© 2010 mandy elizabeth blackburn - university of...
TRANSCRIPT
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MONITORING POLYMORPHISM AND INHIBITOR-INDUCED CONFORMATIONAL
ENSEMBLE SHIFTS IN HIV-1 PROTEASE VIA PULSED ELECTRON PARAMAGNETIC
RESONANCE
By
MANDY ELIZABETH BLACKBURN
A DISSERTATION PRESENTED TO THE GRADUATE SCHOOL
OF THE UNIVERSITY OF FLORIDA IN PARTIAL FULFILLMENT
OF THE REQUIREMENTS FOR THE DEGREE OF
DOCTOR OF PHILOSOPHY
UNIVERSITY OF FLORIDA
2010
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© 2010 Mandy Elizabeth Blackburn
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To my loving parents and my amazing wife
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ACKNOWLEDGMENTS
I want to thank my wife, Pamela Morris, and my parents, Robert and Sandra Blackburn, for
their encouragement, patience, love and support. I also want to thank my Paul and Susanne
Morris and Joel and Autumn Morris for their support and encouragement.
I want to thank my advisor, Dr. Gail Fanucci, with my deepest gratitude. Her faith in me
inspired faith in myself and helped me to accomplish more than I thought I could. She also
challenged me to constantly improve myself, both as a scientist and a human. Her generosity
also made it possible for me to attend an unusually large number of conferences where I was able
to meet and make contacts with many important people in our field.
I would also like to thank all the professors and teachers along the way who helped inspire
and encourage me to aim higher. Miss Reilly, a high school teacher, for finding the shy kid at
the back of the room and pushing me into honors classes. Drs. Deborah Evans, Mark Ondrais,
Richard Watts, and Joe Ho, at the University of New Mexico, for inspiring my love of science.
Dr Philip Laipis, at the University of Florida School of Medicine, for his advice and mentoring.
Drs. Nicole Horenstein and Phil Brucat, at the University of Florida Chemistry Department, for
their encouragement and many engaging conversations.
I would like to thank our collaborators in this project, specifically Dr. Carlos Simmerling and
Ding Fangyu for Molecular Dynamics simulations on spin-labeled Human Immunodeficiency
Virus (HIV-1) protease, and Dr. Ben Dunn and Dr. Roxana Coman for the DNA for preliminary
studies on HIV-1 protease and their insight on kinetic characterization of aspartic proteases. I
would also like to thank Mrs. Dawn Zbell-Herrick, a Ph.D. student at Dr. David Cafiso‘s group
at the University of Virginia, as well as Dr. Ralph Weber (Bruker Biospin) for their help with the
pulsed electron paramagnetic resonance experiments. Most importantly, I would like to thank
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Dr. Angerhofer for graciously sharing his instrument with me and for his patience and
willingness to help train me on the spectrometer.
I would like to express my gratitude to all the members in my committee, Dr. Joanna Long,
Dr. Ben Dunn, Dr. Maureen Goodenow, Dr. Alex Angerhofer and Dr. Adrian Roitberg for many
valuable discussions and their support.
I also wish to express my gratitude to both the current and past members of the Fanucci
research group, especially Thomas Frederick, Luis Galiano, Jordan Mathias, Natasha Hurst,
Jamie Kear, Jeff Carter, Stacey-Ann Benjamin for their friendship and patience.
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TABLE OF CONTENTS
page
ACKNOWLEDGMENTS ...............................................................................................................4
LIST OF TABLES ......................................................................... Error! Bookmark not defined.
LIST OF FIGURES .......................................................................................................................10
LIST OF ABBREVIATIONS ........................................................................................................11
ABSTRACT ...................................................................................................................................24
CHAPTER
1 INTRODUCTION ..................................................................................................................26
Scope of this Work .................................................................................................................26 Introduction to Human Immunodeficiency Virus (HIV) and HIV Protease (HIV PR) ..........27
Acquired Immunodeficiency Syndrome ..........................................................................27 Human Immunodeficiency Virus ....................................................................................28
Genome ....................................................................................................................28
Virion contents .........................................................................................................30 Structure and organization of the virion ...................................................................32
Role of the HIV-1 Protease in the Viral Life Cycle ........................................................33 Structure of HIV-1 Protease ............................................................................................35
HIV-1 Protease as a Drug Target ....................................................................................41 Protease Inhibitors ...........................................................................................................42
Characterization of Inhibitor Binding .............................................................................45 HIV-1 PR Subtype Polymorphisms and Rates of Mutation ............................................47 Drug-Pressure Selected Mutations ..................................................................................49
Understanding the Flaps of HIV-1 PR ............................................................................50 Protein Structure and Flexibility .............................................................................................58
Protein Structure ..............................................................................................................58 Protein Motion and Flexibility ........................................................................................61
Energy Landscapes, Conformational Ensembles, and Ensemble Shifts .........................63 Experimental Methods for Characterizing Ensembles and Ensemble Shifts ..................67
Nuclear Magnetic Resonance ...................................................................................68
Hydrogen/deuterium exchange ................................................................................70 Fluorescence .............................................................................................................71 X-ray diffraction .......................................................................................................72 Cryogenic studies .....................................................................................................72
Computational Methods ...........................................................................................73 Scope of Dissertation ..............................................................................................................73
2 ELECTRON PARAMAGNETIC RESONANCE ..................................................................75
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Introduction to Electron Paramagnetic Resonance (EPR) ......................................................75
Spin Hamiltonian .............................................................................................................75 Electron Zeeman ......................................................................................................76 Hyperfine interaction ................................................................................................78
Nuclear Zeeman .......................................................................................................80 Zero-field splitting ....................................................................................................80 Nuclear quadrupole ..................................................................................................80 Nuclear spin-spin interactions ..................................................................................81 Electron-electron dipole interactions .......................................................................81
Exchange coupling ...................................................................................................81 Site-Directed Spin-Labeling ............................................................................................82
History of site-directed spin-labeling .......................................................................82 Spin labels ................................................................................................................84
Selection of labeling sites .........................................................................................85 Nitroxide line shapes ................................................................................................85
Spin label conformations ..........................................................................................88 Line shape analysis ...................................................................................................89
Introduction to Distance Measurements Via Pulsed EPR ......................................................90 Dipolar Interaction ...........................................................................................................91 Electron Spin Echo Techniques .......................................................................................91
Double Quantum Coherence (DQC) ........................................................................91 Double electron-electron resonance (DEER) ...........................................................92
Experimental Considerations for Pulsed EPR ......................................................................100 Instrumental Requirements ............................................................................................100 Spin Relaxation .............................................................................................................101
Tm ...........................................................................................................................102
T1 ............................................................................................................................105 Cryoprotectants and Glassing Agents ...........................................................................107 Temperature Selection ...................................................................................................107
Sample Concentration ...................................................................................................108 Analysis of DEER Data ........................................................................................................109
Converting the Dipolar Evolution Curve into a Distance Profile ..................................109 Curve Fitting Approaches ..............................................................................................110
Tikhonov Regularization Method ..................................................................................111 DeerAnalysis Software Package ....................................................................................111
L-curve ...................................................................................................................111 Approximate Pake transformation .........................................................................113 Model fitting ...........................................................................................................113
Background correction options ..............................................................................114 Validation module ..................................................................................................115
Verification of Background Subtraction and Gaussian Reconstruction ........................116 Zero-point selection ................................................................................................116 Self consistent analysis of the background subtraction level .................................117 Gaussian reconstruction .........................................................................................120
Experimental Considerations and the Corresponding Effect on the Results .................123 Signal-to-noise ratio ...............................................................................................123
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Maximum dipolar evolution time, tmax ...................................................................125
Spin-labeling efficiency .........................................................................................127
3 DISTANCE MEASUREMENTS FOR HIV-1PR SUBTYPE B .........................................128
Introduction ...........................................................................................................................128
Experimental Design .....................................................................................................128 Previous Studies ............................................................................................................129 Ensembles Shifts of HIV-1 PR ......................................................................................132
Materials and Methods .........................................................................................................133 Protein Expression and Purification ..............................................................................133
DEER Samples ..............................................................................................................135 Protonated matrix ...................................................................................................135 Deuterated matrix ...................................................................................................136
DEER Experiment .........................................................................................................136 Data Analysis .................................................................................................................137
Results...................................................................................................................................137
Apo and Substrate Mimic ..............................................................................................137 Inhibitors ........................................................................................................................139
Estimation of Error in Distance Profiles and Population Analysis ...............................145 Discussion .............................................................................................................................147 Conclusion ............................................................................................................................151
4 DEER RESULTS FOR HIV PROTEASE SUBTYPE C AND CLINICAL ISOLATE
V6, A DRUG-RESISTANT VARIANT ..............................................................................153
Introduction ...........................................................................................................................153 Subtype C ......................................................................................................................154
Clinical Isolate V6 .........................................................................................................159 Materials and Methods .........................................................................................................163
Protein Expression and Purification ..............................................................................163 DEER Experiments .......................................................................................................164
Results...................................................................................................................................164 DEER Results for Subtype C HIV-1 PR .......................................................................164 DEER Results for the V6 Variant of HIV-1 PR ............................................................172
Discussion .............................................................................................................................180 Conclusion ............................................................................................................................181
5 SOLUTE EFFECTS ON SPIN-LABEL MOBILITY AND PROTEIN
CONFORMATIONS ............................................................................................................182
Introduction ...........................................................................................................................182 Solute Effects on Solution Properties and Protein Structure and Function ...................183
Important considerations for proteins ....................................................................183 Important considerations for water ........................................................................184 Important considerations for solutes ......................................................................185 Solute exclusion .....................................................................................................189
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Macromolecular crowding and confinement ..........................................................190
Osmotic pressure and water activity ......................................................................190 Viscosity .................................................................................................................191
Solute Effects on Continuous Wave (CW)-EPR and Pulsed EPR Data for HIV-1
Protease ......................................................................................................................193 CW-EPR line shapes ..............................................................................................193 Pulsed EPR distance measurements .......................................................................193
Materials and Methods .........................................................................................................194 Materials ........................................................................................................................194
Solute Solutions .............................................................................................................195 Fluorophore Labeling ....................................................................................................195 Steady-State Fluorescence Anisotropy ..........................................................................195 Continuous Wave EPR ..................................................................................................196 15
N Hetronuclear Single Quantum Coherence (HSQC) NMR ......................................196 Results...................................................................................................................................197
Effect of solutes on spin-label correlation times ...........................................................199 Protein-solute interactions .............................................................................................204
Discussion .............................................................................................................................212 Conclusion ............................................................................................................................213
6 FUTURE WORK ..................................................................................................................215
Improving the Data Analysis Process for DEER Experiments ............................................215 Investigation of Point Mutations ..........................................................................................215
Method Validation via Model Systems ................................................................................216 Isothermal Titration Calorimetry and Differential Scanning Calorimetry ...........................217
NMR .....................................................................................................................................218
APPENDICES
A HIV-1 PR DNA AND PROTEIN SEQUENCES .................................................................219
Protein Sequences .................................................................................................................219 Inhibitor Structures ...............................................................................................................220
B SUPPLEMENTAL INFORMATION FOR DEER EXPERIMENTS AND DATA
ANALYSIS...........................................................................................................................222
Subtype B..............................................................................................................................222
Subtype C..............................................................................................................................244 Variant V6 ............................................................................................................................268
LIST OF REFERENCES .............................................................................................................290
BIOGRAPHICAL SKETCH .......................................................................................................306
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LIST OF TABLES
Table page
1-1 FDA approved protease inhibitors for treatment of HIV-1 ...............................................45
3-1 Pulse sequence parameters used with the Xepr software package from Bruker..............137
3-2 Parameters of Gaussian-shaped populations used to reconstruct distance profiles. ........144
3-3 Inhibition constant and dissociation constants for subtype C HIV-1 PR.........................147
3-4 Comparison of percentage closed populations for each FDA-approved inhibitor with
published values of KD, KI, G, H, -T S (25 C), and the number of non-water
mediated hydrogen bonds in the crystal structures (excluding residue D25). .................149
4-1 Kinetic parameters for subtype C HIV-1 PR. ..................................................................157
4-2 Inhibition constant and dissociation constants for subtype C HIV-1 PR.........................159
4-3 Kinetic parameters for variant V6 HIV-1 PR.60
...............................................................161
4-4 Inhibition constants for variant V6 HIV-1 PR.60
.............................................................161
4-5 Parameters of Gaussian-shaped populations used to reconstruct distance profiles for
subtype C. ........................................................................................................................172
4-6 Parameters of Gaussian-shaped populations used to reconstruct distance profiles for
clinical isolate, V6. ..........................................................................................................179
A-1 E. coli codon-optimized HIV-1 Protease Variant Sequence Alignment Residues 1-40. .219
A-2 E. coli codon-optimized HIV-1 Protease Variant Sequence Alignment Residues
41-70. ...............................................................................................................................219
A-3 E. coli codon-optimized HIV-1 Protease Variant Sequence Alignment Residues
71-99. ...............................................................................................................................219
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LIST OF FIGURES
Figure page
1-1 Schematic diagram of the complete HIV-1 genome ..........................................................29
1-2 Pictorial representation of the structural assembly of immature and mature HIV-
Virions with various proteins labeled accordingly. ...........................................................32
1-3 HIV viral life cycle. ...........................................................................................................34
1-4 HIV-1 PR topology. ...........................................................................................................37
1-5 Illustration of the ‗fireman‘s grip‘ in the HIV-1 PR active site. ........................................38
1-6 Structure of HIV-1PR PDB ID 2bpx. ..............................................................................40
1-7 X-ray crystal structure of the semi-open and the MD structure of the wide-open
conformation with a space-filling model of an inhibitor placed in the active site
pocket to illustrate the relative sizes of the inhibitor and the gap between the flap
tips. .....................................................................................................................................41
1-8 Inhibitor structures and scaffolds. ....................................................................................43
1-9 Reaction scheme for competitive inhibition. .....................................................................46
1-10 Phylogenic tree of HIV-1 ...................................................................................................48
1-11 Protein sequence variation among protease inhibitor naïve patients and patients who
have undergone protease inhibitor therapy. .....................................................................49
1-12 Structures of two x-ray crystal structures of HIV-1 PR illustrating the ―handedness‖
of the flaps in the semi-open and closed conformations. .................................................51
1-13 Four x-ray crystal structures illustrating the major conformations of HIV-1 PR. ...........52
1-14 Structures of three predominant HIV-1 protease conformations. A) Closed
conformation (PDB ID 1HVR). B) Semi-open conformation (PDB ID 1HHP).
C) Wide-open conformation. .............................................................................................54
1-15 A) MD structure from a simulation of HIV-1 protease illustrating the curled or
tucked conformation. B) Illustration of the interactions between Ile 50 and residues
79-81 and 32. .....................................................................................................................55
1-16 MD structures from a simulation of HIV-1 protease illustrating the curled or tucked
conformations. ...................................................................................................................55
1-17 A) DEER dipolar evolution curves for apo and inhibitor-bound HIV-1 PR. B)
Corresponding distance profiles.81
.....................................................................................56
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1-18 Inter-spin label distances from DEER experiments and MD simulations. ......................57
1-19 Conformational parameters from Chou et al. illustrating the preference of certain
amino acids for a particular secondary structural element. ................................................60
1-20 Schematic diagram of an energy landscape for a protein with two major
conformations, A and B. ..................................................................................................65
2-1 Energy level diagram for the Zeeman and hyperfine splittings of an S = 1/2 spin on a
nucleus with I=1. ................................................................................................................79
2-2 Structure of spin-labels before and after binding to Cys side chain. .................................84
2-3 Schematic diagram of the possible energy levels (A) for a spin ½ on a nucleus with
spin 1 and corresponding absorption (B) and derivative (C) spectra. Sample line
shapes for nitroxide radicals undergoing rapid motion (D), moderate motion (E), and
no motion (F). ....................................................................................................................86
2-4 Illustration of the three correlation times of a spin label ...................................................87
2-5 Illustration of the 4/ 5 model. The S interacts with the H on the C (indicated by
dotted line), which restricts rotations to the 4 and 5 torsional angles. ..........................89
2-6 Parameters for quantifying the breadth of a CW-EPR line-shape. A) Central line-
width, Hpp and the ratio of the center-field transition to the low-field transition,
ICF/LF. B) Second moment, H2
. .......................................................................................90
2-7 Pulse sequences for A) ―2+1‖ experiment, B) Three-pulse DEER, and C) Four-pulse
DEER. Pulse spacings labeled with remain constant and spacings labeled with t
are incremented. .................................................................................................................93
2-8 Absorption spectra for a nitroxide spin-label with the low-field transition marked as
the observe frequency and the center-field transition marked as the pump frequency. .....95
2-9 Sample dipolar evolution curves before and after background subtraction. ......................97
2-10 Effect of the breadth of the distance profile and the most probable distance on the
dipolar evolution curve. .....................................................................................................98
2-11 Minimum tmax for a given interspin distance based on Equation 2-38.............................100
2-12 Pulse sequence for an echo decay experiment and Tm curves for HIV-1 protease in
various buffer conditions. ................................................................................................104
2-13 Inversion recovery pulse sequence and corresponding sample data. ...............................106
2-14 Plot of the maximum concentration of spins as a function of the inter-spin distance. ..109
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2-15 Example of an L-curve and the corresponding distance profiles and dipolar evolution
curves. ..............................................................................................................................112
2-16 Illustration of the Self-Consistent Analysis process developed to optimize the
background subtraction in the DEER dipolar evolution curves.......................................119
2-17 Illustration of the population validation process used to interrogate the validity of
population containing less than 15% of the total population. ..........................................122
2-18 Example of an L-curve and the corresponding distance profiles and dipolar evolution
curves with a high SNR. ..................................................................................................124
2-19 Example of an L-curve and the corresponding distance profiles and dipolar evolution
curves with a low SNR. ...................................................................................................124
2-20 Illustration of impact that the length of tmax has on the resulting distance profile. ..........126
3-1 A) Dipolar evolution curves for apo (black) and RTV-bound (grey) subtype B HIV-1
PR (curves offset vertically for clarity). B) Corresponding distance profiles. C) L-
curve for apo HIV-1 PR. D) L-curve for RTV-bound HIV-1 PR. ..................................129
3-2 Dipolar evolution curves for apo (black) and RTV-bound (grey) subtype B HIV-1
PR labeled with A) MTSL, B) MSL, C) IAP, and D) IASL. E-F) Corresponding
distance profiles generated. ..............................................................................................130
3-3 A) Dipolar evolution curves for apo subtype B (black), V6 (grey), and MDR769
(light grey) (curves are vertically offset for clarity). B) Corresponding distance
profiles generated by TKR. ..............................................................................................131
3-4 Cartoon illustration of possible energy landscapes for a HIV-1 PR with the three
major conformations ........................................................................................................132
3-5 The four-pulse DEER sequence with the pulse spacings labeled according Bruker‘s
nomenclature in the Xepr software package. ...................................................................136
3-6 DEER data for HIV-1 PR subtype B. ..............................................................................138
3-7 Dipolar Evolution curves for HIV-1 PR subtype B in the presence of various FDA
approved inhibitors. .......................................................................................................140
3-8 Distance profiles for HIV-1 PR subtype B in the presence of various FDA approved
inhibitors ..........................................................................................................................141
3-9 Gaussian-shaped populations used to fit the distance profiles for HIV-1 PR subtype
B. ....................................................................................................................................142
3-10 Gaussian-shaped populations used to reconstruct the distance profiles for HIV-1 PR
subtype B. ........................................................................................................................144
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3-11 DEER data for HIV-1 PR subtype B. ............................................................................145
3-12 DEER data for apo HIV-1 PR subtype B collected with various values. ...................146
3-13 Average distance profile (grey) and average Gaussian-shaped populations for the
data shown in Figure 3-12. .............................................................................................147
3-14 Distance distributions for synthesized HIV-1 PR in the absence and presence of
inhibitors which mimic various stages of the substrate in the catalytic process. ...........151
4-1 Ribbon diagram of apo subtype C HIV-1 PR (PDB ID 2R8N) highlighting the
locations of naturally occurring polymorphisms relative to subtype B. ..........................155
4-2 Ribbon diagrams of apo subtype C HIV-1 PR (blue) (PDB ID 2R8N) overlaid with
apo subtype B HIV-1 PR (gold) (PDB ID 1HHP). ........................................................156
4-3 Ribbon diagram illustrating the difference in packing between residues 36 and 15 in
(A) subtype C HIV-PR (PDB ID 1SGU) and (B) subtype B HIV-PR (PDB ID
2BPX). .............................................................................................................................157
4-4 Ribbon diagram illustrating the locations of the drug-pressure selected mutations in
V6. ..................................................................................................................................160
4-5 Overlay of x-ray structures for V6-PR (I84V, I54V) (yellow) (PDB ID 1SGU) and
B-PR (PDB ID 1HSG) (blue) bound to IDV. ..................................................................162
4-6 Overlay of x-ray structures for V6-PR (I84V, I54V) (PDB ID 1SH9) (yellow) and B-
PR (PDB ID 1HXW) (blue) bound to RTV. ..................................................................163
4-7 A) DEER Dipolar evolution curves for apo subtype C and subtype B HIV-1 PR.
B) Corresponding distance profiles generated by TKR. ..................................................165
4-8 A) DEER Dipolar evolution curves for apo and CA-p2 bound subtype C HIV-1 PR.
B) Corresponding distance profiles generated by TKR. ..................................................165
4-9 A) DEER Dipolar evolution curves for CA-p2-bound subtype C subtype B HIV-1
PR. B) Corresponding distance profiles generated by TKR. ..........................................166
4-10 DEER dipolar evolution curves for C-PR in the presence of nine FDA-approved
inhibitors overlaid with the dipolar evolution curve for apo C-PR. ................................167
4-11 DEER distance profiles for C-PR in the presence of nine FDA-approved inhibitors
(solid line) ........................................................................................................................168
4-12 Distance profiles for C-PR (solid) and B-PR (dashed) in the presence of nine FDA-
approved inhibitors. .........................................................................................................169
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4-13 Gaussian-shaped populations used to reconstruct the distance profiles of apo and
CA-p2-bound C-PR. ........................................................................................................170
4-14 Gaussian-shaped populations used to reconstruct the distance profiles for C-PR in the
presence of nine- FDA-approved inhibitors ....................................................................171
4-15 DEER dipolar evolution curves and distance profiles for apo V6-PR and B-PR. ...........172
4-16 DEER dipolar evolution curves and distance profiles for apo and CA-p2 bound
V6-PR. .............................................................................................................................173
4-17 DEER dipolar evolution curves and distance profiles for CA-p2 bound V6-PR and
B-PR. ................................................................................................................................174
4-18 DEER dipolar evolution curves for V6-PR in the absence and presence of nine FDA-
approved inhibitors. .........................................................................................................175
4-19 DEER distance profiles for the V6 variant of HIV-1 PR in the presence of nine FDA-
approved inhibitors ..........................................................................................................176
4-20 DEER distance profiles for the V6 variant of HIV-1 PR in the presence of nine FDA-
approved inhibitors ..........................................................................................................177
4-21 Gaussian-shaped populations used to reconstruct the distance profiles of apo and
CA-p2-bound V6-PR. ......................................................................................................178
4-22 Gaussian-shaped populations used to reconstruct the distance profiles for V6-PR in
the presence of nine- FDA-approved inhibitors...............................................................179
5-1 Structures of water and various solutes. ..........................................................................183
5-2 Illustration concentration regimes for polymers. ...........................................................187
5-3 Illustration of several common polymers structures. .......................................................188
5-4 Illustration of potential size variations between solutes and proteins which lead to
changes in the translation and rotational diffusion of proteins. .......................................192
5-5 Plots of (A) viscosity and (B) osmolality as a function of percent content for sucrose
(dark grey, circle), glycerol (light grey, star), PEG 3000 (triangle, grey), and
Ficoll400 (square, black). (C) Plot of osmolality versus viscosity. ..............................198
5-6 CW-EPR line shapes for MTSL-labeled HIV-1 PR in the presence of various solutes
with incremented concentrations .....................................................................................200
5-7 CW-EPR line shapes (100 G scans) for MTSL-labeled HIV-1 PR in the presence of
various sizes of PEG and EG with incremented concentrations ......................................200
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5-8 CW-EPR line shapes (100 G scans) for spin-labeled HIV-1 PR in the presence (blue)
and absence (red) of a tight-binding inhibitor, ritonavir (RTV) ......................................201
5-9 Fluorescence anisotropy measurements for BODIPY-labeled HIV-1 PR at sites (A)
T74C and (B) K55C. ......................................................................................................202
5-10 Plots of the percent change in the fluorescence anisotropy BODIPY-labeled HIV-1
PR variants T74C and K55C in presence of four solutes ................................................203
5-11 Hydrophobic surfaces of HIV-1 PR in the (A) closed (PDB ID 2pbx), (B) semi-open
(PDB ID 3hvp), and (C) wide-open (structure from Hornak et al.50
) conformations. ...205
5-12 15
N HSQC NMR spectra of HIV-1 PR with the assignments determined by
comparison to Ref.72
........................................................................................................206
5-13 A)15
N HSQC NMR spectra of HIV-1 PR in the absence (red) and presence (blue) of
150 g/L of Ficoll400. B)15
N HSQC NMR spectra of HIV-1 PR titrated with
Ficoll400. .........................................................................................................................208
5-14 A)15
N HSQC NMR spectra of HIV-1 PR in the absence (red) and presence (blue) of
100 g/L of PEG 8000. B) 15
N HSQC NMR spectra of HIV-1 PR titrated with PEG
8000..................................................................................................................................209
5-15 A)15
N HSQC NMR spectra of HIV-1 PR in the absence (red) and presence (blue) of
250 g/L of sucrose. B)15
N HSQC NMR spectra of HIV-1 PR titrated with sucrose. ....210
5-16 Comparison of the A) hydrophobic surface of HIV-1 PR to resonances changes in
HIV-1 PR (mapped on to PDB ID 2pbx) in the presence of B) PEG 8000, C) sucrose,
and D) Ficoll400. ...........................................................................................................211
A-1 Structures for the nine FDA-approved inhibitors used in this work. ...............................220
A-2 Stick- and space-filling-models for the nine FDA-approved inhibitors used in this
work. ................................................................................................................................221
B-1 DEER data for apo HIV-1 PR subtype B. ......................................................................222
B-2 DEER data for CA-p2 bound HIV-1 PR subtype B. .....................................................223
B-3 DEER data for IDV-bound HIV-1 PR subtype B. .........................................................224
B-4 DEER data for NFV-bound HIV-1 PR subtype B. ........................................................225
B-5 DEER data for ATV-bound HIV-1 PR subtype B. ........................................................226
B-6 DEER data for SQV-bound HIV-1 PR subtype B. ..........................................................227
B-7 DEER data for RTV-bound HIV-1 PR subtype B. ........................................................228
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B-8 DEER data for LPV-bound HIV-1 PR subtype B. ........................................................229
B-9 DEER data for APV-bound HIV-1 PR subtype B. ........................................................230
B-10 DEER data for DRV-bound HIV-1 PR subtype B. ........................................................231
B-11 DEER data for TPV-bound HIV-1 PR subtype B. ........................................................232
B-12 Error Analysis for populations < 15% in HIV-1PR Apo. ................................................233
B-13 Error Analysis for populations < 20% in HIV-1PR CA-p2. ............................................234
B-14 Error Analysis for populations < 20% in HIV-1PR IDV. .............................................235
B-15 Error Analysis for populations < 20% in HIV-1PR NFV. ...............................................236
B-16 Error Analysis for populations < 20% in HIV-1PR ATV. ............................................237
B-17 Error Analysis for populations < 20% in HIV-1PR SQV. .............................................238
B-18 Error Analysis for populations < 20% in HIV-1PR RTV. .............................................239
B-19 Error Analysis for populations < 20% in HIV-1PR LPV. ...............................................240
B-20 Error Analysis for populations < 20% in HIV-1PR APV. ...............................................241
B-21 Error Analysis for populations < 20% in HIV-1PR DRV. ..............................................242
B-22 Error Analysis for populations < 20% in HIV-1PR TPV. .............................................243
B-23 DEER data for apo HIV-1 PR subtype C (collected 5/09). ...........................................244
B-24 DEER data for apo HIV-1 PR subtype C (collected 6/09). ...........................................245
B-25 DEER data for CA-p2-bound HIV-1 PR subtype C. .....................................................246
B-26 DEER data for IDV-bound HIV-1 PR subtype C. .........................................................247
B-27 DEER data for NFV-bound HIV-1 PR subtype C. ........................................................248
B-28 DEER data for ATV-bound HIV-1 PR subtype C. ..........................................................249
B-29 DEER data for APV-bound HIV-1 PR subtype C. ..........................................................250
B-30 DEER data for LPV-bound HIV-1 PR subtype C. ..........................................................251
B-31 DEER data for RTV-bound HIV-1 PR subtype C. ..........................................................252
B-32 DEER data for SQV-bound HIV-1 PR subtype C. ........................................................253
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B-33 DEER data for DRV-bound HIV-1 PR subtype C...........................................................254
B-34 DEER data for TPV-bound HIV-1 PR subtype C. ..........................................................255
B-35 Error Analysis for populations < 20% in apo subtype C HIV-1PR (collected 5/09) .......256
B-36 Error Analysis for populations < 20% in apo subtype C HIV-1PR (collected 6/09). ......257
B-37 Error Analysis for populations < 20% in CA-p2 bound subtype C HIV-1PR. ..............258
B-38 Error Analysis for populations < 20% in IDV bound subtype C HIV-1PR. ..................259
B-39 Error Analysis for populations < 20% in NFV bound subtype C HIV-1PR. .................260
B-39 Error Analysis for populations < 20% in ATV bound subtype C HIV-1PR. ..................261
B-40 Error Analysis for populations < 20% in APV bound subtype C HIV-1PR. .................262
B-41 Error Analysis for populations < 20% in LPV bound subtype C HIV-1PR. ...................263
B-42 Error Analysis for populations < 20% in RTV bound subtype C HIV-1PR. .................264
B-43 Error Analysis for populations < 20% in SQV bound subtype C HIV-1PR. .................265
B-44 Error Analysis for populations < 20% in DRV bound subtype C HIV-1PR. ..................266
B-45 Error Analysis for populations < 20% in TPV bound subtype C HIV-1PR. ...................267
B-46 DEER data for apo HIV-1 PR V6. ...................................................................................268
B-47 DEER data for CA-p2 bound HIV-1 PR V6. .................................................................269
B-48 DEER data for IDV bound HIV-1 PR V6. ....................................................................270
B-49 DEER data for NFV bound HIV-1 PR V6.......................................................................271
B-50 DEER data for ATV bound HIV-1 PR V6. ...................................................................272
B-51 DEER data for APV bound HIV-1 PR V6. ....................................................................273
B-52 DEER data for LPV bound HIV-1 PR V6. ......................................................................274
B-53 DEER data for RTV bound HIV-1 PR V6. A .................................................................275
B-54 DEER data for SQV bound HIV-1 PR V6.......................................................................276
B-55 DEER data for DRV bound HIV-1 PR V6. ...................................................................277
B-56 DEER data for TPV bound HIV-1 PR V6. ......................................................................278
19
B-57 Error Analysis for populations < 20% in apo HIV-1PR V6. .........................................279
B-60 Error Analysis for populations < 20% in NFV bound HIV-1PR V6. ............................282
B-61 Error Analysis for populations < 20% in ATV bound HIV-1PR V6. ............................283
B-62 Error Analysis for populations < 20% in APV bound HIV-1PR V6. ............................284
B-63 Error Analysis for populations < 20% in LPV bound HIV-1PR V6. ..............................285
B-64 Error Analysis for populations < 20% in RTV bound HIV-1PR V6. ..............................286
B-65 Error Analysis for populations < 20% in SQV bound HIV-1PR V6. ............................287
B-66 Error Analysis for populations < 20% in DRV bound HIV-1PR V6. ...........................288
B-67 Error Analysis for populations < 20% in TPV bound HIV-1PR V6. ............................289
20
LIST OF ABBREVIATIONS
HIV Human immunodeficiency virus
PR Protease
EPR Electron paramagnetic resonance
RT Reverse transcriptase
IN Integrase
CW Continuous wave
DEER Double electron-electron resonance
AIDS Acquired immune deficiency syndrome
PCP Pneumocystis jirovecii pneumonia
ORF Open reading frame
PIC Pre-integration complex
RNA Ribonucleic acid
DNA Deoxyribonucleic acid
Gag Group-specific antigen gene
Pol Polymerase gene
Env Envelope gene
Nef Negative factor protein
Rev Anti-repression transactivator protein
Tat Transactivating regulatory protein
Vif Virion infectivity factor
Vpr Viral protein R
Vpu Viral protein U
MA Matrix protein
CA Capsid protein
21
NC Nucleocapsid protein
RT Reverse transcriptase
SU, gp120 Surface protein, glycoprotein 120
TM, gp41 Transmembrane protein, glycoprotein 41
MHC Major histocompatibility complex
CD4 Cluster of differentiation 4
PI Protease inhibitor
II Integrase inhibitor
FI Fusion inhibitor
NRTI Nucleoside reverse transcriptase inhibitor
NNRTI Non-Nucleoside reverse transcriptase inhibitor
PDB Protein DataBank
MD Molecular dynamics
CW-EPR Continuous-wave electron paramagnetic resonance
CD Circular dichroism
PMPR Pentamutated protease
IPTG Isopropyl-β-D-thiogalactoside
EDTA Ethylenediaminetetraacetic acid
BME β-Mercaptoethanol, 2-Mercaptoethanol
diGly Diglycine, 2-[(2-aminoacetyl)amino]acetic acid
MTSL (1-Oxyl-2,2,5,5-Tetramethyl-Δ3-Pyrroline-3-Methyl)
Methanethiosulfonate
IASL 4-(2-Iodoacetamido)-TEMPO
IAP 3-(2-Iodoacetamido)-PROXYL
MSL 4-Maleimido-TEMPO
NHFML National High Field Magnetic Lab
22
DQC Double quantum coherence
SQC Single quantum coherence
ZQC Zero quantum coherence
Tm Phase memory
T1 Spin-lattice relaxation time
T2 Spin-spin relaxation time
APV Amprenavir
TPV Tipranavir
IDV Indivavir
SQV Saquinavir
LPV Lopinavr
FPV Fosamprenavir
RTV Ritonavir
DRV Darunavir
ATZ Atazanavir
NFV Nelfinavir
TKR Tikhonov Regularization
MC Montecarlo
CRF Circular Recombinant Form
ITC Isothermal Titration Calorimetry
DSC Differential Scanning Calorimetry
NMR Nuclear Magnetic Resonance
βe Bohr magneton (9.27400949 × 10-24
J·T-1
)
βN Nuclear magneton (5.05078324 × 10-27
J·T-1
)
e proton electric charge (1.60217653 × 10−19
C)
23
Reduced Plank‘s constant (or Dirac‘s constant, 1.054571628 × 10-34
J·s)
me Electron rest mass (9.10938215 × 10–31
kg)
ge Spectroscopic (Landé) splitting factor
gN Nuclear splitting factor
A0 Hyperfine splitting
η Kinematic viscosity
ωee Electron-electron dipolar coupling
R Spin label diffusion tensor
τ Correlation time
Ms Total electronic spin; Scaled mobility
FB Fraction of spins excited by the pump pulse in the DEER experiment
Regularization parameter
L Tikhonov Matrix
K Tikhonov regularization kernel
Pλ Distance distribution matrix corresponding to the parameter λ
CDC Center for Disease Control
24
Abstract of Dissertation Presented to the Graduate School
of the University of Florida in Partial Fulfillment of the
Requirements for the Degree of Doctor of Philosophy
MONITORING POLYMORPHISM AND INHIBITOR INDUCED CONFORMATIONAL
ENSEMBLE SHIFTS IN HIV-1 PROTEASE VIA PULSED ELECTRON PARAMAGNETIC
RESONANCE
By
Mandy Elizabeth Blackburn
August 2010
Chair: Gail Elizabeth Fanucci
Major: Chemistry
Human Immunodeficiency Virus Type 1 protease (HIV-1 PR) is an enzyme required for viral
replication, and as such represents a major drug target in the treatment of AIDS. HIV-1 PR is
responsible for the cleavage of the viral polyproteins gag and gag-pol, and inhibition of this
enzyme results in the formation of immature non-infectious virus particles. The structure and
function of HIV-1 PR has been studied for over 20 years. However, questions regarding the
conformations, flexibility, dynamics and motion of the beta-hairpin turns, also known as flaps,
which cover the active site cavity, remain. Pulsed EPR methods are emerging as a powerful
method for monitoring protein conformations and flexibility. Here, double electron-electron
resonance (DEER) EPR of spin labeled constructs of HIV-1 PR is used to characterize changes
in flap conformations and domain rotations as a function of various substrates and inhibitors. The
most probable distances and the breadth of the distance distribution profiles provide insights
regarding conformational mobility and flexibility. We also show that drug pressure selected
mutations alter the average conformation of the flaps and the degree of opening of the flaps.
Distance profiles obtained from EPR are validated by molecular dynamic (MD) simulations
performed by the Simmerling group, which provide structural models needed to fully interpret
25
the EPR results. By combining experiment and theory to understand the role that altered flap
dynamics/conformations play in the mechanism of drug resistance, key insights are gained that
maybe useful in the rational development of new inhibitors of this important enzyme.
26
CHAPTER 1
INTRODUCTION
Scope of this Work
The goal of this research was to investigate the conformations and flexibility of the ―flaps‖ in
human immunodeficiency virus (HIV) protease (HIV-1 PR) using pulsed and continuous wave
(CW) electron paramagnetic resonance (EPR). It has been hypothesized that the flexibility of the
flaps, the -hairpin turns that control access to the active site of the protease, is modulated by
drug-pressured selected mutations in the protein and that this altered flexibility imparts resistance
to the inhibitors. Additionally, the effect of the naturally occurring polymorphisms among the
various subtypes on inhibitor binding and on flap flexibility has not been fully characterized. To
characterize the flap conformations, a pulsed technique called double electron-electron resonance
(DEER) was utilized to measure the distance between spin-labels incorporated into the flaps.
The aims of this work were to (1) optimize this technique for addressing these questions and (2)
to determine if the flap flexibility is altered by drug pressure selected mutations and naturally
occurring polymorphisms.
This chapter will provide an introduction to HIV and the important factors of the virus that
contribute to drug resistance. The function, structure, and characteristics of the protease will be
discussed in detail. Finally, the concept of conformational ensembles in proteins will be
introduced as it relates to the flexibility of the flaps. Chapter two will provide an introduction to
both CW and pulsed EPR spectroscopy—the primary techniques utilized in this work. In chapter
three, the distance measurements for HIV-1 PR subtype B will be presented and discussed. In
chapter four, the results of an investigation into the effects of solutes on the conformation and
spin-label mobility of HIV-1 PR will presented and discussed. Chapter five will present and
27
discuss the results of investigations using subtype C PR and a drug-pressure selected variant, V6.
Chapter six will discuss future directions that this work can take.
Introduction to HIV and HIV Protease
Acquired Immunodeficiency Syndrome
Acquired Immunodeficiency Syndrome (AIDS) is the final stage of an infection caused by
the Human Immunodeficiency Virus (HIV)1; 2
. AIDS is defined as a clinical condition in which
the patient develops various opportunistic infections and rare cancers resulting from an HIV
related suppression of the patient‘s immune system. HIV virions bind and enter cells that
contain CD4 proteins in their cellular membrane, including T helper cells, regulatory T cells,
dendritic cells, monocytes, and macrophages. The CD4+ T cells are essential for defense against
infections in the host. As HIV eventually reduces the number of CD4+ T cells from over 800
cells/mm3to less than 200 cells/mm
3, the immune system of the host is progressively
diminished.3 The immune system is considered compromised when the patient becomes
susceptible to opportunistic infections,4 such as Pneumocystis jirovecii pneumonia (PCP)
5, a rare
form of pneumonia, or Karposi‘s sarcoma,6 a rare form a cancer, both of which are common
among people with AIDS.
It is believed that HIV first entered human populations from a primate source as early as 30-
100 years ago.7 The earliest known HIV infection was isolated from a serum sample taken from
a patient in Congo in 1959.8 The identification of AIDS in 1981 resulted from multiple patients
presenting with the same rare conditions, Karposi‘s sarcoma and/or PCP, in rapid succession.
This statistical anomaly was noticed by the Center for Disease Control (CDC) and prompted
further investigation. Two years later, the HIV virus was identified as the potential cause of
AIDS. Since the discovery of AIDS and HIV, the number of HIV-infections around the globe
has increased at astonishing rates. In the last decade, with the advent of anti-retroviral therapy
28
and aggressive efforts for preventing the spread of HIV, the rate of increase for new infections
has decreased. In 2007, there were 2.7 million new infections (down from 3 million in 2001) for
a total of 33 million infections worldwide, with 2 million AIDS related deaths worldwide (up
from 1.7 million in 2001).9
Human Immunodeficiency Virus
There are two human immunodeficiency viruses, HIV-1 (from chimpanzees) and HIV-2
(from sooty mangabeys).7 Although the HIV-1 and HIV-2 genomes are very similar, their DNA
sequences differ by about 55%.3 The antibodies used for detecting HIV-1 are typically non-
reactive towards HIV-2 and thus HIV-2 requires separate antibody-based testing for confirming
infection in patients.10
HIV-2 is less prevalent than HIV-1 because it has lower transmissibility
and delayed pathogenesis relative to HIV-1. One significant result of this difference is that
patients infected with HIV-2 tend to have a longer delay between infection and the onset of
AIDS.11
Both HIV-1 and HIV-2 are classified as members of the genus Lentivirus, a subgroup of the
Retroviridae family.7 Lentiviruses are ―slow moving‖ viruses with long incubation periods, such
that several years can pass between initial infection and disease development. Retroviruses are
characterized by their single-stranded positive-sense RNA (ribonucleic acid) genome that is
reversed transcribed into DNA (deoxyribonucleic acid) for integration into the host cell genome.
Genome
Like most viruses, HIV-1 has a compact genome (Figure 1-1), where the percentage of the
DNA encoding genes versus the DNA not encoding genes is much higher than in other
organisms—whose ratios can be as low as 50%. The viral genome contains several open reading
frames (ORF) that are transcribed into the viral proteins. The three largest genes are transcribed
into polyprotein chains that are proteolytically processed into the individual proteins.
29
The major structural proteins, matrix (MA), capsid (CA), and nucleocapsid (NC), are
encoded in the group specific antigen (gag) gene. The viral enzymes (protease (PR), reverse
transcriptase (RT), and integrase (IN) are encoded in the polymerase (pol) gene. The envelope
(env) gene encodes the surface (SU) and transmembrane (TM) proteins involved in recognizing
and binding the host cell. Additionally, the nef, vpr, vpu, tat, vif, and rev genes encode accessory
proteins, which are responsible for suppression of the cell immune response, formation and
localization of the preintegration complex (PIC), degradation of CD4, and enhancement of virion
release.
Figure 1-1. Schematic diagram of the complete HIV-1 genome (modified from Levy3).
Like most retroviruses, the gag and pol genes of HIV-1 are expressed as polyprotein chains
where transcription of the pol gene occurs only from a frameshift during gag transcription.3 It
has been found that frameshifting in several organisms tend to occur at sites with multiple U
bases or stable hairpin structures that result in ribosomal pauses during transcription. The
frequency of the frameshifting is determined by several factors which include, but are not limited
3’
LTR
5’
LTR
vif vpu nef
vpr
p2
MA CA NCp6
pol
PR RT IN
env
SU TM
tat
rev
MA CA NC p6
MA CA NC
PR RT INMA CA
PR RT INMA CA
SU TM
SU TM
HIV-1PRHIV-1PR Cellular protease
(furin)
gag
p1
p6
p1p2
Gag polyproteinGag-Pol polyprotein
Env polyprotein
30
to, the number of consecutive U bases, the stability of the hairpin, and the presence of proteins
that bind and stabilize the hairpin structure. According the numbering convention used by Wain-
Hobson et al.,12
there are six uracil (U) bases beginning at bp 1631. In the gag reading frame,
these bases are part of the codons for Asn-Phe-Leu. In the pol reading frame, these bases are
part of the codons for Phe-Phe-Arg. Additionally, there is a GC-rich stretch of DNA
downstream of the U bases that has been identified as a potential hairpin. Some viruses have
been shown to have frameshifting events as frequently as 1:4;13
however the rate for HIV-1 has
been shown to be about 1:8.14
It has been suggested that the frameshifting mechanism
contributes to regulation of the pol expression (since it lacks a promoter region and thus the
opportunity to regulated in a traditional fashion) because the virus should not need as many
copies of the enzymes as it does the structural proteins. Interestingly, the myeloblastosis-
associated virus (MAV) encodes the protease in the gag gene;15
however, the MAV PR has been
shown to be significantly less active than the HIV-1 PR (as a result of Ser in the catalytic triad
instead of the Thr). It has been proposed that the myeloblastosis-associated viruses have evolved
to produce more PR because it is less efficient.16
Virion contents
Matrix (p17). Matrix, the N-terminal protein in the gag polyprotein (p55), coats the inner leaflet
of the lipid bilayer of the virion and is responsible for targeting p55 to the membrane via
the myristoylation at the N-terminus.
Capsid (p24). Capsid multimerizes to form the capsid, or core of the virion.
Nucleocapsid (p7). Nucleocapsid interacts with the viral RNA genome in addition to
participating in the inter-p55 interactions during viral assembly on the plasma membrane.
Reverse transcriptase (p66, p51). Reverse transcriptase generates the DNA intermediate for
integration into the host cell genome.
Integrase (p32). Integrase splices the DNA intermediate into the host cell genome.
31
Protease (p10). The protease cleaves the polypeptide chains into the individual proteins during
the viral maturation step.
Envelope surface (gp120). The envelope surface protein binds CD4, a host cell surface protein,
the first step in the binding and fusion process.
Envelope transmembrane (gp41). The envelope transmembrane protein binds gp120, attaching
it to the surface of the virion, and participates in the binding to coreceptors on the host cell
surface required for membrane fusion.
Tat (p14). Tat (transactivating protein) upregulates HIV replication by binding the Tat response
element with an RNA loop in the 3‘ portion of the LTR.
Rev (p19). Rev (regulator of viral protein expressison) binds the Rev response element, a cis-
acting RNA loop in the envelope mRNA. Rev inhibits splicing of the viral mRNA and
also shuttles incompletely spliced mRNAs from the nucleus to the cytoplasm.17
Nef (p27). Nef (negative factor) is a myristoylated 27 kDa protein that interacts with a variety of
host cell proteins to increase the viral infectivity. Nef is also believed to play a role in T
cell activation and down regulation of CD4 expression. As one of the first viral proteins
expressed following infection, Nef has also been suggested to play a role in setting the
tempo or determining the magnitude of the infection.18
Vif (p23). Vif (viral infectivity factor) increases the viral infectivity by antagonizing the cellular
protein APOBECC3G, a cytidine deaminase that is packaged into viral particles in the
absence of Vif. APOBEC3G causes G-to-A hypermutation and thus prevents further
spread of the infection as a result of genetic corruption.18
Vpr (p15). Vpr is a 96-residue protein that plays several important roles in the HIV-1 lifecycle.
Vpr causes G2 arrest in the host cell, transactivates the LTR in the integrated provirus,
induces apoptosis, and is part of the preintegration complex.18
Vpu (p16). Vpu is an 81-residue homodimeric integral membrane protein that binds CD4 in the
ER (endoplasmic reticulum), thus inducing CD4 turnover. Vpu also plays a role in virus-
release in certain cell types18
and in down regulation of MHC Class I cell-surface proteins.
p6. p6, a 6-kDa cleavage product from the Gag polyprotein, contains the L domain which
interacts with ESCRT complexes during assembly to facilitate budding.
p2. p2 is a 2-kDa cleavage product from the Gag polyprotein. During viral assembly, the p2
domain within the Gag polyprotein interacts with other p2 domains leading to higher order
multimerization (>1000 kDa).19
p1. p1 is a 1-kDa cleavage product from the Gag polyprotein.
32
Structure and organization of the virion
The structure of mature HIV-1 virions, shown in Figure 1-2A, is similar to that of many other
viruses. The virions are essentially spherical with an overall diameter 100-120 nm.20
The two
main components of the virion are the cone-shaped core, which contains and protects the
genomic content of the virus, and the envelope, which is comprised of a lipid bilayer and the
viral surface proteins.
The shell of the core is composed of many copies of the capsid protein (CA). Inside the core,
the genomic RNA is bound by multiple copies of the nucleic acid binding protein, nucleocapsid
(NC). The NC proteins help maintain the integrity of the nucleic acid by binding to the RNA
and sterically preventing access to the nucleic acid. The viral enzymes RT, IN, and PR are also
located within the core.
The surface of the virus is a lipid bilayer known as the viral envelope, which was transferred
from the host cell during the budding event. Embedded in the outer leaflet of the lipid bilayer are
up to 72 copies of gp41.21
Each gp41 can bind three copies of gp120 forming an Env spike that
appears to be a ―knob‖ in cryoelectron microscopy tomography.22
The inner leaflet of the bilayer
is coated with a layer of matrix (MA) proteins. The MA proteins are myristoylated,23
which
Figure 1-2. Pictorial representation of the structural assembly of immature and mature HIV-
Virions with various proteins labeled accordingly. Image courtesy of National
Institute of Allergy and Infectious Diseases.
33
means they have been modified with a 14-carbon (myristoyl) fatty acid. The hydrocarbons
region of the myristoyl moiety is embedded in the inner leaflet of the bilayer, which acts to
anchors MA to the bilayer. The remaining viral proteins and some ―hijacked‖ host proteins are
contained within the virion.24
Immature virions differ from the mature virions in the organization of the interior of the
particle. The immature virions do not contain a core because the gag and gag-pol polyproteins
have not been proteolytically processed into the individual components. The myristoyl group on
the N terminus of MA, which is the N-terminal protein in the gag and gag-pol polyproteins is
imbedded in the bilayer. The gag and gag-pol polyproteins extend towards the interior of the
virion. The polyprotein self-associate to coat the inner leaflet of the bilayer. The RNA genome
is bound to the NC region of the gag and gag-pol polyproteins. The gp120 and gp41 are the
same as in mature virions because they are processed by intracellular proteases before the virion
buds.
Role of the HIV-1 Protease in the Viral Life Cycle
Figure 1-3 illustrates the steps in the HIV-1 viral lifecycle. The lifecycle begins with a
binding event between a mature (infectious) virus particle and a host cell. The gp120 protein on
the virion surface binds to a CD4 protein on the host cell surface (step 1). Upon recruiting (step
2) an additional host cell receptor protein (usually CCR5 or CXCR4), the viral membrane begins
to fuse (step 3) with the host cell membrane eventually releasing the contents of the virion into
the host cell. After cell entry, the viral capsid, which contains the viral RNA genome, is
uncoated (step 4). The genomic RNA is reverse transcribed by RT (step 5) into double-stranded
DNA, which is then imported (step 6) into the nucleus. The double-stranded DNA is then
integrated (step 7) into the host cell genome. The integrated DNA remains dormant until the
region is activated for transcription. The host cell transcribes (step 8) the mRNA, which is used
34
Figure 1-3. HIV viral life cycle. Figure courtesy of National Institute of Allergy and Infectious
Diseases. Numbered steps are described in detail in the text.
in the production (step 9) of the viral polyproteins. The viral proteins are trafficked (step 10) to
the host cell membrane where they begin to bud (step 11) and form new viral particles, which are
immature and thus non-infectious. This immaturity refers to the state of the viral proteins, which
are still polypeptide chains consisting of multiple proteins. The viral protease cleaves itself from
the polypeptide chain by an unknown process and then cleaves the remaining polypeptide chain
into the individual proteins. These proteins are then rearranged within the viral particle. The
cleavage and reorganization is called the maturation step (step 12) and is the final step in the
viral life cycle.
Mature Virion
HIV
gp120
gp41
Co-receptor(CCR5 or CXCR4)
CD4Preintegration Complex
Viral RNA
RT
Integrase
Viral DNA
Host DNA
New Viral RNA
4
1
3
5
6
7
8
9
2
11
12
10
35
Structure of HIV-1 Protease
Although, we know now that HIV protease is a dimeric aspartic protease, the following
provides a brief history of the identification and characterization of HIV-1 PR. In 1984, viral
genome was sequenced12; 25
and many viral proteins were identified by homology to other
retroviruses. It was determined that a protease was likely encoded at the 5‘ end of the pol gene
as in several other retroviruses.26
Similar to most retroviral proteases, HIV-1 PR was
homologous to several cellular aspartic proteases, such as pepsin.27
Sequence analysis also
revealed that HIV-1 PR was most likely a dimer because the sequence only included one of the
two necessary catalytic triads (Asp-Thr-Gly).27
In 1986 and 1987, several researchers expressed
a portion of the gag-pol polyprotein including the putative HIV-1 PR in E. coli and demonstrated
that the sequence contained the protein responsible for proteolytic processing of the gag-pol
polyprotein.28; 29
It was unclear from the sequence analysis alone, which residues comprised the
active protease because the protease cleaves itself from the polyprotein chain at two then
unknown cleavage sites. In 1988, two groups synthesized and characterized a 99 amino acid
sequence corresponding to the proposed minimum sequence necessary for HIV-1 PR.30; 31
Both
groups demonstrated that a protein containing just these 99 amino acids had enzymatic function
for the proteolytically processing the gag-pol polyprotein. In order to determine the exact
sequence of the HIV-1 PR, several researchers purified and characterized HIV-1 PR from partial
gag-pol polyproteins expressed in E. coli cells.28; 32
They also discovered that a 10 kDa protein
corresponding to theHIV-1 PR sequence was sufficient for proteolytically processing the gag-pol
polyprotein. By substituting the Asp25 for either Asn, Ala, or Thr residues and monitoring gag-
pol polyprotein processing,33; 34; 35
several other researchers established Asp25 of HIV-1 PR was
necessary for activity. Furthermore, it was demonstrated in an in vitro assay of recombinantly
36
expressed gag-pol that pepstatin A, a naturally occurring inhibitor to pepsin, could prevent gag-
pol processing.33
In 1989, the investigation into potential inhibitors for HIV-1 PR continued vigorously. Many
potential transition state mimetics were identified that could inhibit the HIV-1 PR in vitro36; 37; 38
furthermore, it was demonstrated that some inhibitors could prevent HIV replication in cell
culture39
while others could not.40
In 1989, the first crystal structures of HIV-1 PR were
published (PDB ID 2hvp).41; 42; 43
In 1996, the first structure from data of NMR experiments was determined.44
HIV-1 PR was
studied in the presence of a symmetric cyclic urea-based inhibitor. The results were compared to
the structure obtained from crystallographic studies of HIV-1 PR bound to the same inhibitor.
The two structures were similar but significant differences were observed in the loops and the
overall ―compactness‖ of the two structures. Specifically, the NMR data revealed more
flexibility of the flaps than can be inferred from static x-ray models.
The structure determination of HIV-1 PR confirmed the sequence homology of HIV-1 PR to
other viral and cellular aspartic proteases. The cellular proteases are monomeric; however, they
contain two highly symmetric domains that are analogous to the monomers of viral proteases.45
Thus, the structural features of each domain in the cellular proteases and each monomer from the
viral proteases are similar and can be described by a general template.45
This general template
for aspartic proteases is illustrated in Figure 1-4A and these features are mapped onto the HIV
structure in Figure 1-4C. The protease monomers have a pseudo-twofold symmetry axis. The
structural components are named alphabetically with the pseudo-symmetry partners designated
by the prime symbol (‗). The N-terminal (residues 1-5, -sheet A) of HIV-1 PR comprise the
outer-edges of the four-sheet dimerization domain. Residues 9-15 form the -strand B which,
37
along with -sheet C (residues 18-24) form the fulcrum. The active site triad (Asp25, Thr26, and
Gly27) sits on a loop between -strand C and -strand D (residues 30-35). In the cellular
proteases, the D strand would be followed by a helix H. However, in the smaller viral proteases,
like HIV-1 PR, the D strand is followed by short disordered loop H (residues 36-42) called the
elbow. The A‘ -strand (residues 43-49) and half of the B‘ -strand (residues 52-66) form the
Figure 1-4. HIV-1 PR topology. A) Schematic diagram of secondary structural elements labeled
according the aspartic protease template (modified from Wlodawer et al.45
). B) Top
view of HIV-1 PR ribbon diagram color coded to match the aspartic protease
template (PDB ID 3HVP). C) Front view of HIV-1 PR ribbon diagram.
flap. The other half of the B‘ -strand and the C‘ -strand (residues 69-78) form the cantilever.
The D‘ -strand (residues 83-85) forms part of the active site wall and leads into helix H‘
(residues 86-94). The C-terminal is the Q -strand (residues 95-99), which sits between the A
strands to complete the dimer interface.
The HIV-1 PR dimer is stabilized by inter-monomer interactions, with the majority occurring
in the dimerization domain where the four terminal -sheets from each monomer intercalate,
forming 12 hydrogen bonds. Additional inter-monomer interactions in the active site further
stabilize the dimer structure. Thr26 participates in what is known as the ‗fireman‘s grip‘ (Figure
A
B
Active Site
C
A’
H
D
Q
D’
C’
H’
A B
C
D’
1
59
1518
24 30
35
3642
43
49 52
78
66 69
83
85
8694
95
99
C’B’
A’
H
D
CBA
H’
Q
Active Site Loop
38
1-5) where hydrogen bonds are formed between a side chain hydroxyl and both the backbone
carbonyl of Leu24 and the backbone amide of the Thr26 from the other monomer. Investigation
has confirmed the importance of Thr26 by substitution of other amino acids that are not capable
forming the hydrogen bonding network resulting in a shift of the monomer-dimer equilibrium in
favor of the monomer.46
Figure 1-5. Illustration of the ‗fireman‘s grip‘ in the HIV-1 PR active site. Residues from
second monomer designated with the prime (‗) symbol. A) Side view. B) Top view
The active site of HIV-1 PR has a geometry that is highly conserved among both viral and
cellular aspartic proteases. The catalytic triad, Asp25, Thr26, Gly27, form the same interactions
and same structure. The foundation of this structure is the ‗fireman‘s grip‘ but the structure is
stabilized by additional hydrogen bonds. The backbone carbonyl of Asp25 hydrogen bonds with
the backbone amide of Gly27. The Asp25 residues are typically depicted with one residue being
protonated and the other being deprotonated with the proton being shared between the two
closest oxygen atoms. A water molecule further stabilizes this interaction by hydrogen bonding
with an oxygen from each Asp residue.47
The end result of this hydrogen bonding network is a
Leu24Leu24
Asp25
Asp25
Thr26Thr26
Gly27
Gly27Leu24’
Asp25’
Thr26’
Gly27’ Leu24’Asp25’Thr26’
Gly27’
A B
39
stable, geometrically conserved active site, with the catalytic Asp in the necessary position for
proteolytic activity.
HIV-1 PR contains two -hairpin turns, called the ‗flaps‘, that sit over the active site. In the
inhibitor-bound crystal structures, the flaps make extensive contact with the inhibitor. On
average, the flaps contribute roughly half of the interactions between the inhibitor and HIV-1
PR.48
When bound to an inhibitor or substrate, the flaps are pulled in toward the active site by
the interaction with the ligand. There are also interflap interactions such as the hydrogen bonds
typically observed between the backbone atoms of residue 51. This conformation is typically
referred to as the closed conformation. In the absence of ligand, the flaps sit slightly further
away from the active site, in what is termed the semi-open conformation. For the first few years
after the initial crystal structures were solved, researchers debated which flap conformation was
the most stable in solution and which, if any, were stabilized by crystal contacts. The HIV-1 PR
structures were compared to apo PR structures from other viruses, some of which were closed
(SIV) or semi-open (HIV-2); however some also contained disordered flaps that were unresolved
(Rous Sarcoma Virus). Researchers eventually concluded that closed structures of apo proteases
were stabilized by crystal contacts and that the semi-open form is the most thermodynamically
stable in solution.45
The other major question addressed by researchers was the issue of substrate access to the
active site. The space filling model (Figure 1-6B) and the top view (Figure 1-6C) clearly show
that with the flaps closed, there is insufficient space for the substrate to enter from either the top
or side of the protein. Researchers were quick to identify that in order for substrates or inhibitors
to bind, it is necessary for the protein to undergo a large conformational change to move the flaps
out of the way. Figure 1-7 shows the semi-open and wide-open conformations of HIV-1 PR with
40
an inhibitor placed in the active. This figure illustrates that the interflap distance in the semi-
open conformation not sufficiently large to allow access to the active site and that a wide-open
conformation is necessary. Several experimental techniques as well as computational
approaches were preformed to address this issue. This topic will be discussed in greater detail
later in this dissertation in the section ―Understanding the Flaps of HIV-1 PR‖.
Figure 1-6. Structure of HIV-1PR PDB ID 2bpx. A) Ribbon diagram highlighting the various
structural regions of HIV-1PR. B) Space-filling model of HIV-1PR illustrating the
size of the active site cavity and the inability of a polypeptide substrate to slide
through the active site with flaps closed. C) Top view of the ribbon diagram
illustrating the relative horizontal position of the flaps and how the flaps block access
to the active site.
Based on the results of several molecular dynamic simulations (MD) and by crystal structure
analyses, the main structural components of HIV-1 PR are divided based on rigid domain
movements during flap opening. The active site floor and the active site wall undergo a small
motion during flap movement where symmetry partners move closer together upon flap closing
and slightly farther away during flap opening. The elbows, cantilever, and fulcrum (Figure 1-6)
are also involved in opening the flaps. As the flaps open, the elbows and cantilever shift down
(away from the flaps). The fulcrum pivots slightly around its inner-most point (point closest to
Cantilever
Active site
DimerizationDomain
Flaps
Elbow
Fulcrum
A B
C
41
the active site) to accommodate the shift in the cantilever. These motions allow significant
movement in the outer most edges of the protease (flaps, cantilever, and fulcrum) while the core
of the HIV-1 PR remains relatively immobile.49; 50
Figure 1-7. X-ray crystal structure of the semi-open and the MD structure of the wide-open
conformation with a space-filling model of an inhibitor placed in the active site
pocket to illustrate the relative sizes of the inhibitor and the gap between the flap tips.
Additional studies have revealed that the sequence of the flaps is highly conserved in patients
that have never been exposed to protease inhibitors. However, there is an increase in the number
of amino acid substitutions in the flap sequence found in patients that have been treated with
protease inhibitor. This correlation between protease inhibitor therapy and mutations in flaps
indicates that there is a strong possibility for a connection between mutations in the flaps and
drug resistance.
HIV-1 Protease as a Drug Target
Several viable strategies are currently utilized for drug therapy in HIV-positive and AIDS
patients; most target viral proteins essential in the viral life cycle.51
For HIV-1, this includes the
proteins involved in recognizing and binding to the host cell, the proteins involved in fusing the
A B
42
viral and host membranes, RT,IN, and PR—all of which are targets for FDA-approved
antiretroviral drugs that are currently being used to treat HIV positive patients. Part of the
success of targeting these proteins relies on the fact that the small molecules are specific to viral
proteins which do not have homologous proteins in the host cell. Unfortunately, there are
usually host cell proteins with some degree of homology, which leads to some inhibition of
normal function within the host cell and can cause side effects in the patients.52
An example of side effects resulting from inhibition of cellular enzymes is the inhibition of
DNA polymerase by nucleotide inhibitors for reverse transcriptase (RT). The nucleoside
reverse transcriptase inhibitors (NRTI) are effective in inhibiting RT but typically have no
noticeable effect on most of the cellular polymerases because of differences in the selectivity of
the polymerases for the nucleotides. However, DNA polymerase , the only polymerase for
mitochondrial DNA (mtDNA), is strongly inhibited by NRTIs resulting in a depletion of
mtDNA.53
Consequently, the expression of proteins encoded in the mtDNA, such as those
involved in oxidative phosphorylation, is decreased, which results in clinical symptoms
associated with genetic disorder of the mtDNA. Symptoms include loss of muscle coordination,
muscle weakness, heart disease, liver disease, kidney disease, gastrointestinal disorders, among
others.
Protease Inhibitors
In 1988, the search for protease inhibitors began when it was shown that preventing HIV-1
PR activity via a D25N mutation inhibited the viral lifecycle.35
Within the next year, Deinhardt
et al.39
showed that viral replication could be halted by the addition of an aspartic acid specific
inhibitor, pepstatin A (Figure 1-8B), and Richards et al.36
demonstrated that HIV-1 PR could be
inhibited in vitro by several general aspartic protease inhibitors. Wlodawer et al.43
showed that a
43
non-hydrolysable substrate peptide could bind tightly to the HIV-1 PR active site and inhibit the
HIV-1 PR activity.
The first investigations into inhibitors designed specifically for HIV-1 PR began in 1989, and
were based upon the knowledge gained from studies on other aspartic proteases like rennin.40
These early inhibitors were based upon Pepstatin A, a native inhibitor of pepsin, which contains
an uncommon amino acid statine (Figure 1-8A). Statine (Sta) has the unique structure of a
tetrahedral intermediate or transition state analogue. Thus many peptide mimetics containing a
Figure 1-8. Inhibitor structures and scaffolds. A) Structure of the non-standard amino acid
statine. B) Structure of pepstatin containing two Sta amino acids. C) Structure of
the hydroxyethylene scaffold. D) Structure of the hydroxyethylamine scaffold. E)
Structure of the reduced amide scaffold. F) Structure of saquinavir (based on the
hydroxyethylamine scaffold. G) Structure of Tipranavir, a non-peptidomimetic
inhibitor.
A B
C D E
F G
Saquinavir (SQV) Tipranavir (TPV)
Reduced AmideHydroxyethylamine (HEA)Hydroxyethylene (HEE)
PepstatinStatine (Sta)
44
variety of tetrahedral intermediates substituted for the scissile amide bond36; 38; 40
were tested for
HIV-1 PR inhibition. It was also found that compounds with a specific tetrahedral intermediate,
a hydroxyethylene isostere ( [CH(OH)CH2]) (Figure 1-8), inhibited HIV-1 PR more effectively
than others.54
Other transition state analogues such as the reduced amide (Figure 1-8E),
phosphinates, and -fluoroketones were tested, but few inhibited HIV-1 PR as efficiently as the
hydroxyethylene scaffold.38
As with all drug design and discovery attempts, transitioning the
small molecules which successfully inhibited HIV-1 PR in vitro to viable drugs was complicated
by solubility, bioavailability, stability, and side effect issues. The drug design was additionally
stymied by the fact that in vitro inhibition did not necessarily result in inhibition of the viral
replication in cell cultures.40
The first FDA-approved protease inhibitor for HIV in 1995 was saquinavir (SQV) (Figure 1-
8F)55
followed shortly thereafter by ritonavir (RTV) and indinavir (IDV). There are currently 10
FDA-approved protease inhibitors (structures are shown in Appendix A (Figure A-1), properties
listed in Table 1-1). SQV and most of the FDA approved protease inhibitors are peptidomimetic
inhibitors, meaning that the structures mimic that of a peptide. The structure of the transition
state analogue varies slightly between inhibitors, but they are all based on either the
hydroxyethylamine (HEA) (Figure 1-8D) or the hydroxyethylene (HEE) scaffold (Figure 1-8C).
Tipranavir (Figure 1-8G), the only non-peptidomimetic inhibitor approved by the FDA, was
discovered from refinement of the lead compound phenprocoumon56
and is thus considered to
have a coumarin scaffold.
Peptidomimetic inhibitors are not the only option for inhibiting HIV-1 PR. Technically, any
molecule that can prevent the protease from functioning is an inhibitor. This means that
45
An inhibitor which binds under the elbow regions could stabilize the closed conformation and
prevent flap molecules which prevent dimer formation could be used as inhibitors, since the
monomeric protein is essentially inactive.57
It has been hypothesized that small molecules
designed to bindopening, thus preventing substrate binding to the active site.58
Conversely, large
inorganic compounds have been co-crystallized with the protease and hold the flaps in a wide-
open conformation, thus preventing substrate binding and substrate-flap interactions.59
Table 1-1. FDA approved protease inhibitors for treatment of HIV-1 Inhibitor Abbreviation Year
Approved
Scaffold
Type
Kd (pM)a,b
KI (nM)b,c
# non-water
mediated hydrogen
bondd,e,f,g
Amprenavir APV 1999 HEA 220(±27) 0.17
c 5
d
Tipranavir TPV 2005 Coumarin 19 b 0.019
b 6
g
Indinavir IDV 1996 HEE 590(±93) a 3.9
c 3
d
Saquinavir SQV 1995 HEA 280(±22) a 1.3
c 7
d
Lopinavir LPV 2000 HEE 36(±7) a 0.05
c 3
f
Fosamprenavir FPV 2003 HEE
(modified)
NAh NA
h NA
h
Ritonavir RTV 1996 HEE 100(±11) a 0.7
c 7
e
Darunavir DRV 2006 HEA 10b 0.010
b 6
d
Atazanavir ATV 2003 HEA NAh 0.48
c 3
b
Nelfinavir NFV 1997 HEA 670(±110)a 1.2
c 2
d
a) Data from Clemente et al.60
d) Data from Muzammil et al.61
c) Data from Yanchunas et al.62
d) Data from Prabu-Jeyabalan et al.63
e) Data from Prabu-Jeyabalan et al.64
f) Data from Reddy
et al.65
g) Data from Nalam et al.66
h) Data not available
Characterization of Inhibitor Binding
The FDA-approved protease inhibitors are competitive inhibitors, which means they bind
HIV-1 PR stronger than the substrate, the substrate-binding and inhibitor-binding are mutually
exclusive, and that the binding is reversible. Competitive inhibition follows the reaction scheme
in Figure 1-9, where E, S, I, and P are the enzyme, substrate, inhibitor, and product respectively,
ES and EI are the enzyme-substrate and enzyme-inhibitor complexes respectively.
46
Figure 1-9. Reaction scheme for competitive inhibition.
The binding affinity of an inhibitor is specified in terms of the association constant, Ka
(Equation 1-1), which is in turn determined by the standard Gibbs free energy, G° (Equation
1-2), where R is the molar gas constant, T is the absolute temperature, H° is the standard
]][[
][
IE
EIKa (1-1)
)ln( aKRTSTHG (1-2)
change in enthalpy, and S° is the standard change in entropy. As competitive inhibitors, they
must bind with very high affinity to prevent the substrate from binding. For binding to be
thermodynamically favorable, G° must be negative with larger absolute magnitudes
corresponding to tighter binding. Most of the first generation of inhibitors (IDV, SQV, and
NFV) have small positive H° values and large positive S values to achieve the large negative
G° values needed for effective competitive inhibition.67
RTV, APV, LPV, and ATV have small negative H° values and moderate positive S°
values that combine to give large negative G° values. The most recent inhibitors, DRV and
TPV, have large negative H° values with moderate to small S° values that combine to give
E + S ES E + P
+
I
EI + S No Reaction
k1
k-1
k2
k3
47
large negative G° values. At first glance, one might think these differences are trivial, because
regardless of the size and sign of the entropic and enthalpic contributions, the free energies are
all large and negative. However, these variations are significant because they indicate a
considerable diversity in how the inhibitors bind and determine what conditions affect the
binding.
HIV-1 PR Subtype Polymorphisms and Rates of Mutation
Like most viruses, HIV-1 has a high rate of mutation which gives rise to genetic variability.
The viral reverse transcriptase lacks the proof-reading capability of most eukaryotic polymerases
resulting in a significantly higher rate of mutation relative to eukaryotic cells. The mutation rate
of human DNA polymerase is estimated to be roughly 5x10 -11
mutations/bp/replication68
whereas the mutation rate for HIV-1 is 3.4 x 10-5
mutations/bp/replication.69
Since the viral
genome contains about 10 kb, there is approximately one mutation for every three replication
cycles.
The genetic variability of HIV is manifested in the large number of differing viral genomic
sequences that appear all over the world. The sequences have been divided into groups and
subtypes as illustrated in Figure 1-10 based on their similarities and differences. The sequences
in each group (M-Major, O, N) differ by at least 25% in the gag and env genes. Each group is
subdivided into subtypes (A-L). Each subtype refers to sequences from a common ancestor that
differ by more than 20% in the env gene and 15% in the gag gene.3 The variations in any given
genomic sequence are typically characterized by comparing it to the consensus sequence for
appropriate subtype.
The most studied subtype is B, which is most prevalent in North America and Western
Europe. The consensus sequence for subtype B is from the LAI isolate,3a sample taken from a
48
Figure 1-10. Phylogenic tree of HIV-1 (reproduced from Peeters et al.70
). The scale bar
represents 10% divergence in sequence from the most recent common ancestor.
Group N and O are more closely related to SIV strains than to HIV M strains.
patient designated LAI, and is thus referred to as the LAI sequence. It is listed as
B.FR.83.HXB2 in the Los Alamos HIV database. Worldwide, subtype C is responsible for the
highest number and is predominantly found in sub-Saharan Africa.
It is important to note that the natural sequence variation (not drug pressure selected) in a
subgroup is not random and is found in specific regions of the HIV-1 PR. The functionally or
structurally important regions of HIV-1 PR have little or no significant variation. A comparison
of HIV-1 PR protein sequences (Stanford HIV Database, http://hivdb.stanford.edu) from both
untreated (protease inhibitor naïve) and treated (protease inhibitor therapy) patients (Figure 1-11)
F1
F2
B
D
A1
A2
K
F
B/D
C
H
A
G
J
Group N
Group O
Group M
SIV
SIV
SIV
Scale Bar = 10% divergence
49
Figure 1-11. Protein sequence variation among protease inhibitor naïve patients and patients
who have undergone protease inhibitor therapy. The data are averaged values of
subtypes A, B, C, D, F, G, AE, and AG. The % variation is relative to the consensus
sequence for each subtype. The residue number corresponds to the position in the
amino acid sequence of HIV-1 PR.
reveals that there are multiple conserved regions for the protease in the untreated patients.
Several of these regions are no longer conserved in protease inhibitor-treated patients. As
illustrated in Figure 1-11, the conserved regions correspond to the dimerization domain, the
flaps, the active site, and the active site wall. These domains are functionally important for the
protease. The dimerization domain is essential because the protease monomer is effectively
inactive. Likewise, the flaps are necessary in binding the substrate and holding the substrate
during catalysis, in addition to regulating substrate access to the active site. The active site walls
are also involved in binding and recognizing the substrate and are necessary for enzymatic
activity and specificity.
Drug-Pressure Selected Mutations
The high mutation rate of the HIV genome provides a mechanism of evolving for adaption to
changing environments, which results in immune system evasion and drug resistance. When the
0 10 20 30 40 50 60 70 80 900
10
20
30
40
% V
ari
atio
n
Residue #
PI Naive
PI Therapy
50
virus attempts to replicate in the presence of an inhibitor, viruses containing random mutations
that allow the virus to propagate will survive. The viral fitness of these variants will be honed
over many generations to produce viable drug-resistant viruses.
For HIV-1 PR, the drug-pressure selected mutations can be divided into two categories:
active site and non-active site mutations. The ability of the active site mutations to confer drug
resistance is easily explained because these mutations can reduce inhibitor binding by changing
the shape of the active site pocket. The ability of the non-active site mutations to confer
resistance is not as straightforward. The currently accepted explanation is that the non-active site
mutations affect the dynamics and/or flexibility of HIV-1 PR, either restricting HIV-1 PR from
reaching the wide-open conformation needed to bind the inhibitor or preventing the flaps from
closing before the inhibitor can optimize its geometry for high-affinity binding.71
Thus,
understanding the role of the flaps in inhibitor binding can potentially result in the design of
better drugs that are less susceptible to resistance.
Understanding the Flaps of HIV-1 PR
As an important factor in both drug design and drug resistance, many methods (including
NMR, x-ray crystallography, molecular dynamics (MD) simulations, fluorescence, and others)
have been used to study the structure and flexibility of the HIV-1 PR flaps. Together, these
techniques have elucidated two keys features of the flaps: the conformations and the flexibility of
the flaps—the ability of the flaps to transition between conformations.
The semi-open form has been shown to be the most stable conformation in apo HIV-1 PR by
NMR, x-ray crystallography, and MD studies. NMR relaxation measurements and NMR nuclear
Overhauser effect (NOE) spectroscopy have shown that the flaps are relatively flexible in the
absence of substrate or inhibitors. The -hairpin turn structure (Figure 1-4) is maintained,72
but
51
the flaps undergo large amplitude low frequency motion on the s to ms timescale indicative of
conformational exchange. Additionally, the lifetime of these states is approximately 100 s.
The flap tips, residues 48-52, are even more flexible, undergoing rapid conformational
exchange.73
As result of this flexibility, the flap conformations have been described as an
ensemble of semi-open conformations that can transiently sample closed and wide-open
conformations.
The binding of substrate or inhibitor stabilizes the closed conformations because the flaps
also interact with the substrate or inhibitor and move closer to the active site. These interactions
also result in the flaps becoming rigid72
and only experiencing slight motion in residues 50 and
51.73
Also, the ―handedness‖ of the flaps—the relative position of one flap in front of the
other—changes upon binding substrate or inhibitor as illustrated in Figure 1-12.
Figure 1-12. Structures of two x-ray crystal structures of HIV-1 PR illustrating the ―handedness‖
of the flaps in the semi-open and closed conformations. A) Top view of the closed
conformation (PDB ID 2BPX). B) Front view of the closed conformation. C) Top
view of the semi-open conformation (PDB ID1HHP). D) Front view of the semi-
open conformation.
In addition to the closed and semi-open conformations, MD simulations have also revealed
two other possible flap conformations: wide-open and curled (or tucked). Although the wide-
open form has been known to exist for years, the MD simulations were the first to provide a
A
B
C
D
52
structure.74
An x-ray structure of a drug-resistant clinical isolate, MDR769,75
also shows an
open conformation but MD simulations76
have demonstrated that this conformation is an artifact
of crystal contacts. However, it is possible that this structure contributes to a small fraction of
the conformational ensemble of HIV-1 PR.
The x-ray structure of MDR769 is shown in Figure 1-13 along with 3 other HIV-1 PR x-ray
structures illustrating the conformations seen by x-ray crystallography. The closed form was
Figure 1-13. Four x-ray crystal structures illustrating the major conformations of HIV-1 PR.
The closed conformation (PDB ID 2BPX) is shown in green and the semi-open
(1HHP) in red. The gold structure (1TW7) is an ―open‖ structure that was
crystallized from a drug resistant variant. (It should be noted that the flap
conformations are stabilized by a crystal-crystal contact). The blue structure (1ZTZ)
was crystallized in the presence of a bulky inorganic inhibitor that restricted the flaps
from closing.
crystallized in the presence of an inhibitor and is the conformation in which the flaps sit the
closest to the active site. The semi-open form was crystallized without substrate or inhibitor.
A
B
53
The flaps in this state sit slightly farther away from active site but still interact with each other.
The ―handedness‖ of the flaps is also reversed relative to closed form. One of the open
conformations (PDB ID 1ZTZ) was crystallized in the presence of bulky inorganic molecules in
addition to an inhibitor. These molecules stabilized a horizontal opening of the flaps. The other
open form is MDR769 and was crystallized in the absence of substrate or inhibitor. This
structure also displays more of a horizontal opening (as opposed to the more vertical opening
events seen in MD simulations).
The lengths of all-atom MD simulations are typically restricted to less than 100 ns because of
high computational demands. However, most large conformational changes occur on the s to
ms timescale. To capture these events in a computationally feasible timescale, many
computations utilize activated or restricted MD simulations,58; 74
which typically involve the use
of harmonic force constants on specific atoms to initiate the conformational change. Although
these simulations can provide accurate models, the forces used to activate or restrict the
simulation can obscure relevant information about the protein such as correlations between
domains or the relative populations of each state. Thus, the MD simulations of Simmerling et
al.50; 77
are particularly important because their use of a low-viscosity implicit solvent allowed
them capture apo HIV-1 PR transitioning between the semi-open, closed, and wide-open
conformations and to extract valuable information about the correlations of various domains
throughout these events.
Figure 1-14 shows the front and top views of the closed and semi-open conformations used
as starting points for the simulations, the wide-open conformation from their simulation, and an
overlay of these structures to highlight the changes in various domains. In their simulation, the
opening of the flaps correlated with a downward shift in the cantilever and fulcrum. At the peak
54
of the opening event, the distance between the tips was greater than 30 Å. An additional MD
simulation77
reveals that this open structure will close around an inhibitor placed in the active
site to form the closed conformation. Two of the significant achievements of this work are that
HIV-1 PR returned to the semi-open form after reaching the wide-open state and transiently
sampled the closed conformation in addition to the wide-open state. These results corroborate
the work of Ishima et al.73
which determined that in the absence of substrate or inhibitors, the
flap conformations are predominantly semi-open but can also sample closed and wide-open
forms.
Figure 1-14. Structures of three predominant HIV-1 protease conformations. A) Closed
conformation (PDB ID 1HVR). B) Semi-open conformation (PDB ID 1HHP).
C) Wide-open conformation. Figure modified from Simmerling et al.50
Several MD simulations have also shown that the flaps adopt a curled or tucked
conformation. These conformations include a broad range of flap conformations as illustrated in
Figures 1-15 and 1-16. In the more open curled states,78
the flap tips curl back towards the active
site and the monomers undergo a domain rotation that opens up the active site pocket. In these
A
B
C
D
E
F
55
Figure 1-15. A) MD structure from a simulation of HIV-1 protease illustrating the curled or
tucked conformation. B) Illustration of the interactions between Ile 50 and residues
79-81 and 32. Figure reprinted with permission from Scott et al.79
structures, Ile50 typically interacts with residues 79-81 and 32 as shown in Figure 1-15B. Other
curled structures are more closed,79
with the flaps curling into the active site pocket but without
the domain rotation that opens the pocket as illustrated in Figure 1-16. Ishima et al.80
recently
demonstrated via NMR relaxation measurements and chemical shift analysis that the
Figure 1-16. MD structures from a simulation of HIV-1 protease illustrating the curled or tucked
conformations. A) X-ray structure (PDB ID 1HHP), the starting structure of the
simulation. B) Structure at 2500 ps. C) Structure at 5000 ps. Figure reprinted with
permission from Toth et al. J. Mol. Graph. Model. 2006.
A B
56
predominant conformation in the absence of substrate or inhibitors involves interactions between
the flap tips. Thus, the curled or tucked conformations may constitute a small fraction of the
conformational ensemble but are not the dominant conformation.
Recently our group utilized site-directed spin-labeling (SDSL) in conjuction with double
electron-electron resonance (DEER) to characterize the flap conformations.81
These experiments
measured the interflap distance between spin-labels grafted at position 55 in the flaps. Figure
1-17 shows the dipolar evolution curves and corresponding distance profiles for HIV-1 PR in the
absence and presence of ritonavir (RTV). In the presence of RTV, an inhibitor of HIV-1 PR, the
most probable distance was 32.6 Å, corresponding to the distance predicted for the closed
conformation. The breadth of the distribution was 3.0 Å which corresponds to the motion of the
spin-label about the flexible linker that attaches the label to the protein. In the absence of the
inhibitor, the most probable distance was 35.5 Å, which corresponds to the distance expected for
the semi-open conformation. The breadth of the profile was 10 Å and corresponds to the both
the motion of the label and the motion of the flaps. Most significantly, this distance profile
includes distances greater than 39 Å which likely correspond to a wide-conformation.
Figure 1-17. A) DEER dipolar evolution curves for apo and inhibitor-bound HIV-1 PR. B)
Corresponding distance profiles.81
0.0 0.5 1.0 1.5 2.0
Ech
o In
ten
sity
Time ( s)
A
20 30 40 50
P(r
)
Distance (Å)
B
35.4 Å
32.6 Å
57
These results were corroborated by additional simulation from Simmerling et al.82
Figure
1-18 shows the overlay of the MD results with the DEER distance profiles in the absence and
presence of RTV. Their results confirmed that the breadth of the profile for inhibited HIV-1 PR
does correspond to the motion of the label about the flexible linker. Likewise, the breadth of the
profile for apo HIV-1 PR results from a significant increase in the motion in the flaps. Their
results also demonstrated that the larger distances (>39 Å) can only be achieved in a wide-open
form.
Figure 1-18. Inter-spin label distances from DEER experiments and MD simulations. A)
Inhibitor-bound HIV-1 PR. B) Apo HIV-1 PR. MD simulation initiated from closed
conformation. C) Apo HIV-1 PR. MD simulation initiated from semi-open
conformation. Figure reprinted with permission from Ref.82
These results have collectively provided significant insight into the conformations and
flexibility of HIV-1 PR. However, they are mostly specific to subtype B. A few MD
simulations58; 74; 76; 83
have investigated the effect of mutations on the flaps. The conclusion
drawn from these simulations are that the various mutations alter the stability of each
conformation in such a way that inhibitor binding becomes less favorable than with wild-type
HIV-1 PR. In the case of the V82A I84V double mutant, the flaps preferred a more open
conformation. Thus, inhibitor binding would include a larger entropic penalty relative to wild-
type.58
In the case of M46I,74
the flaps were shown to prefer the closed conformation in the
A B C
58
absence of an inhibitor. A large number of x-ray structures exist for HIV-1 PR constructs
including various single point mutations and combinations of mutations. These structures show
that the largest effects are seen in the shape and size of the active site binding pocket and that the
rest of the protein is relatively consistent. This trend implies that a significant portion of the drug
resistance arises from changes in the flap flexibility and not in just the closed conformation. In
order to gain a better understanding of the mechanisms of drug resistance, more investigations
need to be performed to ascertain the effects of each mutation and various combinations of
mutations.
Protein Structure and Flexibility
Protein Structure
Proteins consist of a polypeptide chain, many of which fold into a specific tertiary structure.
The structure of proteins has been divided into four categories: primary, secondary, tertiary, and
quaternary structure. The primary structure of the protein—the sequence of amino acids in the
polypeptide—is determined by the DNA encoding for the protein. The secondary structure of
the protein is determined by the preferred rotomeric conformations of the amino acid side chains
about the N-C bond and the C -C bond (as defined by the and angles, respectively). The
secondary structure is usually classified as being a helix, a -sheet, a loop, or disordered. The
helices can adopt several different turn radii which correspond to the -helix, the 310 helix, and
-helix, although the -helix is by far the most common. The tertiary structure is determined by
the interactions between the various secondary structure elements in the protein—the packing of
helices or the stacking of -sheets. The quaternary structure, if present, is the interaction
between multiple proteins in the formation of a macromolecular complex. References to a
59
protein‘s structure typically refer to the unique tertiary structure that the protein assumes in
solution.
The secondary structural elements, namely the helix and the -sheet, are stabilized by a
network of hydrogen bonds between the atoms in the peptide backbone. Certain amino acids
seem to have a preference for being structured and some unstructured. Proline for example, is
very rarely found in helices and is essentially limited to the ends of the helix which are more
tolerant of non-helical and angles. A data mining study of the structures in the PDB had
revealed that disordered regions in proteins are typically enriched in charged residues (lysine
(Lys), arginine (Arg), aspartate (Asp), glutamate (Glu)) in addition to proline (Pro) and serine
(Ser). The disordered regions are also typically lacking in hydrophobic residues such as
tryptophan (Trp), phenylalanine (Phe), isoleucine (Ile), and Tyrosine.84
Additionally, certain
amino acids seem to have a preference for the type of secondary structure in which they occur.
This preference results from balancing the optimization of the peptide backbone hydrogen
bonding network and the packing of the bulky side chains together and is not as pronounced as
the preference between order and disorder.
This structural preference was initially investigated in the early 1970‘s85; 86; 87
but has seen a
resurgence in popularity as a result of efforts to engineer proteins that will fold into a desired
structure.88
The known structures of 15 proteins were analyzed to determine the frequency of
each amino acid occurring in each of the major secondary structural elements. The total number
of times an amino acid appeared in each element was divided by the total number of occurrences
in all elements to give a normalized frequency (f). The frequency was divided by the relative
percent that each element occurred (36 % helix, 17.1 % -sheet, and 46.9 % coil) to yield the
conformational parameter (P). Figure 1-19 plots the conformational parameters from Chou et
60
al.85
for each amino acid. An amino acid such as Asp with roughly equivalent P values for each
element would be said to have said to have no preference for a particular structural element.
Whereas an amino acid such as Glu clearly has a preference for helical structures and Ile has a
moderate preference for -sheets. It should clarified that these numbers should not be
extrapolated to large disordered regions in proteins as these numbers were determined from—
and thus apply to—structurally well-defined regions and short loops.
Figure 1-19. Conformational parameters from Chou et al. illustrating the preference of certain
amino acids for a particular secondary structural element.
The tertiary structure of a protein is not as straightforward to determine as the secondary
structure and has been the subject of numerous studies. It has been determined that the tertiary
structure is largely created from and stabilized by hydrophobic collapse. Essentially, the
hydrophobic portions of the protein self-associate to reduce the number of ordered water
molecules necessary to solvate these regions. This step results in a collapsed structure that lacks
order called a molten globule.89
After the molten globule is formed, additional interactions act to
stabilize the native state, including electrostatic interactions and hydrogen bonds between polar
groups on the protein‘s surface.
Ala
Arg
Asn
Asp
Cys Gln
Glu
Gly
His Ile Leu
Lys
Met
Phe Pro
Ser Thr
Trp
Tyr
Val
0.0
0.2
0.4
0.6
0.8
1.0
1.2
1.4
1.6
1.8
Con
form
atio
nal P
aram
eter
helix
sheet
coil
61
It has long been understood that there is an important relationship between the structure of a
protein and its function. In 1893, Emil Fisher demonstrated that enzymes could selectively
function on a particular enantiomer and thus developed the ―lock and key‖ model—the ideas the
structure of the enzyme and the substrate should fit together like a lock and key.90
In the late
1920‘s and early 1930‘s several studies were published on denaturing proteins which established
that proteins maintain a unique structure which is lost upon denaturation.91; 92
The first protein
structures were determined in 1958 using x-ray crystallography by Max Perutz93
and Sir John
Cowdery Kendrew,94
who shared a Nobel prize for their work. There are currently over 34,500
protein structures deposited in the protein database (PDB). The formation of the protein
structure-function paradigm makes sense in the context of the available technology to the early
protein scientists. The first proteins studied were either the structural proteins, which were
typically sufficiently abundant to be easily purified, or enzymes, which could be easily identified
and tracked through a purification process by their enzymatic function, all with well defined
structures which are critical to their functions.
Protein Motion and Flexibility
Although structures provide invaluable atomistic information about the protein and its
function, it does not provide all of the information necessary to understand the protein dynamics
and how the protein converts from one structure to other.
As Richard Feynman astutely recognized, ―everything that living things can do can be
understood in terms of the jigglings and wigglings of atoms‖95
Stated another way by Dorothee
Kern, ―Biological function is ultimately rooted in the physical motion of biomolecules.‖96
Thus
the function of a protein, although largely dependent upon its structure, is also dependent upon
the protein‘s movement and flexibility. Many proteins undergo conformational changes which
are necessary for accomplishing their function. Others rely upon changes in their vibrational
62
freedom to bind ligands. Without movement and flexibility, these proteins would cease to
function.
Proteins undergo a large variety of motions that each occur within a certain timescale. The
smallest motions are the bond vibrations that occur on a ps – fs time scale, followed by bond
rotations which occur on the ps- s timescales (depending on the size of the moieties at each end
of the bond). These motions result from the thermal energy in the system. There are also small
conformational changes within the protein such as loop movements or shifting the position of a
helix which occur in the ns- s timescale. The largest motions are the domain movements, where
an entire domain in the protein shifts its location relative to the rest of the protein; these typically
occur on the s-ms timescale. Recent developments in computations and simulations have
shown that motions associated with the larger conformational changes (i.e. loop movements and
larger) frequently correspond to the collective low energy normal modes of the bond vibrations.97
Each motion in a protein carries with it a certain energy barrier that must be overcome. For
the fast motions in the ns or faster timescales, the energy barriers are typically less the 1 kT
(equivalent to 1 RT for a mole of the protein), where k is the Boltzman constant
(1.380 6504×10−23
J K-1
) and T is the absolute temperature (typically 298 K). Slow motions on
the s-ms timescale typically have energy barriers on the order of several kT. Since the thermal
energy in the system is approximately 1 kT, the barriers less than 1 kT are easily and frequently
crossed whereas the larger barriers are more difficult to cross and thus crossed less frequently. It
is the magnitude of these energy barriers that determines the rate of inter-conversion between the
two states.
The population of each state or conformation is determined by the relative free energy of
each state according to Equation 1-3, where R is the gas constant, T is the absolute temperature,
63
][
][ln
A
BRTGGGGG abab (1-3)
[B] and [A] are the concentrations of the B and A states respectively, Gb and Ga are the
corresponding molar free energies, and Gb° and Ga° are the molar free energies of the standard
states. At equilibrium, G=0, so Equation 1-3 can be rearranged to form Equation 1-4, which
can also be rearranged to form Equation 1-5. According to Equation 1-5, if the relative
][
][ln
A
BRTG (1-4)
RTGO
eA
B /
][
][ (1-5)
populations of the states can be experimentally determined, then the free energy difference
between the states can be estimated with reasonable certainty. These are the same fundamental
equations used earlier to discuss inhibitor binding, but the focus here is on the population
difference between state A and state B as opposed the entropic and enthalpic contributions to
each state.
Energy Landscapes, Conformational Ensembles, and Ensemble Shifts
The concept of an energy landscape was initially applied to proteins in terms of protein
folding funnels. The top of the folding funnel represented the protein in the unfolded state,
which has a large number of different conformations available that have the same energy level.
As the hydrophobic regions collapse, the energy of states decreases and the number of accessible
states decreases so the funnel deepens and narrows. As the specific stabilizing interactions are
formed, the energy and number of states will continue to decrease so the funnel will continue to
deepen and narrow. As the conformations sampled become more like the native state, the energy
levels continue to decrease until finally the protein reaches the native state which has the lowest
64
energy of all of the states. It has also been described that proteins in the process of folding can
reach a meta-stable state (a local minimum, but not the global minimum) and become kinetically
trapped—where the protein cannot reach the global minimum which is the native state.
The idea of energy landscapes applies to protein conformations as well. Instead of starting at
the top of the funnel, the focus is primarily on the bottom where the global and energetically
accessible local minima are located. Each local minimum in the landscape corresponds to a
stable conformation that the protein can form. Although the landscapes are typically portrayed
as being smooth, each local minimum is actually composed of multiple local minima of
approximately equal energy. These local minima are divided by small energy barriers because
the structures differ only by bond lengths and bond rotations (Figure 1-20). The landscape is
highly multidimensional because proteins have many atoms and many possible conformations.
Each conformation or conformational state of the protein corresponds to a group of highly
related structures. Collectively, all the conformational states form the protein conformational
ensemble. Thus, the ensemble includes the predominant low-energy conformations that
dominate the average structure of the protein, as well as the higher energy conformations that the
protein will rarely sample. The determination and characterization of protein conformational
ensembles is an important aspect of understanding protein function.
The energy landscape is specific for a certain set of conditions, such as solvent, temperature,
or pH, in addition to the presence of a substrate, inhibitor, or other ligand. Changing any one of
the above can, and most frequently does, remodel the energy landscape. This remodeling can be
thought of in a variety of ways, e.g. shifting the energy levels of the local minima to change the
population distribution.
65
Figure 1-20. Schematic diagram of an energy landscape for a protein with two major
conformations, A and B. The black and grey traces illustrate an ensemble shift
induced by some change in condition that stabilizes the B state and destabilizes the A
state. Figure modified from Henzler-Wild et al.96
The conformational change that a protein undergoes upon binding to a ligand can be
discussed in terms of remodeling the energy landscape. One form of remodeling is the
narrowing of breadth of the local minimum upon binding a ligand. This corresponds to an
increase in the rigidity of the protein resulting from a decrease in the mobility of the atoms and
residues although maintaining the same average structure. An example of this form of
remodeling is the homodimeric cAMP-binding transcriptional activator, which is highly dynamic
upon binding the first cAMP but rigid after binding the second cAMP.98
Another form of remodeling is the alteration of the relative energies of the local minima, thus
shifting the relative populations of each state. This is a very common theme among most
proteins that undergo a conformational change upon binding to a ligand. The implication of this
trend is that the bound form is energetically accessible to the apo protein and is stabilized by the
interaction of the partner. An example of this is the human proto-ocogene Vav, which has an
GAB
G‡(kA→B)
G‡(kB→A)
State AState B
ns
ps
s to ms
Free
En
ergy
Conformational Coordinate
66
acidic ―latch‖ domain (Ac) that binds to the guanidine nucleotide exchange factor (GEF)
substrate binding domain, resulting in autoinhibition. It was shown that Vav occasionally
samples a conformation on the s-ms timescale where the latch is displaced and autoinhibition is
relieved. Phosphorylation of Tyr174 also leads to the release of the latch and relieves the
inhibition.99
Thus, the uninhibited conformation is the higher energy state, but it is still
energetically accessible to the unphosphorylated protein. However, phosphorylation shifts the
relative energy levels between the inhibited and uninhibited states, making the uninhibited state
the more populated form.
Another mode of remodeling can occur when the higher energy state is an intermediate in the
pathway to the stable ligand-bound state. In this case, the ligand bound structure is not
energetically accessible to the apoprotein, and the minimum corresponding to the higher energy
state is shifted to correspond to the new bound state.100
An example is maltose binding protein
(MBP) which has been shown to have two unique predominant conformations (95 % open and
5% minor) in the apo state and one predominant conformation (closed) in the maltose-bound
state. The difference between the open and closed states is a 35° domain rotation of the CTD (C-
terminal domain) relative to the NTD (N-terminal domain). The minor state is very similar to
the closed state, but corresponds to only a 33° domain rotation. This difference results from an
increased distance between the domains because the interdomain interface is lined with
positively charged residues on both sides. The binding of the maltose shields these charges and
permits the domains to move closer together to form the closed state.101
In this case, the minor
conformation is the higher energy state that is energetically accessible to the apoprotein and is an
intermediate in the formation of the bound state upon ligand binding.
67
Experimental Methods for Characterizing Ensembles and Ensemble Shifts
There is a variety of techniques suitable for characterizing protein conformations, ensembles,
and ensemble shifts. Most of the techniques are only applicable for a set range of timescales and
thus can only characterize certain regions of the energy landscape. Many techniques also have
sensitivity limitations, in that signals from sparsely populated states are sufficiently weak to not
be detectable in the presence of signals from the highly populated states. Thus, the most
complete characterization requires the combination of multiple techniques.
The easiest motions to characterize are the slow timescale motions, which interconvert
slowly enough to either be studied directly. Alternatively, the higher energy states can be
trapped and studied via structure determination techniques, such as x-ray crystallography, NMR,
cryo-electron microscopy, small angel x-ray scattering, and hydrogen/deuterium exchange. The
trapping of the higher energy states is usually accomplished by careful selection of conditions
(salt concentration, temperature, pH, etc) or by binding of a ligand (frequently an altered ligand
that traps the protein in an intermediate state).
Most of these techniques have limitations or difficult-to-meet requirements. X-ray
crystallography requires that the state of interest be amenable to crystallization. For NMR, the
protein must weigh less than 100 kDa (although anything above 70 kDa is incredibly difficult).
NMR also requires that the protein can be isotopically labeled, which typically involves
recombinant expression and thus rules out proteins that must be isolated from natural sources.
The motions occurring on the faster timescales are more difficult to characterize. They
typically have been discussed in terms of statistical distributions, because there are often many
more states, which cannot usually be trapped individually.
68
NMR
Paramagnetic relaxation enhancement. Paramagnetic relaxation enhancement (PRE)
NMR utilizes a paramagnetic center to increase the relaxation rates of nuclei within a certain
radius. The paramagnetic moiety is typically introduced into the protein via site-directed spin-
labeling (discussed in detail in Chapter 2), where an amino acid is replaced by a cysteine (Cys)
and is subsequentially modified with a spin-label—a small molecule containing a stable nitroxide
radical or metal chelating group. Alternatively, if the protein contains a diamagnetic ion
cofactor, a paramagnetic transition metal ion can sometimes be substituted for the native metal
ion. The spin relaxation rates of the nuclei under investigation will be measured in the presence
of the paramagnetic species and a corresponding diamagnetic species. The difference between
the two is the enhancement resulting from the paramagnetic species. The relaxation
enhancement results from the dipolar interaction between the spins (discussed in Chapter 2)
which is proportional to the 1/r3, where r is the distance between the spins. The distance range
varies with the magnitude of the gyromagnetic ratio ( ) for the nuclei and can thus be selected by
choosing the appropriate nuclei. Typically, the spin-spin relaxation, T2 (discussed in Chapter 2),
is the preferred relaxation measurement for this technique. However, spin-lattice relaxation, T1,
measurements are also suitable.
Paramagnetic relaxation enhancement is especially useful because the range of distances over
which it is sensitive can be changed by measuring the relaxation rates for a different nucleus.
However, the true power of PRE, in terms of characterizing an energy landscape for a protein,
the sensitivity to sparsely populated states as long as the distance measured is shorter for the
higher energy state relative to the low energy state. As a result, Clore et al.101
were able to
69
determine the structure of the minor conformation in MBP, even though it represented only 5%
of the population.
Relaxation dispersion. Relaxation dispersion (RD)102
is another NMR technique that is
gaining in popularity for the characterization of conformational ensembles and sparsely
populated states. The major and minor conformations must have different chemical shift values
and different relaxation rates, both resulting from the structural differences. The RD experiment
measures the apparent relaxation rate as a function of the spacing between refocusing pulses,
which requires that the motions being studied occur on an intermediate timescale relative to the
experiment (exchange rate of the motion (1/s) chemical shift difference (rad/s) between the
states). The apparent relaxation rate is the combination of the relaxation rates of both states
relative to the amount of time spent in each state. The data are typically plotted to give a
relaxation profile (Reff( CMPG), where Reff is related to change in signal intensity and CMPG is
repetition rate of the pulses in the Carr-Purcell-Meiboom-Gill pulse sequence), from which the
exchange rate between the two states and their chemical shift differences can be determined by
fitting the data to the modified Bloch equations.103
Residual dipolar coupling. Residual dipolar coupling (RDC) NMR is a technique that uses
residual alignment of the protein with the magnetic field to investigate the relative alignment of
bonds within the protein. The protein alignment can be enhanced by adding large, non-spherical
moieties which align within the magnetic field to the sample such as lipid bicelles—discoid
shaped lipid bilayers resulting from the combination of short and long chain lipids which forms a
planar bilayer with the long chain lipids and is ringed by the short chain lipids. The degree of
ordering of the protein can be controlled by adjusting the concentration of the bicelles.104
70
Depending on the assumptions made during the data analysis, both structural and dynamical
information can be elucidated.105
Order parameter determination. NMR relaxation techniques can also be useful by fitting
the data to determine the model-free order parameter, S, and the correlation time e.106
The T1,
T2, and nuclear Overhauser effect (NOE) values can be measured using inversion recovery, spin
echo, and NOESY pulse sequences respectively. These data are fit to the equations described in
Szabo et al.106
to extract S and e, which correspond to magnitude and rate of the motion
respectively. Because this technique characterizes each residue in protein, different residues can
compared to residues in regions of the protein that experience a larger change in motion upon
ligand binding than other sites. It can also compare alterations in the motion at a particular site
as a result of amino acid substitutions in the protein sequence, which can elucidate important
residues for the motion and flexibility in the protein.
Hydrogen/deuterium exchange
Hydrogen/deuterium exchange utilizes the pH dependent exchange between the amide proton
and water to replace amide protons with deuterium atoms. It has been shown107
that the amide
bonds involved in hydrogen bonds exchange at a slower rate relative to amide bonds solvated by
water. It is also known that buried amides (the amides not exposed to the solvent) are not
accessible for exchange. The effective rate of deuterium exchange will be a convolution of the
time spent by a particular proton in an exchangeable conformation vs. a non-exchangeable
conformation. For example, an amide proton in an active site that is protected by a ―lid‖ would
only be accessible when the lid is open. Thus, measurement of the exchange rate of such a
proton would provide information on the dynamics of the lid domain. This technique requires a
detection method sensitive to the small differences between hydrogen and deuterium and is thus
71
predominantly performed using either NMR or mass spectrometry (MS). Fast timescales can be
probed by NMR and either method can be used to probe the slow timescales. The slower
timescales are typically monitored via quenching, i.e., the sample is allowed to exchange for a
certain period of time at an acidic pH, after which it is quenched by raising the pH above 7.
Fluorescence
Intrinsic tryptophan fluorescence. A large variety of fluorescence-based techniques can
provide insight into the conformations and ensembles in proteins. Intrinsic tryptophan (Trp)
fluorescence is sensitive to the polarity of its environment, and can distinguish between
conformations with differing environments. Fluorescence lifetime measurements of the intrinsic
Trp fluorescence can reveal the number of different Trp environments. If there is only one Trp
and it has multiple lifetimes (i.e., the lifetime data are best fit by a multi-exponent) then that Trp
has multiple conformations. The lifetimes can be studied as a function of ligand concentration,
pH, temperature, or other conditions to monitor the relative number of Trp in each conformation
as well as changes to each conformation. For example, consider a protein has a Trp residue with
two lifetimes, one short and one long. As ligand is added, the relative contribution from each
state will change and be detected. It is also possible, however, that the ligand can also change
the lifetime of a state, making it either longer or shorter. This can also be identified and tracked
as a function of ligand concentration.
Single molecule fluorescence. Another increasingly common technique is single molecule
fluorescence. This method typically relies on modifying a residue on the protein with a very
high quantum yield fluorescent probe (the quantum yield of Trp is too low for these
experiments). By measuring the time-dependence of the lifetime, this method can reveal
information about the conformation of the protein. This technique can also be used for FRET
(Forester‘s or Fluorescence Resonance Energy Transfer) in which case the time-dependence of a
72
single distance can be measured and directly related to a conformation. There are multiple
benefits to observing single molecules. One is that it is possible to monitor both how long it
takes for a conformational change to occur and how long the state persists. It has been observed
that the conformational changes are typically faster than the observation time but that the
―slowness‖ of the change results from the infrequency of the transition. Another powerful
benefit is that events can be observed in order. Many techniques can show that a protein has
multiple conformations, but few techniques can determine the exact order they occur in. For
example, single molecule FRET revealed several additional rotational steps between the three
major conformations and also revealed that the steps are reversed in ATP synthesis relative to
ATP hydrolysis.108
X-ray diffraction
X-ray crystallography is powerful technique for discovering structural information about a
protein on an atomistic scale. This technique is even powerful in conjunction with biochemical
tricks for capturing or stabilizing higher energy or transient states. These tricks include the use
of transition state mimetics, substrate or products mimetics, and non-reactive substrates, as well
as variant proteins that are enzymatically incompetent or impaired. Because the technique
requires the protein to assume a conformation amenable to crystallization, it is primarily limited
to the study of slow timescales. However, faster motions can be studied by analyzing the B
factors, as long as care is taken to avoid effects from crystal contacts and the lattice.
Cryogenic studies
Because the transition between states relies on the thermal energy of the system, reducing the
thermal energy available will reduce the rate at which the protein can switch states. This practice
facilitates the study of transient states too short-lived to study at room temperature. Enzymes are
frequently studied by freezing quenching the sample immediately after mixing the enzyme with
73
the substrate. For light-triggered events, the sample is frozen in the dark and then exposed to
light.
Computational Methods
The ability to calculate the position and trajectories of atoms as a function of time provides
dynamic and atomistic insight into a protein‘s structure and flexibility. Computational studies in
conjuction with experimental data form a particularly powerful combination because the
computations can provide insight into the interpretation of the experimental results. Likewise,
the experimental results can confirm the accuracy of the computation. It should be noted that the
computations are only as good as the force fields used whereas the experimental results tend to
be more reliable so long as they were preformed correctly and with the proper control
experiments
Scope of Dissertation
This dissertation reports on the investigation into the conformations and flexibility of the
―flaps‖ in HIV protease using pulsed and CW EPR. The aims of this work were to (1) optimize
this technique for addressing these questions and (2) to determine if the flap flexibility is altered
by drug pressure selected mutations and naturally occurring polymorphisms. To optimize this
technique, the data analysis process was thoroughly examined and expanded to include
additional refinements in the final distance profiles. Additionally, the effects of solutes were
investigated to determine the effect of solutes on the flap conformation and spin-label mobility.
This technique was applied to three HIV-1 PR variants—subtype B, subtype C, and a clinical
isolate with drug-pressure selected mutations, V6. The distance between the spin-label on the
flaps was investigated for the apoenzyme and for the enzyme in the presence of nine FDA-
approved inhibitors and one substrate mimic. One of the major goals of this work was also to
74
demonstrate that distance measurements via pulsed EPR can also be used to characterize the
conformational ensemble of sampled proteins.
75
CHAPTER 2
ELECTRON PARAMAGNETIC RESONANCE
Introduction to Electron Paramagnetic Resonance
Electron Paramagnetic Resonance (EPR) is a spectroscopic technique for studying the
interactions between electronic magnetic moments and their immediate environments including
externally applied magnetic fields. There are many excellent reviews for a deeper understanding
of this material.109; 110; 111; 112; 113; 114
Presented here is a brief overview in sufficient detail for the
reader to understand the topics presented in the later chapters.
Spin Hamiltonian
The Hamiltonian is an operator that corresponds to the energy of a system. In an externally
applied magnetic field which is independent of time, the energy of the spin system can be
determined from the static spin Hamiltonian (Equations 2-1 and 2-2)—as opposed to the
oscillatory Hamiltonian that corresponds to the energy of the system in a time-dependent
magnetic field. The static Hamiltonian includes a variety of terms (discussed in subsequent
sections) some of
exchddNNNQNZHFZFSEZ HHHHHHHHH 0 (2-1)
ki
k
ki
i
I
kkk
m
k
kknn
m
k
kke
k
g IdIIPIIBIASDSSgSBTTTTTT ),(
2
11
0,
1
00 H (2-2)
which contribute significantly only in pulsed experiments and some which contribute
significantly in both CW and pulsed EPR. In Equation 2-1HEZ is the electron Zeeman term,
HZFS is the zero-field splitting term, HHF is the hyperfine interaction term, HNZ is the nuclear
Zeeman term, HNQ is the nuclear quadrupole interactions, HNN is the spin-spin interaction term
76
which includes all inter-nuclear interactions, Hdd is the electron-electron dipolar interaction, and
Hexch is the exchange coupling term..
The oscillatory Hamiltonian results from the time-dependence of the applied magnetic field
expressed in Equation 2-3. Substitution of BMW(t) for B0 in Equation 2-2 only affects the
)cos(2)( tt MW0MW BB (2-3)
electron and nuclear Zeeman terms, which can be rewritten as Equation 2-4 and Equation 2-5
respectively.
gSBT
MW )(t(t) eEZ H (2-4)
m
k
kknnNZ tg(t)1
, )( IBT
MW H (2-5)
Electron Zeeman
All particles with spin angular momentum (S) also have a spin magnetic moment ( ) which
is related to S by a proportionality constant, the gyromagnetic ratio ( = q/2m), where q and m
are the charge and mass, respectively, of the particle and ħ is Plank‘s constant (h= 6.626×10−34
J
s) divided by 2 (Equation 2-6). For an electron, this relationship can be rewritten as Equation
2-7, where g is the spectroscopic g-factor (or Landé g-factor) and e is the Bohr magneton
(written as B in some literature) (Equation 2-8), where e is the charge on an electron
(-e = 1.602 x 10-19
C), and me is the rest mass of the electron (9.109 x 10 -31
kg). The value of the
g factor for a free electron is 2.0023193043737, but this value will deviate as a result of spin-
orbit coupling for bound electrons.
SSμ γ2m
q (2-6)
77
Sμ ee g (2-7)
gm
eJTx
e
e
210274.9 124
(2-8)
Additionally, the g factor is actually a tensor and can be anisotropic for some systems. These
two factors make g a useful parameter for characterizing a spin system. Equation 2-4 can be
rewritten as Equation 2-9 to include the tensorial nature of g.
gSμ ee (2-9)
In the presence of an applied magnetic field, the spin magnetic moment will interact with the
field with the energy described by the Hamiltonian in Equation 2-10, where B0 is the applied
0
TT
0 BμμB ee H (2-10)
field, and B0T is the transpose of B0. This interaction causes the spins to align themselves
parallel or antiparallel to the applied field. The spins aligned antiparallel to the field will be at a
lower energy than the spins aligned parallel thus the degeneracy of the spin states is broken.
Because the electron is negatively charged, the electron spin alignment is opposite of the nuclear
spin alignment. Substitution with e yields Equation 2-11, where S is the spin vector for the
SgBBgSTT
00 eeEZ H (2-11)
system. If B0 is applied in z direction of the laboratory frame then the Hamiltonian can be
simplified to Equation 2-12. For a single unpaired electron S = ± ½ so the corresponding
0BSg zeEZ H (2-12)
eigenstates are ms = ± ½. The ms = + ½ state is designated as and the ms = - ½ state is
designated as . The wave functions for these states are | and | , respectively. The
corresponding energies for the spin energy levels are calculated in Equations 2-13 and 2-14.
78
02
1BgE eEZ H (2-13)
02
1BgE eEZ H (2-14)
Thus the difference in energy levels, E, is shown in Equation 2-15, which is also the resonance
condition for EPR. It should be noted the E and thus —the resonant frequency—depend on
the magnitude of B0.
hBgEEE e 0|| (2-15)
Hyperfine interaction
The hyperfine interaction is the result of the electron spin interacting with the additional
magnetic field induced by the spins of neighboring nuclei that have a net magnetic moment and
is described by Equation 2-16, where I is the nuclear spin quantum number, A is the hyperfine
m
k
kkHF
1
IAST
H (2-16)
tensor, and the index k is for all interacting nuclei. This interaction results in a further splitting
of the energy levels based on the spin quantum number of the nucleus as shown in Figure 2-1.
H HF is characterized by a tensor (A) and is anisotropic. The anisotropy makes the hyperfine
interaction a useful parameter for characterizing a spin system.
The hyperfine interaction can also be expressed as Equation 2-17, which is composed of
DDFHF HHH (2-17)
the isotropic Fermi contact term (HF) and anisotropic electron-nuclear dipole interaction (HDD).
HF can be expressed as Equation 2-18, where aiso is the isotropic hyperfine coupling constant
79
Figure 2-1. Energy level diagram for the Zeeman and hyperfine splittings of an S = 1/2 spin on a
nucleus with I=1. Selection rules require that only one quantum number changes
during a transition so the mS number changes while the mI number remains constant
resulting in the three possible transitions illustrated.
(Equation 2-19) and | (0)|2 is the electron spin density at the nucleus, which typically includes
k
TISisoF aH (2-18)
2
00 |)0(|
3
2nneeiso gga
(2-19)
only the contribution of the s orbital. More rigorous calculations should include contributions
from configuration interactions and spin-polarization mechanisms when the unpaired electron is
in a p, d, or f orbital.115
The electron-nuclear dipole interaction, HDD, can be expressed as Equation 2-20, where r is
35
0 ))(3(
4 rrgg nneeDD
ISIrrSTTT
H (2-20)
the vector connecting the electron spin and the nuclear spin. Integration of Equation 2-20 over
the spatial distribution of the electron yields Equation 2-21, where T is the traceless and
TIST
DDH (2-21)
symmetric dipolar coupling tensor with the elements in Equation 2-22 (for spin-only electron-
nuclear dipolar coupling).
mI = -1
mI = 0
mI = 1
mI = 1
mI = 0
mI = -1
mS = 1/2
mS = -1/2
h =ge eB0
Field off
Field on
80
05
2
00
3
4 r
rrrggT
ijji
nneeij
(2-22)
Selection rules dictate that only one quantum number can change in a magnetic resonance
transition so the only allowed transitions are between the mS states while the mI state remains
constant. For a nucleus with I = 1, this leads to the three available transitions illustrated in
Figure 2-1.
Nuclear Zeeman
The nuclear Zeeman term (Equation 2-23) results from the interaction of the nuclear spin
m
k
kkn
nNZ
g
1
0,
IBT
H (2-23)
with the applied magnetic field, where gn ranges from 0.097 for 191
Ir to 5.58 for 1H. This term is
generally considered to be isotropic and is typically small and hard to detect in EPR experiments,
although it is responsible for spin-flip transitions.
Zero-field splitting
The zero-field splitting term (Equation 2-24), where D is the zero field interaction tensor,
DSST
ZFSH (2-24)
results from the special case where the spin energy levels are not degenerate in the absence of an
applied magnetic field. This only occurs with spins > ½ and thus is beyond the scope of this
work.
Nuclear quadrupole
The nuclear quadrupole term (Equation 2-25), where P is the nuclear quadrupole tensor,
2
1kI
kkkNQ IPIT
H (2-25)
81
results from nuclei with spin >1 that also have a non-spherical charge distribution. The lack of
symmetry with the charge distribution interacts with the electric field gradient resulting from
nearby electrons and nuclei. The effects of this term are small and typically negligible for EPR
experiments.
Nuclear spin-spin interactions
The nuclear spin-spin interaction term (Equation 2-26), where d is the nuclear dipole
ki
k
ki
iNN IdIT ),(
H (2-26)
coupling tensor, results from the dipole-dipole interactions between two nuclei. This term
provides much of the structural information gained from NMR experiments but is negligible for
most EPR applications.
Electron-electron dipole interactions
The electron-electron dipole interaction term (Equation 2-27) results from the dipolar
21 DSST
ddH (2-27)
interaction between electrons (the interaction of the electron with the magnetic field from a
nearby electron). This term is the basis for the distance measurements via pulsed EPR and will
be discussed later in more detail.
Exchange coupling
The exchange coupling term (Equation 2-28) results from the Heisenberg exchange coupling
21 JSST
exchH (2-28)
that occurs when there is orbital overlap between the orbitals of two electrons, where J is the
exchange coupling tensor. The orbital overlap permits the electrons to swap orbitals, thus
confusing the knowledge of the respective spin states of each electron. This exchange occurs at
82
distances much shorter than those used for DEER and thus does not contribute to the
experiments performed for this work.
Site-Directed Spin-Labeling
History of site-directed spin-labeling
The history of site-directed spin-labeling began in 1965, when three papers were published
which utilized a persistent nitroxide radical to enable EPR studies of biological molecules. Two
of the papers combined the nitroxide radical with a reactive group to covalently attach the radical
to a protein.116; 117
The third paper used a nitroxide radical with a 2,4-dinitrophenyl moiety to
bind antibodies specific for the 2,4-dinitrophenyl moiety.118
These radicals were termed ―spin-
labels‖ following the nomenclature developed in the 1950‘s for fluorescent dyes which would
label—covalently bind—the biological molecule of interest. It was established that the nitroxide
labels were inert—stable in the presence of water or oxygen,119
sensitive to motion, and
correspond to simple spectra,116
which make the nitroxide labels ideal for probing the
conformational changes in biomacromolecules. This technique increased in popularity over the
next 20 years and was used to study a large variety of systems. However, there were three
significant limitations that hindered the technique from being almost universally applicable—
selectivity, sensitivity, and versatility.
The selectivity issue arose from the limited selection of suitable labeling sites in
biomolecules. There was a small variety of labeling chemistries available that permitted some
selection of the labeling sites. However, most proteins contain multiple labeling sites reactive to
each of the labeling chemistries. Consequently, it was very difficult to obtain protein selectively
labeled at one site.
83
The sensitivity issue arose from the difficulty of preparing samples in sufficient quantity.
This issue was essentially solved in 1982 with the development of the loop-gap resonator.120
This resonator permitted single-scan spectra from picomole quantities of proteins.
The versatility issue arose from the inability to selectively choose the site for labeling.
Researchers were limited to using native sites within the proteins for labeling. However, the
domains of interest do not always contain suitable labeling sites, which limited the applicability
of the method.
The development of site-directed mutagenesis —a technique wherein the DNA bases can be
manipulated at a specific site— permitted researchers to remove all the native labeling sites and
introduce a unique labeling site at the position desired. This combination of site-directed
mutagenesis and spin-labeling was introduced in a 1989 manuscript by Altenbach et al.121
Cys
mutations were introduced into bacteriorhodopsin and subsequentially labeled with thiol-
selective spin-labels.
The term ―site-directed spin-labeling‖ (SDSL) has been coined to describe this combination
of site-directed mutagenesis and spin-labeling. In general, the DNA encoding the protein of
interest is mutated such that the codon for a specific residue is mutated to encode a Cys residue.
The mutant DNA is used to express the Cys-variant in a recombinant expression system such as
E. coli or yeast. The protein is purified and labeled with a thiol-reactive spin-label.
Alternatively, small proteins and peptides can be synthesized with a Cys residue for labeling or
with an amino acid derivative that incorporates a spin label such as TOAC.122
Site-directed spin-labeling can also refer to studies using spin-labeled nucleic acids. A
variety of labels have been developed for incorporation into nucleic acid strands that attach via
84
the base, the sugar, or phosphate group. Typically, the nucleic acid is synthesized and the label
is incorporated via the addition of a derivatized nucleotide that contains the label.
Spin labels
By definition, a spin-label is any molecule containing an unpaired electron—an EPR-active
probe—and reactive moiety for binding to another molecule. The majority of spin-labels used
for investigating the structure and flexibility of biomolecules are nitroxide radicals because their
simple line shape is highly sensitive to motion making them well-suited for investigating the
structure and flexibility of a biomolecules. The nitroxide radical is protected by bulky methyl
groups which prevent collisions. The geometry of the radical and surrounding methyl groups is
typically preserved by inclusion in a five- or six-member ring. The reactive moiety is typically
attached to the ring structure via four-five bonds as is necessitated by the synthesis process. A
large variety of spin-labels are available commercially including variations in the ring structure
and in the reaction chemistry of the flexible linker. Figure 2-2 illustrates the structures of four
common nitroxide spin-labels with thiol-based linkers as well as the structures of the modified
Cys residues after reaction with the spin-label.
Figure 2-2. Structure of spin-labels before and after binding to Cys side chain. A) and B) MTSL:
(1-Oxyl-2,2,5,5-Tetramethyl-Δ3-Pyrroline-3-Methyl) Methane-thiosulfonate; C) and
D) IAP: 3-(2-Iodoacetamido)-PROXYL E) and F) MSL: 4-Maleimido-TEMPO; and
G) and H) IASL: 4-(2-Iodoacetamido)-TEMPO. Rectangular box represents protein
backbone.
ONNH
O
I
O
ONN
O
ONNH
I
O
ONNH
O
S
O
ONN
O
SS
ONS ONNH
S
O
OSN
S
O
O
A
H
G
F
E
D
C
B
.
.
.
.
. .
..
85
Selection of labeling sites
The choice of labeling sites within biological systems is not trivial. Obviously, the site
should be chosen to report on the relevant aspect of the system under study. However, care must
also be taken to preserve the structure and function of the system. For inter-flap distance
measurements in HIV-1 PR, it is necessary to pick sites within the flaps that have been shown to
be highly conserved and intolerant of amino acid substitution. However, there is one site,
position 55, that is able to tolerate a variety of amino acid substitutions and is a suitable choice
for a labeling site.123
Additionally, the extent of solvent exposure at the site should be considered. For distance
measurements via pulsed EPR, solvent exposed sites that report only on the motion about the
flexible linker, (e.g. the line shape do not change upon ligand binding or other changes to the
system) are ideal. However, for characterizing conformational changes via CW-EPR, the label
should be sensitive to changes in the conformation upon ligand binding (e.g. one conformation
gives rise to motionally restricted line shape and the other conformation to a highly mobile line
shape).
Nitroxide line shapes
The unpaired electron in the nitroxide radical is strongly associated with the nitrogen atom
(I=1). This leads to hyperfine splitting with three transitions (ms=+1/2, mI=+1 ms=-1/2,
mI=+1, ms=+1/2, mI=0 ms=-1/2, mI=0, ms=+1/2, mI=-1 ms=-1/2, mI=-1) as illustrated in
Figure 2-1 and Figure 2-3A. When the nitroxide is tumbling quickly in solution, as is the case
for unattached nitroxides and nitroxides attached to small biomolecules (MW < 18 kDa) the
transitions give rise to sharp features in the line shape as illustrated in Figure 2-3D. If the motion
of the nitroxide is restricted, either as a result of slower tumbling from being attached to large
86
molecule or from contacts with neighboring molecules (such as amino acid side chains), the
transitions give rise to features that are broadened from incomplete averaging of anisotropic
components in the spin Hamiltonian, namely the g and A tensors. Figure 2-3E shows a typical
line shape for a nitroxide bound to a 20 kDa protein at a solvent-exposed site. This site displays
some broadening relative to the line shape in Figure 2-3D because of the slower rate of tumbling
in solution. Figure 2-3F shows a line shape typical for completely immobile spin-label.
Figure 2-3. Schematic diagram of the possible energy levels (A) for a spin ½ on a nucleus with
spin 1 and corresponding absorption (B) and derivative (C) spectra. Sample line
shapes for nitroxide radicals undergoing rapid motion (D), moderate motion (E), and
no motion (F).
Three primary modes of motion affect the mobility of the spin-label and the resultant EPR
spectrum: (1) the tumbling of the entire protein, characterized by the correlation time, R; (2)
torsional oscillations about internal bonds within the nitroxide moiety and its attachment to the
3300 3350 3400 3300 3350 3400
d(A
bs)/
dB
0d
(Ab
s)/
dB
0d
(Ab
s)/
dB
0
d(A
bs)/
dB
0
Magnetic Field B0 (Gauss)
En
erg
y
Ab
so
rptio
n
Magnetic Field B0 (Gauss)
E
ms = +1/2
ms = -1/2
mI = 1 0 -1
A
B
C
D
E
F
87
CYS residue side chain, defined at the internal correlation time, I; and local macromolecular
fluctuations of the protein at the labeling site, referred to as local dynamics, B as illustrated in
Figure 2-4.
Figure 2-4. Illustration of the three correlation times of a spin label, where R is the overall
tumbling of the protein, B is the movement of the protein backbone including local
oscillations and conformational changes, and I is the movement of the label about the
flexible linker.
Changes in R are useful for studying the binding of small molecules (peptide or RNA
fragments) to larger biomolecules such as complex protein systems, membrane bilayers, or
RNA/protein complexes. However line shapes that are dominated by R do not contain site-
specific information about protein dynamics. In order to gain site-specific information, it is
necessary that the line shape is not dominated by R. This condition is usually met for
biomolecules greater than 18 kDa, and can be creatively circumvented for most biomolecules
smaller than 18kDa. The major source of structural information in SDSL studies comes from
line shape analysis from nitroxide labeled sites where molecular motions are dominated by
changes in I and B.
B
R
88
Spin label conformations
It is important to understand the intrinsic flexibility and preferred conformations of the
flexible linker that are used to attach the spin-label because of the potential impact these factors
can have on the mobility of the spin-label. Spin-labels can be attached to Cys residues in any
secondary structural element. Each structural element has a different degree of backbone
flexibility and tightness in the packing of the side-chains. These factors strongly affect the
mobility of the spin-label and thus the line shape.
It has been found, that on -helical sites, the delta sulphur atom (S ) can form a stable
interaction with the hydrogen atom (H ) on the alpha carbon (C ). This arrangement restricts
rotations about the first three bonds in the linker thereby reducing the rotational freedom to the
fourth and fifth bonds (corresponding to torsional oscillations about the 4 and 5 dihedral
angles respectively). These constrained motions are the basis for the 4/ 5 model124
illustrated
in Figure 2-5. It has been demonstrated that this model is valid on -helices in a variety of
proteins. However, every protein can potentially have unique or rare factors which cause the
spin-label motion to deviate from this model.
Crystallographic studies of spin-labeled proteins provide direct information regarding the
preferred conformation of the spin-label. This is particularly useful for distinguishing between
rotomeric states of the spin-label versus different protein conformations when the CW line shape
has multiple components. Additionally, computer simulations can be performed to predict the
preferred spin-label conformations. These computations can include full MD simulations of the
entire protein or they can be simplified such that the atoms in the protein are motionally
restricted still while the spin-label is allowed to move.
89
Figure 2-5. Illustration of the 4/ 5 model. The S interacts with the H on the C (indicated by
dotted line), which restricts rotations to the 4 and 5 torsional angles.
Line shape analysis
The line shape analysis typically involves quantifying the breadth of the spectrum as a
measure of the spin-label mobility. If the spin-label is tumbling rapidly and isotropically in
solution, the features of the line shape will be very narrow and sharp resulting from the
averaging of the anisotropy in the A and g tensors. If the motion of the spin-label is restricted,
the averaging of the anisotropy in the A and g tensors will be incomplete and the spectrum will
be broadened. The extent of the broadening correlates with the extent of restriction in the
motion.
Figure 2-6 illustrates several methods commonly used for quantifying the breadth of the line-
shape including measuring the peak-to-peak distance ( Hpp125
or 124
), the ratio between the
intensity of the center field transition to the low field transition (ICF/ILF or H(0)/H(+1)),126
and the
second moment of the spectrum ( H2
).124
The Hpp can be normalized by conversion to the
scaled mobility (MS) as shown in Equation 2-29, where m is the most mobile Hpp reported in
the literature and im is the immobile. The H2
is proportional to the sum of distance squared
11
11
imm
imSM (2-29)
O
O OO
OH
N
SS
NHNH
NHNH
O
NH
NH
O
NH
O
X1
X2
X3X4
X5
H
.
90
between every point and the center of mass of the spectrum times the intensity at that point
(Equation 2-30).
N
i
iji IrrH1
22 *)( (2-30)
Figure 2-6. Parameters for quantifying the breadth of a CW-EPR line-shape. A) Central line-
width, Hpp and the ratio of the center-field transition to the low-field transition,
ICF/LF. B) Second moment, H2
.
Introduction to Distance Measurements Via Pulsed EPR
All experimental techniques that measure distances rely on a distance dependant interaction
between two moieties. For fluorescence resonance energy transfer (FRET), the distance
dependent interaction between the fluorophores is an energy transfer that stems from a long
range dipole-dipole interaction which is distance dependent.127
For NMR, various experiments
use the dipolar couplings, the J-coupling, or spin polarization transfer between various nuclei, all
of which are distance dependent.128
For EPR, both pulsed and continuous wave (CW), the
distance dependent interaction is the dipolar coupling between two unpaired electrons. CW-EPR
is used for distances less than 15- 20 Å129
and pulsed EPR is used for distances between 15-80
Å130
(although 60 Å is the upper limit for most non-model systems).131
Magnetic Field
I
ro
rj
ri
Hpp
ICF
ILF
A B
91
Dipolar Interaction
The dipolar interaction between two spins is essentially the force of the magnetic field
generated by one spin on the magnetic dipole of the other spin. The dipole interaction between
two electrons can be described by the Hamiltonian in Equation 2-31132
, where r is the
5
21
3
210 ))((3
4 rr(r)dd
rμrμμμTT
H (2-31)
inter-electron vector. This can be rewritten as Equation 2-32 or Equation 2-33 by substituting
5
21
3
210 ))((3
4)(
rrrdd
rSrSSSTT
H (2-32)
2
2121
2
210
3
))((3
4
1)(
rgg
rr edd
rSrSSS
TTT
H (2-33)
the magnetic moment operators with the corresponding spin operators, which is usually
represented as STDS.
Electron Spin Echo Techniques
All electron spin echo (ESE) techniques have the same foundation, which is simply that the
dipolar interaction between two electrons takes the form of an additional modulation or
decay/recovery. This manifestation is the result of the instantaneous change in the effective
magnetic field of spin when a coupled spin is flipped via a pulse.133
There are several pulse
sequences that utilize ESE to measure the dipolar interaction between two spins including double
quantum coherence (DQC) and double electron-electron resonance (DEER) (also known as
pulsed electron double resonance, PELDOR).
Double Quantum Coherence (DQC)
Multiple Quantum Coherence (MQC) EPR is analogous to MQC NMR, which has been
explained thoroughly elsewhere.111
The most significant difference has been the difficultly in
92
adapting the technique to the instrumental limitations inherent in the EPR spectrometers.134
However, recent improvements in technology and improved pulse sequences have made DQC
EPR a viable option for distance measurements in many systems, including biological
systems.135
Double electron-electron resonance (DEER)
All DEER experiments have the same general outline: microwave pulses are used to
selectively excite two separate spin populations (generally referred to as spins A and spins B).
The B spins are flipped, which causes a perturbation on the coupled A spins that is manifested as
an additional modulation on the A spins.
‘2+1’. One significant instrumental limitation in the three- and four-pulse DEER
experiments is the need for two separate microwave frequencies and a sufficiently broad
spectrum that two populations of spins exist that can be excited independently. When these
conditions cannot be met, the dipolar interaction can still be probed using a ‗2+1‘ pulse sequence
illustrated in Figure 2-7A. The ‗2+1‘ sequence needs only one microwave frequency but
involves an additional complication resulting from the lack of separation between the A and B
spins. These complications arise from the possibility of flipping the A spins with the second
pulse or flipping B spins with the third pulse and are manifested as phase changes for the spins.
In a DEER experiment with two frequencies, the spins can only gain an additional phase but in a
‗2+1‘ experiment, the spins can either gain an additional phase or recover their original phase.
Three-pulse DEER. The first DEER experiment published136
used the three-pulse DEER
sequence illustrated in Figure 2-7B. This sequence generates a Hahn echo using a two-pulse
Hahn echo sequence on 1)
(the observe frequency). The intensity of the echo is measured as a
93
function of the timing of a third pulse on 2)
(the pump frequency). One of the major limitations
of the three-pulse DEER was the ~100 ns delay in the data acquisition after the third pulse,
Figure 2-7. Pulse sequences for A) ―2+1‖ experiment, B) Three-pulse DEER, and C) Four-pulse
DEER. Pulse spacings labeled with remain constant and spacings labeled with t are
incremented.
because the highly sensitive detector cannot be switched on until the power from the microwave
pulse has sufficiently dissipated from the resonator. This delay is commonly referred to as the
t t
(2)
mw
(1)
mw
t
1 2
(2)
mw
(1)
mw1
t
2
A
B
C
echo
echo
echo
94
experimental dead-time. The largest consequence of the experimental dead-time is that data
from the early part of the dipolar evolution curve area is lost, which is the only region in the
curve that contains information on the shortest distances. This problem was overcome in the
four-pulse DEER sequence by refocusing the Hahn echo, using an additional observer pulse, at
2· 2 after the Hahn echo appears (Figure 2-7C).137
Because of the similarity to the four-pulse
DEER, the three-pulse DEER will not be discussed in detail; most, if not all, of the discussion for
four-pulse will hold true for the three-pulse DEER.
Four-pulse DEER. Figure 2-7C illustrates the pulse sequences used for four-pulse DEER.
Similar to three-pulse DEER, the sequence also begins with a two-pulse Hahn echo sequence on
1). After the appearance of the Hahn echo, a pump pulse is applied on
2) with a varying time
delay after the echo. At 2, the echo is refocused by an additional -pulse on 1)
. Again, the
echo intensity is recorded as a function of the time delay between the first echo and the pump
pulse.
The effect of the pump pulse is to flip the B spins at time t, which alters the effective
magnetic field for the A spins that are coupled to a B spin. This change in the magnetic field
alters the precession frequency of the coupled A spins by ee (electron-electron coupling,) which
results in the magnetization being out-of-phase by the angle ee= eet. Thus ee can be
determined by integrating the echo intensity as a function of t. Equation 2-34 defines ee,
Jr
ggJ AB
AB
eBAddee )1cos3(
1
4
2
3
2
0
(2-34)
where rAB is the distance between the spins, AB is the angle between the static field B0 and the
vector between the spins, J is the exchange coupling, and dd is the dipolar coupling between the
electrons. Equation 2-34 is valid as long as the positions of the electron spins are relatively well
95
defined in relation to the distance between them (i.e. the point-dipole approximation holds). This
restriction is easily met for spins more than 15 Å apart, which is the lower limit for a DEER
experiment. The J-coupling is significant only at smaller distances and is considered negligible
for distances greater than 20 Å.131
As with three-pulse DEER, 1)
is the observer frequency (corresponding to A spins) and 2)
is the pump frequency (B spins). Both frequencies are chosen such that there is no overlap (or
minimal overlap) between the excitation windows of the pulses and that the most spins are
excited. This condition is relatively simple to achieve for nitroxide spin labels, because the low-
field and center-field transitions are >26 G apart (which corresponds to ~72 MHz) as illustrated
in Figure 2-8. Typically, the pump frequency is chosen to correspond to the center-field
transition, because it is the most populated region of the spectrum and the observe frequency is
selected to correspond to the low field transition, because it is the second most populated region
Figure 2-8. Absorption spectra for a nitroxide spin-label with the low-field transition marked as
the observe frequency and the center-field transition marked as the pump frequency.
of the spectrum (that is at least 26 G from the center field transition). These positions can be
reversed, to produce a stronger signal. However, pumping on the larger population leads to
3420 3450 3480 3510
Field (Gauss)
Pump
Observe
~26 G~72 MHz
96
deeper oscillations in the dipolar evolution curve.131
The presence of deeper oscillations
improves the quality of the analysis (these topics will be discussed in more detail later).
The theory behind DEER is typically explained by considering a single macromolecule, e.g.,
a protein, with two spins—an A spin and a B spin. However, the reality is that there are a large
number of macromolecules in the sample tube, most containing two spin labels but some
containing only one label due to incomplete spin-labeling. Thus, not every protein will have
both an A spin and B spin. Inspection of Figure 2-8 reveals that the majority of spins are neither
A nor B spins (the portions of the spectrum not highlighted in grey). Thus, most proteins will
contain neither A nor B, some will contain only an A spin, some will contain only a B spin, and a
small percent will contain both A and B spins. This has two significant consequences.
First, only ~5 % of the sample will contain both A and B spins.131
The percentage can be
determined by calculating the bandwidths of the pump and observe pulses, determining the
number of spins excited by each pulse, and calculating the statistical probability of an A spin and
B spin residing on the same macromolecule. These calculations assume that the sample was
labeled with 100% efficiency. Incomplete labeling can drastically reduce the percentage of the
sample that contributes to the dipolar evolution signal.
Second, every A spin will be surrounded by other spins on other macromolecules, some of
which will be B spins. These intermolecular interactions give rise to the background signal,
which comes from a random distribution of large distances, and thus takes the form of an
exponential decay.
The signal from the intramolecular interactions takes the form of a damped oscillation as
illustrated in Figure 2-9. The raw dipolar evolution curve is shown as the solid black line. This
97
signal is usually designated V(t). The background contribution is plotted as a dashed grey line
and is represented by B(t). The background corrected signal, F(t), is plotted as a solid grey line.
Figure 2-9. Sample dipolar evolution curves before and after background subtraction.
The relationship between the signal, the background, and the background-corrected signal is
given by Equation 2-35. The decay time for the oscillations in F(t), tdecay, and the maximum
dipolar evolution time, tmax, are also illustrated in Figure 2-9. The modulation depth, (also
)()()( tBtFtV (2-35)
represented by in some literature), is a correction factor that compensates for the incomplete
excitation of all B spins by the pump pulse.
As illustrated in Figure 2-10, the frequency and decay rate of the oscillations depend on the
length of the most probable distance and the breadth of the distance distribution respectively. By
varying the breadth of a distance profile centered at 36 Å (Figure 2-10A) from 1 to 10 Å and
generating the theoretical dipolar evolution curves (Figure 2-10B), it can be seen that the
0 1 2 3
Background Corrected
TKR Fit
Dipolar Evolution
Background
( s)
Ech
o I
nte
nsi
ty
tdecay tmax
Background: (1- )B(t)
Uncorrected Dipolar Evolution Curve: V(t)
Background Corrected Dipolar Evolution Curve : F(t)
, modulation depth
98
narrowest distributions have the most well-defined oscillations, corresponding to the longest
decay rates. The frequency of oscillations can likewise be illustrated by comparing the dipolar
evolution curves (Figure 2-10D) corresponding to distance profiles (Figure 2-10C) that have the
Figure 2-10. Effect of the breadth of the distance profile and the most probable distance on the
dipolar evolution curve.
same breadth (7 Å) and vary in the most probable distance from 18 to 78 Å. These dipolar
evolution curves have different decay rates, but because the frequency of the oscillations also
changes, the curves have the same number of oscillations before being completely damped. The
inset in Figure 2-10D highlights the dipolar evolution curves that decay within the first 2 s, a
tmax frequently reported in the literature. These curves are plotted as solid lines and correspond
to center distances of 36 Å or less. The dipolar evolution curves corresponding to center
distances larger than 36 Å are plotted as dashed lines and do not decay within 2 s.
20 30 40 50 0 1 2 3
15 30 45 60 75 0 2 4 6 8 10
0.0 0.5 1.0 1.5 2.0
P(r
)
Distance (Å)E
cho
Inte
nsity
( s)
1 Å
2 Å
3 Å
4 Å
5 Å
6 Å
7 Å
8 Å
9 Å
10 Å
P(r
)
Distance (Å)
Ech
o In
tens
ity
( s)
18 Å
24 Å
30 Å
36 Å
42 Å
48 Å
54 Å
60 Å
66 Å
78 Å
A B
C D
99
Because the acquired signal—V(t)—is the combination of both the intramolecular signal F(t)
and the background signal B(t), it is useful to be able to separate B(t) from V(t). If the V(t) is
collected such that tdecay is much shorter than tmax, then the portion of the curve between tdecay and
tmax will contain only contributions from B(t) and can thus be fit to the appropriate function to
determine B(t). Alternatively, the ln(V(t)) can be used in an identical fashion to determine
ln(B(t)). Strictly speaking B(t) should be an exponential function of the form in Equation 2-36,
)exp()( 3/DkttB (2-36)
where D is the dimensionality of the background—typically three dimensions for soluble
proteins and two dimensions for membrane proteins. However, ln(B(t)) can be described as a
simple low-order polynomial, such as the one in Equation 2-37, where q is the order of the
polynomial.
q
i
i
itatB1
))(ln( (2-37)
The distance limitations for DEER experiments are frequently cited as being from 15 Å to
either 60 Å or 80 Å. The lower limit arises from the requirement that the excitation bandwidth
should exceed the electron-electron coupling, which can be met only for distances at or above 15
Å. The upper limit is determined by the Tm of the system. For nitroxide radicals that can be
dissolved in a variety of organic solvents, the Tm can be extended by using a deuterated solvent
with no methyl protons, such as o-terphenyl. Using this solvent, Jeschke et al.131
were able to
collect a dipolar evolution curve with tmax = 24 s for a shape-persistent biradical with an
interspin distance of 75 Å. For biological molecules, however, the solvent is typically restricted
to aqueous solutions. Furthermore, the biological molecule typically contains many methyl
protons, which contribute to shorter Tm values. These restrictions typically limit the Tm to less
100
than 5 s, although 3-4 s is much more common. These Tm values correspond to distances of 60
Å or less with 45 -50 Å being a more practical limit.
In general, tmax should be twice tdecay, so that the second half of the dipolar evolution curve
can be fit to B(t). This minimum tmax can be determined using Equation 2-38131
and is plotted as
2
0
3
max
8
BBA
AB
gg
rht (2-38)
the solid line in Figure 2-11. The dashed line corresponds to the minimum tmax at a given
distance if detailed information is desired from the distance profiles.
Figure 2-11. Minimum tmax for a given interspin distance based on Equation 2-38.
Experimental Considerations for Pulsed EPR
Instrumental Requirements
A large variety of resonators have been employed in ESE experiments. The resonator (or
cavity) is responsible for converting the microwave power into the B1 field necessary for flipping
the spins. There are three critical aspects of the resonator‘s performance for pulsed EPR
experiments. First, it must efficiently convert the microwave power into the largest B1 field
possible. Second, the resonator must be able to handle the large bandwidth of microwave
frequencies necessary to cover the difference in frequencies between the pump and observe
20 30 40 50 60 70 80
0
5
10
15
20
t max (
s)
Distance (Å)
101
pulses. Finally, the resonator must have a short ring-down time—i.e., it allows the microwave
power to dissipate quickly—so that the detector, which must be protected from the microwave
pulses, can be turned on in time to capture the small signal.
A bimodal resonator was used by Larsen et al.138
so that each mode of the resonator needed
to handle only the bandwidth of one pulse. However, this resonator suffered from a low filling
factor—a measure of the fraction of microwave energy that interacts with the sample—and thus
performed poorly. The commercially available dielectric and split-ring resonators are currently
the most popular. The dielectric resonators, EN4118X-MD4 and ER4118X-MD5 from Bruker
Biospin, offer a large filling factor and variable Q—ratio of microwave power stored in the
resonator to power lost via heat absorption—which provides a high degree of sensitivity and
adaptability for a variety of experiments. The split-ring resonators, ER 4118X-MS5/3/2 from
Bruker Biospin, however, generate the highest B1 fields and have the largest bandwidths. Both
the dielectric and spilt-resonators are suitable for use with DEER, although each offers distinct
advantages.
The sample volumes necessary for DEER vary depending on the resonator. Generally, the
signal-to-noise ratio is highest when the greatest number of spins is in the active area of the
resonator. This criterion is met by using the largest sample tubes that will fit in the cavity and
filling them with sufficient sample so that the active area is full. For a 4 mm (outer diameter)
tube, this corresponds to ~100 L of sample.
Spin Relaxation
One of the major limiting factors in any pulsed magnetic resonance experiment is the time
required by the magnetization to return to thermal equilibrium. Spin relaxation is characterized
by two time constants: T1 or spin-lattice relaxation time (or longitudinal relaxation), which is the
102
time constant for relaxation between different Zeeman energy levels and equivalently the
relaxation of the bulk magnetization along the z-axis; and T2 or spin-spin relaxation time (or
transverse relaxation), which is the time constant for relaxation in the x-y plane. There are also
several other processes that affect the relaxation times. For example, TD, or the spectral
diffusion time, is the time constant during which the spin moves between positions in an EPR
spectrum. (If an excited spin diffuses outside of the spectral window, then it appears to have
relaxed.) There is also the spin-echo dephasing time, Tm, which includes all processes that lead
to a loss of electron spin phase coherence (which includes T2). In addition, there are the nuclear
spin diffusion rate, which is the rate of mutual nuclear spin flips, and cross relaxation, which is
the mutual spin flip of two unlike spins. The two relaxation times that will have the greatest
impact on the ESE experiments are Tm and T1.
Tm
At first glance, it might seem that T2 should play a more prominent role in pulsed EPR
experiments. However, the spin-echo dephasing time, Tm, which includes T2, is the more
relevant term, because it encompasses all processes that affect the refocusing of spins into an
echo, not just the time constant for spins dephasing in the x-y plane.
Tm is highly temperature dependent and is the reason that ESE experiments are preformed at
cryogenic temperatures where the Tm is sufficiently long to accommodate a pulse sequence. The
magnitude of the temperature dependence depends on the relaxation mechanism that is dominant
in the range of temperatures involved. Two major contributing mechanisms to Tm are
instantaneous diffusion and nuclear spin diffusion. Instantaneous diffusion contributes only at
high spin concentrations and results from incomplete excitation of the entire spectrum. Nuclear
spin diffusion results from the flipping of the nuclear spins which are coupled to the electron
spins. The simplest method for minimizing the effect of nuclear spin diffusion on the Tm is to
103
replace neighboring nuclei (usually in the solvent, but can also include isotopically labeling a
protein) with nuclei that have smaller magnetic moments. Replacing protons with deuterons can
extend the Tm by almost 50-fold.
Tm is also dependent upon the solvent used. Solvents with methyl groups display Tm curves
with a different shape, which is indicative of contributions from an additional relaxation process.
One potential explanation for this could be that methyl group rotation can persist down to a few
K,139
leading to an averaging of the couplings between the spin and the three protons (which is a
dephasing process).
Since any two pulses will create an echo, the spin dephasing can be measured by simply
increasing the spacing between the two pulses and measuring the echo intensity as a function of
that spacing (Figure 2-12A). This simple method is typically referred to as an echo decay
experiment, because the echo intensity decays as the pulse spacing increases (Figure 2-12B).
This experiment is also used as a way to estimate the effective T2 of a system, with the
understanding that it is not the true T2 value. The data collected are typically fit to a stretched
exponential of the form in Equation 2-39, where Tm is the rate of decay and A, t0, B, y0 are the
00 )/)(exp()( yTttAty B
m (2-39)
constants to account for the initial intensity, time offset, the extent of stretching for the
exponential function, and value of y as t approaches infinity, respectively. The data in
Figure 2-12B were fit to Equation 2-39 with Tm values of 3.8 s, 5.1 s, and 10.8 s for the
same sample in H2O with 30 % glycerol, H2O with 30% deuterated glycerol, and D2O with 30%
deuterated glycerol, respectively..
There is no standard rule that directly relates the measured Tm to the longest acceptable tmax.
However, the tmax needs to be less than Tm, or the data collection time becomes inordinately long.
104
Figure 2-12. Pulse sequence for an echo decay experiment and Tm curves for HIV-1 protease in
various buffer conditions. A) Echo decay pulse sequence. B) Intensity normalized
Tm curves for HIV-1 PR in 2 mM NaOAc buffer pH 5.0 with H2O and 30% glycerol
(black), 2 mM NaOAc buffer pH 5.0 with H2O and 30% deuterated-glycerol (dark
grey), 2 mM NaOAc buffer pH 5.0 with D2O and 30% deuterated-glycerol (light
grey) with corresponding fits to Equation 2-39.
This limitation on the length of the dipolar evolution curve also limits the amount of information
collected from the experiment. As was discussed previously, if the dipolar evolution curve does
not capture a sufficient number of oscillations, then the quality and resolution of the distance
profile will be compromised. Thus, efforts to extend the Tm can improve the quality of the
results garnered from a DEER experiment. The simplest way to extend the Tm is through the
selection of the matrix (solvents and cosolutes). The better solvents (and buffers) are the ones
without methyl groups. Likewise, using deuterated water and buffers will also help dramatically
as illustrated in Figure 2-12B. The selection of the cryoprotectant can also make a large
difference. The use of glycerol extends the Tm to a greater extent than other solutes including
Ficoll400, sucrose, and various sizes of PEG. However, it should be noted that changes to the
solvents and solutes will only impact surface accessible sites. If the labeling site is buried within
the protein or if the site is buried within the hydrophobic portion of membrane, then the Tm
extension achieved by switching to D2O will be minimal.
t t
A B
0 5 10 15
0.0
0.2
0.4
0.6
0.8
1.0
Ech
o I
nte
nsity
( s)
H2O Gly
H2O D-Gly
D2O D-Gly
echo
105
T1
T1 is the time constant for a spin to establish equilibrium between electron Zeeman energy
levels. Because the ms value changes as transitions are made between levels, the energy of the
system must also change by absorbing energy from or emitting energy to the lattice. According
to the Bloch equations, T1 is defined as the time constant for the z-axis component of the bulk
magnetization to return to equilibrium after the pulse. These definitions are equivalent because
the z axis component of the magnetization results from population differences in the Zeeman
energy levels. Theoretically, it should be straightforward to measure T1 experimentally.
However, there are other processes (primarily spectral diffusion and spin diffusion) that can take
a spin off resonance without changing the populations of the energy levels, thus contributing to
the apparent T1 of the system.
The parameter in the DEER experiment that depends on T1 is the delay between pulse
sequences, usually referred to as the shot repetition time (SRT). Typically the SRT is set to be
five times the value of T1 to allow ~99% of the magnetization to relax back to the z axis. The
effective T1 can be measured using an inversion recovery experiment, although there are other
options as well, including saturation recovery134
or stimulated echo decay.132
As illustrated in Figure 2-13, inversion recovery uses a three-pulse sequence to measure the
rate of recovery. The first -pulse inverts the magnetization, which is then allowed to relax for a
time t, which is incremented. A spin echo is then formed using a /2-pulse followed by a
-pulse. The intensity of the echo will change as a function of t. This experiment is very
straightforward to perform and provides a convenient measure of the effective T1. However, it is
very susceptible to spectral diffusion because of the short inversion pulse (the inversion pulse
can be lengthened but the decreased spectral excitation window will decrease the signal
106
strength). The data from an inversion recovery experiment can be fit using either single or
multiple exponential decays. Fitting to a single exponential (Equation 2-40) is usually sufficient
for estimating the effective T1
01)/exp()( yTtAty (2-40)
for determining the appropriate shot repetition time for a pulsed experiment, although the double
exponential frequently provides the superior fit.
Figure 2-13. Inversion recovery pulse sequence and corresponding sample data.
Similar to Tm, T1 is strongly temperature dependent with different mechanisms dominating in
different temperature ranges. These various mechanisms and their temperature dependence were
reviewed thoroughly in Berliner et al.134
In general, the T1 value will increase as the temperature
decreases, although the extent to which T1 changes will depend on the dominating mechanism.
T1 is also solvent dependent. Hydrogen-bonded solvents have longer T1 values than solvents
with little to no hydrogen bonding. This results from the decreased molecular motion in a
solvent system with more hydrogen bonding (for glassy systems < 200 K).
t
A B
0 200 400 600 800 1000
0
Ech
o In
ten
sity
Time ( s)
T1 = 380 s
107
Cryoprotectants and Glassing Agents
The addition of a solute to a protein sample can have several benefits, including reducing the
likelihood of the sample tube cracking upon being frozen. One of the most commonly cited
reasons for adding the solute is its function as a glassing agent. A glassing agent is an agent (is
this case, solute) that reduces the glass transition temperature, so that the sample remains in a
glass state throughout the experiment. The key benefit to keeping the sample in a glass state is
the prevention of protein aggregation during the process of the sample freezing. (Water tends to
reject impurities as it freezes, thus concentrating the impurities—which includes salts and
proteins). An increase in the effective protein concentration is the decrease in the distance
between neighboring molecules, which can complicate the analysis for measuring the
intramolecular distances.
Glycerol is by far the most common glassing agent and cryoprotectant used, although many
other solutes can be used, including sucrose, ethylene glycol, and PEG. The minimal
requirement for a solute to be a glassing agent is that it reduces the glass transition temperature.
However, it is also important that the solute does not significantly alter the conformational
ensemble of the protein. A simple way to check for this is to perform DEER experiments using a
variety of solutes to see how the distance profile varies for each solute or to perform other
biophysical characterizations in the presence of the solute.
Temperature Selection
The tmax of the DEER experiment is limited strongly by the Tm, which in turn is strongly
dependent upon temperature as previously discussed. The ideal temperature is the one at which
the Tm is most strongly affected by the spin diffusion of nuclear spins, as opposed to being
dominated by the modulation of the hyperfine or g tensor resulting from molecular
reorientation.130
For nitroxide radicals in aqueous buffers, this point is usually at or below 80 K.
108
Most research groups typically choose temperatures between 55 K and 80K. Although the Tm
will continue to increase at lower temperatures, the T1 will also increase which lengthens the
necessary experiment time.
Sample Concentration
Typically, the simplest way to improve the signal to noise ratio (SNR) in an experiment is to
increase the sample concentration. Unfortunately, increasing the spin concentration in ESE
experiments does not always translate into greater sensitivity. The most intuitive limitation is
that at high concentrations, the distance between neighboring molecules is reduced, leading to
increased contributions to the signal from intermolecular dipolar couplings, which complicate the
mathematical separation of the two contributions. However, there is an additional concentration
limitation imposed by the phase memory loss associated with instantaneous diffusion at high
concentrations.131
For most soluble proteins, these concentration limitations will not apply, as
the protein will most likely aggregate before these concentrations are reached. However, the
limitations are relevant for membrane proteins, because the localization of the protein in the
membrane drastically increases the local effective concentration.
Figure 2-14 shows the plots of the concentration limits as a function of the inter-spin distance
for both the intermolecule distance restrictions (dotted line) and the instantaneous diffusion
restrictions (solid lines). The intermolecular distance restriction assumes that the spin-labels are
on the surface of a protein with a 60 Å diameter. The optimal concentration based on the
instantaneous diffusion restriction (black line) is calculated from Equation 2-41131
where tmax can
be expressed in terms of rAB using Equation 2-38 and fA, =0.25 (for a 32 ns observer pulse).
For extracting information about the shape of the profile for narrower profiles, the tmax should be
three times as long, corresponding to a concentration one-third as large (grey line).
109
AABeBAAA,π
optNrπβμggNftπ
c32
0max
1
2
39
2
39 (2-41)
Figure 2-14. Plot of the maximum concentration of spins as a function of the inter-spin distance.
Solid black line corresponds to the restriction imposed by instantaneous diffusion.
Solid grey line corresponds to the restriction imposed by instantaneous diffusion for
minimum concentration when attempting to recover detailed information from the
distance profile. Dashed line corresponds to the restriction imposed by
intermolecular distances.
Analysis of DEER Data
For a complete understanding of how to properly collect and analyze data from a DEER
experiment, the reader is directed to a number of excellent sources130; 131; 140; 141; 142; 143
including
the DeerAnalysis2008 user‘s manual (available online at www.epr.ethz.ch) for those wishing to
analyze their data with this software. This section will cover the material in sufficient detail to
understand the process and ramifications of certain choices on the results.
Converting the Dipolar Evolution Curve into a Distance Profile
The dipolar evolution curve is the manifestation of the additional modulation imposed upon
the A spins by their coupling with the B spins. The frequency of this additional modulation can
2 3 4 5 6 7 80.0
0.5
1.0
1.5
2.0
2.5
3.0
Co
nce
ntr
atio
n (
mM
)
Distance (nm)
Instantaneous Diffusion
Intermolecular Distance
110
be determined in a variety of ways. Most simply, it can be Fourier transformed into a frequency
domain spectra where the splitting between the singularities in the Pake pattern is proportional to
1/r3 where r is the interspin distance. However, this only gives an estimate of the most probable
distance and works better for narrower distance distributions. To extract a distance profile from
the dipolar evolution, a more sophisticated technique is required. A handful of these techniques
are currently employed but each has shortcomings in one aspect or another.
The source of difficulty in converting the dipolar evolution curve into a distance profile is
that there is no unique distance profile. Significantly distinct distance profiles can give rise to
strikingly similar dipolar evolution curves. Additionally, the solution can be non-trivially
influenced by small amounts of noise in the data. Several groups have come up with ways to
either deal with the ill-posedness or to circumvent it. These solutions typically involve solving
the inverse problem, which is finding a distance profile that satisfies the experimental data.
Curve Fitting Approaches
A common approach to finding the best distance profile involves the use of curve fitting to
optimize the solution. There are many variations of this method, but all include a modeling of
the distance profile based on current knowledge of the system and generating the corresponding
theoretical dipolar evolution curve for comparison with the experimental data. The process
involves changing the distance profile to optimize the fit between the theoretical and
experimental dipolar evolution curves.
One variation on this approach utilizes Monte Carlo (MC) methods to generate a distance
profile with an assumed form, such as a Gaussian or Lorentizian shape by combining random
functions. The theoretical and experimental dipolar evolution curves are compared and the
process repeated until the fit between the curves meets the pre-defined level. These approaches
can yield high quality feasible results but have the limitations that they are either model
111
dependant or assume a form for the distance profile, which can impose an artificial symmetry on
the solution.
Tikhonov Regularization Method
Tikhonov regularization (TKR)144
is a mathematical method used for solving an ill-posed
problem by introducing a penalty for smoothness. TKR uses the function in Equation 2-42 to
balance the quality of fit to the experimental data (first term) with the smoothness of the solution
222 ||||||||][ LPSKPP (2-42)
(second term) by varying the magnitude of the regularization parameter (also denoted in
some literature), where P is the probability distribution of the interspin distance, K is an operator
that maps the function P onto S, S is the experimental data vector, L is an operator, usually the
identity of second derivative operators, and is the regularization parameter.
DeerAnalysis Software Package
The DeerAnalysis software uses a combination of shell factorization (to simulate the dipolar
evolution curves) and Tikhonov regularization (to optimize the solution) to convert dipolar
evolution curves into distance profiles. It also includes several other options for data analysis
including approximate Pake transformation (APT) and model fitting (to either Gaussian
functions or user defined functions). There are also a variety of options for background
corrections.
L-curve
The L-curve is the visual result of the TKR process (Equation 2-43) where the log of ( )
(Equation 2-44) is plotted against the log of ( ) (Equation 2-45). As illustrated in Figure
2-15A, each point on the curve corresponds to a particular value of —the regularization
2
2
22 ||)(||||)()(||)( rPr
tDtSPG (2-43)
112
2||)()(||)( tDtS (2-44)
2
2||)(||)( rP
r (2-45)
parameter. For small , G(P) is dominated by ( )—the quality of the fit between the
experimental dipolar evolution curve and the theoretical curve. As increases, the contribution
by ( ) increases more than the contribution from ( ) so the L-curve has a steep slope. At
large values of ( ), G(P) is dominated by ( )—the smoothness of the solution. As
increases, the contribution from ( ) is minimal because the solution is already smooth so the
contribution from ( ) dominates and the slope is flat. There is a point between these two
regimes where the slope changes. This point corresponds to the optimal solution because it is the
point where the smoothness of the solution and the quality of fit are balanced. The value that
corresponds to this point is the optimal value of regularization parameter and the corresponding
distances profiles and dipolar evolution curve fit are the optimal distance profile and fit.
Figure 2-15. Example of an L-curve and the corresponding distance profiles and dipolar
evolution curves.
20 30 40 50
-4.2 -4.0 -3.8
-24
-20
-16
-12
0.0 0.5 1.0 1.5
0.0 0.5 1.0 1.5
20 30 40 50
20 30 40 50
0.0 0.5 1.0 1.5 log
log Time ( s) Distance (Å)
Under-smoothed
Small
Optimal
Over-smoothed
A B
D
F
C
E
GLarge
Optimal
113
Figure 2-15 also illustrates the effect of non-optimal values on the distance profile and the
TKR fit. The distance profile in Figure 2-15B is under-smoothed and corresponds to a value
that is too small. The corresponding dipolar evolution curve in Figures 2-15C is over-fit,
meaning that the theoretical dipolar evolution curve was fit to some of the noise. The distance
profile in 2-15D is qualitatively similar to the distance profile in Figure 2-15B in that the most
probable distance is the same and the breadth at the base of the first two peaks in Figure 2-15B is
only slightly smaller than the breadth of the peak in Figure 2-15D. However, the distance profile
in Figure 2-17D is smoother and corresponds to the optimal value. The dipolar evolution
curve in Figures 2-15D is optimal. The distance profile in Figure 2-15F is over-smoothed and
thus overly broad. The corresponding dipolar evolution curve in Figures 2-15G is under-fit,
meaning that some of the oscillations in the signal are neglected in the TKR fit.
Approximate Pake transformation
The approximate Pake transformation (APT) uses a discrete integral transformation—
analogous to the Fourier transformation—that has been corrected for cross-talk to convert the
dipolar evolution curve to a frequency domain spectrum. The distance profile is extracted from
the shape of the frequency domain spectrum. This method is very quick computationally also for
a quick estimation of the distance profile while determining the optimal background subtraction.
However, APT frequently includes negative probabilities for some distances in the distribution,
which lessens the overall accuracy of the profile.
Model fitting
In some cases, the use of a model-based analysis can provide better results than a model-free
analysis. For example, a semi-rigid polymer with spin-labels at the end will not give a Gaussian
distribution of distances. However, the form of the distribution has been defined accurately in
114
the worm-like chain model. Fitting a distribution to this model uses only two degrees of
freedom—the persistence length, Lp, and the end-to-end distance L—instead of the large number
of degrees of freedom associated with the model-free analysis—the number of r values for which
P(r) is defined. This reduction in the degrees of freedom reduces artifacts from noise but it can
also impose a shape on the distribution profile that may not be valid. Care must be used to
ensure the model accurately represents the system.
The DeerAnalysis software includes a module to perform such analyses. The included
models include fitting a one or two Gaussian functions, the surface of a sphere, a random coil, a
semi-rigid worm-like chain, and a semi-rigid worm-like chain that includes a Gaussian
distribution of the label. Users can also define their own models by following the template in the
DeerAnalysis2008 user‘s manual.
Background correction options
The dipolar evolution curve is described by V(t), which is a function of the dipolar evolution
time t. V(t) is the product of the two functions shown in Equation 2-51. F(t) is the form factor—
analogous to the form factor in scattering techniques—and B(t) is the background factor.
)()()( tBtFtV (2-51)
Likewise, the spin-spin interactions can be divided into intramolecular interactions—between
spins on the same macromolecule—and intermolecular interactions—between spins on different
macromolecules. The distance between the intramolecular spins should be shorter than the
distances between the intermolecular spins. The only exceptions are for very large
intramolecular spin-spin distances or very concentrated samples where the intermolecular
distance is short. Thus F(t) corresponds to the intramolecular spin-spin interactions and B(t)
corresponds to the intermolecular spin-spin interactions.
115
It follows that F(t) and B(t) will have different forms because F(t) corresponds to the
distribution of distances between labels on a macromolecule while B(t) corresponds to the
distribution of the macromolecules. As a result, many algorithms require the separation of B(t)
to correctly analyze F(t).
The DeerAnalysis software comes with three modules for subtracting the background. One
option is to experimentally determine the background contribution by performing an identical
experiment with singly labeled sample. However, this cannot be performed for all samples, in
particular polymers and oligomeric proteins. The other two modules include fitting the
background to a simple polynomial of various degrees and fitting the background to an
exponential function corresponding to a homogeneous background with variable dimensions,
which is particularly useful for membrane samples where the background signal is restricted to
two dimensions.
Subtracting out the correct level of background contribution to the dipolar evolution curve is
not trivial. Because the background contribution results from intermolecular spin-spin
interactions, the corresponding distances are large and the effect of the background contribution
is distributed over the whole dipolar evolution curve. The intramolecular spin-spin
interactions—which should be shorter distances than the intermolecular interactions—contribute
only high frequency oscillations to the dipolar evolution and thus strongly affect the dipolar
evolution curve at small t values. As long as the dipolar evolution curve is collected such that
tmax > 2·tdecay, the background can be determine from the portion of the curve at t > tdecay.
Validation module
Because the error in TKR does not propagate in a manner that can be predicted analytically,
the error must be determined by other means. The DeerAnalysis2008 includes a Validation
module that estimates the error by determining distance profiles for all the combinations of the
116
variables that contribute to the error—background density, modulation depth, and background
dimensionality. The user selects the upper and lower limits for each variable and the number of
data points to test between limits and the Validation module determines the distance profile and
corresponding dipolar evolution curve for each combination of variables. Because of the large
number of calculations, this process is typically slow. The module contains two options for
narrowing down the number of reasonable distance profiles. The user can trim out distance
profiles with corresponding dipolar evolution curves that are a poor fit to the experimental data.
The user can also discard distance profiles with populations at large distances as these profiles
tend to correlate with incorrect background. The remaining profiles can then be compared to
give an estimate of the error in the distance profile. Figure 2-15 displays a sample image of a
distance profile with error estimates.
Verification of Background Subtraction and Gaussian Reconstruction
In addition to the processes included in the DeerAnalysis software package, we developed
additional steps in the analysis to further refine our results and to extend the analysis into
conformational ensemble analysis. These steps include manual selection of the zero-point in the
dipolar evolution spectra, a self-consistent analysis of the background subtraction level, and a
Gaussian function-based fitting of the distance profiles called Gaussian reconstruction.
Zero-point selection
In pulsed magnetic resonance experiments, data is frequently collected as a function of t,
which is the spacing between select pulses in the sequence. In cases where t should vary
between 0–tmax, t actually starts at a small negative time so that the data can be corrected for any
discrepancy between the instrumental zero time and that actual zero time. The correction utilizes
the symmetry in the dipolar evolution curve—the curve is symmetric about the zero-point—to
mathematically find the true zero-point.
117
The DeerAnalysis software contains a subroutine that uses a first moment analysis for
identifying the zero-point and shifting the data accordingly.142
The first moment analysis utilizes
the fact that the zero point should be a local maximum and that the function should be symmetric
about the maximum. Thus, the first moment of small range of distance centered on the zero
point should be zero. Accordingly, the data near t=0 are divided in small overlapping regions
and the center of the region with the smallest first moment is selected as the true zero-point.
This subroutine has been tested and is reasonably robust for accurately correcting the data except
in datasets that are negatively phased, e.g., data that has been phased such that the DEER echo
intensity is negative. Since a large portion of the data in this work was collected in this fashion,
it was necessary to manually find the zero-point and correct the data accordingly.
To accomplish this correction, the raw dipolar evolution curves are imported into Origin7.5
or Origin8.0. Both the first derivative method and fitting to a Gaussian function have been tested
on several datasets. It was found that fitting all the data points < 400 ns to a Gaussian function
and using the center of that Gaussian function for the zero-point is more consistent than taking
the first derivative of the data and using the point where the first derivative was zero. This was
largely due to the small amount of noise in the data near the zero-point in some datasets that
skewed the results. The zero-point determined is manually entered into the DeerAnalysis
software as the zero-point.
Self consistent analysis of the background subtraction level
In a DEER experiment the background results from intermolecular interactions—the dipolar
interactions between spin-labels on different protein molecules. The most accurate analysis of a
dipolar evolution curve depends on having the most accurate background subtraction possible.
The DeerAnalysis software package utilizes the APT module to optimize the background
subtraction as was discussed previously. Although the APT generates a good estimate of the
118
correct level of background to subtract, it actually tends to generate a small range of acceptable
background. It can be shown that the typically small variations in the background subtraction
levels can lead to small differences in the distances profiles. These small differences typically do
not affect the most probable distance in the profile, nor do they affect the full width at half
maximum (FWHM). The small differences are typically manifested in the fine features of the
distance profiles which correspond to lowly populated states in the protein. This variation in the
fine features is problematic because it is these lowly populated states that are of interest. The
best solution is to identify the most accurate level of background subtraction which should
correspond to the most accurate distance profile.
We have developed a self consistent method to analyze the level of background subtraction
and identify the most accurate level. As illustrated in Figure 2-16, the first step is to analyze the
data using the DeerAnalysis software with the recommended level of background subtraction.
This will generate several output files including a distance profile and a background subtracted
dipolar evolution curve. The distance profile is input into the DeerSim software package which
has been incorporated into the DeerAnalysis software for ease of use. The DeerSim uses the
distance profile to generate a corresponding theoretical dipolar evolution which is completely
free of any background contributions. This theoretical curve is compared with the background
subtracted curve (also called the TKR fit) from DeerAnalysis. If the two curves do not overlay
exactly as illustrated in Figure 2-16, then the background subtraction was not correct and the
process needs to be repeated beginning with a slightly different background subtraction in
DeerAnalysis. These steps are repeated until the TKR fit and theoretical dipolar evolution curve
overlay exactly.
119
Figure 2-16. Illustration of the Self-Consistent Analysis process developed to optimize the background subtraction in the DEER
dipolar evolution curves. Steps explained in detail in the text.
5) Alter background subtraction in DeerAnalysis as necessary and repeat analysis
20 30 40 50 60
Distance (Å)
20 30 40 50 60
Distance (Å)
0 1 2 3
( s)
Ech
o I
nte
nsity
0 1 2 3
( s)
Echo
In
ten
sity
0 1 2 3
( s)
Echo
In
ten
sity
Experimental Dipolar modulation
Distance DistributionDistance Profile fit to Gaussian Functions
Theoretical Dipolar Modulation
Compare Dipolar Modulations
1) Analyze data with DeerAnalysis software to generate distance profile
3) Input Gaussian functions into DeerSim to generate theoretical dipolar evolution curve
(Software upgrade that allows direct input of distance profile just completed)
2) Convert distance profile to a series of Gaussian functions
4) Overlay experimental and theoretical dipolar evolution curves
120
If necessary, this process can be modified to probe the validity of different populations
within a distance profile. For example, if the level of background subtraction is too low,
meaning that not enough background was subtracted, then populations can appear at distances
too long to be relevant to the system. These populations can be suppressed in the distance profile
that is used to generate the theoretical echo. In this case, the theoretical curve will not overlay
with the TKR fit so the level of background subtraction selected in DeerAnalysis would be
adjusted accordingly. If the resulting theoretical curve and TKR fit overlay, then the population
at the large distance can be assigned to background and can be neglected.
This process is extremely helpful in cases where tmax is too short to capture more than one or
two oscillations or in cases where tmax is moderately short but the oscillations are strongly
damped from a broad distribution.
Gaussian reconstruction
The distance profiles of various samples can be compared in a variety of different ways. The
earliest papers published discussed the distance profiles in terms of the most probable distance
and the FWHM of the profile. This type of analysis is sufficient for demonstrating that a
conformational change took place, resolving which direction the change occurred in, and
providing insight into the magnitude of the change. Although this analysis is simple, it was
appropriate considering the available methods for converting the dipolar evolution curve into a
distance profile. In other words, the distance profiles lacked a high degree of accuracy because
of assumptions used in the analysis process, such as fitting to model or forcing an artificial
symmetry onto the distance profile. It has been shown that the most probable distance and
FWHM are very robust to a variety of assumptions that are frequently used and thus these
analyses were sufficiently accurate.
121
In light of the improvements made in the process of converting the dipolar evolution curves
to distance profiles, the accuracy of the distance profiles have increased. Thus it is possible to
discuss the distance profiles in more detail, especially for distance profiles with fine features
instead of a featureless peak. One option includes fitting the distance profile to a series of
Gaussian functions that will sum to regenerate the original profile. This fitting can be
accomplished in a variety of ways, including a brute force manual fitting. However, Origin8.0
service release 1 (sr1) and newer contains an easy to use process to fit the profile to any number
of Gaussian functions with independent breadths and intensities using a variety of peak-finding
techniques. This is especially useful for finding hidden peaks—when one peak has significant
overlap with a larger peak and thus appears as one distorted peak. For the work presented in this
dissertation, the distance profiles were fit to Gaussians using the second-derivative method in
Origin8.0 sr5 unless stated otherwise. The second-derivative method takes the second derivative
of the distance profile and assumes that each local minimum corresponds to a Gaussian function.
In general, any Gaussian function corresponding to less than 1 % of the total population was
discarded as unnecessary.
One caveat to including the fine features of a distance profile in the interpretation of the data
is that TKR distance profiles are known to include occasional artifacts, which are manifested as
small populations. Thus, it is necessary to verify that any population contributing to less than
15% of the total population is actually representative of an actual conformation in the protein.
This validation can be accomplished by suppressing the population in question and generating
the corresponding dipolar evolution curve. If any portion of the theoretical curve lies outside of
the noise in the experimental dipolar evolution curve then the population can be attributed to a
protein conformational state. Conversely, if the theoretical curve lies within the noise then the
122
population can be attributed to part of the background signal and discarded. Occasionally, a
theoretical curve will lie at the edge of the noise in the experimental. In this case, it remains
unclear whether the population is real.
This process is illustrated in Figure 2-17. The Gaussian-shaped populations used to
reconstruct the distance profile is shown in Figure 2-17A and the distance profile is shown in
Figure 2-17B. The background-subtracted experimental dipolar evolution curve and the TKR fit
are shown in Figure 2-17C. The theoretical dipolar evolutions curves with the populations at 20
Å and 42 Å suppressed are shown in Figures 2-17D-E, respectively and the theoretical curve for
Figure 2-17. Illustration of the population validation process used to interrogate the validity of
population containing less than 15% of the total population. A) Gaussian-shaped
populations used to reconstruct the distance profile. B) Distance profile with (solid)
and without (dashed) the 20 Å population. C) Background subtracted experimental
dipolar evolution curve (black), fit from TKR (red), and theoretical curve generated
by Gaussian reconstruction. D) Same as C with the 20 Å population suppressed in
the Gaussian reconstruction. E) Same as C with the 42 Å population suppressed in
the Gaussian reconstruction. F) Same as C with both the20 and 42 Å populations
suppressed in the Gaussian reconstruction.
20 Å27 Å
33 Å 35 Å
39 Å42 Å
20 Å Population Suppressed
Gaussian Reconstruction
A
B
C
E
D
F
20 30 40 50
20 30 40 50
P(r
)
Distance (Å)
0 1 2 3
20 Å Population
Supressed
( s)
Ech
o In
ten
sity
0 1 2 3
20 & 42 Å Populations
Supressed
( s)
Ech
o In
ten
sity
0 1 2 3
42 Å Population
Supressed
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
0 1 2 3
Gaussian
Reconstruction
( s)
Ech
o In
ten
sity
123
both populations suppressed simultaneously is shown in Figure 2-17F.. It can clearly be seen
that the theoretical curve for the 42 Å population is on the edge of the experimental noise and
that the theoretical curve for the 20 Å population is inside of the noise. However, suppressing
both populations results in a theoretical curve that lies outside of the experimental noise. Thus,
the 20 Å population can be regarded as an artifact and the 42 Å can be deemed real because it
cannot be suppressed in conjuction with the 20 Å population.
It should also be noted that the suppression of multiple peaks can have a smaller net effect on
the theoretical curve because of cancellation. Essentially, the suppression of the singular peaks
might be significant but because each peak shifts the theoretical dipolar evolution curve in
opposite directions, the result of simultaneous suppression is that the theoretical curve remains in
the noise. For this reason, it is also prudent to test all linear combinations of peaks that constitute
less than 15% of the total population.
Experimental Considerations and the Corresponding Effect on the Results
Signal-to-noise ratio
The signal-to-noise ratio (SNR) has a large impact on the quality and accuracy of the
distance profile. In a dataset with low SNR, the oscillations in the noise mask oscillations in the
data. This effect can clearly be seen by comparing the L-curves for identical data sets with
different levels of noise. Figure 2-18 shows the L-curve for a data set with a SNR of 28. Each
of the three distances profiles correspond to values that are too low (under-smoothed), optimal,
and too high (over-smoothed). The arrows indicate the location of each value on the L-curve.
Additionally, the background subtracted experimental dipolar evolution curve (thin grey line) is
shown overlaid with the three TKR fits (thick black line) corresponding to the values. Figure
2-19 shows same data with a SNR of 14.
124
Figure 2-18. Example of an L-curve and the corresponding distance profiles and dipolar
evolution curves with a high SNR.
Figure 2-19. Example of an L-curve and the corresponding distance profiles and dipolar
evolution curves with a low SNR.
A comparison of the L-curves reveals that the lower SNR has a strong effect on the shape of
the L-curve. The corner is obscured making it more difficult to identify the optimal value.
This distortion primarily occurs at small values where the curve is dominated by changes in
log ( ) (the smoothing function) with only small changes in log ( ) (the fit function). The
increased noise results in larger changes in log ( ) thus distorting the curve.
20 30 40 50
-8.4 -7.7 -7.0 -6.3 -5.6 -4.9
-21
-18
-15
-12
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.0
0.0 0.5 1.0 1.5 2.020 30 40 50
20 30 40 50
1E-3
0.00
50.
010.
030.
070.
10.
30.
50.
71
235710
3050
80 100
300
500
700
1000
3000
7000
1000
0
3000
070
000
1000
00
log
log Tau ( s)Distance (Å)
Under-smoothed
Small
Optimal
Over-smoothed
A B
C
D
E
F
G
Large
Optimal
-4.26 -4.20 -4.14 -4.08
-24
-21
-18
-15
-12
-9
0.0 0.5 1.0 1.5 2.02 3 4 5 6
0.0 0.5 1.0 1.5 2.02 3 4 5 6
0.0 0.5 1.0 1.5 2.02 3 4 5 6
log
log Tau sDistance (Å)
Under-smoothed
Optimal
Over-smoothed
A B
C
D
E
F
G
Small
Large
Optimal
125
A comparison of the TKR fits for both SNR reveals that the oscillations in the lower SNR
data are more damped, which translates into broader distance profiles, for values.
Furthermore, the TKR fits for the lower SNR contain additional features, such as the shoulder at
0.25 s that is present in all three TKR fits and the shifted minimum near 1.0 s for the lowest
value. These features contribute to the additional populations seen in the distance profiles. It
should be noted that these additional populations are larger than the populations arising from
artifacts in the TKR process. Additionally, the population validation method used to test the
validity of these populations is not reliable if the SNR is too low because the suppression of
populations will not shift the theoretical dipolar evolution curves outside of the experimental
noise.
Maximum dipolar evolution time, tmax
The maximum dipolar evolution time, tmax, as was discussed previously, is strongly limited
by the Tm of the system. As tmax increases, the length of the pulse sequence increases and the
echo intensity decreases. This decrease in the signal requires that data collection times must be
extended or the SNR will decrease. Figure 2-20A shows two Gaussian-shaped distance
distributions centered at 48 Å with FWHM values of 1 Å and 7 Å. The corresponding theoretical
dipolar evolution curves are shown in Figure 2-20B. These theoretical curves were analyzed by
TKR with tmax values of 10, 4, and 2 s. White noise was convoluted onto the curves using the
white noise generator in Origin8.0 to achieve a SNR of 40. These curves are shown in Figures 2-
20C-E with the corresponding distance profiles in Figures 2-20F-H. The most probable
distances for all curves were 48.00 Å ±0.01 Å. The breadths for the 7 Å FWHM distance
profiles were 7.0 Å ± 0.1 Å. However, for tmax = 2 s, the breadth of the 1 Å FWHM profile was
broadened to 6.8 Å. The distances profiles for the 1 Å FWHM curves were more accurate for
126
tmax = 4 and 10 s with breadths of 1.4 and 1.1 Å respectively. These results clearly
demonstrated that the accuracy of distance profile breadth depends strongly on collecting the
dipolar evolution curve to a sufficiently large tmax value.
Figure 2-20. Illustration of impact that the length of tmax has on the resulting distance profile. A)
Two Gaussian-shaped distance profiles centered at 48 Å with FWHM = 1 Å (solid), 7
Å (dashed) and B) the corresponding theoretical dipolar evolution curves. C, E, and
G) The same echo curves as in (B) truncated to 10, 4, and 2 s respectively with
random SNR of 40 convoluted onto the curve and D, E, and F) the distance profiles
resulting from analysis of the echo curves in (C), (E), and (F) respectively with
DeerAnalysis2008.
Although it is unlikely to encounter distance profiles as narrow as 1 Å in a biological system,
these results illustrate the extreme effect that short tmax values can have on the breadth of a
distance distribution. The dipolar evolution curves at tmax = 2 s contain less than one-half of an
oscillation while the curves at tmax = 4 s contain almost two full oscillations. Thus, it is
advisable to collect experimental dipolar evolution curves with sufficiently long tmax such that at
least two oscillations are captured.
40 50 60
0 2 4 6 8 10 40 50 6040 50 6040 50 60
P(r
)
Distance (Å)
Ech
o In
ten
sity
Time ( s)
FWHM = 1 Å
FWHM = 7 Å
P(r
)
Distance (Å)
0.0 0.5 1.0 1.5 2.0
Time ( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
0 2 4 6 8 10
Time ( s)
Ech
o In
ten
sity
0 1 2 3 4
Time ( s)
Ech
o In
ten
sity
A
B
C
D
E
F
G
H
= 2 s= 4 s= 10 s
127
Spin-labeling efficiency
Poor spin-labeling efficiency can drastically increase the length of time needed to collect the
data to a desired SNR. As illustrated in Figure 2-8, the majority of the spins are not affected by
either the pump or observe pulses and can are designated C spins. Thus, the majority of the
proteins will contain non-productive spin pair combinations such as A-A, B-B, A-C, B-C, and C-
C. Because the dipolar evolution signal only results from proteins that have both an A spin and
B spin, only a small fraction of the sample contributes to the DEER signal. If the spin-labeling
efficiency is low then the amount of singly-labeled protein increases. This in turn decreases the
number of proteins with both A and B spins which in turn decreases the signal. It is not
necessary to quantify exactly what the spin-labeling efficiency is, but it is worth the effort to
optimize the labeling protocols to ensure that the protein is labeled with the greatest efficiency
possible. There is no standard set of conditions that will result in maximal labeling for all sites
on all proteins, but the pH and temperature can usually be optimized for a protein in general
based on the stability of the protein. In general, the labeling reaction will proceed faster at
higher temperatures however, not all proteins are sufficiently stable at room temperature and thus
must be labeled at colder temperatures. Likewise, the labeling reactions tend in proceed faster at
higher pHs however the reaction also tends to be less specific at higher pHs. Thus is necessary
to confirm that only the desired sites were labeled. Solvent-exposed sites will naturally be easier
to label than buried sites. It is possible to increase the labeling efficiency of buried sites by
adding a small amount of denaturant to allow the protein to unfold a little thereby increasing
solvent and thus spin-label access to the interior of the protein. Alternatively, the protein can be
labeled in the unfolded state and then refolded to the native state if the necessary folding
conditions for the protein are known and if the presence of the spin-label does not interfere with
folding significantly.
128
CHAPTER 3
DISTANCE MEASUREMENTS FOR HIV-1PR SUBTYPE B
Introduction
As discussed in Chapter 1, the flaps of HIV-1 protease (HIV-1 PR) play an important role in
the function of the enzyme. It has been shown through several experimental methods that the
flaps are inherently flexible and that this flexibility is necessary for proper function. The flaps
are characterized by three major conformations—closed, semi-open, and wide-open. Ishima et
al.73
summarized the flap conformations in solution as being an ensemble of conformations,
which are predominantly semi-open but can also include small populations of open and closed
forms. Results of recent molecular dynamics (MD) simulations50
of HIV-1 PR are consistent
with the NMR results.
Experimental Design
This chapter describes the characterization of the conformational ensembles of HIV-1 PR,
the distances between two spin-labels on the flaps by four-pulse double electron-electron
resonance (DEER) experiments. Protein constructs containing the lysine (K) to cysteine (C)
mutations at position 55 (K55C) in the flaps were expressed, purified, and labeled with
methanethiosulfonate spin label (MTSL). It has been demonstrated that HIV-1 PR is tolerant to
amino acid substitutions at the K55 position, so the substitution to Cys and the incorporation of
the spin-label should not significantly alter the structure of the HIV-1 PR nor interfere with the
activity of the HIV-1 PR. A comparison of the distance between the terminal amine nitrogen
atoms in the available x-ray structures of HIV-1 PR at K55 varies from 25 Å to 36 Å which is
well suited for DEER experiments.
129
Previous Studies
Galiano et al. recently showed that the DEER technique can be used to measure distances
between spin-labels incorporated into the flaps of HIV-1 PR and that these distances provide
insight into the flap conformations.81
The dipolar evolution curves, distance profiles, and L-
curves for HIV-1 PR in the absence and presence of ritonavir (RTV) are shown in Figure 3-1.
Apo HIV-1 PR yielded a broad distance profile with a most probable distance of 35.4 Å,
corresponds to the distance expected for the semi-open conformation. The breadth of this
profile, 12.7 Å, is larger than the value predicted for just the semi-open conformation and is
indicative of the flaps sampling conformations ranging from the closed form to wide-open
conformations.
Figure 3-1. A) Dipolar evolution curves for apo (black) and RTV-bound (grey) subtype B HIV-1
PR (curves offset vertically for clarity). B) Corresponding distance profiles. C) L-
curve for apo HIV-1 PR. D) L-curve for RTV-bound HIV-1 PR.81
-3.36 -3.29 -3.22 -3.15
-24
-21
-18
-15
-12
-9 1E-3
0.01
0.1
1
10
100
1000
10000
25000
50000
75000
100000
log
(
)
log ( )
0.0 0.5 1.0 1.5 2.0
Ech
o I
nte
nsity
Time ( s)
20 30 40 50
P(r
)
Distance (Å)
-4.0 -3.6 -3.2 -2.8
-24
-21
-18
-15
-12
-9 1E-3
0.01
0.1
1
10
50100
250
500
1000
5000
10000
50000
100000
log
log
Ritonavir
Apo
A
B
C
D
35.4 Å
32.6 Å
Apo
Ritonavir
130
The distance profile for RTV bound HIV-1 PR shows a most probable distance of 32.6 Å
which is consistent with predictions for the closed conformation based on x-ray structures. The
breadth of the profile is 3.6 Å, which is narrower than that for the apoenzyme. Because the flaps
undergo only very small and rapid oscillations when bound to an inhibitor,73
the breadth of the
RTV-bound distance profile can be attributed to the motion of the spin-label about the flexible
linker.
In this study, Galiano and co-workers utilized four different spin-labels to compare the effect
of varying the linker flexibility on the distance profiles (Figure 3-2). The most probable
distances for spin labels closely approximated the distances for MTSL with the slight differences
being attributable to the different lengths of the linkers. The breadths of the profiles varied more
noticeably but were consistent with predictions based on the known flexibility of the linkers.
Figure 3-2. Dipolar evolution curves for apo (black) and RTV-bound (grey) subtype B HIV-1
PR labeled with A) MTSL, B) MSL, C) IAP, and D) IASL. E-F) Corresponding
distance profiles generated.81
0 1 2 3 0 1 2 3 0 1 2 3 0 1 2 3
20 30 40 50 20 30 40 50 20 30 40 5020 30 40 50
Ech
o In
ten
sity
Time ( s)
Ech
o In
ten
sity
Time ( s)
Ech
o In
ten
sity
Time ( s)
Ech
o In
ten
sity
Time ( s)
P(r
)
Distance (Å)
RTV (MTSL)
Apo (MTSL)
P(r
)
Distance (Å)
RTV (MSL)
Apo (MSL)
P(r
)
Distance (Å)
RTV (IASL)
Apo (IASL)
P(r
)
Distance (Å)
RTV (IAP)
Apo (IAP)
A B C D
E F G H
131
The IAP linker is the same length as the MTSL and MSL linkers but is more flexible. The IASL
linker contains an additional bond and is also more flexible than the MTSL and MSL linkers.
Galiano et al.145
extended this study to include two drug-resistant variants, V660
and
MDR769,146
which are clinical isolates from patients who have received protease inhibitor
therapy. The distance profiles shown in Figure 3-3 demonstrated that the semi-open
conformation of V6 is more closed—has a shorter interflap distance—than subtype B, whereas
MDR769 is more open—has a longer interflap distance. This trend is consistent with predictions
based on the x-ray crystal structures. This important result showed that the flap‘s motion and
flexibility is affected by polymorphisms in the protein sequence.
Figure 3-3. A) Dipolar evolution curves for apo subtype B (black), V6 (grey), and MDR769
(light grey) (curves are vertically offset for clarity). B) Corresponding distance
profiles generated by TKR.145
These results were also confirmed by molecular dynamic (MD) simulations preformed by
Simmerling et al.82; 145
The distance profiles for apo and RTV-bound protease were very similar
to the experimental results, and most importantly, the change in the breadths of the profiles was
also observed. Likewise, the MD simulations for V6 and MDR769 also captured the differences
in the semi-open conformations.
0 1 2 3 20 30 40 50
Echo Inte
nsity
( s)
P(r
)
Distance (Å)
Subtype B
V6
MDR769
A B
V6
Subtype B
MDR769
Subtype B
V6MDR769
132
The goal of the present work is to characterize the flap conformations of the inhibitor-bound
protease to determine if the effect of inhibitor binding on the flaps is universal for all inhibitors
or if the effect varies among the inhibitors. The nine inhibitors have similar binding affinities
but they show varying enthalpic and entropic contributions to the free energy of binding. It is
possible that these differences could result in different effects on the flap conformations
monitored by DEER.
Ensembles Shifts of HIV-1 PR
Because the apo HIV-1 PR has been characterized as having some population in the closed
and open conformations,73
it follows that the addition of an inhibitor could simply shift the
ensemble to favor the closed conformation. This concept is illustrated in Figure 3-4. Two
energy landscapes are shown, one corresponding the apoenzyme (Figure 3-4A) and one
Figure 3-4. Cartoon illustration of possible energy landscapes for a HIV-1 PR with the three
major conformations (closed, right, semi-open, middle, wide-open, left) in the
presence and absence of an inhibitor. A) The semi-open conformation is the lowest
in energy and thus the most populated, but the closed and wide-open conformations
are close enough in energy and have low enough energy barriers that they will be
sampled as well. B) The ensemble shifts in the presence of an inhibitor, so that the
energy of the closed conformation is the lowest. The closed conformation will now
be the most populated with a small sampling of the semi-open and wide-open states.
inhibitor
A B
133
corresponding to an inhibitor-bound protease (Figure3-4B). Each local minimum corresponds to
a group of highly related structures which compose the major conformations of HIV-1 PR. In
the apoenzyme, the semi-open conformation is the most populated and lowest in energy. The
closed and wide-open conformations are energetically accessible but have a slightly higher
energy than the semi-open form as illustrated in Figure 3-4A. Upon binding an inhibitor, the
closed conformation becomes the most stable. The presence of the inhibitor in the active site
remodels the energy landscape so that the energy of the closed conformation is lower than that of
the semi-open and wide-open forms. The closed conformation is the same, regardless of whether
the inhibitor is present or absent, so the conformational coordinates of the minimum do not
change, just the relative energy level.
Materials and Methods
Protein Expression and Purification
The codon- and expression-optimized DNA encoding HIV-1 PR was purchased from DNA
2.0 (Menlo Park, CA) and was cloned into the pET 23a vector (Novagen, Gibbstown, NJ) using
standard cloning techniques. This DNA also included three additional amino acid substitutions
(Q7K, L33I, L36I) to reduce auto-proteolysis and two amino acid substitutions to remove the
native cysteines (C67A, C95A). The active site of HIV-1 PR was removed via a D25N
substitution and the labeling site was introduced (K55C) using site-directed mutagenesis.
The HIV-1PR was expressed into inclusion bodies using BL21*(DE3) pLysS E. coli cells
(Invitrogen, Carlsbad, CA). Cells were grown at 37 °C with shaking (250 rpm) to OD600 (optical
density at 600 nm) = 1.0, at which time the protein expression was induced with 1 mM IPTG
(isopropyl- -D-thiogalactoside). Expression was allowed to continue at 37 °C for 4 to 6 hours
until OD600 = 1.6. Cells were pelleted via centrifugation at 7500 x g for 20 mins at 4 °C, and the
pellet resuspended in 40 mL Buffer A (20 mM Tris, 1 mM EDTA, 10 mM BME pH 7.5). Cells
134
were lysed via sonication (2 mins total, with 5 sec on and 5 sec off) on ice, followed by three
passes through a 35 mL French pressure cell (Thermo Scientific). The inclusion bodies and
cellular debris were pelleted by centrifugation at 18500 x g for 30 mins at 4 °C. The inclusion
body pellet was resuspended in 40 mL of Buffer 1 (25 mM TrisHCl, 2.5 mM EDTA, 0.5 M
NaCl, 1 mM diGly, 50 mM BME, pH 7.0). The inclusion bodies were then sonicated as before,
homogenized using a 40 mL dounce homogenizer, and re-pelleted via centrifugation. The
inclusion bodies were washed twice more using two different buffers (Buffer 2: 25 mM TrisHCl,
2.5 mM EDTA, 0.5 M NaCl, 1 mM diGly, 50 mM BME, pH 7.0, 1 M Urea; Buffer 3: 25 mM
TrisHCl, 1 mM EDTA, 1 mM diGly, 50 mM BME, pH 7.0). The inclusion bodies were then
solubilized in 9 M urea (also containing 25 mM TrisHCl, 5 mM NaCl, 1 mM EDTA, 1 mM
diGly, 50 mM BME) with pH adjusted to be about 0.5 pH units below the pI of the HIV-1 PR
(pI = 9.35, pH = 8.85) to minimize binding to the Q column.
The solubilized inclusion bodies were then passed through two 5 mL Q columns (Amersham
Biosciences). The HIV-1 PR flowed through the column while the majority of the contaminating
protein bound the column. The column flow through was acidified by the addition of formic
acid (to a final concentration of 25 mM) and allowed to set overnight at 4°C to maximize
precipitation of contaminating proteins. The precipitate was removed by centrifugation at 38500
x g for 30 mins at RT. The supernatant was added drop-wise to 10 mM formic acid (pH ~ 3.0)
solution on ice in a tenfold dilution for optimal refolding of HIV-1 PR. The refolded protein was
then allowed to equilibrate to roughly 25°C, at which time the pH was adjusted to 5.0 by adding
2.5 M sodium acetate (NaOAc) buffer pH 5.5. Samples were spun again at 18500 x g for 25
mins at 4° to remove precipitated contaminants.
135
The HIV-1 PR was then concentrated to OD280 = 0.5 using an Amicon 8200 stirred cell with
a polyethersulfone (PES) membrane (Millipore) (MWCO 10 kDa) and was then buffer
exchanged into 10 mM Tris buffer pH 6.9 using a 53 mL HiPrep desalting column (Amersham
Biosciences). The sample was then concentrated back to OD280 = 0.5. A single crystal of spin
label (approximately a 20-fold molar excess) was dissolved in 100% ethanol (EtOH) and was
added to the sample. The reaction was allowed to proceed in the dark for 8-16 hours at room
temperature (20 to 24°C). The labeled protein was desalted into 10 mM NaOAc buffer pH 5.0
(to prevent non-specific interactions between the protein and the column), diluted to reduce the
buffer concentration to 2 mM NaOAc buffer pH 5.0 (to maximize protein stability and minimize
aggregation) and concentrated to OD280 > 1.0 using the stirred cell with a PES membrane. The
sample was subsequently stored at -20°C. Labeling efficiency was checked by collecting CW
EPR spectra.
DEER Samples
Protonated matrix
The HIV-1 PR was concentrated to OD280 > 1.6 using an Amicon Ultra-4 Centrifugal Filter
Unit with Ultracel-3 membrane. To avoid multiple freeze/thaw cycles, 70 L of the protein was
aliquoted into 0.2 mL PCR tubes for storage at -20 C. To prepare for a DEER experiment, one
aliquot was allowed to thaw at room temperature. For substrate-bound or inhibited samples, a
4:1 molar excess of substrate or inhibitor (typically 3 to 6 L) was added to the 70 L of protein
and allowed to sit for 15 to 30 mins to ensure sufficient time for binding. The substrate mimic
used in this work is a nonhydrolyzable synthetic peptide corresponding to the CA-p2 cleavage
site in the gag-pol polyprotein. The glycerol (either deuterated or protonated) was then added to
the sample to give a final concentration of 30% (typically 30 to 32.6 L). The sample was
136
mixed thoroughly with a pipet tip and transferred to a 4 mm quartz EPR tube using a syringe
fitted with a ~30 cm long tube (outer diameter ~2 mm).
Deuterated matrix
The HIV-1 PR was concentrated to OD280 > 1.6 using an Amicon Ultra-4 Centrifugal Filter
Unit with Ultracel-3 membrane. A 5-mL HiPrep desalting column was equilibrated with 11 mL
of 50 mM deuterated NaOAc buffer pH 5.0 in D2O. The sample was loaded onto the column
(volume ≤ 1.0 mL), and 1.5 mL of flow through was collected and discarded. The sample was
collected in the next 2.0 mL. The column was then washed with three column volumes each of
water, 1 M NaCl, water, 0.5 M NaOH, and water. The sample was concentrated back to OD280
> 1.6 and EPR signal was checked again. The sample was then treated as described above for
protonated matrices.
DEER Experiment
All DEER experiments were performed on a Bruker E580 spectrometer at 65 K with an ER
4118X-MD5 resonator. Samples were ―flash frozen‖ in a liquid nitrogen bath before being
placed into the resonator. The four-pulse DEER sequence discussed in chapter two (Figure 3-5)
was used in all experiments unless noted otherwise. The pulse parameters used with the Xepr
Figure 3-5. The four-pulse DEER sequence with the pulse spacings labeled according Bruker‘s
nomenclature in the Xepr software package.
(2)
mw
(1)
mw
2
Integration Gate (PG)
d0 d1 d2
d3
d1 d2
dx
137
Table 3-1. Pulse sequence parameters used with the Xepr software package from Bruker.
Matrix type d0 d1 d2 d3 PG dx
Protonated 100 200 3000 100 220 12
Deuterated 100 400 3000 100 220 12
All times listed in units of ns.
software package from Bruker Biospin are listed in Table 3-1. The length of the d1 spacing
varies depending on whether or not the matrix is protonated or deuterated. The 200 ns spacing is
used for protonated matrices and the 400 ns spacing is used for deuterated matrices.
Data Analysis
All DEER data were analyzed as discussed in Chapter two. Briefly, the dipolar evolution
curves were analyzed via Tikhonov regularization (TKR) to generate distance profiles and
background-subtracted dipolar evolution curves. The level of background subtraction was
optimized via the self-consistent analysis (SCA). The distance profile from TKR was used to
generate a theoretical dipolar evolution curve that was compared to the background-subtracted
dipolar evolution curve. If the two dipolar evolution curves did not match, then the TKR
analysis was repeated with an adjusted level of background. This process was repeated until the
theoretical and background dipolar evolution curves matched. The final distance profile was fit
to series of Gaussian functions.
Results
Apo and Substrate Mimic
The background-subtracted dipolar evolution curves for the apo and substrate mimic (CA-p2)
bound HIV-1 PR subtype B with amino acid substitutions D25N, Q7K, L33I, L36I, and K55C
and labeled with MTSL are shown in Figure 3-6A. It is clear that the dipolar evolution curves
for the apo and substrate bound forms of HIV-1 PR are very different. The first minimum in the
apo curve is shifted to right relative to the CA- p2 bound curve indicating that the most probable
138
Figure 3-6. DEER data for HIV-1 PR subtype B. A) Background subtracted dipolar evolution
curves for apo and CA-p2 bound HIV-1 PR overlaid with the fit from TKR. B) The
corresponding distance profile generated via analysis with TKR for apo and CA-p2.
distance is larger. Also the oscillations in the CA-p2 bound curve have a shorter periodicity
indicative of a narrower distribution. These trends are also seen in the distance profiles
generated by TKR. The most probable distance for the apoenzyme is 36.3 Å compared to 33.0 Å
for the CA-p2 bound HIV-1 PR. Likewise, the FWHM (full width at half maximum) of the
apoenzyme is 5.2 Å relative to 3.2 Å for the CA-p2 bound HIV-1 PR. This change in the
distance profile results from an alteration in the flap conformations of HIV-1 PR upon binding to
a substrate mimic, as seen in the x-ray structures. The ~3 Å shift to a smaller distance is
indicative of the flap conformation changing from predominantly semi-open to predominantly
closed in the presence of the substrate, thus bringing the spin labels closer together. Likewise,
the decrease in the FWHM is indicative of the decrease in the flexibility of the flaps as they close
around the substrate. The 3 Å breadth of the CA-p2 distance is consistent with the small cone of
motion of the spin label around the flexible linker even when the flaps are essentially
immobilized.
20 30 40 500 1 2 3
Apo
Ca-P2
( s)
Ech
o I
nte
nsity
P(r
)
Distance (Å)
Apo
Ca-P2
A B
139
Inhibitors
A comparison of the dipolar evolution curves for HIV-1 PR in the presence of the nine FDA-
approved inhibitors (Figure 3-7) reveals that the inhibitors do not all have the same effect on the
interflap distances. Some inhibitors (RTV, APV, LPV, DRV, TPV, and SQV) shift the first
minimum to the left and increase the frequency of the oscillations (Figure 3-7D-I). These
changes are indicative of a narrower distance distribution centered at a shorter distances. Other
inhibitors (IDV, NFV, and ATV) have little to no effect on the dipolar evolution curves (Figure
3-7A-C).
The distance profiles resulting from the TKR analysis of the dipolar echo curves for HIV-1
PR subtype B in the presence of the nine FDA approved inhibitors are not as identical as might
be expected considering their similar binding affinities (nM level). Figure 3-8 shows the
distance profiles for the PR in the presence of the nine inhibitors, as well as the apoprotease,
grouped according to the inhibitor‘s effect on the interflap distance measurements. It can clearly
be seen that the inhibitors in Figure 3-8D-I, have a strong effect on the flaps, shifting the most
probable distance from 36 Å to 33 Å and narrowing the breadth from 5 Å to 3 Å in the same
fashion as the substrate mimic. Likewise, it can clearly be seen that the inhibitors in Figure3-5A-
C have little to no effect on the flaps, with the largest shift being from 36 Å to 35 Å and the
breadth actually increasing from 5.2 Å to 5.5 Å. Interestingly, the distance profiles for all three
of these inhibitors contain a pronounced shoulder at 33 Å (indicated by the dashed vertical lines).
This shoulder is indicative of a population in the closed conformation.
The distance profiles can be fit to a series of Gaussian functions as discussed in Chapter 2.
The Gaussian functions used to reconstruct these TKR distance profiles for both the apo and
CA-p2 samples are centered at distances that correspond to the predominant conformations of
140
Figure 3-7. Dipolar Evolution curves for HIV-1 PR subtype B in the presence of various FDA
approved inhibitors. Apo protease is shown in black and the inhibitor-bound protease
is shown in grey. A) Nelfinavir (NFV), B) Indinavir (IDV), C) Atazanavir (ATV),
D) Amprenavir (APV), E) Lopinavir (LPV), F) Daurunavir (DRV), G) Saquinavir
(SQV), H) Ritonavir (RTV), I) Tipranaivr (TPV).
HIV-1 PR (Figure 3-9). The 33 Å distances correspond to the closed conformation, the 35-
36 Å distances to the semi-open conformation, and the 41-40 Å distances to the wide-open
conformation. The profile for the apoprotease was fit to four Gaussian functions. The Gaussian
function centered at 36 Å with a full-width at half-max (FWHM) value of 4.9 Å corresponds to
the expected distance and breadth expected for the semi-open conformation. This population
0 1 2 3
IDV
( s)
Ech
o In
ten
sity
0 1 2 3
TPV
( s)
Ech
o In
ten
sity
0 1 2 3
APV
( s)
Ech
o In
ten
sity
0 1 2 3
ATV
( s)
Ech
o In
ten
sity
0 1 2 3
RTV
( s)
Ech
o In
ten
sity
0 1 2 3
SQV
( s)
Ech
o In
ten
sity
0 1 2 3
NFV
( s)
Ech
o In
ten
sity
0 1 2 3
LPV
( s)
Ech
o In
ten
sity
0 1 2 3
DRV
( s)
Ech
o In
ten
sity
A D G
B E H
C F I
ApoNFV
Apo
Apo
Apo
ApoApo
ApoApo
ApoIDV
ATV
APV
LPV
DRV
SQV
RTV
TPV
141
Figure 3-8. Distance profiles for HIV-1 PR subtype B in the presence of various FDA approved
inhibitors (dashed vertical at 33 Å highlights the shift of the most probable distance).
Apo distance profile is represented as a dashed line. A) Nelfinavir (NFV), B)
Indinavir (IDV),) C) Atazanavir (ATV), D) Amprenavir (APV), E) Lopinavir
(LPV), F) Daurunavir (DRV), G) Saquinavir (SQV), H) Ritonavir (RTV), I)
Tipranaivr (TPV).
accounts for 86% of the total population. The Gaussian function centered at 33 Å with a FWHM
of 3 Å corresponds to the distance and breadth expected for the closed conformation with a 3%
population. The Gaussian function centered at 41 Å with a FWHM of 3.4 Å corresponds with
the wide-open conformation captured in Simmerling‘s MD simulation. The Gaussian function at
25 Å with a FWHM of 2.3 Å does not correspond with a well-known conformation of the
A D G
B E H
C F I
20 30 40 5020 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
RTV
Apo
P(r
)
Distance (Å)
IDV
Apo
P(r
)
Distance (Å)
NFV
Apo
P(r
)
Distance (Å)
ATV
Apo
P(r
)
Distance (Å)
APV
Apo
P(r
)
Distance (Å)
LPV
Apo
P(r
)
Distance (Å)
SQV
Apo
P(r
)
Distance (Å)
DRV
Apo
P(r
)
Distance (Å)
TPV
Apo
142
Figure 3-9. Gaussian-shaped populations used to fit the distance profiles for HIV-1 PR subtype
B. A) Apo HIV-1 PR. B) CA-p2 bound HIV-1 PR.
protease. However, several MD simulations have obtained results that indicate the flaps can tuck
or curl into the active site cavity. The distance for the 25 Å population is consistent with the
distance expected for a ―curled‖ or ―tucked‖ conformation. Populations appearing at this
distance will be putatively referred to as ―curled‖ in this work, although more data is needed for
a confirmed assignment.
The profile for the CA-p2 bound protease was also fit to four Gaussian functions. In this
sample the most populated conformation was the closed form, constituting 80% of the total. The
corresponding Gaussian function was centered at 33 Å with a FWHM of 2.7 Å. The two
Gaussian functions near 36 Å were combined to form the population for the semi-open
conformation and had a most probable distance of 36.3 Å and a FWHM of 3.3 Å. The fourth
Gaussian function was centered at 41.7 Å with a FWHM of 2.1 Å and corresponds to the wide-
open conformation. These results can be interpreted to mean that 86% of the apoprotease is in
20 30 40 5020 30 40 50
P(r
)
Distance (Å)
Closed
Semi-open
Wide-open
P(r
)
Distance (Å)
Curled
Closed
Semi-open
Wide-open
A B
Apo Ca-P2
Curled
Closed
Semi-open
Wide-open
ClosedSemi-open
Wide-open
143
the semi-open conformation, but upon binding an inhibitor, the closed conformation becomes
more stable and thus the closed conformation becomes populated with 80% of the protein.
Figure 3-10 shows the Gaussian reconstruction for each of the inhibitor bound HIV-1 PR
samples overlaid with the distance profile generated by TKR. Table 3-2 lists the most probable
distance, FWHM, and percent population for each of the Gaussian functions used in the
reconstruction. Interestingly, populations with similar characteristics appear in all the samples
and vary primarily in their relative populations. For example, in the distance profile for CA-p2
bound HIV-1 PR, the most probable distance is 33 Å, which corresponds to the expected
distance for the closed conformation of the flaps. The apo HIV-1 PR distance profile has a most
probable distance of 36 Å which corresponds to the semi-open conformation of the flaps.
However, the CA-p2 distance profile also contains a small population at 36Å and the apo profile
contains a small population at 33 Å. The Gaussians for all the samples can be divided into four
categories that correspond to the four major conformations of the flaps: populations between 25–
30 Å which correspond to tucked or curled conformations, populations around 33 Å which
correspond to the closed conformation, populations around 36 Å that correspond to the semi-
open form, and populations between 39 45 Å that correspond to the wide-open conformation.
Additionally, the breadths of the populations correspond to the expected flexibility of the spin
labels in each conformation. It is known that the flaps are more rigid in the closed conformation
than in the semi-open conformation73
and this trend is reflected in the distance profiles. The
populations at 33 Å are narrower in breadth than are the populations for the open and semi-open
populations.
144
Figure 3-10. Gaussian-shaped populations used to reconstruct the distance profiles for HIV-1 PR
subtype B. Populations were assigned to the closed (black), semi-open (grey), and
wide-open (white) conformations. A) Nelfinavir (NFV), B) Indinavir (IDV), C)
Atazanavir (ATV), D) Amprenavir (APV), E) Lopinavir (LPV), F) Daurunavir
(DRV), G) Saquinavir (SQV), H) Ritonavir (RTV), I) Tipranaivr (TPV).
Table 3-2. Parameters of Gaussian-shaped populations used to reconstruct distance
profiles. Sample Curled Closed Semi-open Wide-open
Center FWHM % Center FWHM % Center FWHM % Center FWHM %
Apo 24.7 Å 2.3 Å 4 33.0 Å 3.0 Å 3 36.4 Å 4.9 Å 86 41.3 Å 3.4 Å 7
CA-p2 33.0 Å 2.7 Å 80 36.3 Å 3.3 Å 16 41.7 Å 2.1 Å 4
NFV 32.8 Å 2.6 Å 14 35.9 Å 4.9 Å 78 41.8 Å 3.2 Å 8
IDV 32.8 Å 2.6 Å 14 35.9 Å 4.8 Å 79 41.2 Å 3.3 Å 7
ATV 32.8 Å 3.2 Å 41 35.9 Å 3.9 Å 49 41.3 Å 2.5 Å 6
APV 33.2 Å 2.8 Å 76 37.0 Å 2.4 Å 18 41.7 Å 2.0 Å 6
LPV 32.9 Å 2.9 Å 84 36.2 Å 3.9 Å 11 42.8 Å 2.8 Å 5
DRV 33.2 Å 2.9 Å 87 36.6 Å 2.5 Å 13
TPV 32.9 Å 2.3 Å 91 36.3 Å 1.7 Å 9
RTV 33.0 Å 2.6 Å 90 37.4 Å 2.1 Å 10
SQV 32.9 Å 2.8 Å 93 37.4 Å 2.1 Å 7
Error is estimated to be ± 5% in the percent population, ±0.5 Å for the center distances, and
±0.5 Å for the FWHM values.
A D G
B E H
C F I
20 30 40 50
20 30 40 5020 30 40 50
20 30 40 50
20 30 40 5020 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
NFV
P(r
)
Distance (Å)
LPV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
IDV
P(r
)
Distance (Å)
RTV
145
Estimation of Error in Distance Profiles and Population Analysis
The Figure 3-11 shows the dipolar evolution curves for apo subtype B HIV-1 PR in H2O
(discussed above) and D2O (both contain 30% D8-glycerol and 2 mM NaOAc buffer pH 5.0).
The use of deuterated water shifts the first minimum in the dipolar evolution curve to 46 ns
lower, leading to a slightly shorter most probable distance. The most probable distance for
HIV-1 PR in H2O is 36.3 Å compared to a most probable distance of 35.2 Å in the presence of
D2O. Although this difference is small, it is most likely real given the high SNR ratio of both
dipolar evolution curves. The most likely cause for the difference in the distance distributions is
Figure 3-11 DEER data for HIV-1 PR subtype B. A) Background subtracted dipolar evolution
curves for apo and CA-p2 bound HIV-1 PR overlaid with the fit from TKR. B) The
corresponding distance profile generated via analysis with TKR for apo and CA-p2.
the slightly higher viscosity of the D2O solution relative to the H2O solution. This data also
suggests that given sufficiently high SNR, subtle changes in the conformational ensemble can be
detected via DEER.
Figure 3-12 show the dipolar evolution curves for apo subtype B HIV-1 PR in D2O collected
as function of (the length of the dipolar evolution curve) and the corresponding distance
profiles. These data were collected on the sample without thawing the sample to ensure the
20 30 40 50
P(r
)
Distance (Å)
0 1 2 3
( s)
Ech
o In
ten
sity
H2O36.3 Å
D2O35.2 Å
H2OD2O
A B
146
highest degree of similarity possible between the curves. The curves were also analyzed with the
same level of background subtraction (global analysis). Collecting and analyzing the data in this
fashion provides an estimate of error in the distance profiles in addition to confirming that the
dipolar evolution curves are independent of .
Figure 3-12 DEER data for apo HIV-1 PR subtype B collected with various values. A)
Background subtracted dipolar evolution curves for apo HIV-1 PR vertically offset
for clarity. B) The corresponding distance profile generated via analysis with TKR
for apo HIV-1 PR.
Figure 3-13 shows the average of the distance profiles in Figure 3-12B in addition to the
average Gaussian-shaped populations. The individual distance profiles were fit to individual
series of Gaussian functions to generate the Gaussian-shaped populations, which were
subsequentially averaged. The error bars indicate the local error propagated through the
calculation of the average. It can be seen that the largest relative errors correlate with the least
populated conformations. This figure provides an estimate of the error in the distance profiles
that arises from the TKR process but not sample to sample variation.
0 1 2 3 4
Ech
o In
ten
sity
Time ( s)
20 30 40 50
P(r
)
Distance (Å)
A B
3.5 s3.0 s
2.5 s2.0 s
1.8 s1.5 s
3.5 s
3.0 s
2.5 s
2.0 s
1.8 s
1.5 s
A B
147
Figure 3-13. Average distance profile (grey) and average Gaussian-shaped populations for the
data shown in Figure 3-12. Error bars indicate the local error propagated through
calculating the average.
Table 3-3. Inhibition constant and dissociation constants for subtype C HIV-1 PR.
Most
Probable
Distance
(Å)
Std
Dev
95% CI FWHM
(Å)
Std
Dev
95% CI %
Population
Std
Dev
95% CI
Unassigned 15.5 2.5 2.0 4.1 1.7 1.4 1.9 1.7 1.4
Curled 24.7 1.9 1.6 4.1 1.8 1.5 3.2 1.3 1.1
Tucked 28.5 0.5 0.4 3.5 0.4 0.3 1.2 2.0 1.7
Closed 33.1 0.20 0.17 4.2 0.7 0.6 26 8 6
Semi-open 39.8 0.24 0.20 5.0 0.4 0.4 64 7 6
Wide-open 39.6 0.7 0.6 7.0 11 9 4.8 3.5 2.9
Discussion
These DEER results provide a measure of the percent of the protease in the closed
conformation for comparison to other measures of the inhibitor‘s interaction with the protease.
Table 3-3 lists the inhibitors in order of increasing percent closed and contains literature values
for the inhibition constant (KI), the dissociation constant (KD), the number of non-water mediated
20 30 40
Curled
Tucked
Closed
Semi-open
Wide-open
P(r
)
Distance (Å)
148
hydrogen bonds in the crystal structure (excluding hydrogen bonds to the D25 residues), and the
thermodynamic parameters of the inhibitor binding ( G, H, and S). There is a strong
correlation between the percent closed population and the number of non-water mediated
hydrogen bonds (excluding the hydrogen bonds to the D25 residues) in the x-ray structures. The
inhibitors with the largest percent closed populations also have the most hydrogen bonds. There
is a weak correlation between the percent closed population and the KD, in that all inhibitors with
a KD value > 300 pM also have a percent closed value < 50%. There is also a weak correlation
between the thermodynamic parameters ( G, H, and -T S) and the percent closed
conformation, with the exception of TPV, RTV and SQV. The inhibitors with the most
unfavorable G, H, -T S values (most positive or least negative) also have the smallest percent
closed populations. The exception of TPV can potentially be explained by the non-
peptidomimetic structure of TPV. This structural difference also gives rise to a unique feature of
TPV, which is that the H for TPV binding drug-resistant protease variants is actually more
favorable than the H than the binding to the wild-type protease.61
However, there is no obvious
explanation for the exception of RTV and SQV, since the thermodynamic parameters are almost
identical to those for IDV and NFV but the two groups have drastically different percent closed
populations. Additionally, the percent closed populations do not track with the KI values.
The caveat with comparing these DEER results to parameters from the literature is three-fold.
First, and probably most important, is that the DEER data were collected using protease
constructs with the D25N mutation that renders the protease catalytically incompetent. All of the
inhibitors contain a transition mimic that specifically hydrogen bonds with both of the D25
residues. Replacing the D25 residues with Asn (N) disrupts the formation of these hydrogen
149
Table 3-4. Comparison of percentage closed populations for each FDA-approved inhibitor with
published values of KD, KI, G, H, -T S (25 C), and the number of non-water
mediated hydrogen bonds in the crystal structures (excluding residue D25).
Inhibitor Abbreviation % Kd KI # of G H -T S
Closed (pM)a,b
(nM)b,c
Hydrogen
Bondsd,e,f,g
(Kcal/mol)d,i,j,
Nelfinavir NFV 14 670 a 1.2
c 2
d -9.7
i 2.8
i -14.2
i
Indinavir IDV 14 590 a 3.9
c 3
d -11.8
i
-13.1 d
3.9 i
1.3 d
-15.7 i
-14.4 d
Atazanavir ATV 41 NAh 0.48
c 3
b -14.3
d -4.2
d -10.1
d
Lopinavir LPV 84 36 a 0.05
c 3
f -14.3
d -2.4
d -11.9
d
Amprenavir APV 76 220 0.17c 5
d -13.2
j
-13.3 d
-6.9 j
-6.7 d
-6.9 j
-6.6 d
Darunavir DRV 87 10b 0.010
b 6
d -15.0
d -12.7
d -2.3
d
Tipranavir TPV 91 19 b 0.019
b 6
g -14.6
d -0.7
d -13.9
d
Ritonavir RTV 90 100 a 0.7
c 7
e -13.5
i -2.3
i -11.2
i
Saquinavir SQV 93 280 a 1.3
c 7
d -11.8
i 2.2
i -14.0
i
a) Data from Clemente et al.60
d) Data from Muzammil et al.61
c) Data from Yanchunas et al.62
d) Data from Prabu-Jeyabalan et al.63
e) Data from Prabu-Jeyabalan et al.64
f) Data from Reddy
et al.65
g) Data from Nalam et al.66
h) Data not available. i) Data from Todd et al.147
j) Data
from Ohtaka et al.67
bonds and reduces the Kd‘s from the nanomolar range to the micromolar range. It is possible
but unlikely that the D25N mutation could also lead to other differences in the interaction of the
inhibitors with the HIV-1 PR, as crystal structures of both the D25 and D25N protease have been
co-crystallized with DRV, and the structures contain no significant differences.148
Second, the
DEER data were collected at 65K, which requires that the samples be frozen. The freezing
process, submerging the sample tube in liquid nitrogen, is generally considered ―rapid‖ but
occurs over 2 to 3 seconds, which is significantly slower than the timescale of the conformational
changes. Thus, it is possible that the populations in the lowest energy conformational are larger
in the frozen sample than at ambient temperatures. Third, the DEER data is collected in the
presence of 30% w/v glycerol. The presence of the glycerol, which is preferentially excluded
from the protein surface, can potentially shift the ensemble of conformations. Exploring the
effects of the solutes on the flap conformations and spin-label mobility is the focus of Chapter 5.
150
However, the correlation between percent closed populations with the number of non-water
mediated hydrogen bonds in the crystal structures, as well as the weak correlation with the Kd
and thermodynamic parameters, suggest that, although the percent populations determined by
DEER may not absolutely correlate with the ensemble in solution, the trends in ensemble shifts
reflect the changes at ambient temperatures.
Recently, Kent et al.149
utilized DEER distance measurements to investigate the effects of
three inhibitors that mimic different phases of the substrate throughout the catalytic process.
Their study used both active (D25) and inactive (D25N) chemically synthesized HIV-1 PR
labeled at site K55C with MTSL. Similar to our results, their apo HIV-1 PR had a broadest
distance profile with three distinct populations corresponding to the closed, semi-open, and wide-
open conformations. Figure 3-14 shows the distance profiles for both active (D25) and inactive
(D25N) HIV-1 PR in the absence and presence of three inhibitors. In the presence of the MVT-
101 inhibitor, which mimics an ―early‖ transition state, the flap conformations are strongly
shifted to the closed conformation with a distribution breadth comparable to the breadth seen in
our RTV-bound HIV-1 PR. In the presence of the KVS-1 inhibitor, which mimics the full
tetrahedral intermediate, the flaps are also strongly shifted to the closed conformation but the
breadth of the distribution is slightly broader than was seen for MVT-101. In the presence of the
JG-365 inhibitor, which mimics a ―late‖ transition state, the profile is shifted approximately 1 Å
to left and has the same breath as the profile for apo HIV-1 PR. These results also corroborate
that apo HIV-1 PR is predominantly in the semi-open form and transiently samples the wide-
open and closed conformations. Additionally, their works demonstrates that even inhibitors
which do not strongly close the flaps in D25N HIV-1 PR have a similar effect in active HIV-1
PR.
151
Figure 3-14. Distance distributions for synthesized HIV-1 PR in the absence and presence of
inhibitors which mimic various stages of the substrate in the catalytic process. Figure
reproduced with permission from Torbeev et al.149
Conclusion
Our results are significant because they demonstrate that careful analysis of DEER data with
sufficiently high SNR can provide information on the conformational ensembles of proteins,
which is significantly more information than just the most probable distance and breadth of the
distance distribution. Additionally, these results demonstrate that DEER is sensitive to less
populated conformational states, as long as the SNR is sufficiently high. The ability to detect
these less populated states means that pulsed EPR can be added to a very short list of techniques
that are capable of detecting the signal from a small minority of the protein population. In light
152
of the growing interest in the dynamics and conformational ensembles of proteins and
macromolecular complexes, this technique will prove to be incredibly useful. Additionally,
many proteins which are not amenable to study by other powerful techniques, such as x-ray
crystallography and NMR, can be successfully studied via pulsed EPR.
153
CHAPTER 4
DEER RESULTS FOR HIV PROTEASE SUBTYPE C AND CLINICAL ISOLATE V6, A
DRUG-RESISTANT VARIANT
Introduction
As discussed in Chapter 1, HIV has a high rate of mutation which gives rise to the large
variety of protease sequences observed that include both naturally occurring polymorphisms,
found in the various subtypes, and drug-pressure selected mutations, found in clinical isolates
from patients receiving protease inhibitor therapy. The effects of both naturally occurring
polymorphisms and drug-pressure selected mutations on the structure and function of the
protease have been studied by a variety of techniques although the drug-pressure selected
mutations have been studied more thoroughly than the naturally occurring polymorphisms.
The polymorphisms are typically grouped according to their location within the HIV-1 PR
structure and are divided into active site (AS) and non-active site (NAS) mutations.150
The effect
of the AS mutations on the inhibitor binding is intuitively obvious; they alter the shape and size
of the active site binding pocket. Because inhibitors are rigid and designed to match the shape
and size of the active site pocket, their binding affinities are more strongly affected by changes in
the active site than the more flexible substrates.151
The effects of the NAS mutations, however, are not so obvious. Many x-ray crystallography
studies and several MD simulations have shown that some, but not all, of the NAS mutations
alter the packing of the hydrophobic core in such a way that the shape and size of the active site
is altered. It has also been shown that some NAS mutations alter the flexibility of the flaps or
shift the conformational ensembles of HIV-1 PR in favor of either more closed or more open
forms.150
The effects of the NAS mutations are especially important because the majority of naturally
occurring polymorphisms occur outside of the active site. In order to understand and predict
154
how the various subtypes will interact with the inhibitors, the mechanisms by which the NAS
mutations alter the effectiveness of the inhibitors must be understood.
This work seeks to characterize the flap conformations of subtype C and clinical isolate, V6
which is a drug-resistant variant, in the absence and presence of FDA-approved inhibitors.
These results can be combined with thermodynamic, kinetic, x-ray crystallography, and MD
studies to further understand the effects of mutations in these HIV-1 PR variants and to develop
more effective therapies.
Subtype C
World-wide, subtype C is responsible for more HIV infections than any other subtype and is
predominantly found in sub-Saharan Africa. However, most of the HIV-related research has
focused on subtype B, which is most prevalent in North America and Western Europe.
Additionally, all of the FDA-approved protease inhibitors (PIs) have been developed against
subtype B. Because the protease sequences of the various subtypes can vary by up to 30%
relative to subtype B, it cannot be assumed that currently available PIs will be effective against
these other subtypes. Thus, the susceptibility to FDA-approved inhibitors and the relative
vitality of subtype C HIV-1 PR are of great interest.
Figure 4-1 shows the x-ray crystal structure of apo subtype C HIV-1 PR (C-PR). The
naturally occurring polymorphisms typically found in C-PR, relative to subtype B, are
highlighted by spheres and include T12S, I15V, L19V, M36I, S37A, H69K, L89M, and I93L.
As with most naturally occurring polymorphisms, these occur outside of the active site. Of
particular interest, is occurrence M36I, which has been associated with drug-resistance in
subtype B. Additionally, two polymorphisms occur in the elbow (M36I and S37A), three in the
fulcrum (T12S, I15V, and L19V), and one in the cantilever (H69K). These regions are involved
in the opening of the flaps; thus, we hypothesize that the flexibility of the flaps in C-PR differs
155
Figure 4-1. Ribbon diagram of apo subtype C HIV-1 PR (PDB ID 2R8N) highlighting the
locations of naturally occurring polymorphisms relative to subtype B.
from the flexibility of the flaps in B-PR. In particular, the side-chain of L89 packs into the
hydrophobic core and mutations at this position could alter the packing of the core subsequently
affecting the shape of the active site. The L93 side-chain faces towards the cantilever.
Mutations at this site could alter the flap flexibility by altering the interactions of the cantilever
with the core of the protease.
Figure 4-2 shows an overlay of the C-PR structure with a structure of apo subtype B HIV-1
PR (B-PR). Both structures were crystallized in the P41212 space group. Overall, these
structures are highly similar with an average root mean squared deviation (RMSD) value of
1.09 Å152
; however, there are several regions with potentially significant differences including
the flaps, elbows, and 80‘s loop in the active site pocket. Considering the number of
polymorphisms in these regions, it is not surprising that they differ from those in B-PR. This
also reinforces the prediction that the flap flexibility in C-PR may differ from that observed in B-
PR. Additionally, the flap conformations are dramatically different as can be seen in top view of
the overlay (A). The closest atomic distance between the flap tips in B-PR is 4.4 Å, but is
H69K
M36I
S37A
I15V
L19I
T12S
L89M
I93L
156
increased to 12.2 Å for C-PR. Interestingly, apo subtype B has also been crystallized in a
structure (PDB ID 2PC0)153
almost identical to that of apo subtype C with an average RMSD of
0.28 Å.152
Figure 4-2. Ribbon diagrams of apo subtype C HIV-1 PR (blue) (PDB ID 2R8N) overlaid with
apo subtype B HIV-1 PR (gold) (PDB ID 1HHP). A) Top view. B) Front view.
These figures are generated using Chimera154
and overlays were generated by
aligning the alpha-carbons of one monomer.
These differences could result from the altered side-chain packing between the M36I and
I15V polymorphisms. M36I is located near the elbow and the side-chain faces towards the
fulcrum. I15V is in the fulcrum and the side chain faces towards the elbow. Both naturally
occurring polymorphisms involve replacing larger side chains with smaller residues thus
decreasing the steric hindrance between the flap elbows and the fulcrum. M36I in C-PR has
two-fold less van der Waals contacts than M36 in B-PR.152
This variation is illustrated in Figure
4-3, which shows the space filling models for the residues at position 36 and 15 for C-PR (A)
and B-PR (B). It can clearly be seen that there is more crowding for these residue in B-PR
relative to C-PR. One potential consequence of this disparity is that the flaps of C-PR might be
more likely to favor an open conformation.
A B
157
Figure 4-3. Ribbon diagram illustrating the difference in packing between residues 36 and 15 in
(A) subtype C HIV-PR (PDB ID 1SGU) and (B) subtype B HIV-PR (PDB ID 2BPX).
The enzymatic properties of C-PR are similar to those of B-PR and are summarized in Table
4-1. The Michaelis-Menten constants (Km), an indicator of substrate binding affinity, are almost
identical for C-PR and B-PR, with values of 17 M and 19.5 M, respectively. The catalytic
constants (kcat) show a slightly larger difference. The kcat is 5.6 s-1
for C-PR but is 10 s-1
for
B-PR, which is an almost two-fold decrease. The catalytic efficiencies (kcat/Km) were
0.32 M-1
s-1
and 0.55 M-1
s-1
for C-PR and B-PR respectively.155
These values are comparable
to those determined for two other subtype C variants, C and C-SA by Velázquez-Campoy et
al.156
They found Km values of 11.6 M, 5.4 M, and 14 M, kcat values of 5.8 s-1
, 7.7 s-1
and
Table 4-1. Kinetic parameters for subtype C HIV-1 PR.
Coman et al.155
Velázquez-Campoy et al.156
Km ( M) kcat (s-1
) kcat/Km
( M-1
s-1
)
Km ( M) kcat (s-1
) kcat/Km
( M-1
s-1
)
B-PR 19.5 10 0.55 14 8.9 0.64
C-PR 17 5.6 0.32
C-SA 11.6 5.8 0.5
C 5.4 7.7 1.43
A B
158
8.9 s-1
, and kcat/Km values of 0.32 M-1
s-1
, 1.43 M-1
s-1
, and 0.64 M-1
s-1
for C-SA, C, and B-
PR, respectively. The sequence of their C-SA variant, which is more prolific in South Africa, is
closer to the C-PR variant used by Coman et al. than the variant designated C. The results of
these two studies show that the naturally occurring polymorphisms in these variants of subtype C
do not provide a catalytic advantage over subtype B, although other variants have been shown to
have such an advantage.157
Coman et al.155
also determined the inhibition constants (KI) for eight of the FDA-approved
PIs for C-PR; this work is summarized in Table 4-2. The KI values for most of the inhibitors
were higher for C-PR than for B-PR, which is indicative of weaker inhibitor binding. This result
is not surprising since the inhibitors were designed to inhibit B-PR. The largest difference was
seen for RTV, with KI increased 3.8-fold relative to B-PR. However, the KI values for all
inhibitors remained in the nM range, suggesting they would still be effective at inhibiting C-PR.
Interestingly, the KI values for APV and TPV were lower for C-PR than for B-PR, indicating
tighter inhibitor binding.
Velázquez-Campoy et al.156
measured the dissociation constants (Kd) for IDV, SQV, NFV,
RTV, APV, and LPV for C-PR, which are also summarized in Table 4-2. They found that, for
all inhibitors tested, the Kd values were larger for C-PR than for B-PR, indicating the inhibitors
bind more weakly to C-PR. The smallest increase seen was 3.1-fold increase for APV (0.0465
nM for C-PR compared to 0.015 nM for B-PR). Similar to the trend seen for the KI constants, all
the Kd values remained in the nM range, indicating the inhibitors still bind sufficiently to inhibit
the enzyme.
159
Table 4-2. Inhibition constant and dissociation constants for subtype C HIV-1 PR. B-PR C-PR
KI155
(nM) KD156
(nM) KI155
(nM) KD156
(nM)
Indinaivir (IDV) 1.8 0.48 3.3 2.784
Nelfinavir (NFV) 1.7 0.26 2.7 1.014
Atazanaivr (ATV) 0.07 0.13
Amprenavir (APV) 0.04 0.015 0.29 0.0465
Lopenavir (LPV) 0.11 0.008 0.19 0.0624
Ritonavir (RTV) 0.07 0.03 0.27 0.726
Saquinavir (SQV) 2.2 0.40 2.6 2.32
Tipranavir (TPV) 0.4 0.11
Clinical Isolate V6
As discussed in Chapter one, the high mutation rate of the HIV genome provides an
evolutionary mechanism for adapting to the presence of protease inhibitors. The currently
accepted explanation for why the non-active site mutations affect the efficacy of protease
inhibitors is that they change the dynamics and/or flexibility of HIV-1 PR by either preventing
HIV-1 PR from reaching the wide-open conformation needed to bind the inhibitor or by
preventing the flaps from closing before the inhibitor can optimize its geometry for high-affinity
binding.71
Thus, understanding the role of the flaps in inhibitor binding can potentially result in
the design of better drugs that are less susceptible to drug-selected resistance.
The drug-resistant variant V6 was isolated from a pediatric patient undergoing RTV therapy.
It contains two AS mutations, V32I and V82A, and six NAS mutations, K20R, L33F, M36I,
L63P, A71V, and L90M. In addition to RTV resistance, these mutations are also associated with
IDV and NFV resistance. The V82 mutation is frequently seen in resistance to all clinically used
inhibitors. The positions of these mutations are highlighted in Figure 4-4. The combination of
V32I and V82A alters the shape of the active site, which typically results in significant decreases
in inhibitor binding. The side-chain of L90M faces into the hydrophobic core and can alter the
shape of the active site by changing the packing of the hydrophobic core. Residues L33, M36,
and K20 pack together in the region between the fulcrum and the flap elbows. Mutating these
160
residues most likely impacts the mechanics of flap opening. Likewise, residues A71 and L63 are
located in the cantilever, which is also involved in the opening of the flaps. Thus mutations in
these positions can also affect the ability of the flaps to open.
Figure 4-4. Ribbon diagram illustrating the locations of the drug-pressure selected mutations in
V6. Active site mutations are shown in black and non-active site mutations are
shown in grey. Mutations on mapped on a structure of subtype B HIV-1 PR (PDB ID
2BPX).
A previous study by Molla et al.158
found that drug-pressure selected mutations appeared in a
particular order for patients on RTV therapy. V82A is the first mutation to appear and is
associated with the initial decrease in the effectiveness of RTV. It is most frequently followed
by the mutations I54V, A71V, and, M36I, with the mutations I84V, K20R, L33F, and L90M
appearing later.
Similar to many drug-resistant HIV-1 PR variants, the V6-PR variant does not performs as
well enzymatically as the wild-type HIV-1 PR (subtype B).60
The Km value for V6-PR shows a
three-fold increase relative to B-PR (47 M for V6-PR compared to 18.2 M for B-PR). The kcat
value for V6-PR is 27 s-1
, which is 1.3-fold higher than the kcat value for B-PR, which is 21 s-1
.
V32I
V82A
A71V
L63P
L90M
M36I
L33F
K20R
161
The catalytic efficiency of V6-PR is roughly half that of B-PR (0.58 M s-1
for V6-PR compared
to 1.2 M s-1
for B-PR), which largely results from the three-fold increase in Km.
Table 4-3. Kinetic parameters for variant V6 HIV-1 PR.60
Km ( M) kcat (s-1
) kcat/Km ( M-1
s-1
)
B-PR 18 21 1.2
V6-PR 47 27 0.58
Error is estimated to be ± 5% in the percent population, ±0.5 Å for the center distances, and
±0.5 Å for the FWHM values.
Clemente et al.60
determined the KI values for RTV, IDV, and NFV for V6-PR, which are
summarized in Table 4-4. As expected, V6-PR shows a large decrease in susceptibility to RTV
because these mutations were selected for by RTV therapy. The KI value for RTV was 42-fold
higher for V6-PR relative to B-PR (30 nM for V6-PR versus 0.7 nM for B-PR). However, V6-
PR also shows some level of cross-resistance to IDV and NFV with 22-fold and 14 fold increase,
respectively. This result is also not unexpected given that a number of the mutations observed in
V6-PR also occur in IDV-selected and NFV-selected variants.
Table 4-4. Inhibition constants for variant V6 HIV-1 PR.60
B-PR V6-PR
KI (nM) KI (nM)
Indinaivir (IDV) 3.1 69
Nelfinavir (NFV) 1.2 17
Ritonavir (RTV) 0.7 30
Although there are no x-ray crystal structures for V6-PR, there are two x-ray structures for a
V6-PR variant containing the additional mutations I84V and I54V60
. These structures can be
compared to those of B-PR to provide insight into the structural effects induced by the drug-
pressure selected mutations. However, the V6 and subtype B structures are from crystals with
162
different symmetry point groups (V6 = P61, subtype B (1HSG, 1HXW) = P21212) so some
differences might be attributable to crystal contact artifacts. Figure 4-5 shows the IDV-bound
V6-PR structure overlaid with a comparable IDV-bound B-PR structure. Comparison of the
active sites reveals that the mutations lead to small changes in the shape of the active site pocket.
Because the inhibitors are much more rigid than the peptide substrates, even subtle changes in
the active site can have a large impact on inhibitor binding with only small affects on the
substrate binding. However, the structures are very similar overall, including the position of the
bound IDV. Comparison of the C backbone trace (A) shows that the regions in V6-PR with the
largest deviations relative to B-PR are the elbow and fulcrum and are the regions with the most
NAS mutations.
Figure 4-5. Overlay of x-ray structures for V6-PR (I84V, I54V) (yellow) (PDB ID 1SGU) and
B-PR (PDB ID 1HSG) (blue) bound to IDV. A) Backbone trace to highlight regions
of variation. B) Ribbon diagram to highlight extent of the similarities.
Figure 4-6 shows the RTV-bound x-ray structure of C-PR overlaid with RTV-bound B-PR.
Although these structures have a high degree of similarity, they are more different than the
structures for IDV. In addition to differences in the flaps, elbows, and 80‘s loops, these
structures also have significant differences in the fulcrum and cantilever domains. Additionally,
A B
163
the position of the bound RTV is not same for C-PR as for B-PR. Because the overall structures
for both RTV- and IDV-bound C-PR are similar to B-PR and the largest deviations are seen in
regions that are involved in the flap opening, it has been hypothesized that the contributions of
the NAS mutations to drug resistance are via alterations in the mechanics of flap opening.
Figure 4-6. Overlay of x-ray structures for V6-PR (I84V, I54V) (PDB ID 1SH9) (yellow) and B-
PR (PDB ID 1HXW) (blue) bound to RTV. A) Backbone trace to highlight regions
of variation. B) Ribbon diagram to highlight extent of the similarities.
Thus, characterizing the flaps conformations of variant V6-PR can elucidate the effect of the
NAS mutations on the flap dynamics. To this end, double electron-electron resonance (DEER)
was used to measure the distance between spin-labels covalently attached to K55C in the flaps.
Distance distributions were determined for apo and substrate (CA-p2)-bound V6-PR, in addition
to V6-PR in the presence of nine FDA-approved inhibitors. These distance profiles correlate
with changes in the population profiles for the various flap conformations described below.
Materials and Methods
Protein Expression and Purification
Subtype C HIV-1 PR and variant V6-PR were expressed and purified as discussed in Chapter
three with the following the exception. The pH of buffer 4 (9 M urea, 25 mM TrisHCl, 5 mM
A B
164
NaCl, 1 mM EDTA, 1 mM diGly, 50 mM BME) was adjusted to be about 0.5 pH units below the
pI of the HIV-1 PR (for subtype C pH = 9.05 (pI = 9.55) was used and for V6 pH = 8.42 (pI =
8.92) was used) to minimize binding to the Q column.
DEER Experiments
All samples were prepared as described in Chapter three. DEER data was collected as
described in Chapter three. The dipolar evolution curves were converted to distance profiles via
Tikhonov regularization (TKR) as implemented in the DeerAnalysis2008 software package.142
Distance profiles were reconstructed using a series of Gaussian-shaped populations. Any
populations contributing to less than 15% of the total population were validated using the method
described in Chapter two.
Results
DEER Results for Subtype C HIV-1 PR
Figure 4-7 shows the dipolar evolution curves and corresponding distance profiles for apo
subtype C and apo subtype B HIV-1 PR. The dipolar evolution curves are similar but not
identical. The first minimum in the curve for C-PR is shifted 33 ns higher than that of B-PR,
which is indicative of a longer most probable distance. The oscillations in the curve for C-PR
are similar to those for B-PR but have a slightly smaller intensity, leading to broader
corresponding distance profile for C-PR relative to B-PR. The most probable distance for apo
B-PR is 35.4 Å compared to 37.6 Å for apo C-PR. The breadth of distance distribution for C-PR
is 6.9 Å, which is broader than the breadth seen for B-PR (5.1 Å).
Figure 4-8 shows the dipolar evolution curves for apo and CA-p2 bound C-PR and the
corresponding distance profiles. A comparison of the dipolar evolution curves shows that the
first minimum in the curve for CA-p2 bound C-PR is shifted 153 ns lower, leading to a shorter
most probable distance. Additionally, the oscillations in the curve for CA-p2 bound C-PR have a
165
Figure 4-7. A) DEER Dipolar evolution curves for apo subtype C and subtype B HIV-1 PR.
B) Corresponding distance profiles generated by TKR.
higher intensity than those of apo C-PR which indicates the breadth of the distance distribution
for CA-p2 bound C-PR is narrower than that of apo C-PR. The most probable distance for CA-
p2 bound C-PR is 33.5 Å and the breadth of the distribution reduced to 3.9 Å. The change in the
distance profile for C-PR upon binding CA-p2 is similar to the change observed for B-PR
binding CA-p2; for B-PR the most probable distance shifts from 35.4 Å to 33.0 Å and the
breadth narrows from 5.1 Å to 3.2 Å. These changes represent a shift in the flap conformations
from being predominantly semi-open to predominantly closed.
Figure 4-8. A) DEER Dipolar evolution curves for apo and CA-p2 bound subtype C HIV-1 PR.
B) Corresponding distance profiles generated by TKR.
20 30 40 50
P(r
)
Distance (Å)
Bsi Apo
Csi Apo
0 1 2 3
Bsi Apo
Bsi Apo TKR Fit
( s)
Ech
o In
ten
sity
A BA
Apo B PR
Apo C PR
Apo B PR
Apo C PR
20 30 40 500 1 2 3
P(r
)
Distance (Å)
Apo
CA-p2
Ech
o In
ten
sity
( s)
AA BA
CA-p2 C-PR
Apo C-PRApo C PR
CA-p2 C-PR
166
Figure 4-9 shows the dipolar evolution curves and corresponding distance profiles for CA-p2
bound C-PR and B-PR. It can clearly be seen that both the dipolar evolution curves and distance
profiles are nearly identical. This similarity suggests that substrate-bound structure of C-PR
highly resembles the substrate bound structure of B-PR.
Figure 4-9. A) DEER Dipolar evolution curves for CA-p2-bound subtype C subtype B HIV-1
PR. B) Corresponding distance profiles generated by TKR.
Figure 4-10 shows the dipolar evolution curves for C-PR in the presence of nine
FDA-approved protease inhibitors. It can clearly be seen that the inhibitors affect the dipolar
evolution curves differently. NFV, IDV, and ATV affect only minor changes, whereas the other
inhibitors induce more significant changes. Interestingly, this trend is almost identical to the
trend observed for inhibitor binding in B-PR as shown in Chapter three. For all the inhibitors
except IDV, the first minimum is shifted lower indicating smaller most probable distances. The
magnitude of this shift ranges from 17 ns for IDV to 182 ns for TPV. Additionally, the intensity
of the oscillations is higher for APV, LPV, DRV, TPV, SQV, and RTV than those for apo C-PR.
As mentioned previously, the higher intensity oscillations correspond to narrower distance
distributions.
Figure 4-11 shows the distance profiles for C-PR in the presence of nine FDA-approved
inhibitors. It can clearly be seen that IDV, NVF, and ATV have minimal effects on the flap
20 30 40 500 1 2 3
P(r
)
Distance (Å)
CA-p2
Ech
o In
ten
sity
( s)
CA-p2
A B
B PR CA-p2
C PR CA-p2B PR CA-p2C PR CA-p2
167
conformations. The distance profile for IDV is almost identical to that of apo C-PR. NFV and
ATV shift the most probable distance to a slightly shorter distance (~36 Å) but do not change the
breadth of the distribution. APV shifts the most probable distance to below 34 Å, similar to the
remaining inhibitors, but does not narrow the distribution to the same extent. Likewise, LPV and
Figure 4-10. DEER dipolar evolution curves for C-PR in the presence of nine FDA-approved
inhibitors overlaid with the dipolar evolution curve for apo C-PR.
RTV affect less drastic reductions in the distribution breadths than do SQV and DRV. TPV
induces the largest shift in the most probable distance and narrowest distance distribution.
These changes in the distance profiles for C-PR can be compared to the inhibitor-induced
changes seen in the distance profiles from B-PR. Figure 4-12 show the overlays of the distance
0 1 2 3
0 1 2 3 0 1 2 3
0 1 2 3
0 1 2 3 0 1 2 3
0 1 2 3
IDV
( s)
Ech
o In
ten
sity
Ech
o In
ten
sity
( s)
LPV
Ech
o In
ten
sity
( s)
RTV
0 1 2 3
SQV
( s)
Ech
o In
ten
sity
Ech
o In
ten
sity
( s)
TPV
Ech
o In
ten
sity
( s)
APV
0 1 2 3
ATV
( s)
Ech
o In
ten
sity
Ech
o In
ten
sity
( s)
NFV
Ech
o In
ten
sity
( s)
DRV
Apo
Apo ApoApo
Apo Apo
Apo
Apo Apo
NFV
APV
TPV
IDV
LPV
RTVATV
DRV
SQV
A D G
B E H
C F I
168
profiles for C-PR and B-PR with each of the nine- FDA-approved inhibitors. The differences
seen between the distance profiles of C-PR and B-PR for IDV, NFV, and ATV are similar those
observed for apo C-PR and apo B-PR. The differences between the profiles for C-PR and B-PR
with APV, LPV,
Figure 4-11. DEER distance profiles for C-PR in the presence of nine FDA-approved inhibitors
(solid line) (vertical dotted line at 33 Å highlights the shift in the most probable
distance) overlaid with the distance profile for apo C-PR (dashed line).
SQV, DRV, and TPV are strikingly minor. In each case, the most probable distances are
essentially the same and the breadths of the distance distributions for C-PR are slightly broader
than those of the B-PR profiles. Interestingly, this is not the case for RTV. The most probable
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
20 30 40 50
P(r
)
Distance (Å)
LPV
P(r
)
Distance (Å)
RTV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
NFV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
IDVA D G
B E H
C F I
36.6 Å
37.2 Å
35.6 Å
33.6 Å
33.0 Å33.3 Å
32.8 Å
33.6 Å
33.5 Å
Apo37.6 Å
169
distance for C-PR with RTV is 0.7 Å longer and the breadth of the profile significantly broader
than for B-PR. However, a comparison of the inhibition constants (Table 4-2) for C-PR reveals
that largest change in the inhibition constant between C-PR and B-PR is with RTV.
Figure 4-12. Distance profiles for C-PR (solid) and B-PR (dashed) in the presence of nine FDA-
approved inhibitors.
The distance profiles for apo and CA-p2 bound C-PR can be reconstructed using a series of
Gaussian-shaped populations, which are shown in Figure 4-13. The apo C-PR distance profile
was fit to four Gaussian-shaped populations that are centered at 29, 33, 37, and 41 Å. The 41 Å
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
20 30 40 50
P(r
)
Distance (Å)
LPV
P(r
)
Distance (Å)
RTV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
NFV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
IDVA D G
B E H
C F I
36.6 Å
37.2 Å
35.6 Å
33.6 Å
33.0 Å33.3 Å
32.8 Å
33.6 Å
33.5 Å
B-PR32.9 Å
B-PR35.6 Å
B-PR32.8 Å
B-PR33.0 Å
B-PR32.9 Å
B-PR32.9 Å
B-PR33.3 Å
B-PR33.8 Å
B-PR35.6 Å
170
population corresponds to the wide-open conformation and constitutes 21% of the total protein
population. The population centered at 37 Å corresponds to the semi-open form of C-PR and
contributes 58% to the total population. The closed form corresponds to the population centered
at 33 Å, which is 9% of the population. The population centered at 29 Å (12%) does not
correspond to any of the well-known conformations of HIV-1 PR and is distinct from the
populations that appear around 25 Å and are designated as curled as discussed in Chapter three.
However, it is likely that this population also represents a curled or tucked conformation that
brings the flaps closer together. Thus, for now, populations centered near 30 Å are putatively
assigned to the tucked conformation for the purposes of discussion. The distance profile for
CA-p2 bound C-PR was fit to three Gaussian-shaped populations, which are centered at 31.8,
33.7, 38.1 Å. These populations correspond to the tucked, closed and semi-open conformations,
respectively and represent 13%, 79%, 7% of the total population, respectively.
Figure 4-13. Gaussian-shaped populations used to reconstruct the distance profiles of apo and
CA-p2-bound C-PR.
Likewise, the distance profiles for C-PR in the presence of the inhibitors can be reconstructed by
a series of Gaussian-shaped populations. These reconstructions are shown in Figure 4-14 and are
20 30 40 5020 30 40 50
CA-p2
P(r
)
Distance (Å)
Apo
P(r
)
Distance (Å)
A B
Closed
Semi-open
Closed
Semi-open Wide-open
Tucked
Tucked
171
summarized in Table 4-5. For IDV, NFV, and ATV, the most populated conformation is the
semi-open form, with increasingly larger populations of the closed conformation, respectively.
Interestingly, the percentage of wide-open conformation does not change appreciably between
these inhibitors. The distance profiles for APV, RTV, and LPV are all predominantly closed but
still have appreciable populations in the semi-open form. The conformations for SQV, DRV,
and TPV are almost entirely all closed. This trend is very similar that observed for B-PR except
that most of the inhibitors lead to a slightly smaller percent closed population for C-PR relative
to B-PR.
Figure 4-14. Gaussian-shaped populations used to reconstruct the distance profiles for C-PR in
the presence of nine- FDA-approved inhibitors
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 5020 30 40 50
P(r
)
Distance (Å)
IDV
P(r
)
Distance (Å)
RTV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
NFV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
LPV
A D G
B E H
C F I
Closed
Semi-open
Wide-open
Closed
Semi-open
Wide-open
Closed
Semi-open
Wide-open
Semi-open
Wide-open
Closed
Tucked
Semi-open
Closed
Semi-open
Wide-open
Closed
Semi-open
Closed
TuckedSemi-open
Closed
Tucked
Semi-open
Closed
Tucked
172
Table 4-5. Parameters of Gaussian-shaped populations used to reconstruct distance profiles for
subtype C. Sample Curled/Tucked Closed Semi-open Wide-open
Center FWHM % Center FWHM % Center FWHM % Center FWHM %
Apo 29.6 Å 3.1 Å 12 33.1 Å 4.4 Å 9 36.9 Å 4.6 Å 58 40.3 Å 3.4 Å 21
CA-p2 31.8 Å 1.9 13 33.7 Å 3.4 Å 80 38.1 Å 3.4 Å 7
NFV 32.7 Å 3.9 Å 12 36.5 Å 4.7 Å 78 39.6 Å 2.9 Å 10
IDV 30.5 Å 2.6 Å 4 33.0 Å 3.2 Å 6 37.3 Å 5.4 Å 81 41.0 Å 3.1 Å 9
ATV 33.0 Å 3.7 Å 17 36.0 Å 5.2 Å 68 39.6 Å 4.3 Å 15
APV 33.3 Å 3.2 Å 54 36.6 Å 5.1 Å 42 41.4 Å 2.5 Å 4
LPV 33.0 Å 3.3 Å 76 37.3 Å 4.4 Å 24
DRV 33.2 Å 2.8 Å 84 37.0 Å 2.2 Å 12 41.3 Å 1.6 Å 4
TPV 32.8 Å 2.8 Å 97 36.3 Å 1.2 Å 3
RTV 31.7 Å 1.7 Å 8 33.8 Å 3.4 Å 77 38.0 Å 3.4 Å 15
SQV 32.0 Å 1.8 Å 21 34.0 Å 3.0 Å 72 39.0 Å 2.0 Å 7
Error is estimated to be ± 5% in the percent population, ±0.5 Å for the center distances, and
±0.5 Å for the FWHM values.
DEER Results for the V6 Variant of HIV-1 PR
Figure 4-15 shows the dipolar evolution curves and corresponding distance profiles for apo
V6-PR overlaid with those of apo B-PR. A comparison of the dipolar evolution curves reveals
that apo V6-PR and B-PR should have similar distance profiles although the most probable
distance for V6-PR should be slightly shorter than for B-PR. The most probable distance for V6-
PR is 35.7 Å, which is just shorter than the 36.3 Å seen for B-PR. The breadth of the profile for
V6-PR is 7.1 Å, which is broader than the breadth of 5.1 Å for B-PR.
Figure 4-15. DEER dipolar evolution curves and distance profiles for apo V6-PR and B-PR.
20 30 40 500 1 2
Bsi TKR Fit
V6 Apo
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
V6 Apo
Bsi Apo
A BAA
Apo B PR
Apo V6 PR
Apo B PR
Apo V6 PR
173
Figure 4-16 shows the dipolar evolution curves and distance profiles for apo and CA-p2
bound V6-PR. Similar to C-PR and B-PR, the binding of CA-p2 to V6-PR shifts the first
minimum in the dipolar evolution 114 ns lower and increases the intensity of the oscillations,
indicative of a shorter most probable distance with a narrower distribution. The most probable
distance is 32.9 Å for CA-p2 bound V6-PR with a breadth of 3.5 Å.
Figure 4-16. DEER dipolar evolution curves and distance profiles for apo and CA-p2 bound
V6-PR.
Figure 4-17 shows the dipolar evolution curves and distance profiles for CA-p2 bound V6-
PR and B-PR. The first minimum in the dipolar evolution curve for V6-PR is shifted slightly
lower, by ~58 ns, indicative of a slightly shorter most probable distance. However, this
difference not what is seen in the distance profiles. The most probable distances are the same but
the distribution of distances around the most probable distances differ. In the case of V6-PR,
there is more population for distances below the most probable distance. Whereas, for B-PR,
there is more population at distances greater than the most probable distance. However, the SNR
for the CA-p2 bound V6-PR is substantially higher than the SNR for B-PR and it is likely that
the differences seen in the dipolar evolution curves and distance profiles are a result of the noise.
20 30 40 50
P(r
)
Distance (Å)
Ca-P2
0 1 2 3
CA-p2
( s)
Ech
o In
ten
sity
A BA BAA
CA-p2 V6 PR
Apo V6 PRApo V6 PR
CA-p2 V6 PR
174
Figure 4-17. DEER dipolar evolution curves and distance profiles for CA-p2 bound V6-PR and
B-PR.
Figure 4-18 shows the dipolar evolutions curves for V6-PR in the presence of nine FDA-
approved inhibitors. Similar to C-PR and B-PR, IDV, NFV, and ATV have minimal effects in
the dipolar evolution curves, shifting the first minimum by ~30 ns. However, RTV, which had a
more drastic effect on C-PR and B-PR, has a much smaller effect on V6-PR. The first minimum
is shifted by only 67 ns. This result is not unexpected because the drug-pressured selected
mutations in V6 were selected for under RTV therapy. The trend in the remaining inhibitors is
similar to that seen with C-PR and B-PR. TPV, SQV, and DRV have a strong effect on the
dipolar evolution curve, shifting the first minimum by ~115 ns. LPV and APV have slightly less
effect in the dipolar evolution curves and shift the first minimum by only 86 ns.
This trend is also seen in the distance profiles for V6-PR in the presence of the inhibitors,
which are shown in Figure 4-19. NFV and IDV shift the most probable distance to ~34 Å and
increase the breadth of the profile slightly. ATV and RTV shift the most probable distance to
~ 34 Å but do not change the breadth of the profiles. APV shifts the most probable distance to
33.7 Å and narrows the breadth to 3.8 Å. SQV and DRV shift the most probable distances
20 30 40 50
P(r
)
Distance (Å)
Ca-P2
0 1 2 3
CA-p2
( s)
Ech
o In
ten
sity
A BA BAA
CA-p2 V6 PR
CA-p2 B PR
CA-p2 V6 PRCA-p2 B PR
175
Figure 4-18. DEER dipolar evolution curves for V6-PR in the absence and presence of nine
FDA-approved inhibitors.
to~33.3 Å and narrow the distance profile significantly to ~3.4 Å. LPV also shifts the most
probable distance to 33.5 Å and narrows the breadth to 2.2 Å but retains a large population of
distances around 30 Å. TPV, as with C-PR and B-PR, has both the largest shift in the most
probable distance, to 32.9 Å, and the largest decrease in profile breadth, to 2.6 Å.
With the exception of RTV, this trend is similar to that seen for B-PR. Figure 4-20 show the
distance profiles for V6-PR and B-PR in the presence of nine FDA-approved inhibitors. In
0 1 2 3
Ech
o In
ten
sity
Time ( s)
RTV
0 1 2 3
NFV
( s)
Ech
o In
ten
sity
0 1 2 3
LPV
( s)
Ech
o In
ten
sity
0 1 2 3
ATV
( s)
Ech
o In
ten
sity
0 1 2 3
APV
( s)
Ech
o In
ten
sity
0 1 2 3
SQV
( s)
Ech
o In
ten
sity
0 1 2 3
TPV
( s)
Ech
o In
ten
sity
0 1 2 3
IDV
( s)
Ech
o In
ten
sity
0 1 2 3
DRV
( s)
Ech
o In
ten
sity
Apo Apo Apo
Apo Apo Apo
Apo Apo Apo
NFV
APV
TPV
IDVLPV
RTV
ATVDRV
SQV
A D G
B E H
C F I
176
Figure 4-19. DEER distance profiles for the V6 variant of HIV-1 PR in the presence of nine
FDA-approved inhibitors (vertical dashed line at 33 Å highlights the shift in the most
probable distance) overlaid with the distance profile for apo V6-PR.
general, the shifts of the most probable distance are the same for V6-PR and B-PR but the
breadths for V6-PR are slightly broader than those for B-PR. The exceptions are LPV, which is
narrower for V6-PR than for B-PR, TPV, which is the same for V6-PR and B-PR, and RTV,
which is drastically different in both the shift and breadth of the profile as a result of the RTV-
resistance of V6-PR.
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
P(r
)
Distance (Å)
NFV
P(r
)
Distance (Å)
RTV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
LPV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
IDV
A D G
B E H
C F I
34.0 Å
34.0 Å
34.4 Å
34.3 Å
35.8 Å33.7 Å
33.4 Å
33.2 Å
33.5 Å
32.9Å
177
Figure 4-20. DEER distance profiles for the V6 variant of HIV-1 PR in the presence of nine
FDA-approved inhibitors (vertical dashed line at 33 Å highlights the shift in the most
probable distance) overlaid with the distance profile for the same inhibitor bound to
B-PR.
Figure 4-21 shows the Gaussian reconstructions for the apo and CA-p2 bound V6-PR
distance profiles. The distance profile for apo V6-PR was fit to three Gaussian-shaped
populations corresponding to the tucked (29 Å), closed (33 Å), semi-open (36 Å), and wide-open
(39 Å) conformations, representing 10%, 21%, 61%, and 8 % of the total population,
respectively. Interestingly, the CA-p2 bound distance profile was fit to only one population,
which corresponds to the closed conformation and is centered at 33 Å.
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50
P(r
)
Distance (Å)
NFV
P(r
)
Distance (Å)
RTV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
LPV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
IDV
A D G
B E H
C F I
34.0 Å
34.0 Å
34.4 Å
34.3 Å
33.2 Å33.7 Å
33.4 Å
33.2 Å
33.5 Å
32.9Å
35.9 Å
33.0 Å
32.8 Å
33.2 Å
32.8 Å
33.8 Å
32.9 Å
35.8 Å
178
Figure 4-21. Gaussian-shaped populations used to reconstruct the distance profiles of apo and
CA-p2-bound V6-PR.
Figure 4-22 shows the Gaussian reconstruction for the inhibitor-bound distance profiles for
V6-PR. The largest semi-open populations are seen for NFV, IDV, RTV, and ATV and
correspond to 39%, 54%, 51%, 63%, respectively. The second largest populations for these
inhibitors corresponds to the closed conformation and represent 30%, 30%, 34%, and 30%,
respectively. The third largest population is the tucked conformation, which constitutes 14%,
10%, 15%, and 7%, respectively. NFV and IDV also have wide-open populations that contribute
17% and 6% of the total population. The largest population for APV, SQV, DRV, LPV, and
TPV is in the closed conformation, which represents 72%, 87%, 89%, 83%, and 92%,
respectively. APV has three additional populations corresponding to tucked (7%), semi-open
(16%), and wide-open (4%). SQV has one additional population in the semi-open conformation
(13%). DRV has four additional populations corresponding to the curled (3%), tucked (3%),
semi-open (3%), and wide-open (2%).. LPV has an additional tucked populations of 17% and
TPV has three additional populations, curled (5%), tucked (2%), and wide-open (2%).
20 30 40 5020 30 40 50
P(r
)
Distance (Å)
CA-p2
P(r
)
Distance (Å)
ApoA B
Closed
Closed
Semi-open
Tucked Wide-open
179
Figure 4-22. Gaussian-shaped populations used to reconstruct the distance profiles for V6-PR in
the presence of nine- FDA-approved inhibitors.
Table 4-6. Parameters of Gaussian-shaped populations used to reconstruct distance profiles for
clinical isolate, V6. Sample Curled/Tucked Closed Semi-open Wide-open
Center FWH
M
% Center FWHM % Center FWHM % Center FWHM %
Apo 29.6 Å 3.9 Å 10 33.2 Å 3.8 Å 21 36.4 Å 4.8 Å 861 39.9 Å 3.1 Å 8
CA-p2 33.1 Å 4.0 Å 100
NFV 27.3 Å 6.1 Å 14 32.9 3.8 Å 30 35.4 Å 4.3 Å 39 39.2 Å
42.4 Å
3.4 Å
3.3 Å
17
IDV 27.5 Å 6.1 Å 10 32.8 Å 5.4 Å 30 36.8 Å 7.2 Å 54 46.8 Å 4.5 Å 6
ATV 29.6 Å 4.0 Å 7 32.8 Å 3.7 Å 30 36.0 Å 5.5 Å 63
APV 29.8 Å 2.8 Å 8 33.3 Å 3.1 Å 72 37.7 Å 3.5 Å 16 45.0 Å Å 2. Å 8 4
LPV 30.0 Å 3.0 Å 17 33.4 Å 2.2 Å 83
DRV 25.9 Å
28.5 Å
1.1 Å
1.1 Å
3
3
33.2 Å 3.2 Å 89 38.5 Å 1.5 Å 3 43.7 2.4 Å 2
TPV 25.0 Å
29.2 Å
2.1 Å
1.0 Å
5
2
32.9 Å 3.4 Å 92 40.9 Å 1.9 Å 2
RTV 31.1 Å 4.5 Å 15 33.7 Å 4.7 Å 34 36.0 Å 6.2 Å 51
SQV 33.2 Å 3.1 Å 87 38.2 Å 1.8 Å 13
Error is estimated to be ± 5% in the percent population, ±0.5 Å for the center distances, and
±0.5 Å for the FWHM values.
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
20 30 40 50
20 30 40 50
20 30 40 50 20 30 40 50
20 30 40 50
P(r
)
Distance (Å)
IDV
P(r
)
Distance (Å)
ATV
P(r
)
Distance (Å)
SQV
P(r
)
Distance (Å)
TPV
P(r
)
Distance (Å)
DRV
P(r
)
Distance (Å)
RTV
P(r
)
Distance (Å)
APV
P(r
)
Distance (Å)
LPV
P(r
)
Distance (Å)
NFVA D G
B E H
C F I
Closed
Semi-open
Wide-open
Closed
Semi-open
Wide-open
Closed Semi-open
Semi-openClosed
Tucked
Semi-open
Wide-open
Closed
ClosedTucked
Wide-openCurled
Closed
TuckedSemi-openClosed
Semi-open
Wide-open
Closed
Tucked
Tucked
Tucked
Tucked
Curled
180
Discussion
In this work, we characterized the flap conformations of subtype C HIV-1 PR and a drug-
resistant variant of HIV-1 PR, V6, in the absence and presence of a substrate mimic, CA-p2, and
in the presence of nine- FDA-approved inhibitors. This was accomplished by measuring the
distance between spin-labels incorporated at site K55C in the flaps using DEER.
Our results for apo C-PR correlate with the differences seen between the x-ray crystal
structures for C-PR and B-PR. The most probable distance in the semi-open conformation for C-
PR is longer than that of B-PR by ~ 1 Å. This difference is smaller than that seen in the x-ray
structures but the trend is consistent. Additionally the apo C-PR has a larger wide-open
population than B-PR, which is consistent with the predictions that the M36I and I15V
polymorphisms would increase the flexibility of the flaps in C-PR. Our results also show that
CA-p2 bound C-PR is highly similar to that of B-PR. This indicates that the substrate bound
conformations of C-PR and B-PR are most likely very similar as well.
The changes in the distance profiles for C-PR in the presence of the nine FDA-approved
inhibitors are similar to those seen for B-PR. The noticeable difference is that the distance
profiles are slightly broader for C-PR, which likely results from the decreased binding affinity of
the inhibitors for C-PR. Also, the distance profile for RTV with C-PR showed the largest
difference relative to B-PR, which is consistent with RTV having a significantly larger increase
in KI for C-PR.
Our results for apo V6-PR, which showed the V6-PR is less open then B-PR, are also
consistent with the predictions based on the locations and known effects of several of the
polymorphisms in V6-PR. The side-chains of L33, M36, and K20 pack together in the region
between the fulcrum and elbows. Thus, the combined effect of mutating all three of these
residues is most likely to alter the flexibility of the flaps and to stabilize a slightly more closed
181
conformation. This trend is also seen in the CA-p2 bound V6-PR, which in more closed than
that of B-PR.
Our results for V6-PR in the presence of the nine FDA-approved inhibitors is also consistent
with the trend seen in the inhibition constants for V6-PR. The distance profile for RTV shows
the most largest difference relative to B-PR, which correlates with the large increase seen in the
KI value. This result is expected because the polymorphisms in V6 were selected for under RTV
therapy. The KI values for other inhibitors also increased for V6-PR compared to B-PR. This
trend is also seen in our results. The distance profiles for all the inhibitors except DRV and TPV,
showed an increased breadth relative to B-PR. Although the KIs have not been determined for
all the inhibitors, this indicates that these inhibitors might also have increased KI values.
Furthermore, the lack of change between the distance profiles of DRV and TPV for V6-PR and
B-PR suggests that these inhibitors might be the most effective at inhibiting V6-PR.
Conclusion
These results demonstrate that DEER is sufficiently sensitive to detect subtle changes in the
conformational ensembles resulting from polymorphisms in the protein sequence. Furthermore,
the correlations seen between the changes in the KI values for C-PR and V6-PR variants relative
to B-PR, suggests that DEER can potentially predict changes in the effectiveness of inhibitors for
variants of HIV-1 PR. Additionally, the details of the conformational ensembles of HIV-1 PR
can confirm the predicted effects of polymorphisms on the flap flexibility and conformation and
provide a measure of the magnitude of the effects.
182
CHAPTER 5
SOLUTE EFFECTS ON SPIN-LABEL MOBILITY AND PROTEIN CONFORMATIONS
Introduction
The addition of solutes to protein samples is often required for a variety of experimental
techniques. In x-ray crystallography, the solutes aid in the crystallization process and protect the
crystals during the freezing process. In SDSL EPR studies of proteins and biological molecules,
solutes are frequently added to increase the correlation time for isotropic tumbling ( R) of
molecules under 20 kDa so that the line shape is not dominated by R (e.g., fully averaged) and
can thus reveal local information about the spin-label‘s mobility about a flexible linker ( I) and
about the flexibility of the protein backbone ( B). For pulsed EPR studies, which are preformed
at cryogenic temperatures, solutes are added as glassing agents to prevent phase separation and
protein aggregation.
However, it has been shown that solutes can alter the structure and function of proteins.
Solutes can increase or decrease the rate of an enzymatic reaction, stabilize or destabilize the
native state of the protein, and enhance or hinder a protein‘s ability to undergo a conformational
change. These effects result from the differences between solute-water, solute-protein,
protein-water, and water-water interactions. Consequently the effects of the solute on the protein
will depend on the size, concentration, and chemical composition of both the solute and protein.
To simplify the discussion, it is useful to deconstruct the various types of solutes and the
various impacts the solutes have on the solution. Furthermore, it useful to deconstruct the
various aspects of the protein in order to delineate how the various effects of solutes on the
solution properties collectively affect the protein.
183
Figure 5-1. Structures of water and various solutes. A) Water, B) urea, C) ammonia, D)
glycerol, E) sucrose, and F) poly(eythlene glycol).
Solute Effects on Solution Properties and Protein Structure and Function
Important considerations for proteins
In general, proteins can be considered to have two primary components—the peptide
backbone and the amino acid side chains. The peptide backbone is hydrophobic and generally
prefers to self-associate in the presence of aqueous solutions. The amino acid side chains are
typically grouped into four categories—polar, charged, aromatic, and hydrophobic (non-polar).
The surface of a folded protein is a combination of each of these groups. Typically, the more
hydrophobic side chains and peptide backbone are buried in the core of the protein or buried in
the hydrophobic region of a bilayer with the charged and polar groups exposed to the solvent.
However, the solvent-exposed surface of the protein is heterogeneous and comprised of both
polar and non-polar regions that vary for every protein. The water and solutes interact with each
region differently and the overall effect of the solute on the protein will depend on the
OH OH
OH
NH2 NH2
O
N H
H
H
O
OH OH
O
O
OH
OH
OH
OH
OH
OH
OHH
OOH OH
n
A B DC
FD
184
contribution of each region to the whole. Thus, each protein can potentially have a unique
response to various solutes.
Important considerations for water
Water is unique in its interactions, and despite the long history of investigations into the
structure and nature of water, a full understanding has yet to be accomplished. Few molecules, if
any, can hydrogen bond as efficiently as water. Water has the unique ability to either donate or
accept hydrogen bonds at all four positions on the oxygen creating a tetrahedral structure.
Additionally, water can donate the same number of hydrogen bonds as it can accept which
maximizes the ability of water to form hydrogen bonding networks. Other small polar
compounds such as alcohols and acetone contain carbon residues and thus are only polar on one
side of the molecule. Other polar compounds like ammonia, which can also donate and accept
up to four hydrogen bonds lacks the symmetry of water because it can donate three hydrogen
bonds but only accept one. Consequently, the addition of any compound to an aqueous solution
raises the chemical potential ( ) of the solution by disrupting the hydrogen bonding network.
This disruption is typically manifested as an increase in the structure of the water near the
molecule. For non-polar molecules, the water molecules are structured around the molecule to
form a cage. For ions, the water molecules strongly hydrogen bond with ion creating a layer of
rigid water. For polar compounds, there is typically no significant ordering of water molecules,
just a small disruption in the hydrogen bonding network.
The chemical potential for each species in a solution can be described by Equation 5-1,
jj
s
j aRT ln*ln (5-1)
where j is the index for each component, jsln
is the chemical potential in solution, j* is the
chemical potential in the pure state, aj is the activity of component j, R is the molar gas constant,
185
and T is the absolute temperature. For an ideal solution, the activity of component j is equal to
j, the mole fraction of component j. Thus, the addition of a solute to an aqueous solution
reduces the mole fraction of water and the activity of water which decreases the chemical
potential of water.
Important considerations for solutes
Solutes can vary greatly in their size, structure, and chemical compositions and each facet
impacts the effects of the solute on the protein and the solution differently. Additionally, certain
combinations of features can also have collective effects that differ from effects of either feature
alone. In general, the size, density, polarity, hydrophobicity, concentration, and number of
hydrogen bond donors and acceptors are considered to be the most important aspects of the
solutes.
Size. Solutes can be divided into two important categories based on their size—small
molecules whose size is on the same order as water and larger molecules whose size varies from
peptides to large proteins. The effects of large solutes are dominated by the solute‘s exclusion
from the surface of the protein resulting from steric restraints. However, the
polarity/hydrophobicity of the solute can also contribute to the effect of the solute on the protein.
The effect of small solutes is determined solely by their chemical composition and concentration.
Polarity/hydrophobicity. The polarity/hydrophobicity of the solute will determine whether
the solute interacts more favorably with the water or with the protein. A more favorable
solute-water interaction results in the solute being excluded from the surface of the protein
(generally referred to as preferential hydration meaning the protein is preferentially hydrated by
water, which will be discussed in more detailed below). Solutes like urea interact more
favorably with the protein which tends to destabilize the protein structure. Solutes like glycerol
186
and sucrose tend to interact more favorably with the water which tends to stabilize the protein
structure.
Hydrogen bond donors and acceptors. Each solute has a set number of hydrogen bond
donors and acceptors. The number and ratio of these sites determines to a large extent how the
solute will behave in each of the concentration regimes. Glycerol, for example, has three
hydroxyl groups which can each donate and accept one hydrogen bond. At low concentrations,
each hydroxyl group will hydrogen bond to two water molecules and the rest of the glycerol
molecule will be solvated by a cage of water molecules. All the water molecules involved in
solvating the glycerol are removed from the bulk solvent. As the concentration increases, the
bulk will be depleted as the glycerol molecules are solvated. At low concentrations of bulk
water, the water molecules from the solvation cages will be ―borrowed‖ to coordinate the
hydroxyl groups and will be replaced by other glycerol molecules. Thus solutes with more
hydrogen bonding sites deplete the bulk water faster.
Concentration. The effect of each solute depends on the concentration of the solute, which
can be divided into three regimes based on the solvation of the solutes as illustrated in Figure
5-2. At low concentrations (dilute regime, Figure 5-2A), the solute will effectively only interact
with bulk water. The net amount of bulk water will decrease as some of the water molecules will
be required to solvate the solute. Polymers in the dilute regime occupy a space determined by
their radius of gyration (Rg). As the concentration increases (semi-dilute regime, Figure 5-2B),
the amount of bulk water decreases and the solute becomes more likely to interact with other
solutes. Polymer molecules will begin to intertwine with other polymer molecules as the
solution becomes more crowded and as the available bulk water for solvation decrease. The
187
concentration at which the polymers changes from predominantly interacting with only itself to
intertwining with other polymer
Figure 5-2. Illustration concentration regimes for polymers. Molecules and can be a
protein-ligand pair or two proteins that bind. A) Dilute regime where polymers
interact predominantly with themselves. The dotted line around the polymers
indicates the radius of gyration (Rg). B) Crossover concentration, defined as the
concentration where the polymers switch from interacting with themselves to
interacting with other polymer molecules. C) Semi-dilute regime where the polymers
interact with other polymer molecules and begin to intertwine. D) Concentrated
regime where polymer molecules are tightly intertwined. Figure modified from
Kozer et al.159
molecules is called the crossover concentration (Figure 5-2C) and depends primarily on the Rg
of the polymer. At high concentrations (concentrated regime, Figure 5-2D), there is insufficient
bulk water to solvate all of the solutes so the solutes must interact with one another. Polymers
will be highly intertwined.
It is intuitively obvious that the effect of solutes on the solution and the protein in each of
these concentration regimes will differ. In the dilute regime, diffusion-limited processes like
protein-protein and protein-ligand interactions will be hindered because of the decrease in
translation diffusion. Changes in the protein conformation may be affected as a result of
188
preferential hydration. At the crossover concentration and in the semi-dilute regime, protein
interactions will tend to be increased as the solutes form effective cages around the protein. The
cage tends to increase the lifetime of the collision complex which increases the amount of time
available for the protein and its binding partner to find the correct binding geometry. In the
concentrated regime, protein interactions will tend to be decreased as the tightly intertwined
polymer network can occupy the space between the protein and its binding partner.
Density (polymer structure). Polymers can by synthesized with a variety of structures
ranging from linear to dendritic. With regards to the polymer‘s effect on the protein, it is the
density of each structure that matters. Several polymer structures are illustrated in Figure 5-3.
The linear polymers are the least dense and will be more likely to intertwine at lower
concentrations. The dendritic polymers are the most dense and, depending on the number of
generations present (number of layers extending from the central monomer), may be unable to
intertwine because the density at the edge of the protein is already maximized. Other structures,
such as block or brush polymers, can have a range of densities that can be as low as the linear
polymers. The density of the polymer determines the concentration at which the polymers begin
to interact with polymer molecules (crossover concentration). Polymers which lower crossover
concentrations will tend to be more excluded strongly and excluded at lower concentrations.
Figure 5-3. Illustration of several common polymers structures. A) Dendritic polymer with three
generations. B) Brush polymer. C) Linear polymer in the random coil conformation.
D) Branched polymer.
A B C D
189
Solute exclusion
There are several factors that can contribute to a solute being excluded from the surface of a
protein, including preferential hydration, steric exclusion, and surface tension. The exclusion of
the solute from the surface requires energy which is proportional to the surface area.
Consequently, the energy is minimized when the surface area is minimized, which means that
solute exclusion favors the most compact form of the protein. Any conformational change in the
protein that exposes more surface area will be hindered whereas any conformational change that
reduces the surface area will be favored.
Preferential hydration means that the protein is predominantly solvated by water molecules
with a corresponding exclusion of solute molecules. In a protein-solute solution, there is a
balance among the water-water interactions and the protein-water, solute-water, and protein-
solute interactions. If the protein-water or solute-water interactions are more favorable than the
protein-solute interactions, then the solute will be excluded from the surface of the protein.
Steric exclusion results from the solute being excluded from the protein surface because the
solute is significantly larger than the water and is sterically hindered from approaching the
protein. When steric hindrance is a factor, the protein conformation with the smallest amount of
excluded volume is stabilized.
Surface tension was believed to be an important factor in the stabilizing effect that many
solutes have on protein structure. The water molecules at the air-water interface are unable to
maintain the favorable tetrahedral hydrogen bonding network of bulk water and thus experience
a higher degree of order. This increase in the ordering of the water leads to the exclusion of ions
and solutes from the surface similar to the solute exclusion from the surface of proteins.
According to this theory, any solute that increases the surface tension of water should have a
190
stabilizing effect on the protein and any solute that decreases the surface tension of water should
have a destabilizing effect on the protein structure. It has been shown that sucrose increases the
surface tension and has a stabilizing effect. However, glycerol reduces the surface tension but
also has a stabilizing effect on protein structure. Thus surface tension may play a role in the
effect of solutes on the protein, but is not a reliable predictor of the effect.
Macromolecular crowding and confinement
Macromolecular crowding is a term used to describe the intracellular environment and refers
to the high concentration of macromolecules present. The effects of macromolecular crowding
on proteins are generally mediated by reduced volume effects. Essentially the crowders occupy
a fraction of the solution volume and therefore increase the effective concentrations of other
species in the solution.
Osmotic pressure and water activity
A decrease in the chemical potential of water also results in a decrease in the water activity
and an increase in the osmotic pressure as demonstrated in Equation 5-2,160
where pW and pW
are the vapor pressure of water in the solution and in the pure state
VmRTppRTaRT s
sWWWW
s
WW
ln
ln
*ln )5.55/()/ln(ln (5-2)
respectively, msln is the solute concentration in molal units, sln
is the osmotic coefficient of the
solution, is the partial molar volume of water, and is the osmotic pressure. Thus osmotic
pressure can be used to measure the activity of water. The activity of water is essentially a
measure of the effective concentration of water, or in other words, the amount of bulk water.
The availability of bulk water in a protein-solute solution will affect the balance between the
protein-water and solute interactions can lead to preferential hydration.
191
Viscosity
The viscosity of a solution is defined as the resistance of a fluid to deformation under stress.
Solutions with low viscosity, like water, deform easily whereas solutions with high viscosity,
like molasses, do not deform easily. Because the viscosity of water is so low, the addition of any
solute tends to increase the viscosity of the solution. The magnitude of the increase is dependent
upon the size and shape of the solute added. Large polymers increase the viscosity more than
smaller polymers or monomers—such as glycerol. However, the shape of the polymer is also
important to consider because a linear polymer will increase the viscosity to a greater extent than
a branched polymer of equal mass. This trend results from the effective density of the solute in
solution, the branched polymers are more dense than a linear polymer and thus do not contribute
as effectively to resisting shear forces. The change in viscosity upon solute addition is also
concentration dependant. The higher the concentration of solute, the greater the solution
viscosity will be.
Assuming the solute is inert, meaning it has no significant interactions with the protein, the
primary effect of solution viscosity on the protein is to slow down the rate of diffusion. Proteins
are considered to have two kinds of diffusion, translational diffusion and rotational diffusion.
The translational diffusion rate of molecules is described by the translational diffusion
coefficient (Dt) in Equation 5-3 and can be predicted from the Stokes-Einstein (SE) relation,
where k is the Boltzman constant, T is the temperature, is the viscosity of the solution, and R is
the radius of the particle (assumed to be spherical). The rotational diffusion coefficient (Dr) in
Equation 5-4 is also predicted from the SE relation. It has been demonstrated that Dt for
R
kTDt
6 (5-3)
192
38 R
kTDr
(5-4)
poly(ethylene glycol) (PEG) polymers of various sizes as well as monomers such as glycerol and
sucrose follow this SE relation. However, Dr only follows the SE relation for very small
polymers and monomers,161
and deviates from the SE relation for larger polymers. This
deviation is typically attributed to different microscopic environments created by large and small
solutes in solution as illustrated in Figure 5-4. Small solutes like glycerol are much closer to size
to that of the solvent when compared to the size of the protein as illustrated in Figure 5-4A.
However, polymers can range from 200 Da to 100‘s KDa which places them on the same scale
as the protein (Figure 5-4B). The large polymers reduce translational diffusion but because the
protein occupies a small pocket that is free of solute, the rotational diffusion is only slightly
damped. The viscosity of the solution in these pockets differs from the viscosity measured for
the bulk solution and is referred to as the microviscosity. The viscosity of the bulk solution is
referred to as both the bulk viscosity and macroviscosity. Because the term bulk viscosity has
other connotations as well, the term macroviscosity will be used in this work.
Figure 5-4. Illustration of potential size variations between solutes and proteins which lead to
changes in the translation and rotational diffusion of proteins.
BA
193
Solute Effects on CW-EPR and Pulsed EPR Data for HIV-1 Protease
CW-EPR line shapes
As discussed in Chapter 2, the CW-EPR line shapes are sensitive to the motion of the spin-
label, which is the combination of the protein tumbling in solution, the motion of the protein
backbone at the labeling site, and the motion of the label about the flexible linker. Each of these
motions will be impacted differently by the various solute effects. The protein tumbling in
solution will be most sensitive to the microviscosity. The backbone motion, which combines
both the conformational changes of the protein and the small oscillations of the backbone
between energetically accessible bond angles, will be most sensitive to the changes in the
preferential hydration and solute exclusion. In the case of HIV-1 protease (HIV-1 PR), it is
difficult to separate the contributions from conformational changes in the flaps and the small
oscillations of the backbone for labeling sites on the flaps because both motions change upon
binding inhibitors.73
The motion of the spin-label about the flexible linker will also be sensitive
to changes in preferential hydration and solute exclusion.
As the motion of the spin-label decreases, the features in the line shape will broaden. The
increase in spectral breadth can be qualitatively compared by visual inspection of the high field
transition because it is the most sensitive to motion. The spectral breadth can be quantitatively
compared by measuring the change in the intensity of the central transition ( Hpp) or the ratio of
the intensities of the low field and center field transitions (ILF/ICF) or by calculating the second
moment ( H2
) or scaled mobility (MS) as discussed in Chapter 2.
Pulsed EPR distance measurements
The distance profiles for HIV-1 PR from DEER experiments are sensitive to the flexibility of
the spin-label about the flexible linker and to changes in the flaps conformations as demonstrated
in Chapter 3. The breadth of the distance distribution in an inhibitor-bound sample represents
194
the distribution of the spin-label around the flexible linker because the flaps have been shown to
be essentially rigid when bound to an inhibitor. If the motion of the spin-label about the linker is
decreased in the presence of solute, this change will most likely be manifested as a change in the
breadth of the distribution. If a higher energy conformation of a protein is more compact than
the lowest energy conformation, then the presence of the excluded solutes will favor the higher
energy conformation. This shift in the conformational ensemble will be manifested as a shift in
the distance profile.
For the apo form of HIV-1 PR, the semi-open conformation has both the smallest volume and
the least surface area. In the presence of solutes which are excluded from the surface, the
conformational ensemble will be shifted in favor of the semi-open conformation. However, the
closed conformation of the inhibitor-bound HIV-1 PR has the smallest volume and least surface
area if the volume and surface of the inhibitor are in included in the calculations. Thus, in the
presence of excluded solutes, the ensemble will be shifted in favor of the closed conformation.
Materials and Methods
Materials
(1-Oxyl-2,2,5,5-Tetramethyl-Δ3-Pyrroline-3-Methyl) Methanethiosulfonate (MTSL) was
purchased from Toronto Research Chemicals (North York, ON, Canada). 4-Maleimido-TEMPO
(MSL), 3-(2-Iodoacetamido)-PROXYL (IAP) and 4-(2-Iodoacetamido)-TEMPO (IASL) were
purchased from Acros Organics (Belgium) through Sigma Aldrich. Glycerol, sucrose, Ficoll400,
sodium acetate (NaOAc), Tris-HCl, and dimethyl sulfoxide (DMSO) were purchased from
Fisher Bioreagents. All molecular weights of poly(ethylene glycol) (PEG) polymers were
purchased from Fluka through Sigma
195
Solute Solutions
Stock solutions of the solutes were prepared by dissolving 6 g of sucrose or PEG (all
molecular weights) in acetate buffer (2 mM NaOAc pH 5.0) to a volume of 10 mL using
volumetric flasks to yield 60% weight/volume (w/v) stock solutions. The 30% w/v Ficoll400
stock solution was prepared by dissolving 3 g in acetate buffer to a volume of 10 mL using
volumetric flasks and incubating in a 42 C water bath until dissolved. The 60% w/v solution of
glycerol was prepared by adding 6 g of glycerol to acetate buffer to a final volume of 10 mL
using volumetric flasks.
Fluorophore Labeling
The Cys variants of HIV-1 PR were desalted into 10 mM Tris pH 7.0 for labeling with the
fluorophores. Dipyrromethane boron difluoride (BODIPY) was dissolved in DMSO to make a
0.5 mg/mL solution. The 5-((((2-iodoacetyl)amino)ethyl)amino)naphthalene-1-sulfonic acid
(IAEDANS) (FW 434.25 g/mol) was dissolved in DMSO to make a 0.5 mg/mL solution. The
fluorophore solutions were added to the protein sample to give an approximately 100-fold excess
of label to protein. The solutions were incubated overnight at 4 C and excess label was removed
via desalting column (Hiprep 26/10, Amersham Biosciences) equilibrated with 2 mM NaOAc
pH 5.0. The labeled protein was concentrated to ~10 M and stored at -20 C. The purity of the
labeled protein was estimated to be greater than 95% pure by SDS-PAGE.
Steady-State Fluorescence Anisotropy
Steady state fluorescence anisotropy measurements were made on a Fluoromax-3 (Horiba
Jobin Yvon, Edison, NJ) equipped with Glan-Thompson polarizers (#FL-1044) in an L-format
configuration. Excitation and emission wavelengths were set to 505 nm and 535 nm respectively
for BODIPY and 336 nm and 490 nm for IEADANS. The silt widths were set to 5 nm and the
196
integration time to 0.3 s. Measurements were made using a 4 mm x 4 mm quartz cuvettes and a
theromstated cell holder set to 20°C. Initial protein concentrations ranged from 0.15 to
0.3 mg/ml (7.5 to 12 M) as determined by absorption at 280 nm, using an extinction coefficient
of 1.15 mg cm-1
ml-1
. Stock solute solutions (made as described below) were titrated into the
protein sample using Hamilton Gastight syringes (Hamilton, Reno, NV) and mixed well by
repeatedly transferring the solution between a large Hamilton syringe and the cuvette.
Anisotropy values ( r ) were calculated from the Equation 5-5, where Ivv, Ivh, Ihv, Ihh are the
intensities of the light
vhvv
vhvv
IGI
IGIr
*2
* (5-5)
when the excitation and emission polarizers, respectively, are in the vertical position or
horizontal position as designated by the subscripts and G = Ihv / Ihh and is a correction factor that
compensates for the instrumental bias in the detection of polarized light.
Continuous Wave EPR
CW X-band EPR spectra were obtained on a modified Bruker ER200 spectrometer with an
ER023M signal channel, an ER 032M field control unit, and equipped with a loop gap resonator
(Medical Advances, Milwaukee, WI). All EPR spectra were collected at 24 C. The temperature
was controlled by utilizing a glass dewar (Wilmad-Labglass, Buena,NJ) to surround the loop gap
resonator and protein. Nitrogen gas was flowed through a copper coil submerged in a waterbath
(Thermo Scientific Neslab RTE-7 digital one (– 25°C to 150°C ± 0.01°C)) of 40% ethylene
glycol in water and over the sample.
15N HSQC NMR
NMR samples were prepared by dissolving various amount of PEG 8000 in a volume of
protein solution containing 125 M HIV-1 PR solution in 2 mM NaOAc buffer pH 5.0. The
197
final PEG 8000 concentrations ranged from 0 to 300 g/L in 50 g/L increments. Sample pH was
verified after the addition of PEG using litmus paper and was corrected if necessary. The 15
N
HSQC NMR spectra were collected at 20 C on a Bruker Avance II 600 MHz NMR spectrometer
with a 14 T magnet and a 5 mm cyroprobe. Spectral widths were set to 13 ppm (1H) and 38 ppm
(15
N). The 1H chemical shifts were referenced to 4,4-dimethyl-4-silapentane-1-sulfonic acid
(DSS).
Results
Because there is a complex relationship between the various attributes of the solute and their
effects on the solution properties, it is important to characterize several aspects of the solute
solutions such as osmolality and viscosity so that connections can be made between solute
properties and corresponding effects on the protein. The solution viscosities for various
concentrations of each solute were measured using a Cannon-Fenske viscometer. The osmotic
pressure of the same solutions were measured using vapor-pressure osmometry.
Figure 5-5A plots the measured viscosity for a series of solutions containing systematically
varied amounts (percent content (w/v)) of Ficoll400, sucrose, PEG 3000, and glycerol in 2 mM
NaOAc buffer pH 5.0. The data for each solute can be fit to an exponential expression such as
Equation 5-6, where the 1/t1 values were smallest for Ficoll400 (6.8 ± 0.2), followed by
PEG3000 (13.0 ± 0.9) and glycerol (36 ± 1) with largest being sucrose (43.8 ± 0.6). Thus the
)/1exp( 1tAy (5-6)
dependence of the viscosity on the solute follows the trend sucrose < glycerol < PEG 3000<
Ficoll400. It is also noteworthy that the concentration dependence (percent content in terms of
weight/volume) of the solution viscosity for glycerol and sucrose are very similar which
corresponds with the similarity of their sizes relative to PEG 3000 and Ficoll400. The high
198
viscosity of Ficoll400 corresponds with the highly branched nature of Ficoll400‘s polymeric
structure.
Figure 5-5. Plots of (A) viscosity and (B) osmolality as a function of percent content for sucrose
(dark grey, circle), glycerol (light grey, star), PEG 3000 (triangle, grey), and
Ficoll400 (square, black). (C) Plot of osmolality versus viscosity. Figure modified
from Galiano et al.162
Viscosity measurements performed by LG and osmolality
measurements performed by GEF.
Figure 5-5B plots the measured osmolality for the same solutions in Figure 5-5A. The 30%
and 40% glycerol solutions were not measureable via vapor-pressure osmometry and are thus
extrapolated from data in the literature measured via vapor-pressure deficit.163
The osmotic
pressure follows the trend glycerol > sucrose> PEG 3000 > Ficoll400, which is different than the
trend for viscosity. It is also important to note that the measurements for Ficoll400 were on the
order of the osmolality for the NaOAc buffer. The osmolality for glycerol however, spanned two
orders of magnitude. At low concentrations (<10% w/v), glucose and sucrose have a strong
effect on the osmolality of the solution and PEG 3000 and Ficoll400 have almost no effect. At
A
B
C
0 10 20 30 40 50
100
1000
10000
1 2 3 4 5 6
100
1000
10000
1
2
3
4
5
6
0 3 6 9
6
12
18
6
12
18
24
12.61
25.22
37.83
50.44
Osm
ola
lity (
mm
ol kg
-1)
% Content (w/v)
Ficoll400
Sucrose
PEG 3000
Glycerol
Osm
ola
lity (
mm
ol kg
-1)
Viscosity (cS)
Vis
co
sity (
cS
)
Ficoll400
glycerol
PEG 3000
sucrose
Ficoll400
glycerol
PEG 3000sucrose
Ficoll400
glycerol
PEG 3000
sucrose
199
intermediate concentration ranges (10% to 20% w/v), the osmolalities for glycerol and sucrose
diverge with the glycerol values being almost double the values of the sucrose. The osmolality
for PEG 3000 also begins to increase but is still roughly half of the sucrose values.
Figure 5-5C plots the measured osmolality versus the measured viscosity. There is a clear
distinction between glycerol and sucrose—small viscogens—and the polymers. The polymers
exhibit large changes in the viscosity with only small changes in the osmolality and the small
viscogens exhibit moderate changes in the viscosity with large changes in the osmolality.
Effect of solutes on spin-label correlation times
A comparison of the CW-EPR line shapes (Figures 5-6 and 5-7) for HIV-1 PR labeled with
MTSL at site K55C in the presence of several solutes at various concentrations reveals that the
motion of the spin-label (the convolution of R, I, and B) depends on the nature and
concentration of the solute. The high field transition (marked by the arrow in Figure 5-6B) is the
most sensitive to the solute and can be used as an indicator for the reduction in the spin-label
motion.
Of all the solutes tested, glycerol had the most pronounced effect in changing the line shapes,
followed by PEG, ethylene glycol (EG), sucrose, and then Ficoll400. This trend does not
correlate with the size, viscosity, or osmolality of the solute. Instead, the trend correlates with
the hydrophobic character of the solute. Of the solutes investigated, Ficoll400 has the most
hydrophilic character followed by sucrose and both these solutes have minimal effects on the line
shapes. The hydrophobicity of the PEG polymers scales with the size of the polymer, which is
consistent with the line shape changes seen in Figure 5-7. EG has more hydrophobic character
than PEG 300 but less hydrophobic character than glycerol.
200
Figure 5-6. CW-EPR line shapes for MTSL-labeled HIV-1 PR in the presence of various solutes
with incremented concentrations in 2 mM NaOAc buffer pH 5.0. Spectra were
collected at 24 C. Data collected by LG.162
Figure 5-7. CW-EPR line shapes (100 G scans) for MTSL-labeled HIV-1 PR in the presence of
various sizes of PEG and EG with incremented concentrations in 2 mM NaOAc
buffer pH 5.0. Spectra were collected at 24 C.
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
DC
A B
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
CA
D
B
0%3%
6%9%12%
0%10%20%30%40%
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLGly10
MTSLOSmo_MTSLGly20
MTSLOSmo_MTSLGly30
MTSLOSmo_MTSLGly40
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLFic3
MTSLOSmo_MTSLFic6
MTSLOSmo_MTSLFic9
MTSLOSmo_MTSLFic12
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLP3K6
MTSLOSmo_MTSLP3K12
MTSLOSmo_MTSLP3K18
MTSLOSmo_MTSLP3K24
MTSLOSmo_MTSLBUF
MTSLOSmo_MTSLSuc6
MTSLOSmo_MTSLSuc12
MTSLOSmo_MTSLSuc18
###
0%
6%
12%
18%
0%6%12%18%24%
G
A
E
B
Ficoll400
Sucrose
PEG 3000
Glycerol Ethylene Glycol
0%6%12%18%24%
PEG 8000
0%6%
12%18%24%
PEG 300
0%6%12%18%
24%
D F
C
C
201
The CW-EPR line shapes are sensitive to changes in I, R, or B but EPR line shape analysis
alone cannot distinguish which correlation times have changed. However, it is well known the
motion of the flaps ( B) decreases significantly upon binding an inhibitor. Thus, comparing the
line shapes of HIV-1 PR in the absence and presence of an inhibitor will determine if the line
shape is reporting on changes in B. Shown in Figure 5-8 are the line shapes for apo and RTV-
bound HIV-1 PR labeled with four common spin-labels. It can be seen that the line shapes do
not change in the presence of inhibitor regardless of the spin-label used. This result indicates
that the spin-labels at site K55C are not sensitive to changes in B.
Figure 5-8. CW-EPR line shapes (100 G scans) for spin-labeled HIV-1 PR in the presence (blue)
and absence (red) of a tight-binding inhibitor, ritonavir (RTV) (2 mM NaOAc buffer,
pH 5.0). Spectra were collected at 24 C. Data collected by LG.162
In general, proteins larger than 18 kDa tumble sufficiently slow in solution that the X-band
EPR line shapes for nitroxide radicals are not sensitive to any decrease in R. The HIV-1 PR
dimer is roughly 22 kDa which should be sufficiently large that the line shapes will not report on
IASLMSL
IAPMTSL
A C
B D
202
R. This assumption can be tested by comparing the trends in the line shapes to the trends in the
fluorescence anisotropy measurements of HIV-1 PR in the presence of the same solutes. The
steady-state fluorescence anisotropy measurements are sensitive to changes in the fluorophore‘s
orientation that occur within the fluorescent lifetime of the probe fluorophore (~5 ns for
BODIPY). Thus, the anisotropy is sensitive to changes in all three correlation times but is
dominated by changes in R because the protein tumbling will result in much larger changes in
the orientation of the fluorophore.
Figure 5-9 plots the change in anisotropy of BODIPY-labeled HIV-1 PR as function of the
solution viscosity. HIV-1 PR was labeled at two sites, K55C and T74C—a relatively rigid site
on a -strand near the core of the protease—so that a comparison can be made between the more
Figure 5-9. Fluorescence anisotropy measurements for BODIPY-labeled HIV-1 PR at sites (A)
T74C and (B) K55C. The error bars for these data are smaller than the symbols and
are not shown.
mobile K55C site on the flaps and a rigid site. The anisotropy for both sites increased the most
for sucrose and glycerol, which is indicative of the largest decrease in motion. Both Ficoll400
and PEG 3000 resulted in a smaller increase in the anisotropy. This trend is not the same as the
trend observed for the CW-EPR line shapes where glycerol and PEG 3000 induced the largest
1 2 3 4 5 6 7
0.12
0.16
0.20
0.24
0.28
1 2 3 4 5 6 7
0.08
0.12
0.16
0.20
Ficoll
Sucrose
PEG3000
Glycerol
An
iso
tro
py
Viscosity (cS)
An
iso
tro
py
Viscosity (cS)
A B
203
change in the line shape broadening. From these results, we can conclude that the change seen in
the X-band EPR line shapes do not result solely from changes in R.
Figure 5-10 plots the same anisotropy data as shown in Figure 5-7 but now grouped
according to the solute instead of labeling site. A clear a difference can be seen between the
T74C site and the K55C site in the presence of glycerol (A) and PEG 3000 (C) that is absent in
sucrose (B) and Ficoll400 (D). In the presence of high glycerol and PEG 3000 concentrations,
K55C experiences a larger decrease in motion than T74C. This difference could potentially
result from changes in the fluorophore motion
Figure 5-10. Plots of the percent change in the fluorescence anisotropy BODIPY-labeled HIV-1
PR variants T74C and K55C in presence of four solutes, (A) glycerol, (B) sucrose,
(C) PEG 3000, and (D) Ficoll400.
A B
C D
1 2 3
0
60
120
1 2 3 4 5
0
50
100
150
0 5 10 15 20
0
50
100
150
200
0 5 10
0
25
50
75
100
Sucrose%
Ch
an
ge
in
An
iso
tro
py
Viscosity (cS)
Glycerol
% C
ha
ng
e in
An
iso
tro
py
Viscosity (cS)
PEG 3000
% C
ha
ng
e in
An
iso
tro
py
Viscosity (cS)
Ficoll400
% C
ha
ng
e in
An
iso
tro
py
Viscosity (cS)
K55C
K55C
K55C
K55C
T74C
T74C
T74C T74C
204
about its flexible linker. The fluorophore is large and hydrophobic and has a longer linker region
than the spin-labels used in this work. Additionally, the fluorphore is more exposed to the
solvent at the K55C site. Thus the fluorphore should have a large degree of motion about the
flexible linker at the K55C site. In the presence of excluded solutes, the preferential hydration
could decrease these motions by constraining the fluorophore to lie against the protein.
However, the difference in anisotropy between K55C and T74C can potentially result from
preferential hydration induced changes in the flap motion. Measuring the anisotropy of the
K55C for inhibitor-bound HIV-1 PR would easily distinguish between these scenarios as the
flaps in the inhibitor-bound HVI-1 PR are essentially immobile. Therefore, any change in the
anisotropy would result from changes in the fluorophore motion about the linker.
Protein-solute interactions
In several reports, PEG polymers were found to bind to hydrophobic regions of the protein
surface.164; 165; 166; 167
In these studies, a variety of solution NMR techniques were utilized to
detect the residue-specific changes induced by the presence of PEG. A straightforward method
to monitor residue level interactions is by 1H-
15N HSQC NMR. When applied to
15N-labeled
cytochrome-C as a function of PEG concentration, it was determined that PEG molecules
specifically interact with a hydrophobic patch on the surface that constitutes the ligand-binding
domain.164
The surface of HIV-1 PR contains several hydrophobic patches including the flap tips as
illustrated in Figure 5-11. In order to characterize sites of specific interactions between the
polymers and the surface of HIV-1 PR, I preformed an analogous experiment on 15
N-labeled
HIV-1 PR.
Figure 5-12 shows the HSQC spectrum for 15
N-labeled HIV-1 PR (containing the D25N
mutation to prevent autoproteolysis) with the resonance assignments labeled. This spectrum is
205
Figure 5-11. Hydrophobic surfaces of HIV-1 PR in the (A) closed (PDB ID 2pbx), (B) semi-
open (PDB ID 3hvp), and (C) wide-open (structure from Hornak et al.50
)
conformations. The colors range from blue to orange with the darker blue being the
most polar and the darker orange being the most hydrophobic. Surfaces generated
using Chimera.154
very similar to the published HSQC spectrum for active 15
N-labeled HIV-1 PR containing the
same three stabilizing mutations utilized in our HIV-1 PR constructs (Q7K, L33I, and L63I).
Our spectrum contains 93 resonances which correspond to the 93 non-proline residues in HIV-1
PR. The additional peaks correspond to nitrogen containing side-chains.
Based on the results of our CW-EPR and fluorescence anisotropy experiments and the
hydrophilic nature of Ficoll400, it is reasonable to predict that the presence of Ficoll400 will not
interact with the surface of HIV-1 PR. Figure 5-13A shows an overlay of the HSQC spectra for
15N-labeled HIV-1 PR in the absence and presence of 150 g/L Ficoll400. It can be seen, that in
the presence of the Ficoll400, some of the resonances are broadened and thus less intense.
However, none of the resonances are shifted significantly. The overlay of the HSQC spectra for
each of the six Ficoll400 concentrations (0-300 g/L) is shown in Figure 4-13B, with the 1H-axis
shifted by 0.05 ppm and the 15
N-axis shifted by 0.25 ppm per spectrum to highlight the
concentration dependence of the broadening. Although the concentration dependence varies
slightly among the resonances, the broadening effects in the presence of Ficoll400 can be
attributed to an increase in the rotational correlation time, R.
A B C
206
Figure 5-12. 15
N HSQC NMR spectra of HIV-1 PR with the assignments determined by
comparison to Ref.72
The HSQC spectra are shown in Figure 5-14A for 15N-labeled HIV-1 PR in the absence and
presence of 100 g/L of PEG 8000. In the presence of PEG, many of the resonances are
broadened and some of the resonances are shifted. Figure 4-14B shows an overlay of the spectra
collected as a function of PEG concentration (0-300 g/L). Each spectrum is offset by 0.05 ppm
in the 1H-axis and 0.25 ppm in the
15N-axis. The broadening of many of the resonances in the
G27
T91
G68
G17G40
G52
G94 I93T96
G48
G73 G51
T26 G49
G86
N88
R87
L5/V11
G16
Q58
I84
I3
Y59
A67
A22
A71N38/V32 L10
L38
A28
K35
Q92M36
D30K7 V82
L89W42
A95
W6
I63
L76K55K70
D25
I85
I33I64
I66
V75 I15
V77
I13
I54
I47
V56
Q61
R57
I50
L20
K20/D29E65
T12 K43
T4
S37
L90
F99
L24
L19M46
K14/E21
I62 R8F53
L97T31
H69
T80
Q18
E34
R41 T72
I50
207
presence of PEG is also attributed to an increase in R. However, the shifted resonances
correspond to sites that specifically bind to the polymer.
Spectroscopically, shifted resonances result from changes in the chemical environment of the
nuclei that alter the magnetic shielding. In a titration experiment, the gradual shifting of
resonances between the chemical shifts of the start-point and end-point of the titration indicates
that the nucleus in question in undergoing exchange on a timescale faster than the NMR
experiment. If the exchange was slower than the NMR timescale, the intensity of the resonance
would be split between the start and end points with the ratio changing as a function of
concentration. Likewise, if the exchange is on similar timescale to the NMR experiment, the
resonance will be broadened as the intensity is blurred between the start and end points.
Phenomenologically, the shifts indicate that the corresponding residues are interacting with the
PEG molecules. This interaction alters the chemical environment of these residues resulting in a
change in their chemical shifts.
I also investigated the residue-specific effects of sucrose on 15
N-labeled HIV-1 PR. Figure
4-15A shows the HSQC for 15
N-labeled HIV-1 PR in the absence and presence of 250 g/L
sucrose. Similar to the PEG 8000, the presence of the sucrose broadened many resonances and
shifted many others. Likewise, the broadening of the resonances in the presence of sucrose can
be attributed to an increase in R. Interestingly, many of the resonances that shifted in the
presence of PEG also shifted in the presence of sucrose but in the opposite direction. This result
is likely due to the different chemical natures of PEG and sucrose. Although some of the
resonances shifted in the presence of both PEG and sucrose, many resonances shifted in only one
solute or the other. This result shows that the residue-specific interactions of PEG and HIV-1 PR
are not the same as the interaction between sucrose and HIV-1 PR.
208
Figure 5-13. A)15
N HSQC NMR spectra of HIV-1 PR in the absence (red) and presence (blue) of 150 g/L of Ficoll400. B)15
N HSQC
NMR spectra of HIV-1 PR titrated with Ficoll400. 0 g/L (black), 50 g/L (red), 100 g/L (blue), 150 g/L (green), 200 g/L
(magenta), 250 g/L (purple), 300 g/L (cyan). 15
N axis offset by 0.25 ppm and 1H axis offset by 0.05 ppm per spectra.
A B
209
Figure 5-14. A)15
N HSQC NMR spectra of HIV-1 PR in the absence (red) and presence (blue) of 100 g/L of PEG 8000. B) 15
N
HSQC NMR spectra of HIV-1 PR titrated with PEG 8000. 0 g/L (black), 50 g/L (red), 100 g/L (blue), 150 g/L (green),
200 g/L (magenta), 250 g/L (purple), 300 g/L (cyan). 15
N axis offset by 0.25 ppm and 1H axis offset by 0.05 ppm per
spectra.
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
v
A B
210
Figure 5-15. A)15
N HSQC NMR spectra of HIV-1 PR in the absence (red) and presence (blue) of 250 g/L of sucrose. B)15
N HSQC
NMR spectra of HIV-1 PR titrated with sucrose. 0 g/L (black), 50 g/L (red), 100 g/L (blue), 150 g/L (green), 200 g/L
(magenta), 250 g/L (purple). 15
N axis offset by 0.25 ppm and 1H axis offset by 0.05 ppm per spectra.
A B
211
The changes in the resonances can mapped onto the surface of the HIV-1 PR as illustrated in
Figure 5-16. A comparison of these surfaces to the hydrophobic surface area of the HIV-1 PR
reveals that the resonances that shifted in the presence of PEG 8000 correspond to the
hydrophobic patches on the protease surface. The resonances that shifted in the presence of
sucrose have some degree of correlation with the hydrophobic patches, but this correlation is not
as clear as with PEG 8000. These results show that although PEG 8000 does not bind to a
specific site on the protease, as was the case with cyt-c164
, PEG 8000 does interact more
significantly with HIV-1 PR than do either sucrose or Ficoll400.
Figure 5-16. Comparison of the A) hydrophobic surface of HIV-1 PR to resonances changes in
HIV-1 PR (mapped on to PDB ID 2pbx) in the presence of B) PEG 8000, C) sucrose,
and D) Ficoll400. A) The most hydrophobic regions shown in dark orange and the
most hydrophilic regions shown in dark blue. B-D) Shifted resonances indicated in
red and broaden resonance in blue with unaffected resonances in white.
A B
C D
212
Discussion
The goal of this work was to characterize the effects of solutes on two important aspects of
our DEER experiments: the spin-label mobility and flap conformations. We tested the effects of
glycerol, sucrose, PEG, and Ficoll400 using CW-EPR, steady-state fluorescence anisotropy, and
1H-
15N HSQC NMR spectroscopy.
Our results show that the X-band EPR line shapes are dominated by change in I.
Furthermore, our results show that I is sensitive to the presence of excluded solutes. Thus, we
have shown that the spin-label mobility is sensitive to the effects of preferential hydration. In the
presence of solutes that are preferentially excluded from the protein, the mobility of the spin-
label is decreased because the label is forced to lie against the protein surface. The magnitude of
this reduction in mobility depends on the concentration of the solute and the extent to which the
solute is excluded from the protein surface. Solutes like glycerol and PEG, which are more
strongly excluded than sucrose and Ficoll400, result in larger reductions of the spin-label
mobility. We have also shown that the effects of the solutes are the result of preferential
hydration and not the result of osmotic pressure effects which have been seen in other
proteins.168
However, a decrease in the spin-label mobility may not have a corresponding impact on the
DEER distance distributions. If the local environment of the spin-label is such that the label is
randomly oriented along the protein surface when preferentially hydrated then the distance
profiles should not be noticeably different than in the presence of non-excluded solutes.
Conversely, if the local environment is such that the label has a preferred conformation, then it is
possible that the DEER distance profiles will be narrower in presence of excluded volumes.
Position K55C, the labeling site used in our DEER experiments is solvent exposed and has
213
minimal steric hindrance resulting from neighboring side-chains. Thus, it is likely that
spin-labels at this site will be randomly oriented when preferentially hydrated and should not
result in differences in the DEER distance distributions in presence of excluded or non-excluded
solutes.
Our fluorescence anisotropy results show that R is affected by all the solutes tested to
varying degrees. However, we also demonstrated that changes in R are not reported in the
X-band CW-EPR line shape. Likewise, changes in R will not affect the DEER distance
distributions because the samples are frozen and thus the proteins do not tumble during the
DEER experiments.
Furthermore, our fluorescence anisotropy results indicate that B could be affected by the
presence of excluded solutes such as glycerol and PEG. Additionally, the NMR results
demonstrate that PEG interacts specifically with the residues in the flap tips. Because of the
correlation between the effects of PEG and glycerol in the CW-EPR and fluorescence
experiments, it is likely that glycerol also interacts with the flap tips. Consequently, it is possible
that the presence of excluded solutes could alter either the conformational ensemble on the flaps
or conformation of the flaps. However, further studies need to be performed in order to
determine the effect of the solutes on B and to elucidate how these changes could affect the
DEER distance profile.
Conclusion
In this work, we have shown that solutes affect both I and R, but that the spin-label only
reports on changes in I for X-Band EPR experiments. Furthermore, we demonstrated that the
solute effects seen for HIV-1 PR result from preferential hydration and not osmotic pressure.
We also demonstrated that PEG interacts specifically with hydrophobic patches on the surface of
214
HIV-1 PR which includes the flaps tips. This finding can potentially affect the flap conformation
determined from DEER distance measurements.
215
CHAPTER 6
FUTURE WORK
Improving the Data Analysis Process for DEER Experiments
This work utilized a large number of improvements in the data analysis process for DEER
data, however, there are still many improvements needed. To date, no statistical analysis has
been preformed to demonstrate the repeatability of our distance profiles. Likewise, the inherent
variation in the distance profiles for the apo protease has not been fully investigated. We have
demonstrated that a simple change such as replacing the H2O in the buffer with D2O can alter the
most probable distance by approximately 1 Å. This difference suggests that other environmental
changes can alter the distance profile as well but has not been investigated further. Similarly, the
distance profiles for HIV-1 PR in the presence of IDV or NFV, which strongly resemble the
profiles of the apo protease could also potentially be sensitive to environmental change.
Investigation of Point Mutations
The high rate of mutation in HIV has lead to a large number of studies on the variations in
the HIV DNA and protein sequences resulting in several important findings. Two of these
findings include the discovery that mutations occur sequentially in drug-therapy patients and that
some mutations tend to occur in combination with other mutations. As discussed in Chapter 2,
the mutations in HIV-1 PR can be divided in active site and non-active site mutations and that
the non-active site mutations have been hypothesized to affect the enzymatic activity by
modulating the flexibility of the flaps. Although many of these mutations have been
characterized by kinetic and x-ray crystallography studies, which provides insight into how the
mutations affect both the function and structure of the protease, the effects of the mutations on
the flap movement and flexibility remains unclear. This relationship, between the mutations and
216
the flap flexibility, can be investigated by using the inter-flap DEER distance measurements
discussed in this work.
The M36I mutation occurs in several HIV subtypes as well as the two drug-resistant variants
studied by Galiano et al.145
In x-ray structures, the native M36 residue makes several van der
Waals contacts with the neighboring residues. However, the shorter Ile residue cannot occupy
the same volume, so the protein backbone shifts downward to partially compensate.169
This has
been hypothesized to make the flaps more rigid.
The active site mutation, V82A is commonly seen in patients receiving most protease
inhibitors. However, V82A frequently occurs in combination with the I54V mutation, which in
turn frequently occurs in combination with L90M, and M46I. I54 sits in a hydrophobic pocket
lined by P79, I47, and V56. Substituting I54 for a Val residue is believed to affect the ability of
the flaps to open and close.60
These mutations can be investigated as single point mutations and
combinations of mutations to explore the singular and combined effects on the flap
conformational ensembles.
Method Validation via Model Systems
The use of distance distributions from DEER experiments to characterize the conformational
ensembles of a protein in this work is a novel application of DEER. However, these experiments
are preformed at cryogenic temperatures and the in the presence of solutes, both of which can
affect the conformational distribution. The effect of these conditions on the conformational
ensembles of proteins can be investigated by using model systems with well characterized
ensembles such as calmodulin (CaM)170
or maltose binding protein (MBP).101
CaM is well-suited for validating the population analysis method because the conformations
of CaM are well-known and easily controlled. CaM contains four Ca2+
binding EF-hand motifs,
two in the N-terminal domain and two in the C-terminal domain. These domains are connected
217
by an -helical linker region. Upon binding Ca2+
, each domain undergoes a conformational
change which exposes hydrophobic surfaces. In this state, CaM has a high affinity for its many
substrates. Upon binding a substrate, the linker helix bends and CaM wraps around the substrate
bringing the N- and C-terminal domains closer together. This conformational change can be
monitored by DEER by labeling a site in each terminus. The populations of CaM in each state
can be controlled by adjusting the Ca2+
concentrations. A variety of distances ranging from 20 to
45 Å can be studied by using different combinations of labeling sites.
MBP also contains well-studied conformations which are easily controlled. Upon binding
maltose, the C-terminal domain of MBP undergoes a rigid body rotation that moves it closer to
the N-terminal domain. In the apo state, roughly 5 % of MBP occupies a minor conformation
similar to the closed state. The conformations of MBP can be monitored by labeling a site in
each terminus and the relative population of each concentration can be controlled by varying the
concentration of maltose.
Isothermal Titration Calorimetry and Differential Scanning Calorimetry
The DEER experiments in this work have provided novel insight into the role of the flaps in
binding various inhibitors. As this work expands into other protease subtypes and variants, it
will be important to have other experimental data for comparison and for contributing to a better
understanding of the distance distributions. Isothermal titration calorimetry (ITC) is a powerful
technique for simultaneously determining the enthalpic and entropic contributions to free energy
of inhibitor binding and can be used to determine the thermodynamic parameters of the protease
constructs binding to the inhibitors. Additionally, differential scanning calormietry (DSC) can
be used to monitor the effect of binding an inhibitor on the stability of the protein.
218
NMR
Nuclear magnetic resonance is an especially powerful tool for investigating the dynamics of
proteins. The inhibitor-binding to a variety of HIV-1 PR constructs can be investigated by 1H-
15N HSQC NMR. These experiments will reveal the specific residues involved in binding the
inhibitors and can also provide information about how point mutations affect the
inhibitor-binding. Similarly, relaxation measurements can reveal information about the
inhibitor-binding affects the dynamics of various residues in the HIV-1 PR and how these
changes vary among different HIV-1 PR constructs.
219
APPENDIX A
HIV-1 PR DNA AND PROTEIN SEQUENCES
Protein Sequences
Table A-1. E. coli codon-optimized HIV-1 Protease Variant Sequence Alignment Residues 1-40.
Subtype B: PQITLWKRPL VTIKIGGQLK EALLNTGADD TVIEEMSLPG
Subtype C: PQITLWKRPL VSIKVGGQIK EALLNTGADD TVIEE I ALPG
V6: PQITLWQRPL VTIKIGGQLR EALLNTGADD TI F EE I SLPG
Table A-2. E. coli codon-optimized HIV-1 Protease Variant Sequence Alignment Residues
41-70.
Subtype B: RWKPKMIGGI GGFICVRQYD QII IEIAGHK
Subtype C: RWKPKMIGGI GGFICVRQYD QII IEIAGKK
V6: RWKPKMIGGI GGFICVRQYD QIPIEIAGHK
Table A-3. E. coli codon-optimized HIV-1 Protease Variant Sequence Alignment Residues
71-99.
Subtype B: AIGTVLVGPT PVNIIGRNL L TQI GATLNF
Subtype C: AIGTVLVGPT PVNIIGRNM L TQLGATLNF
V6: V IGTVLVGPT PANIIGRNLM TQI GATLNF
220
Inhibitor Structures
Figure A-1. Structures for the nine FDA-approved inhibitors used in this work.
NHO
OO
O
OH
NS
O
O
NH2
HH
OH
O
O
NHS
N
O
O
F
F
F
NN
NHO
NH
O
O
NH O
NH
O
O
NH
OH
NHOH
O
S
N
NHO
O
N
S
N
NH
O
NH
NH2
O
NH
O
NO
NH N
N
NH
O
OH
O
NH OH
NHO
O
O
OHN S
O
O NH2
OH
OH
O
NH N
O NHS
O
O NH
NH
OH
O
N
NH
O
A B C
D E F
IHG
Tipranavir (TPV)Darunavir (DRV)
Saquinavir (SQV)
Ritonavir (RTV)
Atazanavir (ATV)
Nelfinavir (NFV)
Indinavir (IDV)
Amprenavir (APV)Lopinavir (LPV)
221
Figure A-2. Stick- and space-filling-models for the nine FDA-approved inhibitors used in this
work.
Indinavir (IDV) Saquinavir (SQV) Ritonavir (RTV)
Nelfinavir (NFV) Amprenavir (APV) Atzanavir (ATV)
Lopinavir (LPV) Darunavir (DRV) Tipranavir (TPV)
A B C
E
H
D
G
F
I
222
APPENDIX B
SUPPLEMENTAL INFORMATION FOR DEER EXPERIMENTS AND DATA ANALYSIS
Subtype B
Figure B-1. DEER data for apo HIV-1 PR subtype B. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
Apo R (Å) FWHM (Å) %
Semi-Open 36.4 4.9 86
Closed 33.0 3.0 3
Open 41.3 3.4 7
Curled 24.7 2.3 4
A B
C D
E F
-8.5 -8.0 -7.5 -7.0 -6.5
-21
-18
-15
-12
-9
-6 -4 -2 0 2 4 6
20 30 40 50 20 30 40 50
0 1 2 3
log
(a
)
log ( )
Apo
Apo Fit
f (MHz)
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
Semi-Open
Open
Closed
Curled
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
223
Figure B-2. DEER data for CA-p2 bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
-6 -4 -2 0 2 4 6 -9.00 -8.25 -7.50 -6.75
-18
-15
-12
-9
20 30 40 5020 30 40 50
0 1 2 3
CA-p2
CA-p2 Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
CA-p2 R (Å) FWHM (Å) %
Semi-Open 36.3 3.3 16
Closed 33.0 2.7 80
Open 41.7 2.1 4
A B
C D
E F
224
Figure B-3. DEER data for IDV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
IDV R (Å) FWHM (Å) %
Semi-Open 35.9 4.8 79
Closed 32.8 2.6 14
Open 41.2 3.3 7
A B
C D
E F20 30 40 50
-6 -4 -2 0 2 4 6 -9.00 -8.25 -7.50 -6.75
-21
-18
-15
-12
-9
20 30 40 50
0 1 2 3
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
IDV
IDV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
225
Figure B-4. DEER data for NFV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
NFV R (Å) FWHM (Å) %
Semi-Open 35.9 4.9 77
Closed 32.8 2.6 14
Open 41.8 3.2 8
A B
C D
E F
-6 -4 -2 0 2 4 6
20 30 40 5020 30 40 50
-9.00 -8.25 -7.50 -6.75
-21
-18
-15
-12
-9
0 1 2 3
NFV
NFV Fit
f (MHz)
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
log
(a
)
log ( )
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
226
Figure B-5. DEER data for ATV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
ATV R (Å) FWHM (Å) %
Closed 33.3 3.2 41
Semi-Open 35.9 3.9 53
Open 41.3 2.5 6
A B
C D
E F
-6 -4 -2 0 2 4 6 -9.00 -8.25 -7.50 -6.75
-21
-18
-15
-12
-9
20 30 40 50 20 30 40 50
0 1 2 3
ATV
ATV Fit
f (MHz)
log
(a
)
log ( )
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3 ( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
227
Figure B-6. DEER data for SQV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
SQV R (Å) FWHM (Å) %
Semi-Open 37.4 2.1 7
Closed 32.9 2.8 93
A B
C D
E F
20 30 40 50
-6 -4 -2 0 2 4 6 -7.8 -7.2 -6.6 -6.0
-18
-15
-12
-9
-6
20 30 40 50
0 1 2 3
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
SQV
SQV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
228
Figure B-7. DEER data for RTV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
RTV R (Å) FWHM (Å) %
Semi-Open 37.4 2.1 10
Closed 33.0 2.6 90
A B
C D
E F20 30 40 50
-6 -4 -2 0 2 4 6 -7.5 -7.0 -6.5 -6.0
-18
-15
-12
-9
20 30 40 50
0 1 2 3
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
Bsi RTV
Bsi RTV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
229
Figure B-8. DEER data for LPV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
LPV R (Å) FWHM (Å) %
Semi-Open 36.2 3.9 11
Closed 32.9 2.9 84
Open 42.8 2.8 5
A B
C D
E F
-6 -4 -2 0 2 4 6 -8.0 -7.5 -7.0 -6.5
-18
-15
-12
-9
20 30 40 5020 30 40 50
0 1 2 3
LPV
LPV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
230
Figure B-9. DEER data for APV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
APV R (Å) FWHM(Å) %
Semi-Open 37.0 2.4 18
Closed 33.2 2.8 76
Open 41.7 2.0 6
A B
C D
E F
20 30 40 50
-6 -4 -2 0 2 4 6 -9.0 -8.4 -7.8 -7.2
-18
-15
-12
-9
20 30 40 50
0 1 2 3
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
APV
APV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
231
Figure B-10. DEER data for DRV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
DRV R (Å) FWHM (Å) %
Semi-Open 36.6 2.5 13
Closed 33.2 2.9 87
A B
C D
E F20 30 40 50
-6 -4 -2 0 2 4 6 -5.5 -5.0 -4.5 -4.0 -3.5
-21
-18
-15
-12
-9
20 30 40 50
0 1 2 3
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
DRV
DRV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
232
Figure B-11. DEER data for TPV-bound HIV-1 PR subtype B. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
TPV R (Å) FWHM (Å) %
Semi-Open 36.3 1.7 9
Closed 32.9 2.3 91
A B
C D
E F20 30 40 50
-6 -4 -2 0 2 4 6 -7.2 -6.8 -6.4 -6.0
-18
-15
-12
-9
-6
20 30 40 50
0 1 2 3
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
TPV
TPV Fit
f (MHz)
log
(a
)
log ( )
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Ech
o In
ten
sity
( s)
Raw Data
Bachground
Subtraction
233
Figure B-12. Error Analysis for populations < 15% in HIV-1PR Apo. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗*‘ are
considered ―questionable‖, meaning that their population size at the lower limit for
being validated. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue). Note, the presence of 3-4% of closed and curled conformational
populations is questionable. However, given the biological significance of the closed
conformation and computational and crystallographic evidence of the flaps curled in,
we are leaving these populations in the APO state in the analysis but do admit their
significance is questionable at this level of SNR.
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
Semi-Open
Open
Closed
Curled
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open & Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed & Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open & Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
Only Semi-Open
( s)
Ech
o In
ten
sity
Apo R (Å) FWHM (Å) % TKR % Final
Semi-Open 36.4 4.9 86 86
Closed 33.0 3.0 3 3
Open 41.3 3.4 7 7
Curled 24.7 2.3 4 4
A
B C D
E F G
H I J
* *
234
Figure B-13. Error Analysis for populations < 20% in HIV-1PR CA-p2. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). C) Individual populations for the
Gaussian reconstruction. D–F) Background subtracted dipolar echo curve (black)
overlaid with the TKR fit (red) and the modified echo curve for the distance profile
with one or more populations suppressed (blue). (Inset highlights the difference
between the modified dipolar echo curve and the background subtracted echo curve.)
Note, as can be seen here, in certain cases, more than one Gaussian curve was needed
for a given biological population state to regenerate the TKR profiles. In these cases,
the multiple Gaussians were combined together to describe the conformational state.
This seems reasonable as there is no reason why a given conformational state must
have a distance profile that is Gaussian in shape.
CA-p2 R (Å) FWHM (Å) % TKR % Final
Semi-Open 35.4 1.8 6 6
37.0 2.4 10 10
(total 36.3 3.3 16 16)
Closed 32.5 2.0 28 28
33.2 2.4 30 30
34.1 2.4 22 22
(total 33.0 2.7 80 80)
Open 41.7 2.1 4 4
A
B C D
E F20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-Semi-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
& Semi-Open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Closed
Semi-Open
Open
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0.5 1.0 1.5
235
Figure B-14. Error Analysis for populations < 20% in HIV-1PR IDV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue).
IDV R (Å) FWHM (Å) % TKR % Final
Semi-Open 35.9 4.8 78 79
Closed 32.8 2.6 14 14
Open 41.2 3.3 7 7
Curled 27.0 2.5 1 0
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Closed
Semi-Open
Open
0 1 2 3
DeerAnalysis
-Open & Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed & Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open & Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
Only Semi-Open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
A
B C D
E F G
H I J
x
236
Figure B-15. Error Analysis for populations < 20% in HIV-1PR NFV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–H)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue).
NVF R (Å) FWHM (Å) % TKR % Final
Semi-Open 35.9 4.9 78 78
Closed 32.4 2.3 5 5
33.2 2.5 9 9
(total 32.8 2.6 14 14)
Open 41.8 3.2 8 8
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-Open
& Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
& Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
A
B C D
E F G
H
x
237
Figure B-16. Error Analysis for populations < 20% in HIV-1PR ATV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗*‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D) Background
subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and the
modified echo curve for the distance profile with open population suppressed (blue).
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
Semi-Open
Closed
Open
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
ATV R (Å) FWHM (Å) % TKR % Final
Semi-Open 35.9 3.9 49 53
Closed 32.2 2.0 5 5
33.5 2.9 33 36
(total 33.3 3.2 49 41)
Open 41.3 2.5 6 6
A
B C D
238
Figure B-17. Error Analysis for populations < 20% in HIV-1PR SQV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–F)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue).
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Curled
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
SQV R (Å) FWHM (Å) % TKR % Final
Semi-Open 37.4 2.1 7 7
Closed 32.3 1.3 13 13
33.3 2.6 78 80
(total 32.9 2.8 91 93)
Open 43.5 2.5 2 0
A
B C D
E F
x
239
Figure B-18. Error Analysis for populations < 20% in HIV-1PR RTV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–F)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue).
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-Semi-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
RTV R (Å) FWHM (Å) % TKR % Final
Semi-Open 37.4 2.1 10 10
Closed 32.2 1.6 25 25
33.4 2.2 64 65
(total 33.0 2.6 89 90)
Open 44.3 1.6 1 0
A
B C D
E F
x
240
Figure B-19. Error Analysis for populations < 20% in HIV-1PR LPV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. Population marked with ‗!‘ was added as a more biologically relevant
alternative to the split Open populations (marked with ‗*‘) generated by TKR. The
dipolar echo curve for the distance profile containing this population is consistent
with the background subtracted dipolar echo curve. C) Individual populations for the
Gaussian reconstruction. D–I) Background subtracted dipolar echo curve (black)
overlaid with the TKR fit (red) and the modified echo curve for the distance profile
with one or more populations suppressed (blue).
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
-44.9 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
- 41.1 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
+ 42.8 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
LPV R (Å) FWHM (Å) % TKR % Final
Semi-Open 35.0 1.4 3 3
36.7 2.8 8 8
(total 36.2 3.9 11 11)
Closed 31.1 2.9 7 7
33.0 2.8 77 77
(total 32.9 2.9 84 84)
Open 41.1 3.0 3 3
44.9 2.5 2 2
(total 42.8 1.5 5 5)
A
B C D
E F G
H I
x x!
241
Figure B-20. Error Analysis for populations < 20% in HIV-1PR APV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). C) Individual populations for the Gaussian
reconstruction. D–F) Background subtracted dipolar echo curve (black) overlaid with
the TKR fit (red) and the modified echo curve for the distance profile with one or
more populations suppressed (blue).
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Open
( sec)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
Open
APV R (Å) FWHM(Å) % TKR % Final
Semi-Open 37.0 2.4 18 18
Closed 30.4 1.5 2 2
33.2 2.9 74 74
(total 33.2 2.8 76 76)
Open 41.7 2.0 6 6
A
B C D
E F
242
Figure B-21. Error Analysis for populations < 20% in HIV-1PR DRV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–K)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue).
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-51.8 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open & 51.8 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled
& Open & 51.8 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
( s)E
ch
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
0 1 2 3
DeerAnalysis
-Open & Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & 51.8 Å
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
DRV R (Å) FWHM (Å) % TKR % Final
Semi-Open 36.6 2.5 12 13
Closed 33.2 2.9 81 87
Open 41.7 1.7 3.3 0
Curled 25.8 1.0 1.5 0
Unassigned 51.8 1.9 1.9 0
A
B C D
E F G
H I J
K
x x x
243
Figure B-22. Error Analysis for populations < 20% in HIV-1PR TPV. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (red) overlain with the summed
Gaussian population profile (blue dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (red) and
the modified echo curve for the distance profile with one or more populations
suppressed (blue).
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled
& Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-Open
& Curled
& Open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semio-Open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Semi-Open
Closed
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
TPV R (Å) FWHM (Å) % TKR % Final
Semi-Open 36.3 1.7 8 9
Closed 31.0 1.8 4 4
32.9 2.2 79 87
(total 32.9 2.3 83 91)
Open 43.9 1.4 2 0
Curled 22.8 1.1 2 0
24.0 1.5 3 0
26.7 1.2 2 0
A
B C D
E F G
H I J
x x x
244
Subtype C
Figure B-23. DEER data for apo HIV-1 PR subtype C (collected 5/09). A) Background
subtracted dipolar evolution curve (black) overlaid with the fit from TKR (grey) and
the theoretical curve generated from the Gaussian reconstruction (light grey). B)
Raw dipolar evolution curve and background subtraction. C) The corresponding
distance profile generated via analysis with TKR (black) and the sum of Gaussian
functions used in the reconstruction (grey, dotted). D) The individual Gaussian
functions used in the reconstruction labeled according to the corresponding
conformation of HIV-1 PR. E) Frequency domain spectrum. F) L-curve.
A B
C D
E F
-7 -6 -5 -4 -3 -2
-30
-24
-18
-12
-6
-5 0 5
0 1 2 3
20 30 40 50 20 30 40 50
log
log
MHz
Apo
Apo Fit
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
Subtype C: Apo (5/09) R (Å) FWHM (Å) %
Tucked 29.7 3.1 13
Closed 33.3 2.8 8
Semi-open 36.7 4.0 54
Wide-open 40.2 3.3 27
245
Figure B-24. DEER data for apo HIV-1 PR subtype C (collected 6/09). A) Background
subtracted dipolar evolution curve (black) overlaid with the fit from TKR (grey) and
the theoretical curve generated from the Gaussian reconstruction (light grey). B)
Raw dipolar evolution curve and background subtraction. C) The corresponding
distance profile generated via analysis with TKR (black) and the sum of Gaussian
functions used in the reconstruction (grey, dotted). D) The individual Gaussian
functions used in the reconstruction labeled according to the corresponding
conformation of HIV-1 PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: Apo (6/09) R (Å) FWHM (Å) %
Tucked 29.6 3.8 6
Closed 33.3 3.6 12
Semi-open 37.2 4.5 63
Wide-open 40.5 3.9 19
A B
C D
E F
-7 -6 -5 -4 -3 -2
-30
-25
-20
-15
-10
-5
-5 0 5
0 1 2 3
20 30 40 5020 30 40 50
log
log
MHz
Apo
Apo Fit
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
246
Figure B-25. DEER data for CA-p2-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
2 3 4 520 30 40 50
-7 -6 -5 -4 -3
-30
-25
-20
-15
-10
-5
0 1 2 3
-5 0 5
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
CA-p2
CA-p2 Fit
Subtype C: CA-p2 R (Å) FWHM (Å) %
Tucked 31.8 1.9 7
Semi-Open 38.2 3.4 13
Closed 33.7 3.3 80
A B
C D
E F
247
Figure B-26. DEER data for IDV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: IDV R (Å) FWHM (Å) %
Tucked 30.5 2.6 4
Closed 33.0 3.2 6
Semi-open 37.3 5.4 81
Wide-open 41.0 3.1 9
A B
C D
E F
-5 0 5 -7 -6 -5 -4 -3 -2
-30
-25
-20
-15
-10
0 1 2 3
20 30 40 50 20 30 40 50
IDV
IDV Fit
MHz
log
log
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
248
Figure B-27. DEER data for NFV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: NFV R (Å) FWHM (Å) %
Closed 32.7 3.9 12
Semi-open 36.5 4.7 78
Wide-open 39.7 2.9 10
A B
C D
E F
0 1 2 3
-5 -4 -3 -2
-30
-24
-18
-12
-6
-5 0 5
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
log
(
)
log ( )
NFV
NFV Fit
f (MHz)
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
249
Figure B-28. DEER data for ATV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: ATV R (Å) FWHM (Å) %
Closed 33.0 3.7 17
Semi-open 36.0 5.2 68
Wide-open 39.7 4.3 15
A B
C D
E F
-5 0 5 -6 -5 -4 -3 -2
-30
-24
-18
-12
-6
0 1 2 3
2 3 4 520 30 40 50
ATV
ATV Fit
MHz
log
log
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
250
Figure B-29. DEER data for APV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: APV R (Å) FWHM (Å) %
Closed 33.3 3.2 56
Semi-open 36.6 5.1 44
A B
C D
E F
-5 0 5 -5 -4 -3 -2
-30
-24
-18
-12
-6
0 1 2 3
20 30 40 50 2 3 4 5
APV
APV Fit
MHz
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
251
Figure B-30. DEER data for LPV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: LPV R (Å) FWHM (Å) %
Closed 33.1 3.3 76
Semi-open 37.3 4.4 24
A B
C D
E F2 3 4 520 30 40 50
-5 0 5 -7 -6 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
MHz
LPV
LPV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
252
Figure B-31. DEER data for RTV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
Subtype C: RTV R (Å) FWHM (Å) %
Tucked 31.7 1.7 8
Closed 33.8 3.4 77
Semi-open 38.0 3.4 15
A B
C D
E F
20 30 40 50
0 -7 -6 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
20 30 40 50
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
MHz
RTV
RTV Fit
log
log
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
253
Figure B-32. DEER data for SQV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
20 30 40 50 20 30 40 50
-5 0 5 -7 -6 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 30 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
MHz
SQV
SQV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
Subtype C: SQV R (Å) FWHM (Å) %
Tucked 31.8 1.9 7
Semi-Open 38.2 3.4 13
Closed 33.7 3.3 80
A B
C D
E F
254
Figure B-33. DEER data for DRV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
20 30 40 50 20 30 40 50
-5 0 5 -7 -6 -5 -4
-30
-25
-20
-15
-10
0 1 2 30 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
MHz
DRV
DRV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
Subtype C: DRV R (Å) FWHM (Å) %
Closed 33.3 2.8 84
Semi-Open 37.0 2.2 12
Wide-open 41.3 1.6 4
A B
C D
E F
255
Figure B-34. DEER data for TPV-bound HIV-1 PR subtype C. A) Background subtracted
dipolar evolution curve (black) overlaid with the fit from TKR (grey) and the
theoretical curve generated from the Gaussian reconstruction (light grey). B) Raw
dipolar evolution curve and background subtraction. C) The corresponding distance
profile generated via analysis with TKR (black) and the sum of Gaussian functions
used in the reconstruction (grey, dotted). D) The individual Gaussian functions used
in the reconstruction labeled according to the corresponding conformation of HIV-1
PR. E) Frequency domain spectrum. F) L-curve.
2 3 4 520 30 40 50
-5 0 5 -8 -7 -6 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 30 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
MHz
TPV
TPV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
Subtype C: TPV R (Å) FWHM (Å) %
Semi-Open 36.3 1.2 3
Closed 32.8 2.8 97
A B
C D
E F
256
Figure B-35. Error Analysis for populations < 20% in apo subtype C HIV-1PR (collected 5/09).
A) Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F G
D
E
A Subtype C:Apo (5/09) R (Å) FWHM (Å) % TKR % Final
Tucked 29.7 3.1 13 13
Closed 33.3 2.8 8 8
Semi-open 36.7 4.0 54 54
Wide-open 40.2 3.3 27 27
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Closed
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
257
Figure B-36. Error Analysis for populations < 20% in apo subtype C HIV-1PR (collected 6/09).
A) Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F G
D
E
A Subtype C:Apo (5/09) R (Å) FWHM (Å) % TKR % Final
Tucked 29.7 3.1 13 13
Closed 33.3 2.8 8 8
Semi-open 36.7 4.0 54 54
Wide-open 40.2 3.3 27 27
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Closed
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
258
Figure B-37. Error Analysis for populations < 20% in CA-p2 bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
J
N
HG
K
O P
L
D E
I
M
Q
A Subtype C: CA-p2 R (Å) FWHM (Å) % TKR % Final
Curled 24.5 1.3 2 0
Tucked 31.8 1.9 13 13
Closed 33.7 3.3 77 80
Semi-open 38.1 3.4 7 7
Wide-open 42.9 1.8 2 0
2 3 4 520 30 40 50
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
Gauss. Recon.
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o Inte
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ty
0 1 2 3
DeerAnalysis
-Curled &
Wide-open
( s)
Ech
o Inte
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0 1 2 3
DeerAnalysis
-Curled &
Semi-open
& Wide-open
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o Inte
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ty
0 1 2 3
DeerAnalysis
-Semi-open
( s)
Ech
o Inte
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ty
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnlysis
-Semi-open &
Wide-open
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Tucked &
Wide-open
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Curled & Tucked
& Wide-open
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Curled & Tucked
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Curled &
Semi-open
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Tucked &
Semi-open
( s)
Ech
o Inte
nsi
ty
0 1 2 3
DeerAnalysis
-Tucked &
Semi-open
& Wide-open
( s)
Ech
o Inte
nsi
ty
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Recon.
259
Figure B-38. Error Analysis for populations < 20% in IDV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
J
N
HG
K
O P
L
D E
I
M
Q
A Subtype C: IDV R (Å) FWHM (Å) % TKR % Final
Tucked 30.5 2.6 4 4
Closed 33.0 3.2 6 6
Semi-open 37.3 5.4 80 81
Wide-open 41.0 3.1 9 9
Unassigned 52.0 2.4 1 0
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
-30 Ang Closed
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-33 Ang Closed
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-52 & 30
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-52 & 33
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-52 & open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-30 & 33
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-33 & open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-52 & 30 &33
( s)
Ech
o I
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0 1 2 3
DeerAnalysis
-52 & 30 & open
( s)
Ech
o I
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0 1 2 3
DeerAnalysis
-52 & 33 & open
( s)
Ech
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0 1 2 3
DeerAnalysis
-30 & 33 & open
( s)
Ech
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0 1 2 3
DeerAnalysis
-30 & open
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
only Semi-open
( s)
Ech
o I
nte
nsity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
0 1 2 3
DeerAnalysis
-52 Ang
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis Fit
DeerSim
( s)
Ech
o I
nte
nsity
P(r
)
Distance (Å)
R S
260
Figure B-39. Error Analysis for populations < 20% in NFV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
E F
D
A Subtype C: NFV R (Å) FWHM (Å) % TKR % Final
Closed 32.7 3.9 12 12
Semi-open 36.5 4.7 78 78
Wide-open 39.6 2.9 10 10
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Open
( s)
Ech
o In
ten
sity
0.5 1.0 1.5
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0.5 1.0 1.5
261
Figure B-39. Error Analysis for populations < 20% in ATV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
D
E
A Subtype C: ATV R (Å) FWHM (Å) % TKR % Final
Closed 33.0 3.7 17 17
Semi-open 36.0 5.2 68 68
Wide-open 39.6 4.3 15 15
2 3 4 520 30 40 50
0 1 2 3
DeerAnalysis
-Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Closed
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
262
Figure B-40. Error Analysis for populations < 20% in APV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C D
E
A Subtype C: APV R (Å) FWHM (Å) % TKR % Final
Closed 33.2 3.2 54 56
Semi-open 36.6 5.1 42 44
Wide-open 41.4 2.5 4 0
20 30 40 50 2 3 4 5 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
263
Figure B-41. Error Analysis for populations < 20% in LPV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C D
E
A Subtype C: LPV R (Å) FWHM (Å) % TKR % Final
Closed 33.1 3.3 75 76
Semi-open 37.3 4.4 23 24
Wide-open 43.4 1.7 2 0
2 3 4 520 30 40 50
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Csi LPV TKR
DeerSim
264
Figure B-42. Error Analysis for populations < 20% in RTV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
J
HG
K
D E
I
A Subtype C: RTV R (Å) FWHM (Å) % TKR % Final
Tucked 31.7 1.7 7 8
Closed 33.8 3.4 75 77
Semi-open 38.0 3.4 15 15
Wide-open 42.9 2.1 4 0
20 30 40 5020 30 40 50
P
(r)
Distance (Å)
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-open &
Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
Csi RTV
DeerSim
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked &
Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked &
Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked &
Semi-open &
Wide-open
( s)
Ech
o In
ten
sity
265
Figure B-43. Error Analysis for populations < 20% in SQV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
20 30 40 50 20 30 40 50
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-open &
Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
0 1 2 3
Csi SQV TKR Fit
DeerSim
( s)
Ech
o In
ten
sity
B C
F HG
D
A Subtype C: SQV R (Å) FWHM (Å) % TKR % Final
Closed 33.6 3.5 91 100
Semi-open 39.0 2.0 7 0
Wide-open 43.9 2.3 2 0
266
Figure B-44. Error Analysis for populations < 20% in DRV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi DRV TKR Fit
-23
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi DRV TKR Fit
-25
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi DRV TKR Fit
-31
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi DRV TKR Fit
-36
( s)
Ech
o I
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nsity
0 1 2 3
Csi DRV TKR Fit
-41
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi DRV TKR Fit
-20's
( s)
Ech
o I
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0 1 2 3
Csi DRV TKR Fit
-20's & 31
( s)
Ech
o I
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0 1 2 3
Csi DRV TKR Fit
-20's & 41
( s)
Ech
o I
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0 1 2 3
Csi DRV TKR Fit
-20's & 31 & 41
( s)
Ech
o I
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P(r
)
Distance (Å)
Csi DRV TKR
DeerSim
P(r
)
Distance (Å)
Fit Peak 4
Fit Peak 6
Fit Peak 7
Subtype C: DRV R (Å) FWHM (Å) % TKR % Final
Unassigned 23.8 1.5 3 0
Curled 25.7 2.2 3 0
Tucked 31.4 1.5 8 0
Closed 33.2 2.8 72 84
Semi-open 37.0 2.2 10 12
Wide-open 41.3 1.6 4 4
B C
F
J
HG
K L
D E
I
M
A
267
Figure B-45. Error Analysis for populations < 20% in TPV bound subtype C HIV-1PR. A)
Table of values summarizing the populations from TKR analysis and Gaussian
reconstruction procedure. B) Distance profile from TKR analysis (black) overlain
with the summed Gaussian population profile (grey dashed). Populations marked with
‗x‘ were discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
2 3 4 520 30 40 50
0 1 2 3
Csi TPV TKR FIT
DeerSim
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-all
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-all but 36
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-23
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-26
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-36
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-42
( s)
Ech
o I
nte
nsity
0 1 2 3
Csi TPV TKR FIT
-23 &26
( s)
Ech
o I
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0 1 2 3
Csi TPV TKR FIT
-23 &26
( s)E
ch
o I
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0 1 2 3
Csi TPV TKR FIT
-23 &42
( s)
Ech
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0 1 2 3
Csi TPV TKR FIT
-26 &36
( s)
Ech
o I
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0 1 2 3
Csi TPV TKR FIT
-26 &42
( s)
Ech
o I
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0 1 2 3
Csi TPV TKR FIT
-36 & 42
( s)
Ech
o I
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0 1 2 3
Csi TPV TKR FIT
-23 & 26 &36
( s)
Ech
o I
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0 1 2 3
Csi TPV TKR FIT
-23 & 36 &42
( s)
Ech
o I
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0 1 2 3
Csi TPV TKR FIT
-26 & 36 &42
( s)
Ech
o I
nte
nsity
P(r
)
Distance (Å)
Fit Peak 1
Fit Peak 2
Fit Peak 3
Fit Peak 4
Fit Peak 5
P(r
)
Distance (Å)
Csi TPV TKR
DeerSim
Subtype C: TPV R (Å) FWHM (Å) % TKR % Final
Unassigned 23.4 1.3 1 0
Curled 36.5 1.5 1 0
Closed 32.8 2.8 94 97
Semi-open 36.3 1.2 3 3
Wide-open 42.9 1.3 1 0
B C
F
J
N
HG
K
O P
L
D E
I
M
Q
A
R S
268
Variant V6
Figure B-46. DEER data for apo HIV-1 PR V6. A) Background subtracted dipolar evolution
curve (black) overlaid with the fit from TKR (grey) and the theoretical curve
generated from the Gaussian reconstruction (light grey). B) Raw dipolar evolution
curve and background subtraction. C) The corresponding distance profile generated
via analysis with TKR (black) and the sum of Gaussian functions used in the
reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: Apo R (Å) FWHM (Å) %
Tucked 29.7 4.0 10
Closed 33.2 3.8 21
Semi-open 36.4 4.8 61
Wide-open 39.9 3.1 8
-5 0 5 -7 -6 -5 -4
-30
-24
-18
-12
-6
0 1 2 3
20 30 40 50 20 30 40 50
MHz
Apo
Apo Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
269
Figure B-47. DEER data for CA-p2 bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: CA-p2 R (Å) FWHM (Å) %
Tucked 29.7 4.0 10
Closed 33.2 3.8 21
Semi-open 36.4 4.8 61
Wide-open 39.9 3.1 8
20 30 40 50
-5 0 5 -7.0 -6.3 -5.6 -4.9 -4.2
-30
-25
-20
-15
-10
0 1 2 3
20 30 40 50
0 1 2 3
DeerSim
DeerAnalysis
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
MHz
CA-p2
CA-p2 Fit
log
log
Ech
o In
ten
sity
( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
270
Figure B-48. DEER data for IDV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: IDV R (Å) FWHM (Å) %
Tucked 27.5 6.1 10
Closed 32.8 5.4 30
Semi-open 36.8 7.2 54
Wide-open 46.8 4.5 6
20 30 40 5020 30 40 50
0 1 2 3
-5 0 5 -7 -6 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
IDV
IDV Fit
log
log
271
Figure B-49. DEER data for NFV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
20 30 40 50 20 30 40 50
0 1 2 3
-5 0 5 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
NFV
NFV Fit
log
log
A B
C D
E F
V6: NFV R (Å) FWHM (Å) %
Tucked 27.3 6.1 14
Closed 32.9 3.8 30
Semi-open 35.4 4.3 39
Wide-open 40.8 6.7 17
272
Figure B-50. DEER data for ATV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: ATV R (Å) FWHM (Å) %
Tucked 29.6 4.0 7
Closed 32.8 3.8 30
Semi-open 36.0 5.5 63
20 30 40 50
-5 0 5 -8 -7 -6 -5 -4
-30
-24
-18
-12
-6
0 1 2 3
20 30 40 50
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
MHz
ATV
ATV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
273
Figure B-51. DEER data for APV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: APV R (Å) FWHM (Å) %
Tucked 29.8 2.8 8
Closed 33.6 3.7 72
Semi-open 37.8 3.5 16
Wide-open 45.0 2.8 4
20 30 40 50 20 30 40 50
0 1 2 3
-5 0 5 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)Distance (Å)
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
APV
APV Fit
log
log
274
Figure B-52. DEER data for LPV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: LPV R (Å) FWHM (Å) %
Tucked 30.0 3.0 17
Closed 33.4 2.2 83
2 3 4 5
-5 0 5 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
20 30 40 50
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
MHz
LPV
LPV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
275
Figure B-53. DEER data for RTV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: RTV R (Å) FWHM (Å) %
Tucked 30.9 3.9 15
Closed 33.0 3.6 26
Semi-open 35.7 4.5 51
Wide-open 39.1 3.7 8
20 30 40 50 20 30 40 50
0 1 2 3
-5 0 5 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
RTV
RTV Fit
log
log
276
Figure B-54. DEER data for SQV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: SQV R (Å) FWHM (Å) %
Closed 33.3 3.7 87
Semi-open 38.2 1.8 13
-5 0 5 -5 -4 -3
-30
-24
-18
-12
-6
0 1 2 3
20 30 40 50 20 30 40 50
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
MHz
SQV
SQV Fit
log
log
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
277
Figure B-55. DEER data for DRV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: DRV R (Å) FWHM (Å) %
Curled 25.9 1.1 3
Tucked 28.5 1.1 3
Closed 33.2 3.2 89
Semi-open 38.5 1.5 3
Wide-open 43.7 2.4 2
20 30 40 5020 30 40 50
0 1 2 3
-5 0 5 -4.2 -3.6 -3.0
-30
-24
-18
-12
-6
0 1 2 3
DeerAnalysis
-20 Å
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
DRV
DRV Fit
log
log
278
Figure B-56. DEER data for TPV bound HIV-1 PR V6. A) Background subtracted dipolar
evolution curve (black) overlaid with the fit from TKR (grey) and the theoretical
curve generated from the Gaussian reconstruction (light grey). B) Raw dipolar
evolution curve and background subtraction. C) The corresponding distance profile
generated via analysis with TKR (black) and the sum of Gaussian functions used in
the reconstruction (grey, dotted). D) The individual Gaussian functions used in the
reconstruction labeled according to the corresponding conformation of HIV-1 PR. E)
Frequency domain spectrum. F) L-curve.
A B
C D
E F
V6: TPV R (Å) FWHM (Å) %
Curled 25.0 1.6 5
Tucked 29.2 1.0 2
Closed 33.0 3.3 92
Wide-open 40.9 1.9 2
20 30 40 5020 30 40 50
0 1 2 3
-5 0 5 -4.0 -3.5 -3.0
-30
-24
-18
-12
-6
0 1 2 3
DeerAnalysis
Gauss. Reconstr.
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
Ech
o In
ten
sity
Time ( s)
Raw Data
Background
Subtraction
MHz
TPV
TPV Fit
log
log
279
Figure B-57. Error Analysis for populations < 20% in apo HIV-1PR V6. A) Table of values
summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F G
D
E
A V6: Apo R (Å) FWHM (Å) % TKR % Final
Tucked 29.7 4.0 10 10
Closed 33.2 3.8 21 21
Semi-open 36.4 4.8 61 61
Wide-open 39.9 3.1 8 8
20 30 40 50 20 30 40 50
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
280
Figure B-58. Error Analysis for populations < 20% in CA-p2 bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F G
D
E
A V6: CA-p2 R (Å) FWHM (Å) % TKR % Final
Tucked 29.7 4.0 10 10
Closed 33.2 3.8 21 21
Semi-open 36.4 4.8 61 61
Wide-open 39.9 3.1 8 8
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & Tucked
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
281
Figure B-59. Error Analysis for populations < 20% in IDV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
J
HG
K
D E
I
A V6: IDV R (Å) FWHM (Å) % TKR % Final
Curled 23.8 4.6 5 0
Tucked 27.5 6.1 10 10
Closed 32.8 5.4 28 30
Semi-open 36.8 7.2 51 54
Wide-open 46.8 4.5 6 6
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & Tucked
& Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
282
Figure B-60. Error Analysis for populations < 20% in NFV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
G
IH
D
E
A V6: NFV R (Å) FWHM (Å) % TKR % Final
Unassigned 20.7 4.3 8 0
Tucked 27.3 6.1 13 14
Closed 32.9 3.8 27 30
Semi-open 35.4 4.3 35 39
Wide-open 40.8 6.7 17 17
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
-20 Å
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-20 Å & Tucked
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-20 Å & Wide-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o I
nte
nsity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
F
283
Figure B-61. Error Analysis for populations < 20% in ATV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F G
D
E
A V6: ATV R (Å) FWHM (Å) % TKR % Final
Tucked 29.6 4.0 7 7
Closed 32.8 3.8 29 30
Semi-open 36.0 5.5 62 63
Wide-open 40.9 3.0 3 0
20 30 40 5020 30 40 50
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
284
Figure B-62. Error Analysis for populations < 20% in APV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
H
G
D
E
I
A V6: APV R (Å) FWHM (Å) % TKR % Final
Curled 24.1 3.6 8 0
Tucked 29.8 2.8 7 8
Closed 33.6 3.7 67 72
Semi-open 37.8 3.5 15 16
Wide-open 45.0 2.8 4 4
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Curled & Wide-open
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
285
Figure B-63. Error Analysis for populations < 20% in LPV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
JH
G
D
E
I
A V6: LPV R (Å) FWHM (Å) % TKR % Final
Unassigned 20.5 0.6 1 0
Unassigned 22.4 1.0 1 0
Curled 26.9 0.9 1 0
Tucked 30.0 3.0 15 17
Closed 33.4 2.2 79 83
Semi-open 38.2 1.0 1 0
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-20
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-22
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-26
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-38
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-20's
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
-20's & 38
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
DeerSim
286
Figure B-64. Error Analysis for populations < 20% in RTV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C D
A V6: RTV R (Å) FWHM (Å) % TKR % Final
Tucked 30.9 3.9 15 15
Closed 33.0 3.6 26 26
Semi-open 35.7 4.5 51 51
Wide-open 39.1 3.7 8 8
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o In
ten
sity
E F G
287
Figure B-65. Error Analysis for populations < 20% in SQV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F
H
G
D
E
I
A V6: SQV R (Å) FWHM (Å) % TKR % Final
Unassigned 20.3 1.5 7 0
Curled 24.8 1.1 1 0
Tucked 28.8 1.4 7 0
Closed 33.3 3.7 74 87
Semi-open 38.2 1.8 11 13
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
Deersim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-20 Å & Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-20 Å & Tucked
& Semi-open
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-20 Å
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-20 Å & Tucked
( s)
Ech
o In
ten
sity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
J
288
Figure B-66. Error Analysis for populations < 20% in DRV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C F
J
N
HG K
O PL
D E
I
M
Q
A
R S
V6: DRV R (Å) FWHM (Å) % TKR % Final
Unassigned 20.4 1.9 6 0
Curled 25.9 1.1 3 3
Tucked 28.5 1.1 2 3
Closed 33.2 3.2 84 89
Semi-open 38.5 1.5 3 3
Wide-open 43.7 2.4 2 2
20 30 40 50 20 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Curled
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Semi-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-20 Å & Semi-open
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-20 Å & Wide-open
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-Curled & Tucked
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-Curled & Semi-open
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-Curled & Wide-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Semi-open
& Wide-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-Tucked & Semi-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Curled & Tucked
& Semi-open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Tucked & Semi-open
& Wide0open
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-all but 20 Å
( s)
Ech
o I
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0 1 2 3
DeerAnalysis
-all
( s)
Ech
o I
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nsity
0 1 2 3
DeerAnalysis
-20 Å & Tucked
( s)
Ech
o I
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0 1 2 3
DeerAnalysis
-20 Å
( s)
Ech
o I
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nsity
P(r
)
Distance (Å)
DeerAnalysis
Gauss. Reconstr.
P(r
)
Distance (Å)
0 1 2 3
DeerAnalysis
-Tucked
( s)
Ech
o I
nte
nsity
0 1 2 3
DeerAnalysis
-Wide-open
( s)
Ech
o I
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nsity
T U
V
289
Figure B-67. Error Analysis for populations < 20% in TPV bound HIV-1PR V6. A) Table of
values summarizing the populations from TKR analysis and Gaussian reconstruction
procedure. B) Distance profile from TKR analysis (black) overlain with the summed
Gaussian population profile (grey dashed). Populations marked with ‗x‘ were
discarded. C) Individual populations for the Gaussian reconstruction. D–J)
Background subtracted dipolar echo curve (black) overlaid with the TKR fit (black)
and the modified echo curve for the distance profile with one or more populations
suppressed (grey).
B C
F G
D
E
A V6: TPV R (Å) FWHM (Å) % TKR % Final
Unassigned 20.7 2.2 2 0
Curled 25.0 1.6 5 5
Tucked 29.2 1.0 2 2
Closed 33.0 3.3 89 92
Wide-open 40.9 1.9 2 2
20 30 40 5020 30 40 50 0 1 2 3
DeerAnalysis
DeerSim
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-all
( s)
Ech
o In
ten
sity
0 1 2 3
DeerAnalysis
-Tucked & Wide-open
( s)
Ech
o In
ten
sity
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290
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BIOGRAPHICAL SKETCH
Mandy Elizabeth Blackburn was born in 1978 in Denver, Colorado. She obtained her Bachelor
of Science degree in chemistry at the University of New Mexico in Albuquerque in December
2000. After graduation, she served for a year in the United States Navy Reserve in Pensacola,
Florida. Following a four-year hiatus in industry, of which she spent a year in the Quality
Control division of Eppendorf-5 Prime in Boulder, Colorado, she moved to Gainesville, FL. She
worked as a technician in Dr. Philip Lapis‘s laboratory, in the Biochemistry Department of the
medical school at the University of Florida, for a semester, before applying to graduate school.
In January of 2005, she began graduate school in the Department of Chemistry, at the University
of Florida. In April of 2005, she joined Dr. Gail E. Fanucci‘s group.