for biological macromolecules :

For Biological Macromolecules:

For Biological Macromolecules:

• Motion is an integral part of function

For Biological Macromolecules:

• Motion is an integral part of function

• Motion is good for theoreticians like me

For Biological Macromolecules:

• Motion is an integral part of function

• Motion is good for theoreticians like me

• Motion is always bad for experimental structural biologists

Conformational changes in Calmodulin

G-protein transducin

Mechanosensitive channel, MscL

Mechanosensitive channel, MscL

F1-ATP Synthase, molecular motor

Challenges:

Challenges: • Motions occur over a wide range of length scale,

Challenges: • Motions occur over a wide range of length scale,

• Structural data are available at varying resolutions,

Challenges: • Motions occur over a wide range of length scale,

• Structural data are available at varying resolutions,

• How do we simulate, refine & model structures?

Simulating, Refining & Modeling Supermolecular Complexes

at Multi-resolution and Multi-length Scales

Jianpeng MaBaylor College of Medicine

Rice University

I. Simulation and Refinement

at Multi-resolution Scales Quantized Elastic Deformational Model (QEDM)

Proc. Natl. Acad. Sci. USA 99:8620-5 (2002)

modeling structural motions

without atomic coordinates and amino-acid sequence

Discretize low-resolution density maps by• Vector Quantization or• Cubic grid points of cryo-EM density maps

Apply elastic normal mode analysis to the discretized density maps.

For very low-frequency deformational modes, the number of points can be significantly smaller than the number of amino-acids.

Procedures of QEDM

5 Å 7 Å 15 Å

B-factors

Standard NMA

QEDM at 5 Å

QEDM at 7 Å

QEDM at 15 Å

Atomic Displacement of Low-frequency mode

Pyruvate Dehydrogenase Complexes (25Å)

Truncated E2 core Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).

Zhou et al, J. Biol. Chem. 276, 21704-21713 (2001).

Conformational distribution of PDC complex from cryo-EM

PDC is an extraordinarily flexible system

20 % size variation

20 % size variation

Human Fatty Acid Synthase (FAS) at 19 Å Resolution

Proc. Natl. Acad. Sci. USA 99:138-43 (2002)

Experimental Verification&

QEDM-assisted cryo-EM Refinement

Conclusions of QEDM:• Capable of simulating low-frequency deformational motions of proteins based on low-resolution density maps.

• Provide useful insights into protein functions in the absence of detailed atomic model.

• Provide a means to aid structural refinement in cryo-EM measurements.

II. Simulation and Refinement

at Multi-length Scales Substructure Synthesis Method (SSM)

Proc. Natl. Acad. Sci. USA 100:104-9 (2003)

modeling structural motions

of filamentous systems from angstroms to microns

Modal Synthesis Procedure in SSM

• Compute substructure modes by standard normal mode analysis.• Substructures are assembled by imposing geometric boundary conditions. • Calculate the modes for assembled structure by Rayleigh-Ritz principle.• Focus on a set of low-frequency modes.• Does not need to compute Hessian matrix for the assembled structure.

G-actin monomer

A 13-subunit repeat of F-actin filament

37.5 Å

Selected boundary points across the interface

filamentfilament

Bending

Twisting

Stretching

Lowest-frequency modes in the synthesized system

Bending Modes for F-actin Filament of 4.6 Microns

Refining Fibre Diffraction Data by

Long-range Normal Modes

Rosalind Franklin, 1951

In Traditional Fibre Diffraction Refinement:

• The filaments are assumed to be a straight helix.

• But the filaments like F-actin or DNA molecules deform due to their high flexibility.

Challenge:

How do we find proper structural parameters to model the filamentous deformations without overfitting the data?

We chose long-range normal modes of the filaments as refinement parameters.

G-actin monomer

A 13-subunit repeat of F-actin filament

37.5 Å

Bending

Twisting

Stretching

Lowest-frequency modes in the synthesized system

Refinement based on long-range normal modes

Helical selection rule: l=tn+umt=6, u=13 (conventional method)t=6 (or 12, …), u=1 (our method)

l: layerline indexn: order of Bessel functionsm: any integert: number of helical turnsu: number of asymmetric unit in one crossover

Refinement by single low-frequency vibrational normal mode(13-subunit repeat normal modes)

Bending Modes for F-actin Filament

Refinement by multiple modes and different length of repeat

Conclusion:

• Normal modes are good collective variables as structural parameters for refinement. No overfitting of data!!!

• Bending motions dominate the contributions, i.e. the filament wiggling motions must be included in the refinement and errors from them can not be compensated from adjusting other local structural parameters.

III. Refinement of Anisotropic

Temperature Factors for Supermolecular

Complexes in x-ray Crystallography

175,000 A85,000 A

33

GroES

GroEL

Molecular Chaperonin GroEL

I

H

HI

M M

Apical

Equatorial

Intermediate

ATP

Closed Open

E

I

A

25

90 60

Lower hinge

Upper hinge

En bloc rigid-body movements

Chaperonin GroELProteasome

Isotropic Thermal B-factors

Chaperonin GroELProteasome

Isotropic Thermal B-factors

Atomic anisotropic B-factors refined using 100 normal modes,Note: GroEL has more than 50,000 heavy atoms.

Conclusion:

It is finally possible to use collective variables such as low-frequency normal modes to refine the anisotropic thermal parameters for large molecular complexes.

Under harmonic modal analysis, we have unified the schemes in structural refinement for three seemly remote experimental techniques:

X-ray crystallography Electron cryomicroscopy (cryo-EM)Fibre diffraction

Motion is bad news for experimentalists!

AcknowledgementsYifei Kong (Baylor, SCBMB)Yinhao Wu (Rice, RQI)Peng Ge (Rice, RQI)Zhao Ge (Rice, RQI)Jun Shen (Rice, RQI)Billy Poon (Rice, Bioengineering)Terence C. Flynn (Rice, Bioengineering)William H. Noon (Rice, Bioengineering)

Dr. Dengming Ming

National Science Foundation (Early Career Award)National Institutes of Health (R01-GM067801)American Heart AssociationWelch Foundation

Thank You Very Much