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X-ray Crystallography

Biochemistry 412: Proteomics and Functional Genomics

Rongjin Guan

March 7 2008

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Purpose of this class

• Introduce the basic principle of X-ray crystallographySymmetry X-ray diffractionPhase problemMethods to solve the phase problemModel building and refinement

• Give an overview of all steps in structure determination by X-ray crystallography

• Help students understand crystal structure papers

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Overview of X-ray crystallography

1. Grow crystals

3. Solve phases and refine structure

2. Measure diffraction

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Why X-rays?Right wavelength to resolve atoms: C-C bond is 1.54 Å

X-ray crystallography

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How are X-rays produced?

K-orbital

L-orbital

M-orbital

K-absorptionKα1 Kα2

Kβ

Cu(Kα1)= 1.54015 Å; Cu(Kα2)= 1.54433 ÅCu(Kα)= 1.54015 ÅCu(Kβ)= 1.39317 Å

Wave-lengths

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Synchrotron X-rays

Electron/positron injection

Storage RingX-ray

X-rays

Magnetic FieldsElectron/positron beam

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An example of home X-ray source (Rigaku)

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A synchrotron X-ray source at Argonne, IL

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Symmetry in crystals

Why do we need to know the symmetry of the crystals?1) Reduce the size of the asymmetric unit (a unique part of

the crystal) 2) Reduces data collection by reducing the number of

unique reflections to collect3) Symmetry may be useful for phase determination

International Table (volume 1) is a “Bible” for crystal symmetry.

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• A crystal has long range ordering of building blocks that are arranged in an conceptual 3-D lattice.

• A building block of minimum volume defines unit cell

• The repeating units (protein molecule) are in symmetry in an unit cell

• The repeating unit is called asymmetric unit – A crystal is a repeat of an asymmetric unit

Periodicity and Symmetry in a Crystal

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•Arrangement of asymmetric unit in a lattice defines the crystal symmetry.

•The allowed symmetries are 2-, 3, 4, 6-fold rotational, mirror(m), and inversion (i) symmetry (+/-) translation.

•Rotation + translation = screw

•Rotation + mirror = glide

230 space groups, 32 point groups, 14 Bravais lattice, and 7 crystal systems

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Only 65 space groups for chiral molecules

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Steps in structure determination by X-ray crystallography

• Sample preparation chemical, conformational and aggregational homogeneity

• Crystallization • Data collection and process• Phase determination

Isomorphous replacementAnomalous scatteringmolecular replacement, etc

• Model building and refinement• Structural analysis

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Prepare samples for crystallization

Homogeneous protein samples have the best chance to crystallize. (not only pure in SDS PAGE!!!)

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How to grow crystals?

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Phase diagram in crystallization

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Factors that affect crystallization

- pH (buffer)- Protein Concentration- Salt (NaCl, NH4Cl, etc.)- Precipitant- Detergent (e.g. n-Octyl-β-D-glucoside) - Metal ions and/or small molecules- Rate of diffusion- Temperature- Size and shape of the drops- Pressure (e.g. micro-gravity)

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Screening for Crystallization

pH gradient

Precipitant C

oncentration

4 5 6 7 8 9

10 %

15 %

20 %

30 %

Precipitate Crystalline precipitateFiber like Micro-crystals

Small crystals

Ideal crystal

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Monodisperse SeMet SamplesShipped to both Columbia and Hauptman-Woodward Institute (at HWI) for Crystallization Screening

HTP Robotic Screening (1356 conditions) under oil provides initial hits. DeTitta, Luft, et al

Robotic setup of hanging drop crystallization optimization at Columbia is informed by HWI results. Hunt, Tong, et al

Production crystallization conditions include potential ligands assessed by literature search

HTP Crystallization Screening

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A protein crystal gallery

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Crystal

Cryo-loop

DetectorGoniometer

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Crystal characterizations

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An example of diffraction image

ResolutionIce ringMosaicitySpots resolved

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Sometimes, there may be problems

• One cell parameter is too long – spots overlaps• Twinning• High mosaics • Water rings• Radiation damage• Anisotropic diffraction

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A typical data processing output

completeness

Rmerge

Systematic absences

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Phase problem in X-ray Crystallography

The phases are lost during measurement, so electron density cannot be directly calculated. We have to estimate them.

This lack of knowledge of the phases is termed phase problem.

To calculate an electron density map:

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Importance of Phases

Hauptman amplitudeswith Hauptman phases

Hauptman amplitudeswith Karle phases

Karle amplitudeswith Karle phases

Karle amplitudeswith Hauptman phases

Phases dominate the image!Phase estimates need to be accurate

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How to Solve the Phase Problem

• Experimental methods:Multiple/Single Isomorphous Replacement (MIR/SIR)

Heavy atoms (Heavy metals, Xe, Br, I, etc)

Multi/single Wavelength Anomalous Dispersion (MAD/SAD)Heavy atoms (Se-Met, etc),

• Non-experirmental methods:Molecular Replacement

Homologous templates (similar structure fold)Direct Methods (special cases)

high resolution data, small proteins (<2000 atoms)

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Isomorhous Replacement (MIR)

• Heavy atom derivatives are prepared by soaking or co-crystallizing

• Diffraction data for heavy atom derivatives are collected along with the native data

FPH= FP + FH

• Patterson function P(u)= 1/V Σ|F(h)|2 cos(2πu.h)= ρ(r) x ρ(r’) dv

strong peaks for in Patterson map when r and r’ are two heavy atom positions

h

r

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Phase determination by MIR

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The Patterson Function

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Obtaining FH estimate: the isomorphous difference

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Phase determination by MIR once the heavy atom structures are known

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Multiple Anomalous Dispersion (MAD)

At the absorption edge of an atom, its scattering factor fano= f + f’ + if”

Atom f f’ f”Hg 80 -5.0 7.7Se 34 -0.9 1.1

F(h,k,l) = F(-h,-k,-l) anomalous differences positions of anomalous scatterers Protein Phasing

fanoif”

f f’real

imag

inar

y

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Anomalous Scattering breaks the Friedel's Law

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Obtaining FH estimate: the anomalous difference

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Se-Met MAD

• Most common method of ab initio macromolecule structure determination

• A protein sample is grown in Se-Met instead of Met.

• Minimum 1 well-ordered Se-position/75 amino acids

• Anomolous data are collected from 1 crystal at Se K-edge (12.578 keV).

• MAD data are collected at Edge, Inflection, and remote wavelengths

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The ISAS process is carried twice, once with heavy atom site(s) at refined

locations (+++), and once in their inverted locations (---).

Data FOM1 Handedness FOM2 R-Factor Corr. Coef RHE 0.54 Correct 0.82 0.26 0.958

0.54 Incorrect 0.80 0.30 0.940 NP With I3 0.54 Correct 0.80 0.27 0.955

0.54 Incorrect 0.76 0.36 0.919 NP With I & S4 0.56 Correct 0.82 0.24 0.964

0.56 Incorrect 0.78 0.35 0.926 1: Figure of merit before solvent flattening 2: Figure of merit after one filter and four cycles of solvent flattening 3: Four Iodine were used for phasing 4: Four Iodine and 56 Sulfur atoms were used for phasing Heavy Atom Handedness and Protein Structure Determination using S ingle-wavelength Anomalous Scattering Data, ACA Annual Meeting, Montreal, July 25, 1995.

Resolve the SIR or SAS phase ambiguity (Handedness) by Solvent Flattening

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• If the structure of a similar molecule is known, structure factors of this known model may be calculated, allowing placement of the model in the unit cell by minimizing the R factor as a function of the orientation and position of the model within the unit cell:

R-factor = Σ ||Fobs| - |Fcalc|| / Σ|Fobs|hkl hkl

Molecular Replacement

The templates for a successful molecular replacement must be structural homologues (Cα rmsd < 1.5Å), not necessarily, though often, homologous in sequence.

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How phases are calculated in MR

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Two step process in Molecular Replacement

1. find orientation of model (red ==> black)Rotation Function

2. find location of orientated model (black ==> blue)Translation Function

X1: unknown X2: known model

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Once phases are determined, an electron density map can be calculated

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Maps at different resolution show different levels of details

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Phase refinement by solvent flattening

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Model building is the fitting of atomic models into electronic density

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What to refine?• Atom coordinates: (x, y, z)s• B factors and occupancy

Steps in refinement1. Rigid body refinement2. Energy minimization3. Simulated annealing refinement4. Model building in graphics by hand5. Add waters and other molecules6. B factor refinement

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Geometric Restraints in Refinement

Each atom has 4 (x,y,z,B) parameters and each parameters requires minimum 3 observations for a free-atom least-squares refinement. A protein of N atoms requires 12N observations.

For proteins diffracting < 2.0 Å resolution observation to parameter ratio is considerable less.

Protein Restraints (bond lengths, bond angles, planarity of an aromatic ring etc.) are used as restraints to reduce the number of parameters

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R-factor

Rcryst = Σhkl |Fobs(hkl) - kFcal(hkl)| / Σhkl |Fobs(hkl)|

Free-R

R-factor calculated for a test-set of reflections that is never included in refinement.

R-free is always higher than R.

Difference between R and R-free is smaller for higher resolution and well-refined structures

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Free R Factor

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Refinement Validation

• Free R factor

• Ramachandran plot

• Luzzati plot

• MolprobityWhen you believe you have done the best model building and Refinement, you can deposit your structural factors and atomicCoordinates to PDB: www.pdb.org

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The famous “Table 1”: crystallographic refinement statistics

In this case, even at 2.0 A resolution, reflection/parameters ratio= 12396/4*(1331+80) = 2.2, very under-determined.

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Structural analysis

• Can you explain biological data from this structure?

• What is the structural basis of the biological function?

• What implication can you get from the structure? Can you design better inhibitor or substrate (drug design, protein engineering…)

• Are what you observed from this crystal structure believable (or artifact from crystallization?)

• Paper writing

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Further reading if you are interestedCrystallography Made Crystal Clear, by Gale RhodesPrinciples of Protein X-ray Crystallography, by Jan DrenthInternational Tables for Crystallography, vol F, edited by

M. G. Rossmann & Eddy Arnold

http://www.ruppweb.org/Xray/101index.htmlhttp://www.iucr.org/cww-top/edu.index.html

Crystallography history (fun reading)From the Structures of simple Salts to Those of Sophisticated

Viruses, by M. G. Rossmann, Acta Crystal. A54, 1998, 716-728Fifty Years of X-ray Diffraction, Edited by P. P. Ewald, 1962.

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NMR vs Xray pI

010203040506070

3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11

pI Range

# in

PD

B

nm

xra

PSI2 NESG pI Distribution

050

100150200250300350

0-1 1-2 2-3 3-4 4-5 5-6 6-7 7-8 8-9 9-10 10-11

pI

# ta

rget

s

NMR vs Xray HI

020406080

100120

-.25 -

-.20

-0.2 -

-0.15

-0.15

- -0.

1-0.

1 - -0

.05-0.

05 -

00

- .

0505

. - .1

.1 - .1

5.15

- .2

.2 - .2

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Mean Hydrophobicity

# in

PD

B

nmr

xray

Biophysical Features of 230 NESG Structures in PDB

M. Baran, J. Locke, D. Snyder,J. Huang, J. Hunt Poster

25%75%

% of NESG NMR Struc

New NESG PSI2 targets

NESG PSI2 Targets< 20 kDa

X-RayNMR

NMR

NMR

X-RayX-Ray

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Other possible topics

• Time-resolved X-ray crystallography• Direct method to solve phase problem• Small angle X-ray scattering• X-ray powder diffraction to solve protein structures• Difference between NMR and X-ray crystallography• Neutron diffraction • Drug design• Virus/supercomplex crystallography

powerpoint presentation - x-rays · pdf filecrystallography history (fun reading) from the...

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