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X-ray Crystallography Kalyan Das

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Page 1: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

X-ray Crystallography

Kalyan Das

Page 2: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Electromagnetic Spectrum

10-1 to 10 nm

400 to 700 nm

10-4 to 10 -1 nm

10 to 400 nm

700 to 104 nm

X-ray radiation was discovered by Roentgen in 1895. X-rays are generated by bombarding electrons on an metallic anode

Emitted X-ray has a characteristic wavelength depending upon which metal is present.e.g. Wavelength of X-rays from Cu-anode = 1.54178 Å

E= h= h(c/)

Å)= 12.398/E(keV)

NMR 10 um - 10 mm

Page 3: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

X-ray Sources for Crystallographic Studies

Home Source – Rotating Anode

K-orbital

L-orbital

M-orbital

K-absorptionK1 K2

K

Cu(K1)= 1.54015 Å; Cu(K2)= 1.54433 Å

Cu(K)= 1.54015 Å Cu(K)= 1.39317 Å

Wave-lengths

Page 4: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Synchrotron X-rays

Electron/positron injection

Storage RingX-ray

X-rays

Magnetic Fields Electron/positron beam

Page 5: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Crystallization

Slow aggregation process

Protein Sample for Crystallization:

Pure and homogenous (identified by SDS-PAGE, Mass Spec. etc.)

Properly folded

Stable for at least few days in its crystallization condition (dynamic light scattering)

Page 6: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Conditions Effect Crystallization

- pH (buffer)- Protein Concentration- Salt (Sodium Chloride, Ammonium Chloride

etc.)- Precipitant- Detergent (e.g. n-Octyl--D-glucoside) - Metal ions and/or small molecules- Rate of diffusion- Temperature- Size and shape of the drops- Pressure (e.g. micro-gravity)

Page 7: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Precipitant

Drop containing protein sample for crystallization

Hanging-drop Vapor Diffusion

Cover Slip

Well

Page 8: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Screening for Crystallization

pH gradient

Pre

cipita

nt Co

ncentra

tion

4 5 6 7 8 9

10 %

15 %

20 %

30 %

Precipitate Crystalline precipitateFiber like Micro-crystals

Small crystals

Ideal crystal

Page 9: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

• 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

Page 10: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation
Page 11: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

•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

Page 12: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Crystal

Cryo-loop

DetectorGoniometer

Page 13: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Diffraction

Page 14: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Diffraction from a frozen arginine deiminase crystal at CHESS F2-beam line

zoom

1.6 Å resolution

Page 15: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Bragg Diffraction

d

d sin

For constructive interference 2d sin

d- Spacing between two atoms

-Angle of incidence of X-ray- Wavelength of X-ray

Page 16: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Structure factor at a point (h,k,l)

F(h,k,l)= fnexp [2i(hx+ky+lz)]

f – atomic scattering factor

N – number of all atoms

F is a complex number

F(h,k,l)= |F(h,k,l)| exp(-i)

N

n=1

Phase Problem in Crystallography

amplitude

phase

Measured intensity

I(h,k,l)= |F(h,k,l)|2

Reciprocal Space

h,k,l

background

I(h,k,l)

Page 17: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Electron Density

Structure Factor

Electron Density

F(h,k,l)= fnexp [2i(hx)]

Friedel's law F(h) = F*(-h)

Page 18: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Electron Density Maps

4 Å resolution electron density map 3.5 Å resolution electron density map

Protein Solvent

Page 19: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

1.6 Å electron density map

Page 20: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Solving Phase Problem

Page 21: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Molecular Replacement (MR)

Using an available homologous structure as template

Advantages: Relatively easy and fast to get solution.

Applied in determining a series of structures from a known homologue – systematic functional, mutation, drug-binding studies

Limitations: No template structure no solution, Solution phases are biased with the information from its template structure

Page 22: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

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 |F(h)|2 cos(2u.h)= (r) x (r’) dv

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

h

r

Page 23: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

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 7.7 Se 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

Page 24: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

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

Page 25: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Model Building and Refinement

Page 26: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Least-Squares Refinement

List-squares refinement of atoms (x,y,z, and B) against observed |F(h,k,l)|

Target function that is minimized

Q= w(h,k,l)(|Fobs(h,k,l)| - |Fcal(h,k,l)|)2

dQ/duj=0; uj- all atomic parameters

Page 27: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

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

Page 28: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

R-factor

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

Page 29: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

Radius of convergence in a least-squares refinement is, in general, low. Often manual corrections (model building) are needed.

Model Building and Refinement are carried out in iterative cycles till R-factor converges to an appropriate low value with appreciable geometry of the atomic model.

Page 30: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

                                                   

1.0Å                        2.5Å

                                                   

3.5Å                        4Å

Page 31: X-ray Crystallography Kalyan Das. Electromagnetic Spectrum 10 -1 to 10 nm 400 to 700 nm 10 -4 to 10 -1 nm 10 to 400 nm 700 to 10 4 nm X-ray radiation

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