X-ray crystallography - EMBnet node Switzerland

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Experimental structure determination X-ray crystallography X-ray diffraction Protein crystallization Phasing methods Symmetry and packing 1895 W.C. Röntgen discovers X-rays (Nobel Prize 1901) 1910 Max von Laue: Diffraction Theory (Nobel Prize: 1912) 1915 W.L. Bragg & W.H. Bragg: NaCl, KCl (Nobel Prize Physics) 2 • d • sin Θ = n • λ 1934 D. Bernal & D. Crowfoot examine first Proteins 1950 DNA double helix structure: Watson, Crick, Wilkins (Nobel Prize 1963) 1958 Myoglobin Structure (Nobel Prize 1962 Kendrew, Perutz) 1971 Insulin (Blundell) 1978 First Virus Structure (S.C Harrison) 1988 Nobel Prize: Photosynthetic reaction center (Huber, Michel, Deisenhofer) 1997 Nobel Prize: ATP-synthase structure (Walker) 1997 Nucleosome core particle (T. Richmond) 1999 Ribosome Structures (Steitz, …) 2000 Reovirus core structure (S.C. Harrison) 2000 Rhodopsin structure, GPCR (Palczewski et al.) 2002 ABC-Transporter (D. Rees et al.) 2003 R.MacKinnon: structures of ion channel (Nobel Prize Chemistry 2003) X-Ray diffraction

Transcript of X-ray crystallography - EMBnet node Switzerland

Page 1: X-ray crystallography - EMBnet node Switzerland

Experimental structure determination

X-ray crystallography

X-ray diffraction

Protein crystallization

Phasing methods

Symmetry and packing

1895 W.C. Röntgen discovers X-rays (Nobel Prize 1901)

1910 Max von Laue: Diffraction Theory (Nobel Prize: 1912)

1915 W.L. Bragg & W.H. Bragg: NaCl, KCl (Nobel Prize Physics)

2 • d • sin Θ = n • λ

1934 D. Bernal & D. Crowfoot examine first Proteins

1950 DNA double helix structure: Watson, Crick, Wilkins (Nobel Prize 1963)

1958 Myoglobin Structure (Nobel Prize 1962 Kendrew, Perutz)

1971 Insulin (Blundell)

1978 First Virus Structure (S.C Harrison)

1988 Nobel Prize: Photosynthetic reaction center (Huber, Michel, Deisenhofer)

1997 Nobel Prize: ATP-synthase structure (Walker)

1997 Nucleosome core particle (T. Richmond)

1999 Ribosome Structures (Steitz, …)

2000 Reovirus core structure (S.C. Harrison)

2000 Rhodopsin structure, GPCR (Palczewski et al.)

2002 ABC-Transporter (D. Rees et al.)

2003 R.MacKinnon: structures of ion channel (Nobel Prize Chemistry 2003)

X-Ray diffraction

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Dimensions of life ...

Can we see chemical bonds and atoms?

Dimensions of life ...

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visible light 400 - 700 nm

Optical microscope

X-ray Generation and Detection

Why do we use X-rays?

visible light 400 - 700 nm

X-rays: 0.1 Å < λ < 1000 Å (1 Å = 10-10 m = 100 pm = 0.1 nm)

atomic distances: ~ 1.5 Å

How do we generate X-rays?

X-ray tubes & Rotating Anode Generators

Synchrotron Radiation

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X-ray tubes & rotating anodes

Cu - Kα radiation

Wavelength: 1.54 Å

Synchrotron Radiation

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X-ray diffraction

Experimental setup

n • λ = 2 • d • sin θ

Incoming beam

Diffracted beam

θ θ

dd

d • sin θd • sin θ

n • λ

• •

X-Ray diffraction

Bragg’s Law:

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n • λ = 2 • d • sin θ

a

b

x

y

(010

)

(100)

(010

)

(120)

Incoming beamDiffr

acted beam

θ θ

dd

d • sin θd • sin θ

n • λ

X-Ray diffraction

Bragg’s Law

X-ray Crystallography

Protein Crystals

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Droplet

Silicon oil

Reservoir

Cover Slide

X-ray Crystallography

Protein Crystallization

n • λ = 2 • d • sin θ

a

b

x

y

(010

)

(100)

(010

)

(120)

Incoming beamDiffr

acted beam

θ θ

dd

d • sin θd • sin θ

n • λ

X-ray diffraction

Bragg’s Law

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X-ray diffraction

Diffraction patternHistidine Ammonia Lyase crystalPseudomonas putida

Space group: I222a = 79 Åb = 117 Åc = 129 Å, α = β = γ = 90°Resolution:1.5 Å

Wavelength: 1.54 Å(MAR research Imaging plate)

Crystal parametersUnit cell

a

b

x

y

(010

)

(100)

(010

)

(120)

e.g. α = β = γ = 90°

X-ray diffraction

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F (h,k,l)

The relationship between the electron density ρel(x,y,z) and the structure

factors F(hkl) can be described by a Fourier transformation (FT).

This transformation is accurate and in principle complete. If we know the

structure factors (diffraction by electrons) we can calculate the actual real

structure (the density of the electrons in real space).

ρel (x,y,z)

X-ray diffraction

Fourier Transformations

I = | F 2 |

rdersF rsi

Vol

el

vvv vvπρ 2)()( ⋅= ∫

∑∑∑ ++−⋅=h k l

lzkyhxi

EZel ehklF

Vzyx )(2)(

1),,( πρ

F(hkl) = F(hkl) ⋅ei hklϕ

Structure Factor:

Electron Density:

F (h,k,l)

X-ray diffraction

Fourier Transformations

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F(hkl) = F(hkl) ⋅ei hklϕ

ϕϕϕsincos ⋅+= ie

i

Vector representation of F

Vector representation of F in complex plane:

From: Kevin Cowtan's Book of Fourier; http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

… a molecule, and its Fourier Transform:

… an atom, and its Fourier Transform:

From: Kevin Cowtan's Book of Fourier; http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

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… a crystal, and its Fourier Transform:

→ reciprocal space

… a lattice, and its Fourier Transform:

From: Kevin Cowtan's Book of Fourier; http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

… a duck, and its Fourier Transform:

From: Kevin Cowtan's Book of Fourier; http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

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… and a new friend, a Fourier cat: Phases (colors)

Inten-sities

… again, our Fourier Duck:

From: Kevin Cowtan's Book of Fourier; http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

Intensities and phases

The picture that contributed the phases is still visible, whereas the picture which contributed the magnitudes has gone!

Phases contain the bulk of the structural information.

We need the intensities and phases to calculate a realistic picture.

From: Kevin Cowtan's Book of Fourier; http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

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I = | F 2 |

F(hkl) = F(hkl) ⋅ei hklϕ

Houston, Houston!

we have a

Phase Problem !

We can measure intensities, but ....

From: G. Rhodes; Crystallography Made Crystal Clear

Phasing Methods

Heavy atom method (MIR, multiple isomorphous replacement)Each atom in the unit cell contributes to all observed reflection intensities. The basic principle of the MIR method is to collect diffraction data of several (multiple) crystals of the same protein, that share the same crystal properties (isomorphous), but differ in a small number of heavy atoms. The experimental approach is normally to soak protein crystals with diluted solutions of heavy metal compounds (e.g. mercury or platinum derivatives), that often bind specifically to certain protein residues. These additional atoms cause a slight perturbation of the diffraction intensities. To achieve a perturbation large enough to measured correctly, the added atoms must diffract strongly, i.e. elements with a high number of electrons (heavy atoms) are used. The differences of the reflection intensities can be used to locate the positions of the heavy atoms within the unit cell, which allows to estimate initial phases.

Anomalous scattering (MAD, multiple wavelength anomalous diffraction)The MAD method is based on the capacity of heavy atoms to absorb X-rays of a specific wavelength. Near its characteristic absorption wavelength, the diffraction intensities of the symmetry related reflections (Friedel pairs, h,k,l and -h,-k,-l) are no longer equal. This effect is called anomalous scattering. The characteristic absorption wavelengths of typical protein atoms (N,C,O) are not in the range of the X-rays used in protein crystallography and therefore are not contributing to anomalous scattering. However, the use of synchrotron X-ray sources with adjustable wavelengths allows to collect diffraction data under conditions where heavy atoms exhibit strong anomalous scattering. In practice, several diffraction data sets are collected from the same protein crystal at different wavelengths. From the small differences between the Friedel pairs, the location of the heavy atoms can be determined and initial phases of the native data are estimated.

Molecular replacement (MR)In some cases is structure to be examined is known to be very similar to an other structure, that has already been solved experimentally. This could be e.g. the same protein from an other organism or a mutant of this protein. In these cases the phases computed from of the known protein structure (phasing model) can be used as initial estimates of the phases of the unknown protein.

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∑∑∑ ++−⋅=h k l

lzkyhxi

EZel ehklF

Vzyx )(2)(

1),,( πρ F(hkl) = F(hkl) ⋅ei hklϕ

Phase Problem

From: G. Rhodes; Crystallography Made Crystal Clear

∑ −⋅=hkl

calcobs hklFhklFhklwQ 2))()(()(Least squares refinement:

∑∑ ⋅−

=hkl obs

hkl calcobs

hklF

hklFkhklFR

)(

)()(Crystallographic R-Factor:

∑∑

∈⋅−

=Thkl obs

Thkl calcobs

hklF

hklFkhklFR

)(

)()(freeCrystallographic R-Free:

w(hkl) resolution dependent weight factorReflections of the test set T are excluded from the refinement procedure.

Least squares refinement:

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1 2 3 4 5 6 71234567890123456789012345678901234567890123456789012345678901234567890ATOM 74 N ASP A 10 12.982 78.264 31.707 1.00 48.50 N ATOM 75 CA ASP A 10 14.137 79.163 31.764 1.00 46.20 C

COLUMNS DATA TYPE FIELD DEFINITION---------------------------------------------------------------------------------1 - 6 Record name "ATOM "7 - 11 Integer serial Atom serial number.

13 - 16 Atom name Atom name.17 Character altLoc Alternate location indicator.18 - 20 Residue name resName Residue name.22 Character chainID Chain identifier.23 - 26 Integer resSeq Residue sequence number.27 AChar iCode Code for insertion of residues.31 - 38 Real(8.3) x Orthogonal coordinates for X in Angstroms.39 - 46 Real(8.3) y Orthogonal coordinates for Y in Angstroms.47 - 54 Real(8.3) z Orthogonal coordinates for Z in Angstroms.55 - 60 Real(6.2) occupancy Occupancy.61 - 66 Real(6.2) tempFactor Temperature factor.73 - 76 LString(4) segID Segment identifier, left-justified.77 - 78 LString(2) element Element symbol, right-justified.79 - 80 LString(2) charge Charge on the atom.

Anatomy of a PDB file: Coordinate Section

jatom

rsin

j

Bs

j eesfhklFvv⋅⋅−

⋅⋅= ∑ π24

1 2

)()(

0

20

40

60

80

residue no.

fj X Z Y occ. B-FactorATOM 1 N THR 1 17.047 14.099 3.625 1.00 13.79ATOM 2 CA THR 1 16.967 12.784 4.338 1.00 10.80ATOM 3 C THR 1 15.685 12.755 5.133 1.00 9.19ATOM 4 O THR 1 15.268 13.825 5.594 1.00 9.85ATOM 5 CB THR 1 18.170 12.703 5.337 1.00 13.02ATOM 6 OG1 THR 1 19.334 12.829 4.463 1.00 15.06ATOM 7 CG2 THR 1 18.150 11.546 6.304 1.00 14.23

Anatomy of a PDB file: Coordinate Section

Temperature Factors (B-Factor)

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CRYST1, ORIGXn, SCALEn, MTRIXn, TVECT

1 2 3 4 5 6 71234567890123456789012345678901234567890123456789012345678901234567890...CRYST1 146.100 146.100 93.500 90.00 90.00 120.00 P 32 2 1 18 ORIGX1 1.000000 0.000000 0.000000 0.00000 ORIGX2 0.000000 1.000000 0.000000 0.00000 ORIGX3 0.000000 0.000000 1.000000 0.00000 SCALE1 0.006845 0.003952 0.000000 0.00000 SCALE2 0.000000 0.007903 0.000000 0.00000 SCALE3 0.000000 0.000000 0.010695 0.00000 MTRIX1 1 0.615618 -0.566417 -0.547872 43.95300 1 MTRIX2 1 -0.721915 -0.126974 -0.680103 85.75600 1 MTRIX3 1 0.315683 0.814298 -0.487112 -55.40900 1 MTRIX1 2 0.615585 -0.722198 0.315398 52.48700 1 MTRIX2 2 -0.567238 -0.128436 0.813339 80.93800 1 MTRIX3 2 -0.546941 -0.679684 -0.488774 55.37300 1 ...

Crystallography and Coordinate Transformation Section

Lattice Types & Symmetry

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2-dimensional lattice with 2-fold symmetry axes P21 entry in International Tables of Crystallography

Symmetry

NOTE:

Biological macromolecules are

chiral.

Of all 230 possible space groups, only

those 65 without mirror planes and

centers of symmetry are allowed for

protein crystals.

Symmetry

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PDB - file biologically active state: tetramer

Symmetry

NOTE: the content of a PDB file does NOT necessarily represent the biologically active oligomeric form of a protein!

X-ray crystallography

IntroductionG. Rhodes. Crystallography made Crystal Clear, Academic Press, San Diego, USA.

Advanced Textbooks:Giacovazzo, H.L. Monaco, D. Viterbo, F. Scordani, G. Gill, G. Zanotti, M. Catti. Fundamentals of Crystallography, International Union of Crystallography, Oxford University Press, Oxford, UK.

J. Drenth, Principles of Protein Crystallography, Springer, New York, USA.

Links:PDB: http://www.pdb.org

X-ray 101: http://www.ruppweb.org/Xray/101index.html

SCOP: http://scop.mrc-lmb.cam.ac.uk/scop/

CATH: http://www.cathdb.info