X-Ray diffraction 1895 W.C. Rntgen discovers X-rays (Nobel Prize - PDF document

Experimental structure determination � X-ray crystallography � X-ray diffraction � Protein crystallization � Phasing methods � Symmetry and packing X-Ray diffraction 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)

Dimensions of life ... Dimensions of life ... Can we see chemical bonds and atoms?

Optical microscope visible light 400 - 700 nm X-ray Generation and Detection � Why do we use X-rays? � visible light 400 - 700 nm 0.1 Å < λ < 1000 Å � X-rays: (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

X-ray tubes & rotating anodes � Cu - K α radiation � Wavelength: 1.54 Å Synchrotron Radiation

X-ray diffraction � Experimental setup X-Ray diffraction � Bragg’s Law: Diffracted beam Incoming beam λ • n θ θ d d • • d • sin θ d • sin θ n • λ = 2 • d • sin θ

X-Ray diffraction � Bragg’s Law (010) (010) y m a e b Incoming beam d e t c a r f f i D (120) n • λ θ θ d d d • sin θ d • sin θ b (100) x a n • λ = 2 • d • sin θ X-ray Crystallography � Protein Crystals

X-ray Crystallography � Protein Crystallization Cover Slide Silicon oil Droplet Reservoir X-ray diffraction � Bragg’s Law (010) (010) y m a e b Incoming beam d e t c a r f f i D (120) n • λ θ θ d d d • sin θ d • sin θ b (100) x a n • λ = 2 • d • sin θ

X-ray diffraction � Diffraction pattern � Histidine Ammonia Lyase crystal � Pseudomonas putida Space group: I222 a = 79 Å b = 117 Å c = 129 Å, α = β = γ = 90 ° Resolution: 1.5 Å Wavelength: 1.54 Å (MAR research Imaging plate) X-ray diffraction � Crystal parameters Unit cell e.g. α = β = γ = 90 ° (010) (010) y (120) b (100) x a

X-ray diffraction � Fourier Transformations F (h,k,l) ρ el (x,y,z) The relationship between the electron density ρ el (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). X-ray diffraction � Fourier Transformations I = | F 2 | F (h,k,l) = ∫ v v v v v π ρ ⋅ 2 i s r F ( s ) ( r ) e d r Structure Factor: el Vol 1 ∑∑∑ − π + + ρ = ⋅ Electron Density: 2 i ( hx ky lz ) ( x , y , z ) F ( hkl ) e el V h k l EZ F(hkl) = F(hkl) ⋅ e i ϕ hkl

Vector representation of F � Vector representation of F in complex plane: ϕ F(hkl) = F(hkl) ⋅ e i hkl ϕ = ϕ + ⋅ ϕ i e cos i sin From: Kevin Cowtan's Book of Fourier; http: / / www.ysbl.york.ac.uk/ ~ cowtan/ fourier/ fourier.html … an atom, and its Fourier Transform: … a molecule, and its Fourier Transform: From: Kevin Cowtan's Book of Fourier; http: / / www.ysbl.york.ac.uk/ ~ cowtan/ fourier/ fourier.html

… a lattice, and its Fourier Transform: → reciprocal space … a crystal, 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

… again, our Fourier Duck: Phases (colors) … and a new friend, a Fourier cat: Inten- sities 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

We can measure intensities, but .... Houston, Houston! we have a Phase Problem ! I = | F 2 | ϕ F(hkl) = F(hkl) ⋅ e i hkl 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.

Phase Problem 1 ∑∑∑ − π + + ρ = ⋅ F(hkl) = F(hkl) ⋅ e i ϕ 2 i ( hx ky lz ) ( x , y , z ) F ( hkl ) e hkl el V h k l EZ From: G. Rhodes; Crystallography Made Crystal Clear Least squares refinement: ∑ = ⋅ − Least squares refinement: 2 Q w ( hkl ) ( F ( hkl ) F ( hkl ) ) obs calc hkl ∑ − ⋅ F ( hkl ) k F ( hkl ) = obs calc Crystallographic R-Factor: hkl R ∑ F ( hkl ) obs hkl ∑ − ⋅ F ( hkl ) k F ( hkl ) = ∈ obs calc hkl T R ∑ Crystallographic R-Free: free F ( hkl ) ∈ obs hkl T w(hkl) resolution dependent weight factor Reflections of the test set T are excluded from the refinement procedure.