X-Ray structure analysis

Kay Diederichskay.diederichs@uni-konstanz.de

2

Analysis of what?

Proteins ( /ˈproʊˌtiːnz/ or /ˈproʊti.ɨnz/) are biochemical compounds consisting of one or more polypeptides typically folded into a globular or fibrous form, facilitating a biological function.

A polypeptide is a single linear polymer chain of amino acids bonded together by peptide bonds between the carboxyl and amino groups of adjacent amino acid residues. The sequence of amino acids in a protein is defined by the sequence of a gene, which is encoded in the genetic code. In general, the genetic code specifies 20 standard amino acids. (Wikipedia)

3

What is Macromolecular Crystallography?

● The art of getting a protein to “sit still” …then taking a 3D “picture”

● What are protein crystals?Static, well-ordered arrays of protein molecules

● 3D-pictures are stitched together from 2D ones. How are the 2D-pictures made?By irradiating the ordered protein array with X-rays, collecting the constructively diffracted X-rays, and reconstructing a likely model of the protein’s 3D structure using a computer

3

4

● History and current status● Practical aspects● Theory● Comparison with other techniques

Overview

5

Wilhelm Conrad Röntgen (1845-1923) January 23, 1896

Absorption of X-rays

6

Max von Laue (1879-1960) X-ray diffraction of crystals (1912)Paul Peter Ewald (1888-1985) theoretical explanation (1912)

William Henry Bragg (1862–1942) Bragg's equation: nλ = 2d sin ΘWilliam Lawrence Bragg (1890-1971) (Nobel Prize, 1915)

Diffraction of X-rays

7

X-ray diffraction patterns of DNA Rosalind Franklin and Maurice Wilkins (1953)

The central cross shaped pattern as indicative of a helical structure. The heavy dark patterns (left and right) indicate that the bases are stacked perpendicular to the axis of the molecule. http://www.pbs.org/wgbh/nova/photo51/

8

DNA Structure: History

9

Myo- and haemoglobin models at 5.5 Å resolution (1959)

http://www2.mrc-lmb.cam.ac.uk/about-lmb/archive-service/models-and-artefacts

„sausage“ Balsa wood

10

www.umass.edu/molvis/francoeur/barker/barker.html

2 Å Myoglobin model built by A. A. Barker, Model Maker in Cambridge (UK), 1960

11

12

So far, 29 Nobel Prizes are associated with crystallography

• For a list, see http://www.iucr.org/people/nobel-prize

• Either for physical basis or mathematical treatment („Physics“) or important chemical compounds („Chemistry“) or „Physiology and Medicine“ (DNA; Crick, Watson, Wilkins 1962)

• Most recently: (2013 Karplus, Levitt & Warshel); 2012 Lefkowitz & Kubilka; 2011 Shechtman: Quasicrystals; 2009 Ramakrishnan, Steitz, Yonath: Studies of the structure and function of the ribosome

• 14 of the 29 were awarded in Structural Biology (starting in 1946)

• See http://www.ebi.ac.uk/pdbe/docs/nobel/

13

Examples of high-profile structures

Protein translocation through the SecA–SecY complex

Structure of Ebola virus

Ribosome with mRNA

14

15

From Protein Data Bank (PDB) file 1HSGCrystal Structure at 1.9 Å Resolution of HIV II ProteaseJ.Biol.Chem. v269 pp.26344-26348 , 1994

15

16

HEADER HYDROLASE (ACID PROTEINASE) 31-MAR-95 1HSG 1HSG 2COMPND 2 MOLECULE: HIV-1 PROTEASE; 1HSG 4COMPND 3 CHAIN: A, B; 1HSG 5SOURCE 2 ORGANISM_SCIENTIFIC: HUMAN IMMUNODEFICIENCY VIRUS TYPE 1; 1HSG 10SOURCE 3 GENE: HIV-1 PROTEASE FROM THE NY5 ISOLATE; 1HSG 11EXPDTA X-RAY DIFFRACTION 1HSG 13REMARK 2 1HSG 25REMARK 2 RESOLUTION. 2.0 ANGSTROMS. 1HSG 26REMARK 3 R VALUE 0.166 1HSG 31REMARK 3 RMSD BOND DISTANCES 0.017 ANGSTROMS 1HSG 32REMARK 3 RMSD BOND ANGLES 1.9 DEGREES 1HSG 33SEQRES 1 A 99 PRO GLN ILE THR LEU TRP GLN ARG PRO LEU VAL THR ILE 1HSG 62ATOM 1 N PRO A 1 29.361 39.686 5.862 1.00 38.10 1HSG 107ATOM 2 CA PRO A 1 30.307 38.663 5.319 1.00 40.62 1HSG 108ATOM 3 C PRO A 1 29.760 38.071 4.022 1.00 42.64 1HSG 109ATOM 4 O PRO A 1 28.600 38.302 3.676 1.00 43.40 1HSG 110ATOM 5 CB PRO A 1 30.508 37.541 6.342 1.00 37.87 1HSG 111ATOM 6 CG PRO A 1 29.296 37.591 7.162 1.00 38.40 1HSG 112ATOM 7 CD PRO A 1 28.778 39.015 7.019 1.00 38.74 1HSG 113ATOM 8 N GLN A 2 30.607 37.334 3.305 1.00 41.76 1HSG 114ATOM 9 CA GLN A 2 30.158 36.492 2.199 1.00 41.30 1HSG 115ATOM 10 C GLN A 2 30.298 35.041 2.643 1.00 41.38 1HSG 116ATOM 11 O GLN A 2 31.401 34.494 2.763 1.00 43.09 1HSG 117ATOM 12 CB GLN A 2 30.970 36.738 0.926 1.00 40.81 1HSG 118ATOM 13 CG GLN A 2 30.625 35.783 -0.201 1.00 46.61 1HSG 119ATOM 14 CD GLN A 2 31.184 36.217 -1.549 1.00 50.36 1HSG 120ATOM 15 OE1 GLN A 2 32.006 35.518 -2.156 1.00 53.89 1HSG 121ATOM 16 NE2 GLN A 2 30.684 37.339 -2.061 1.00 51.46 1HSG 122ATOM 17 N ILE A 3 29.160 34.436 2.919 1.00 37.80 1HSG 123ATOM 18 CA ILE A 3 29.123 33.098 3.397 1.00 34.13 1HSG 124ATOM 19 C ILE A 3 28.968 32.155 2.198 1.00 33.19 1HSG 125ATOM 20 O ILE A 3 28.088 32.330 1.368 1.00 32.74 1HSG 126

16

17

Thermus thermophilus 70S ribosome

PDB id 2WDI: 32 chains; 90700 atoms

890.000 reflections, 3.3 Å resolution

Voorhees et al (2009) Nature Structural Molecular Biology 16, 528

18

Structure Determination

Crystal h, k, l, I, (I) (x,y,z) Structure

Phases (hkl)

19

First steps of X-ray structure analysis:

• Choice of protein/organism/expression system• Expression and purification

•Crystallization (http://hamptonresearch.com)

20

Crystals

R32 & R3 P321

C2

21

Synchrotron Radiation

1. high brilliance

1. large spectral range

2. time structure

Synchrotron Radiation occurs when a charge moves at relativistic speed following a curved trajectory.

22

Data collection: Swiss Light Source Paul-Scherrer-Institut (PSI), Villigen (CH)

23

Diffraction Data Collection

The data are 3-dimensional – the crystal has to be rotated through a large angular range, and for each orientation a diffraction image is recorded on the detector. The symmetry of the diffraction pattern means that depending on the space group, e.g. 90° rotation suffice.

24

Diffraction Data Collection

h, k, l Miller indicesI(h,k,l) intensity

I(hkl) std dev of I(h,k,l)

2 pieces of information

25Murakami et al., Nature (2002)

The measured intensity (and the accuracy of its measurement) are influenced by:- Crystal quality- Poisson (counting) statistics- Beam strength and quality; exposure time- Radiation damage- Beamline setup and quality

26

Ewald sphere: Bragg's eqn in 3D

27

28

29

Theory: the electromagnetic wave

... can be mathematically described by Maxwell‘s equations (1864):

30

What does this mean?

Visualization is possible with Radiation2D – see T. Shintake, New Mathematical Method for Radiation Field of Moving Charge, Proc. EPAC (2002) http://accelconf.web.cern.ch/Accelconf/e02/PAPERS/WEPRI038.pdf,

download of binary from http://www-xfel.spring8.or.jp for Linux, Mac, Windows

31

Diffraction maths

• Superposition of all waves emanating from all electrons of an object results in a diffraction image

• Mathematical description of wave from x,y,z is f*e-2i(hx+ky+lz)

• Mathematically, addition of waves is a Fourier transform (array of complex numbers that is 1:1 related to the electrons of the object)

• The amplitude of the Fourier transform can be measured by a detector

• Its phase cannot be measured („Phase Problem“) but is required to calculate the electron density

• A regularly ordered (i.e. crystalline) sample has a diffraction image consisting of regularly spaced reflections that are characterized by their position and intensity on the detector

• All electrons of the object contribute to all reflections!

32

Atomic form factor fj

Phase (hkl)

Structure factor amplitude|F(hkl)| I(hkl)1/2

The Structure Factor Equation

F(hkl) = |F(hkl)| ei(hkl) = j fj e2i(hxj+kyj+lzj)

Complex plane

The calculation of F(hkl) from a structure (xj,yj,zj) is

just a summation of the waves originating from each atom (j) in the direction defined by (hkl).

33

Phase (hkl)

Structure factor amplitude|F(hkl)| I(hkl)1/2

The Electron Density Equation

(x,y,z) = 1/V hkl |F(hkl)| ei(hkl) e-2i(hx+ky+lz)

Mathematically inclined people will notice: this is just the Fourier „back transform“!

34

The Electron Density Equation

The electron density (x,y,z) is a three-dimensional function (with

the unit e/Å3), which describes where in the unit cell of the crystal

the electrons (and therefore the atoms) are. It is basically the

image of the structure we want to determine.

It is important to note that every reflection (hkl) of the diffraction

pattern contributes to the electron density at

each and every position (xyz) in the unit cell of the crystal.

(x,y,z) = 1/V hkl |F(hkl)| ei(hkl) e-2i(hx+ky+lz)

35

Interactive tutorials

● http://www.ysbl.york.ac.uk/~cowtan/fourier/fourier.html

● http://www.ysbl.york.ac.uk/~cowtan/sfapplet/sfintro.html

36

Detectors

● … do not measure amplitudes!● they measure deposited energy● the energy is ~|amplitude|2

● … thus, detectors don't measure phase because |amplitude * ei(hkl)| = |amplitude|

37

Data processing

● Indexing

● Integration (=summation)

● Space group determination

● Scaling

● => alle h,k,l,I(hkl),σ(Ihkl

)

2006 2007 2008 2009 2010 2011 2012 2013 2014 2015 20160

500

1000

1500

2000

2500

3000

3500

4000

4500

5000

PDB depositions

XDS

DENZO or HKL

MOSFLM

38

The Phase Problem

I(hkl) ~ F(hkl) F*(hkl)

= |F(hkl)| ei(hkl) |F(hkl)| e-i(hkl)

= |F(hkl)|2

From the diffraction pattern, we can only obtain the

intensities I(hkl) of the reflections (hkl).

Intensities are the squares of the (complex) amplitudes:

The phase (hkl) cannot be measured.

39

How to solve the Phase problem / an X-ray structure

- Direct Methods: suitable for highest resolution data and few atoms, usually not applicable for macromolecules

- Molecular Replacement: obtain a related/similar (= approximately correct) structure from the PDB, orient it correctly in the crystal lattice, identify and remove errors until the atomic model agrees with the experimental data. Not applicable to new/unknown structures. 2/3 of X-ray entries of PDB.

- Experimental Phase Determination (MIR/MAD/SAD): modify the scattering of the object, measure intensities again, work out phase from change in intensities. Requires highly accurate measurement of intensities. Always applicable. Other 1/3 of X-ray entries of PDB.