Protein crystallography. Garry Taylor

Transcription

1 Protein crystallography Garry Taylor

2 X-ray Crystallography - the Basics Grow crystals Collect X-ray data Determine phases Calculate ρ-map Interpret map Refine coordinates Do the biology.

3 Nitrogen at -180 C X-rays Rotate crystal Detector

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5 European Synchrotron Radiation Facility Grenoble, France

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7 X-ray Crystallography - the Basics Grow crystals Collect X-ray data Determine phases Calculate ρ-map Interpret map Refine coordinates Do the biology.

8 Importance of the phase α

9 Fourier Summation Each term is added in with the correct intensity (amplitude) and phase. The object is shown at the foot. The effect of successive summations on the final structure : the more terms included, the higher the resolution.

10 Diffraction from a Series of Objects - 1

11 Diffraction from a Series of Objects - 2

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13 Diffraction by a Crystal The crystal lattice gives rise to the observed spacing between the spots on the diffraction pattern The intensities of the diffraction maxima contain the information about the molecule or The molecular transform is sampled (only observable) at the lattice points (Bragg peaks)

14 Resolution Depends upon the Number of Terms Used The duck (top l.) gives the diffraction pattern top r.). If one recovers the object using only a fraction of the diffracted data, detail is lost (centre and bottom). With X-rays, the same applies and the resolution achieved is usually quoted in Å or nm, the closest spacing of the sets of planes giving rise to the diffraction pattern.

15 Electron Density Equation F hkl = Σ f r.exp{2πi(hx r + ky r + lz r )} summed over all atoms in the unit cell. The Fourier Transform of this equation is ρ xyz = 1/V.Σ F hkl.exp{-2πi(hx r + ky r + lz r )} summed over all measured reflections. ρ xyz = 1/V.Σ F hkl.exp{iα hkl }.exp{-2πi(hx r + ky r + lz r )} Of course, F hkl (I hkl ) 1/2½ but α hkl cannot be measured!

16 Scattering Factors I Interference between electrons within an atom leads to an angular dependent scattering

17 Scattering Factors II In addition, we add a temperature factor, B, to account for atomic motion. This gives further fall-off in scattered intensity with increasing angle. We replace f r by f r.exp{-b r.sin 2 θ/λ 2 } B is sometimes called the Debye-Waller factor. B = 8.π 2.u 2 /3

18 Thermal Motion is Reflected in the Crystallographic B-factors Thermal Motion is reduced by lowering T Static Disorder remains at low temperature

19 Phasing Techniques Multiple Isomorphous Replacement (MIR) Single Isomorphous Replacement (SIR, SIRAS) Multiwavelength Anomalous Dispersion (MAD) Molecular Replacement (MR)

20 The Effect of a Heavy Atom The diffraction pattern has parts with phases of 0º and others with phases of 180º. If a large atom is added with a phase of 0º, then it will add to like phases and subtract from phases of 180º. It is thus possible to determine the phases of each part of the diffraction pattern. A similar technique is used with X-rays (though things are not quite so straightforward!)

21 The Effect of Added Heavy Atom Two diffraction photos superposed but displaced vertically. The differences caused by the addition of an Hg 2+ ion can be seen. Similar effects occur, though less noticeably, with substrates and other ligands.

22 Solving the structure Native crystals Computer Calculate electron density map Crystals soaked in heavy metals - isomorphous to native

23 MAD method of phasing.. example of SeMet Express protein in Met - strain of E. coli Add selenomethionine (Se-Met) to growth media Se-Met becomes incorporated (Se replaces S, 16 electrons v 34 electrons) Go to synchrotron Collect x-ray data around the absorption edge of Se (~0.98Å) - up to 3 wavelengths - advantage is perfect isomorphism Determine positions of Se atoms Use this information to obtain phases Calculate electron density map

24 X-ray Crystallography - the Basics Grow crystals Collect X-ray data Determine phases Calculate ρ-map Interpret map Refine coordinates Do the biology.

25 Electron Density Equation F hkl = Σ f r.exp{2πi(hx r + ky r + lz r )} summed over all atoms in the unit cell. The Fourier Transform of this equation is ρ xyz = 1/V.Σ F hkl.exp{-2πi(hx r + ky r + lz r )} summed over all measured reflections. ρ xyz = 1/V.Σ F hkl.exp{iα hkl }.exp{-2πi(hx r + ky r + lz r )} Of course, F hkl (I hkl ) 1/2½ but α hkl cannot be measured!

26 ...low resolution electron density map using 4000 measurements.begin to see blobs of protein

27 ..using 70,000 intensities...high resolution electron density map begin to see individual atoms..

28 X-ray Crystallography - the Basics Grow crystals Collect X-ray data Determine phases Calculate ρ-map Interpret map Refine coordinates Do the biology.

29 Tracing the initial map bones

30 Tracing the chain With a high quality 2.5Å, or better, map this can now be automated to find every atom in the structure including water molecules

31 Fitting sidechains

32 Resolution 6Å 1Å

33 Resolution 1Å 2.5Å 3Å 4Å

34 X-ray Crystallography - the Basics Grow crystals Collect X-ray data Determine phases Calculate ρ-map Interpret map Refine coordinates Do the biology.

35 What is refinement? Refinement is adjusting the model parameters to optimise some target value e.g. Σ w (F obs F calc ) 2 hkl F calc : F hkl = Σ f r.exp{-b r.sin 2 θ/λ 2 } exp{2πi(hx r + ky r + lz r )} Parameters: atomic coordinates (x,y,z) and temperature factors (B) of all the atoms in protein, ligands, water, ions..etc..

36 Have we got enough observations to refine? For small molecules resolution < 1Å, typically 7 observations per parameter. No problem. For a protein with about 1000 atoms we have 4000 parameters (1000 x,y,z positions and 1000 B factors). At about 2.7Å we have about 4000 reflections (observations) just enough to mathematically solve the equations. We add restraints to improve the obs/param ratio. C-C bond 1.54Å, CH 2 -CH 2 -CH 2 bond 109, rings flat, peptide bond flat, etc..etc..

37 Restraining the stereochemistry.. Refinement involves simultaneously minimising the above equation, and minimising the difference between the observed and calculate F: Σ (F obs - F calc ) 2

38 Monitoring the refinement: the R-factor R = Σ ( F obs - F calc ) hkl Σ F obs hkl Perfect model would give R=0.0 - in reality for proteins, R 0.20

39 Monitoring the stereochemistry