Structure Determination and Analysis : X-ray Crystallography

1. Structure Determination and Analysis : X-ray Crystallography

2. Source Sample Detector Diffraction Intensity of diffracted beam X-rays

3. Energy = hc λ

4. X-rays • Unlike using a light microscope, there is no way of re-focusing diffracted x-rays. • Instead we must collect a diffraction pattern (spots). • It is possible to translate information in the diffraction pattern into atomic structure using Bragg’s law, which predicts the angle of reflection of any diffracted beam from specific atomic planes

5. A typical crystallography experiment Pure protein Grow crystal Characterize crystals Collect diffraction data Solve phase problem Calculate electron density map Build/rebuild model Refine model Analyze structure

6. The Beginning

7. Principles of X-ray diffraction What is a crystal? • The unit cell is the basic building block of the crystal • The unit cell can contain multiple copies of the same molecule whose positions are governed by symmetry rules

8. Proteins and crystallisation • What type of protein is it? Has anything similar been crystallized before? • Proteins must be pure (> 99%) & fully folded Check the activity of your protein if you have an assay Check folding by other spectroscopic methods • Proteins must be homogenous & monodispersed. • Need large amount (mg quantities) • Is it stable ( salt, pH, temp) • Will modifications have to be made?

9. Cover-slip sealed with vacuum grease Protein in “Hanging drop” Precipitant • Crystallisation of proteins ‘controlled’ precipitation of the protein. • Protein aggregates associate & form intermolecular contacts that resemble those found in the final crystal. Aggregates reach the critical nuclear size, growth proceeds by addition of molecules to the crystalline lattice. • The processes of nucleation and crystal growth both occur in supersaturated solutions. • Process controlled by: • Temp • pH • Salt conc • Precipitants (PEG, ethanol)

10. Diffraction Apparatus

11. Synchrotron radiation More intense X-rays at shorter wavelengths mean higher resolution & much quicker data collection

12. Experimental setup

13. Mounting crystals Remove cover slip and fish out crystal with a small nylon loop Surface tension of the liquid in the loop holds crystal in place Mount loop on goniostat in a stream of nitrogen gas

14. Diffraction • Each image represents the rotation of the crystal 1 degree in the X-ray beam. • Each images gives us the position of each spot relative to all the others & there intensity. • Intensity = square of amplitude.

15. Diffraction Principles nl = 2dsinq

16. Diffraction Principles Corresponding Diffraction Pattern A string of atoms

17. X-ray detector X-ray source The reciprocal lattice and the geometry of diffraction

18. Spacing between diffraction spots defines unit cell 1/b 1/a

19. X l A Y Z ? X Waves & the phase problem The amplitudes of the diffracted X-rays can be experimentally measured, but the phases cannot = phase problem. i.e. we don’t know the phase of each diffracted ray relative to the others!

20. The Phase Problem • Diffraction data only records intensity, not phase information (half the information is missing) • To reconstruct the image properly you need to have the phases (even approx.) • molecular replacement • direct methods • isomorphous replacement • anomolous dispersion

21. Structure factors & Fourier transforms unit cell F (h,k,l) = Vx=0 y=0 z=0 (x,y,z).exp[2I(hx + ky + lz)].dxdydz A reflection electron density All reflections phase (x,y,z) = 1/V hkl F (h,k,l)exp[2I(hx + ky + lz) + i(h,k,l) Electron density amplitude At a point • The vector (amplitude and phase) representing the overall scattering from a particular set of Bragg planes is termed the structure factor (F). • Structure factors for various points on the crystal lattice correspond to the Fourier transform of electron density within the unit cell and vice-versa.

22. Fourier Transform of a molecule F T

23. Fourier Transform of a crystal

24. The Phase Problem • Diffraction data only records intensity, not phase information (half the information is missing) • To reconstruct the image properly you need to have the phases (even approx.) • molecular replacement • direct methods • isomorphous replacement • anomolous dispersion

25. Molecular replacement • Requires a starting model for structure • Can calculate back from structure to electron density to structure factors • Works if model is 30 to 40 % identical to correct answer

26. Molecular Replacement By determining the correct orientation and position of a molecule in the unit cell using a previously solved structure as a ‘search model’. This model can then be used to calculate phases

27. Isomorphous replacement (IR) • Provides indirect estimates of the protein phase angles by observing the interference effects of the intensities on scattered beams by a heavy atom marker. • All the electrons in the heavy atom will scatter essentially in the same phase. • We can solve the positions of these heavy atoms because they are few in number and strong in signal. • Using this estimate we can deduce the positions of the protein atoms and their phases

28. Anomalous scattering • Scattering information of an atom whose absorption frequency is close to the wavelength of the source beam produces phase information • Resolved anomalous scattering requires intensity measurements at one wavelength • Multi-wavelength anomalous dispersion, requires intensity measurements at several wavelengths

29. Using the structure factor calculation we can produce electron density maps for the whole protein. • We then fit our protein model (co-ordinates X,Y,Z) inside the map.

30. Resolution 1.2 Å 2 Å 3 Å

31. Resolution 6Å: Outline of the model, feature such as helices can be identified. 3Å: Can trace polypeptide chain using sequence data, establish folding topology. Assign side chains. 2Å: Accurately establish mainchain conformation, assign sidechains without sequence data, I.d water molecules. 1.5Å : Individual atoms are almost resolved, detailed discription of water structure. 1.2Å: Hydrogen atoms may become visible.

32. Final Structure But the work is not over yet!

33. Refinement • The process of building and rebuilding a model can cause many errors in the structure. • Bond length, • Bond angle • Atomic clashes etc • It is necessary to subject the structure to refinement in order to remove these errors and produce a better structure. • Minimization • Thermal parameters • In order to further improve the model, it is refined using a simulated annealing protocol • Refinement progress is monitored by following the agreement between the the observed data ( data collected) and the calculated data (data calculated from current model) =R factor

34. Quality of the structure? • R-factor The agreement between the the observed data (data collected) and the calculated data (data calculated from current model) the lower the number the better; typically around 20% • Resolution The higher the resolution the more detail that can be seen 3.0Å is fairly low whilst 1.1Å is approaching atomic resolution • B-factor Measure of thermal motion. i.e. how much energy each atom contains. Gives us information on mobility & stability • Rms deviation Deviation of bond lengths & angles from ideal

35. Rms deviation of bond length & bond angle Deviation of bond lengths & angles from ideal. All based on the geometry of small molecules. Rms deviation for bond lengths should be less than 0.02Å and less than 4º for bond angles Determined using a Ramachandran plot.

36. Absorption of Light

37. Absorption in the UV and visible range • Protein chromophores: • Peptide bond • Amino acid side chains • Prosthetic groups • Amino acid side chain absorbance: • Asp, Glu, Asn, Gln, His and Arg have transitions at the same wavelength where peptide absorbs • Peptide bond absorbance: • 210 nm due to n   transition • 190 nm due to    transition Protein concentration can be measured by measuring absorbance at 280 nm and by assuming that 1 mg ml-1 solution of protein has absorbance of 1.0

38. Absorption and emission spectra of individual tryptophan residues, in the absence of energy transfer

39. Fourth derivative absorption spectrum • Fourth derivatives ofthe absorption spectra have been documented as a valuable toolfor studying structural changes in proteins. • Proteinfourth derivative spectra have been shown to be very sensitiveto changes in the microenvironment (polarity, hydration, hydrophobicinteractions, packing density) of tyrosine and tryptophan residues Chauhan and Mande, Biochem J, 2001

40. Measurements of conformational properties using optical activity

41. Linearly polarised light Right circular polarisation Left circular polarisation

42. Nearly all molecules of life are optically active • There are four ways that an optically active sample can alter the properties of transmitted light: optical rotation, ellipticity, circular dichroism, circular birefringence Linear Elliptical Circular

43. After passing through an optically active absorbing sample, the light is changed in two aspects: • The maximal amplitude E is no longer confined to a place, instead it traces an ellipse • Ellipticity = tan-1 (minor/major axis) • The orientation of the ellipse is an indication of optical activity. If the sample did not absorb any light, the ellipse would such small axial ratio that it would be equivalent to a plane-polarised light. In this case we will say that the plane polarised light has been rotated. • Orientation of the ellipse is the optical rotation. Optical rotation as a function of wavelength is called the optical rotatory dispersion (ORD).

44. Circular Dichroism

45. CD spectrum of a protein

47. Where can Circular Dichroism be used?

48. Measurements of conformational properties using fluorescence

49. Fluorescence • Chromophores are components of molecules which absorb light • They are generally aromatic rings

50. Fluorescence Jablonski Diagram Singlet States Triplet States Vibrational energy levels S2 Rotational energy levels Electronic energy levels T2 S1 IsC ENERGY T1 ABS FL I.C. PH IsC S0 [Vibrational sublevels] ABS - Absorbance S 0.1.2 - Singlet Electronic Energy Levels FL - Fluorescence T 1,2 - Corresponding Triplet States I.C.- Nonradiative Internal Conversion IsC - Intersystem Crossing PH - Phosphorescence