Title

1. Title ACA Summer School In Macromolecular Crystallography Chicago, July 2006 Use of anomalous signal in phasing Zbigniew Dauter

2. Scattering Normal (elastic) scattering changes with q , not with l Anomalous (resonant) scattering not dependent on q , changes with l

3. Equation Structure factor equation for normal scattering Fh = Sj fj exp(2pih.r) = |Fh|exp(ij) for anomalous scattering f = fo + f’ + if” f” is proportional to absorption and fluorescence f’ and f” related by Kramer-Kronig transformation f’(E) = 2/pò___________ dE’ E’.f”(E’) (E2 – E’2)

4. fSe Black – ideal f” curve by CROSSEC (for isolated atom) Blue – experimental f” curve with white line (affected by environment)

5. fHg Excitation spectrum of Hg (calculated theoretically)

6. f1a Structure factor – vector sum of contributions of individual atoms Fh=Sjfjexp(2pih.rj) = |Fhkl|exp(ij) B factors (ADP’s) omitted for simplicity

7. f1b PH Fh=Sjfjexp(2pih.rj) + Sjfjexp(2pih.rj)

8. f1c /// NA o Fh=Sjfjexp(2pih.rj) + Sj(fj+fj+ifj)exp(2pih.rj) i.exp(ij) = = i.[cos(j) + i.sin(j)] = i.cos(j) - sin(j) = i.sin(j+90o) + cos(j+90o) = exp[i(j +90o)]

9. f1d / // FT= FN + FA+ FA + iFA // FA is perpendicular to FA if all anomalous scatterers are of the same kind

10. f1e / // FT= FN + FA+ FA + iFA // imaginary term iFA breaks Friedel’s law |FT| = |FT| jT = -jT + - / / + -

11. f1f - F represented by its complex conjugate *F -

12. f1g more realistic proportions Bijvoet ratio <D F>/<F> ~ 3–6% for Se for S can be 0.6% (B.C. Wang) <D F>/<F> = (2.NA/NT)1/2.f”/6.7

13. sad2

14. Glucose isomerase: 1 Mn in 388 aa sad2a

15. DFanom is available from experiment DFanom = 2FA”sin(jT–jA) FA” = FA.f”/fo therefore FA ~ DFanom if DFanom is large and DFanom can be used to locate anomalous scatterers instead of FA - using Patterson synthesis - using direct methods sad2b

16. Subtilisin in P212121 , l = 1.54 Å Harker sections of anomalous diffr. Patterson Sav3 anom. Patt. Three calcium sites (f”Ca = 0.70)

17. sad1 Single-wavelength anomalous diffraction SAD phase ambiguity

18. sad3 with experimental errors

19. sad4

20. Idea of B.C.Wang (1985) sad5

21. SAD Fourier maps proper wrong overlap SAD maps solvent flattening

22. Partial structure (Sim) contribution sad6

23. Ferredoxin – 2 Fe4S4 in 55 aa sad6a

24. sad7

25. mad1

26. First SAD result – crambin Hendrickson & Teeter, 1981 6 S among 46 amino acids l=1.54 Å, f”(S)=0.56, <DF>/<F>=1.4% Crambin

27. 7 SeMAD Rice, Earnest & Brünger (2000) re-solved 7 SeMAD structures with SAD and recommended collecting first complete peak data set, and then other MAD wavelengths data, as a sort of insurance policy 1.5-wavelength approach (2002) collecting peak data and rapid phasing, if successful, postponement of next l (now it may be < 1-wavelength)

28. David Blow, Methods Enzymol.374, 3-22 (2003) “How Bijvoet made the difference ?” (written probably in 2001) . . . The future of SAD It seems likely, however, that the various improvements to analyze MAD data more correctly are fading into insignificance. The MAD technique is losing ground to SAD. . . . Blow

29. SAD/(SAD+MAD) structures deposited in PDB PDB statistics 11% 22% 32% 45% 55% 2001 2002 2003 2004 2005

30. Proteinase K 279 amino acids, 1 Ca + 10 S f”(S) = 0.23e, f”(Ca) = 0.35e Proteinase K

31. Prot. K SHELXD Anomalous difference Fourier Results of SHELXD

32. Experimental map after SHELXE Prot. K SHELXE Mean phase error 27.5o

33. Effect of data redundancy Prot. K redundancy

34. Indicators Indicators of anomalous signal - Bijvoet amplitude or intensity ratio - Ranom - c2 difference if Friedels merged - list of outliers - measurability - anomalous signal to noise ratio - correlation between data sets - relation between signal in acentrics and centrics

35. Bijvoet ratio and Ranom GI Bijvoet ratio <DF±>/<F> = (2 NA/NP)1/2. (fA”/6.7) Ranom = S (F+ - F-) / S (F+ + F-)/2 Four data sets from glucose isomerase 1 Mn in 375 a.a.

36. Merging c2 difference Chi2 and Rmerge crystal soaked in Ta6Br12 cluster compound blue – c2 red - Rmerge when Friedels independent orange – c2 green - Rmerge when Friedels equivalent

37. List of outliers Outliers If redundancy if high enough, clearly shows anomalous differences

38. Signal to noise ratio (DF±)/s(F) for proteinase K Signal to noise requires proper estimation of s’s (which is not trivial) signal is meaningful, if this ratio is > 1.3

39. Correlation between data setscorr (DF1±, DF2±) Correlation F1 and F2 may be at different MAD l or merged partial SAD data If higher than 25 - 30% - meaningful (advocated by George Sheldrick for SHELXD resolution cutoff)

40. No indicator is fully satisfactory No indicator these indicators of anomalous signal do not tell if the signal is sufficient for structure solution e.g. difficulties with Cu-thionein (Vito Calderone) 8 Cu in ~53 a.a. (12 Cys), P4332 eventually solved from extremely redundant data

41. Conclusion only one satisfactory indicator of anomalous signal exists: successful structure solution nowadays the structure can be solved in few minutes, when the crystal is still at the beam line