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

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

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/p ò ___________ dE’ E’.f”(E’) (E2 – E’2)

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

Excitation spectrum of Hg (calculated theoretically)

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

Fh = Sj fj exp(2pih.rj) + Sj fj exp(2pih.rj) P H f1b Fh = Sj fj exp(2pih.rj) + Sj fj exp(2pih.rj) P H

Fh = Sj fj exp(2pih.rj) + Sj (fj +fj+ifj)exp(2pih.rj) f1c Fh = Sj fj exp(2pih.rj) + Sj (fj +fj+ifj)exp(2pih.rj) N A o / // 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)]

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

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

f1f F represented by its complex conjugate *F -

more realistic proportions 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

sad2

Glucose isomerase: 1 Mn in 388 aa sad2a Glucose isomerase: 1 Mn in 388 aa

DFanom is available from experiment DFanom = 2 FA” sin(jT – jA) sad2b DFanom is available from experiment DFanom = 2 FA” 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

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

anomalous diffraction sad1 Single-wavelength anomalous diffraction SAD phase ambiguity

with experimental errors sad3 with experimental errors

sad4

sad5 Idea of B.C.Wang (1985)

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

Partial structure (Sim) contribution sad6 Partial structure (Sim) contribution

sad6a Ferredoxin – 2 Fe4S4 in 55 aa

sad7

mad1

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%

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)

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.

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

Proteinase K 279 amino acids, 1 Ca + 10 S f”(S) = 0.23e, f”(Ca) = 0.35e Proteinase K Beamline SER-CAT 22-ID Unit-cell parameters (Å) a=67.55, c=106.88 Space group P43212 Wavelength (Å) 0.98 Distance (mm) 150 Number of images 660 Oscillation (°)/exposure time (s) 0.5 / 2 Transmission 10% Resolution (Å) 50-1.27 (1.32-1.27) Number of unique reflections 63537 Completeness (%) 96.4 (92.7) Overall I/σI 106.1 (31.5) Redundancy 27.1 (26.3) Rmerge (%) 3.3 (13.0)

Anomalous difference Fourier Results of SHELXD Rank Position Height 1 Prot. K SHELXD Results of SHELXD Rank Position Height 1 Ca 1.0000 2 Cys73 0.5105 3 Met111 0.4967 4 Met225 0.4571 5 Met55 0.4560 6 Cys178 0.4417 7 Met238 0.4341 8 Cys123 0.3938 9 Cys249 0.3862 10 Met154 0.3861 11 Cys34 0.3696 12 0.1400

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

Effect of data redundancy Prot. K redundancy Effect of data redundancy Dataset Label Peak Height (σ) Number of sites SHELXD Ca <10S> SO42- 045 25.77 10.48 5.47 - 060 29.07 11.68 6.22 090 35.71 13.95 6.23 120 39.51 15.59 6.54 3 150 43.59 17.20 6.96 8 180 46.81 18.64 7.30 11 210 48.93 19.27 7.44 240 52.17 20.51 7.62 270 54.56 21.24 7.87 300 56.37 21.79 7.80 330 58.13 22.29 8.19

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

Bijvoet ratio and Ranom GI Bijvoet ratio Bijvoet ratio and Ranom <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.

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

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

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

Correlation between data sets corr (DF1±, DF2±) 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)

No indicator is fully satisfactory 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

only one satisfactory indicator of anomalous signal exists: 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