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EMBO course Grenoble, June 2007

EMBO course Grenoble, June 2007. Phasing based on anomalous diffraction Zbigniew Dauter. Structure factor. F P (h) = S j f j . exp (2 p ih • r j ) f j = f º j ( q ) . exp(-B . sin 2 q / l 2 ). Structure factor with heavy atoms.

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EMBO course Grenoble, June 2007

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  1. EMBO courseGrenoble, June 2007 Phasing based on anomalous diffraction Zbigniew Dauter

  2. Structure factor FP(h) = Sj fj. exp (2pih•rj) fj = fºj(q). exp(-B.sin2q/l2)

  3. Structure factor with heavy atoms FPH(h) = Sj fj. exp (2pih•rj) + Sk fk. exp (2pih•rk) FPH(h) = FP(h) + FH(h) |FPH|≠ |FP| + |FH|

  4. Anomalous diffraction normal scattering q q anomalous(resonant) scattering

  5. Structure factor and anomalous effect F(h) = Sj fj.exp(2pih•rj) fj = fºj(q) + f’j (l) + i.f”j (l) Anomalous correction f” is proportional to absorption and fluorescence and f’ is its derivative

  6. l-dependence of anomalous correctionsfor selenium

  7. Structure factor and anomalous vectors FT(h) = Sj fj. exp (2pih•rj) +Sk(fok + f’k + i.f”k). exp (2pih•rk)

  8. Structure factor and anomalous effect FT = FN + FA + F’A + i.F”A Anomalous correction i.f” shifts the phase of atomic contribution in positive direction

  9. Friedel pair – F(h) and F(-h) Anomalous correction f” causes the positive shift of phase of both F(h) and F(-h) in effect |FT(h)| ≠ |FT(-h)| jT(h) ≠ -jT(-h)

  10. Friedel pair – F(h) and *F(-h) |FT(h)| ≠ |FT(-h)| jT(h) ≠ -jT(-h)

  11. Friedel pair – more realistically fº(S) = 16 f”(S) = 0.56 for l = 1.54 Å fº(Hg) = 82 f”(Hg) ≈ 4.5 for l < 1.0 Å

  12. Bijvoet difference DF±= |F+| - |F-|

  13. DF depends on phase difference DF±= 2F”A DF±= 0

  14. Sinusoidal dependence of DF and FA DF±≈2.F”A.sin (jT- jA)

  15. Partial structure of anomalous atoms Anomalous atoms can be located by Patterson or direct methods, since: DF±≈2.F”A.sin (jT- jA) |DF±|2≈ 4.dA2.FA2.sin2 (jT - jA) ≈ 2.dA2.FA2 - 2.dA2.FA2.cos[2(jT – jA)] where dA = f”A/foA sin2a = 1/2 - 1/2.cos2a and anomalous atoms are mutually distant (even low resolution is “atomic”)

  16. Two solutions for a single l (SAD) If anomalous sites are known (DF±, FA, F’A, F”A,jA) there are two possible phase solutions

  17. Selection of mean phase |FSAD| = |FT|.cos[(1/2)(jT1 – jT2)] jSAD = (1/2)(jT1 + jT2) FOM = cos[(1/2) (jT1 – jT2)]

  18. Electron density is then a superpositionof correct structure and noise F1 F2 F1 + F2 iterative solvent flattening indicates correct phase

  19. With errors in measured F+ snd F- With measurement errors and inaccurate anomalous sites the phase indications are not sharp

  20. Phase probability Each phase has then certain probability

  21. Symmetric SAD probability The phase probability is symmetric around jSAD has two maxima

  22. Two solutions not equivalent Vectors FN have different lengths Solution with jT closer to jA is more probable (Sim contribution)

  23. Total SAD probability One solution is slightly more probable (depending how large is the substructure)

  24. Excitation spectrum of Se(not fluorescence spectrum) inflection f’ = -10.5 f” = 2.5 peak f’ = -4.0 f” = 8.0 remote f’ = -0.5 f” = 4.5

  25. Typical MAD wavelengths inflection f’ = -10.5 f” = 2.5 peak f’ = -4.0 f” = 8.0 remote f’ = -0.5 f” = 4.5

  26. Typical MAD wavelengths inflection f’ = -10.5 f” = 2.5 peak f’ = -4.0 f” = 8.0 remote f’ = -0.5 f” = 4.5

  27. MAD 1-st phase

  28. MAD 2-nd phase

  29. MAD two phases

  30. Contributors in analytical MAD approach

  31. Analytical MAD approach(Karle & Hendrickson) FT(±)2 = FT2 + a(l) . FA2 + b(l) . FT.FA .cos (jT - jA) ± c(l) . FT .FA . sin (jT - jA) a(l) = (f’2 + f”2)/fo2 b(l) = 2.f’/fo c(l) = 2.f”/fo Three unknowns: FT, FA and (jT - jA) - system can be solved, and FA used for finding anomalous sites jA (and jT) can then be calculated

  32. MAD treated as MIR Data from different l can be treated as separate derivatives and one native and universal programs (SHARP, SOLVE etc) used for phasing - perfect isomorphism (one crystal) - synchrotron necessary (tunable l) - radiation damage (with long exposures)

  33. Summary MIR MAD SAD home lab or SR synchrotron home lab or SR several crystals one crystal, 2-3 data one data set non-isomorphism perfect isomorphism perfect isomorphism radiation damage ? radiation damage rad. dam. less acute tedious h.a. search easier easy, if works All methods easy thanks to excellent programs SHELXD/E, SnB, SHARP, SOLVE, CNS, PHENIX, CCP4 etc.

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