H.F. Fan & Y.X. Gu Beijing National Laboratory for Condensed Matter Physics

1. Direct Methods in Protein Crystallography H.F. Fan & Y.X. Gu Beijing National Laboratory for Condensed Matter Physics Institute of Physics, Chinese Academy of Sciences P.R. China

2. • The phase problem & direct methods • Sayre’s equation & tangent formula • Use of direct methods in protein crystallography • Direct-method SAD/SIR phasing • Direct-method aided model completion

3. The Phase Problem

4. The Point of View from Direct Methods: Phases are not missing but just hidden in the magnitudes!

5. What is a Direct Method ? It derives phases directly from the magnitudes.

6. Why it is possible ?

7. Each reflection is accompanied by an unknown phase, but yields two simultaneous equations. Hence in theory, a diffraction data set of 3n reflections can be used to solve a structure with n independent atoms (assuming 3 parameters per atom). That is to say, the phases may, at least in theory, be derived from a large enough set of magnitudes given the known quantities of atomic scattering factors. Why it is possible ?

8. Sayre’s Equation Conditions for the Sayre Equation to be valid 1. Positivity 2. Atomicity 3. Equal-atom structure

9. The tangent formula k h, h’ = 2s3s2-3/2|E h E h’E h - h’ | a sinb = å h’ k h, h’ sin (j h’+j h - h’) a cosb = å h’ k h, h’ cos (j h’+j h - h’)

10. Use of direct methods in Protein Crystallography •Locating heavy atoms •Ab initio phasing of protein diffraction data at 1.2Å or higher resolution SnB, SHELXD, ACORN  •Direct-method aided SAD/SIR phasing and structure-model completion OASIS

11. Direct methods breaking the SAD/SIR phase ambiguity

12. Bimodal distribution from SAD Cochran distribution Sim distribution Peaked at Peaked at any where from 0 to2p The phase of F” Phase information available in SAD

13. P+ formula - + Acta Cryst. A40, 489-495 (1984) Acta Cryst. A40, 495-498 (1984) Acta Cryst. A41, 280-284 (1985) Reducing the phase problem to a sign problem Breaking the SAD/SIR phase ambiguity by the Cochran distribution incorporating with partial structure information

14. Direct-method phasing of the 2Å experimental SAD data of the protein aPP Avian Pancreatic Polypeptide Space group: C2 Unit cell: a = 34.18, b = 32.92, c = 28.44Å; b = 105.3o Protein atoms in ASU: 301 Resolution limit: 2.0Å Anomalous scatterer: Hg (in centric arrangement) Wavelength: 1.542Å (Cu-Ka) Df” = 7.686 Locating heavy atoms & SAD phasing: direct methods Acta Cryst. A46, 935 (1990) Data courtesy ofProfessor Tom Blundell

15. Further developments •Direct-method SAD/SIR phasing combined with density modification OASIS + DM, OASIS + RESOLVE, SOLVE/RESOLVE + OASIS  •Direct-methods aided dual-space structure-model completion ARP/wARP + OASIS, PHENIX + OASIS

16. TTHA1634 from Thermus thermophilus HB8 Space group: P21212 Unit cell: a = 100.57, b = 109.10, c = 114.86Å Number of residues in the AU: 1206 Resolution limit: 2.1Å Multiplicity: 29.2 Anomalous scatterer: S (22) X-ray wavelength: l = 1.542Å (Cu-Ka) Bijvoet ratio: <|DF|>/<F> = 0.55% Phasing method: A single run of OASIS2006 + DM (Cowtan) Model building: ARP/wARP Ribbon model plotted by PyMOL ARP/wARP found 1178 of the total 1206 residues, all docked into the sequence. Data courtesy ofProfessor Nobuhisa Watanabe Department of Biotechnology and Biomaterial Chemistry, Nagoya University, Japan

17. Dual-space fragment extension Real-space fragment extension RESOLVE BUILD and/or ARP/wARP Reciprocal-space fragment extension OASIS + DM Partial model OK? No Yes End Partial structure

18. Xylanase S-SAD Synchrotron l = 1.49Å Xylanase S-SAD Synchrotron l = 1.49Å Cycle 3 95% Cycle 0 42% Lysozyme S-SAD Cr-Ka Lysozyme S-SAD Cr-Ka 98% Cycle 6 52% Cycle 0 Azurin Cu-SAD Synchrotron l = 0.97Å Azurin Cu-SAD Synchrotron l = 0.97Å 99% Cycle 6 25% Cycle 0 Glucose isomerase S-SAD Cu-Ka Glucose isomerase S-SAD Cu-Ka Cycle 0 52% Cycle 4 97% Cr-Ka Se, S-SAD Alanine racemase Cr-Ka Se, S-SAD Alanine racemase 17% Cycle 0 97% Cycle 6 Ribbon models plotted by PyMOL Data courtesy ofProfessor N. Watanabe, Professor S. Hasnain, Dr. Z. Dauter and Dr. C. Yang

19. Dual-space fragment extension without SAD/SIR information Direct-method aided MR-model completion

20. Yes No Model completion by ARP/wARP or PHENIX Density modification by DM Phase improvement by OASIS MR model OK? Partial structure End

21. P+ > 0.5 j” + Dj = jmodel <|Dj|> ~ 90o <2|Dj|> ~ 180o |Dj| j” |Dj| • P+ < 0.5 • j” - Dj • jmodel - 2|Dj|

22. MR-model completionof 1UJZ Space group: I222 a=62.88, b=74.55, c=120.44 Number of residuals in AU: 215 Resolution limit: 2.1Å

23. ARP/wARP-OASIS-DM iteration 1UJZ Cycle 7 Cycle 5 Cycle 1 Cycle 3 201 residues all with side chains MR model Final model 46 residues 13 with side chains 215 residues ARP/wARP-DM iteration Cycle 2 Cycle 1 Ribbon models plotted by PyMOL

24. MR-model completionof an originally unknown protein Space group: P212121 a=71.81, b=81.40, c=108.95Å Number of residuals in AU: 728 Solvent content: 0.37 Resolution limit: 2.5Å

25. R-factor: 0.34 R-free: 0.44 No. of residuals: 479 with side chains: 479 Starting model

26. R-factor: 0.33 R-free: 0.40 No. of residuals: 503 with side chains: 503 After phenix.autobuild

27. R-factor: 0.24 R-free: 0.30 No. of residuals: 597 with side chains: 588 After 4 cycles of oasis-phenix

28. What’s the low resolution limit for direct methods?

29. SAD phasing at different resolutions TTHA1634 Cu-Ka data, <|DF|>/<F> ~ 0.55% Very good Marginally traceable 2.1Å 3.5Å 4.0Å Good 3.0Å Still informative Maps at 1s phased by a single run of OASIS + DM (Cowtan) plotted by PyMOL

30. Combining SOLVE/RESOLVE and OASIS + DM dealing with low resolution SIR/SAD data

31. R-phycoerythrin SIR data from the native and the p-chloromercuriphenyl sulphonic acid derivative J.Mol.Biol.262721-731 (1996) Chinese Physics 16, 3022-3028 (2007) Maps plotted by PyMOL Space group: R3Unit cell: a = b = 189.8, c = 60.0Å;g = 120oNumber of residues in the ASU: 668 Resolution limit:2.8ÅReplacing atoms: Hg X-rays: Cu-Ka, λ = 1.542Å SOLVE/RESOLVE & OASIS + DM SOLVE/RESOLVE

32. Tom70p Nature Structural & Molecular Biology 13, 589-593 (2006) Chinese Physics B 17, 1-9 (2008) Space group: P21Unit cell: a = 44.89, b = 168.8, c = 83.4Å;    β = 102.74oNumber of residues: 1086 Resolution limit: 3.3ÅMultiplicity: 3.3Anomalous scatterer: Se (24)X-rays: Synchrotron, λ = 0.9789Å, Δf" = 6.5Bijvoet ratio: <|ΔF|>/<|F|> = 4.3% Maps plotted by PyMOL SOLVE/RESOLVE & OASIS + DM SOLVE/RESOLVE & OASIS + DM SOLVE/RESOLVE SOLVE/RESOLVE

33. OASIS-2006 Institute of Physics Chinese Academy of Sciences Beijing 100080, P.R. China http://cryst.iphy.ac.cn http://www.ccp4.ac.uk/prerelease

35. Acknowledgements Professor Zhengjiong Lin Institute of Biophysics, Chinese Academy of Sciences, Beijing,China Drs Y. He1, D.Q. Yao1, J.W. Wang1, S. Huang1, J.R. Chen1, Q. Chen2, H. Li3, Prof. T. Jiang3, Mr. T. Zhang1, Mr. L.J. Wu1 & Prof. C.D. Zheng1 1 Beijing National Laboratory for Condensed Matter Physics, Institute of Physics, Chinese Academy of Sciences, China 2 National Laboratory of Protein Engineering and Plant Genetic Engineering, Peking University, Beijing, China 3 Institute of Biophysics, Chinese Academy of Sciences,Beijing China The project is supported by the Chinese Academy of Sciences and the 973 Project (Grant No 2002CB713801) of the Ministry of Science and Technology of China.

36. Thank you!