Direct Methods By Fan Hai-fu, Institute of Physics, Beijing cryst.iphy.ac

1. Direct Methods By Fan Hai-fu, Institute of Physics, Beijing http://cryst.iphy.ac.cn 1. Introduction 2. Sayre’s equation and the tangent formula 3. Further developments in the 1990’s 4. Recent progress in solving proteins 1 2 3 4

2. The Phase Problem

3. Direct methods: Deriving phasesdirectlyfrom the magnitudes

4. Why it is possible ?

5. 1947 D. Harker & J. Kasper 1952 D. Sayre 1950’s J. Karle & H. Hauptman 1964 I. L. Karle & J. Karle 1970’s M. M. Woolfson 1985 Nobel Prize awarded to H. Hauptman & J. Karle

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

7. Positivity: Atomicity:

8. Equal-atom structure:

9. Sign relationship¾ an important outcome of the Sayre equation ShSh’Sh - h’ or S-hSh’Sh - h’  +1 Cochran, W. & Woolfson, M. M. (1955). Acta Cryst.8, 1-12.

10. The Probability distribution of three-phase structure invariants ¾Cochran distribution Cochran, W. (1955). Acta Cryst.8, 473-478.

11. The tangent formula 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’)

12. The tangent formula (continued) Maximizing P(jh) Þ jh=b 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’) tanb

13. Direct methods in the 1990’s IUCr Newsletters Volume 4, Number 3, 1996 IUCr Congress Report (pp. 7-18) (page 9) The focus of the Microsym. Direct Methods of Phase Determination (2.03) ¼¼ was the transition of direct methods application to problems outside of their traditional areas from small to large molecules, single to powder crystals, periodic to incommensurate structures, and from X-ray to electron diffraction data. . . . . .Suzanne Fortier http://cryst.iphy.ac.cn

14. Direct methods in protein crystallography 1. For ~1.2Å (atomic resolution) data Sake & Bake Hauptman et al. Half baked Sheldrick et al. Acorn Woolfson et al. 2. For ~3Å SIR, OAS and MAD data OASIS Fan et al.

15. Direct-method phasing of anomalous diffraction 1. Resolving OAS phase ambiguity 2. Improving MAD phases

16. Mlphare + dm Oasis + dm OAS distribution Sim distribution Solvent flattening OAS distribution Sim distribution Cochran distribution Solvent flattening The first example of solving an unknown protein by direct-method phasing of the 2.1Å OAS data Rusticyanin, MW: 16.8 kDa; SG: P21; a=32.43, b=60.68, c=38.01Å ; b=107.82o ; Anomalous scatterer: Cu

17. Direct-method phasing of anomalous diffraction 1. Resolving OAS phase ambiguity 2. Improving MAD phases

18. Direct-method aided MAD phasingSample: yeast Hsp40 protein Sis1 (171-352) Space group: P41212Unit cell:a = 73.63, c =80.76Å Independent non-H atoms: 1380 Number of Se sites in a.s.u: 1 Wavelength (Å): 1.0688 0.9794 0.9798 0.9253 Resolution: 30 ~ 3.0 Å Unique reflections: 4590

19. Direct-method aided MAD phasing (yeast Hsp40 protein Sis1: 171-352) 2w-DMAD 4w-MAD

20. Direct-method aided MAD phasing (yeast Hsp40 protein Sis1: 171-352) DMAD (2w) MAD (4w)

21. Direct-method aided MAD phasing (yeast Hsp40 protein Sis1: 171-352) DMAD (2w) MAD (4w)

22. Acknowledgments Y.X. Gu1, Q, Hao4, C.D. Zheng1, Y.D. Liu1, F. Jiang1,2 & B.D. Sha3 1 Institute of Physics, CAS, Beijing, China 2 Tsinghua University, Beijing, China 3 University of Alabama at Birmingham, USA 4 Cornell University, USA Project 973: G1999075604 (Department of Science & Technology, China)

23. Thank you!