Direct Methods

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Direct Methods By Fan Hai-fu, Institute of
Physics, Beijing http//cryst.iphy.ac.cn
1. Introduction 2. Sayres equation and the
tangent formula 3. Further developments in the
1990s 4. Recent progress in solving proteins
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The Phase Problem
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Direct methods
Deriving phases directly from the magnitudes
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Why it is possible ?
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1947 D. Harker J. Kasper 1952 D.
Sayre 1950s J. Karle H. Hauptman 1964
I. L. Karle J. Karle 1970s M. M.
Woolfson 1985 Nobel Prize awarded to
H. Hauptman J. Karle
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Structure Factors
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Unitary Structure Factors
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Normalized Structure Factors
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Sayres Equation Conditions for the Sayre
Equation to be valid 1. Positivity 2.
Atomicity 3. Equal-atom structure
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Positivity
Atomicity
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Equal-atom structure
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Sign relationship ¾ 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.
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The Probability distribution of three-phase
structure invariants ¾ Cochran distribution
Cochran, W. (1955). Acta Cryst. 8, 473-478.
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Central limit theorem
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(No Transcript)
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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)
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The tangent formula (continued)
Maximizing P(jh) Þ jhb
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
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Saytan
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Direct methods in the 1990s
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
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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.
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Direct-method phasing of anomalous diffraction
1. Resolving OAS phase ambiguity 2. Improving MAD
phases
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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
a32.43, b60.68, c38.01Å b107.82o
Anomalous scatterer Cu
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OASIS (CCP4 Supported Program) DESCRIPTION
OASIS is a computer program for breaking
phase ambiguity in One-wavelength Anomalous
Scattering or Single Isomorphous Replacement
(Substitution) protein data. The phase problem is
reduced to a sign problem once the
anomalous-scatterer or the replacing-heavy-atom
sites are located. OASIS applies a direct method
procedure to break the phase ambiguity intrinsic
to OAS or SIR data. REFERENCES Fan, H. F. and
Gu, Y. X. (1985) Combining direct methods with
isomorphous replacement or anomalous
scattering data III. The incorporation of partial
structure information, Acta Cryst. A41,
280-284. Fan H. F., Hao, Q., Gu, Y. X., Qian, J.
Z., Zheng, C. D. and Ke, H. (1990) Combining
direct methods with isomorphous
replacement or anomalous scattering data VII. Ab
initio phasing of the OAS data from a
small protein, Acta Cryst. A46, 935-939. Y. -D.
Liu, I. Harvey, Y. -X. Gu, C. -D. Zheng, Y. -Z.
He, H. -F. Fan, S. S. Hasnain and Q. Hao (1999)
Is single-wavelength anomalous scattering
sufficient for solving phases? A comparison of
different methods for a 2.1 A structure
solution, Acta Cryst. D55, 1620-
1622. AUTHORS Q. Hao (1, 2), Y. X. Gu, C. D.
Zheng H. F. Fan (2) (1) School of
Applied Sciences, De Montfort University,
Leicester LE1 9BH, England. (2)
Institute of Physics, Chinese Academy of
Sciences, Beijing 100080, P. R. China. Email
qhao_at_dmu.ac.uk or fan_at_aphy.iphy.ac.cn
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Direct-method phasing of anomalous diffraction
1. Resolving OAS phase ambiguity 2. Improving MAD
phases
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Direct-method aided MAD phasing Sample yeast
Hsp40 protein Sis1 (171-352)
Space group P41212

Unit 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
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Direct-method aided MAD phasing (yeast Hsp40
protein Sis1 171-352)
2w-DMAD
4w-MAD
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Direct-method aided MAD phasing (yeast Hsp40
protein Sis1 171-352)
DMAD (2w)
MAD (4w)
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Direct-method aided MAD phasing (yeast Hsp40
protein Sis1 171-352)
DMAD (2w)
MAD (4w)
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Direct phasing of the 2Å SIR data of aPP
with the replacing atoms (Hg) in centrosymmetric
arrangement Space group C2 Unit cell a34.18,
b32.92, c28.22Å b105.3o
SIR
D-SIR
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Recent progress on Direct-methods in Protein
Crystallography is available in
Direct-method_SAD_phasing.ppt
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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)
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Thank you !