h.f. fan & y.x. gu beijing national laboratory for condensed matter physics institute of...

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

Institute of Physics, Chinese Academy of SciencesP.R. China

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

Institute of Physics, Chinese Academy of SciencesP.R. China

Direct Methods inDirect Methods inProtein CrystallographyProtein Crystallography

Direct Methods inDirect Methods inProtein CrystallographyProtein Crystallography

• 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

• 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

The Phase ProblemThe Phase Problem

2 ( )1( , , ) ( , , ) i hx ky lz

h k l

x y z F h k lV

e 2 ( )1( , , ) ( , , ) i hx ky lz

h k l

x y z F h k lV

e

( , , ) ?h k l ( , , ) ?h k l

, ,( , , ) i h k lF h k l e , ,( , , ) i h k lF h k l e

The Point of View fromDirect Methods:

The Point of View fromDirect Methods:

Phases are not missing butjust hidden in the magnitudes!

Phases are not missing butjust hidden in the magnitudes!

What is a Direct Method ?What is a Direct Method ?

It derives phases directly from the magnitudes.

It derives phases directly from the magnitudes.

( , , ) ( , , )F h k l h k l ( , , ) ( , , )F h k l h k l

Why it is possible ?Why it is possible ?

1

, , exp 2N

j j j jj

F h k l f i hx ky lz

Why it is possible ?Why it is possible ?

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.

1

1

, , cos , , cos2

, , sin , , sin 2

N

j j j jj

N

j j j jj

F h k l h k l f hx ky lz

F h k l h k l f hx ky lz

1

1

, , cos , , cos2

, , sin , , sin 2

N

j j j jj

N

j j j jj

F h k l h k l f hx ky lz

F h k l h k l f hx ky lz

Conditions for the Sayre Equation to be valid

1. Positivity2. Atomicity

3. Equal-atom structure

Conditions for the Sayre Equation to be valid

1. Positivity2. Atomicity

3. Equal-atom structure

Sayre’s EquationSayre’s Equation

' ''

sq

fF F F

f V h h h hh

sin = h’ h, h’ sin (h’ +h h’)

cos = h’ h, h’ cos (h’ +h h’)

The tangent formulaThe tangent formula

, ' ' ''

, ' ' ''

sin( )tan

cos( )

h h h h hh

hh h h h h

h

, ' ' ''

, ' ' ''

sin( )tan

cos( )

h h h h hh

hh h h h h

h

1/ 22 2

, ' ' ' , ' ' '' '

sin( ) cos( )

h h h h h h h h h hh h

1

0( ) 2 ( ) exp[ cos( )]P I h h 1

0( ) 2 ( ) exp[ cos( )]P I h h

h, h’ = 2hh’ h - h’

• 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

• 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

Use of direct methods in Protein Crystallography

Use of direct methods in Protein Crystallography

the SAD/SIR phase ambiguity the SAD/SIR phase ambiguity

Direct methods breakingDirect methods breaking

Bimodal distributionfrom SAD

" " "

The phase ofF”

P

Phase information available in SADPhase information available in SAD

Cochrandistribution

Peaked atany where

from 0 to 2

Peaked at

"2

Sim distribution

P+ formulaP+ formula

Acta Cryst. A40, 489-495 (1984)Acta Cryst. A40, 495-498 (1984)Acta Cryst. A41, 280-284 (1985)

' ' , ' 3 ', ','

1 1tanh sin

2 2

sin ' sinbest best

P

m m

h h

h h h h h h h h hh

' h h h Reducing the phase problem to a sign problem

Breaking the SAD/SIR phase ambiguity by theCochran distribution incorporating with partial structure information

+-

Direct-method phasing of the 2Å experimental SAD data of the protein aPP

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; = 105.3o

Protein atoms in ASU: 301Resolution limit: 2.0ÅAnomalous scatterer: Hg (in centric arrangement)Wavelength: 1.542Å (Cu-K) f” = 7.686Locating heavy atoms & SAD phasing: direct methods

Acta Cryst. A46, 935 (1990)

Avian Pancreatic Polypeptide

Space group: C2 Unit cell: a = 34.18, b = 32.92, c = 28.44Å; = 105.3o

Protein atoms in ASU: 301Resolution limit: 2.0ÅAnomalous scatterer: Hg (in centric arrangement)Wavelength: 1.542Å (Cu-K) f” = 7.686Locating heavy atoms & SAD phasing: direct methods

Acta Cryst. A46, 935 (1990) Data courtesy of Professor Tom BlundellData courtesy of Professor Tom Blundell

• 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

• 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

Further developmentsFurther developments

TTHA1634 fromThermus thermophilus HB8

Data courtesy of Professor Nobuhisa WatanabeDepartment of Biotechnology and Biomaterial Chemistry, Nagoya University, Japan

Space group: P21212 Unit cell: a = 100.57, b = 109.10, c = 114.86ÅNumber of residues in the AU: 1206Resolution limit: 2.1ÅMultiplicity: 29.2Anomalous scatterer: S (22) X-ray wavelength: = 1.542Å (Cu-K)Bijvoet ratio: <|F|>/<F> = 0.55%Phasing method: A single run of OASIS2006 + DM (Cowtan)Model building: ARP/wARP

ARP/wARP found 1178 of the total 1206 residues,all docked into the sequence.

Ribbon model plotted by PyMOL

Reciprocal-space fragment extension

OASIS + DM

Reciprocal-space fragment extension

OASIS + DM

Dual-space fragment extensionDual-space fragment extension

, 3

1 1tanh sin

2 2

s s inin

best best

P

m m

h h

h' h h' h h' h' hh h'h'

Real-spacefragment extension

RESOLVE BUILD and/or ARP/wARP

Real-spacefragment extension

RESOLVE BUILD and/or ARP/wARP

Partialstructure

Partialstructure

NoNo

YesYes

OK?OK?

EndEnd

PartialmodelPartialmodel

Glucoseisomerase

S-SADCu-K

17%Cycle 097%Cycle 6

Glucoseisomerase

S-SADCu-K

Cr-K Se, S-SAD Alanine racemase

Cycle 052%

Cr-K Se, S-SAD Alanine racemase

Cycle 497%

25%Cycle 0

Xylanase S-SADSynchrotron = 1.49Å

Xylanase S-SADSynchrotron = 1.49Å

99%Cycle 6

52%Cycle 0

LysozymeS-SADCr-K

LysozymeS-SADCr-K

98%Cycle 6 Azurin

Cu-SADSynchrotron = 0.97Å

Cycle 042%

AzurinCu-SADSynchrotron = 0.97Å

Cycle 395%

Ribbon models plotted by PyMOL

Data courtesy of Professor N. Watanabe,Professor S. Hasnain, Dr. Z. Dauter andDr. C. Yang

Direct-method aided

MR-model completion

Direct-method aided

MR-model completion

Dual-space fragment extension

without SAD/SIR information

Dual-space fragment extension

without SAD/SIR information

, 3

1 1tanh sin

2 2

sin si n

best best

P

m m

h h

h' h h' h h' h' hh h'h'

Partialstructure

Partialstructure

" h 5%

the phase of atoms

randomly selected from the current model

" h h h

" . . "model modeli e h h h h

Density modification

by DM

Density modification

by DM

NoNo

MRmodel

MRmodel

YesYes

EndEndModel completion

by ARP/wARPor PHENIX

Model completion by ARP/wARP

or PHENIXOK?OK?

Phase improvement

by OASIS

Phase improvement

by OASIS

P+ > 0.5

” model

P+ < 0.5

” model

<||> ~

<||> ~

”

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

46 residues13 with side chains

MRmodelMRmodel

Cycle 2

ARP/wARP-DMiterationCycle 1

Cycle 1 Cycle 3

ARP/wARP-OASIS-DM iteration

Cycle 7Cycle 5201 residuesall with side chains Final

modelFinalmodel

215 residues

1UJZ

Ribbon models plotted by PyMOL

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

Starting model

R-factor: 0.34

R-free: 0.44

No. of residuals: 479

with side chains: 479

After phenix.autobuild

R-factor: 0.33

R-free: 0.40

No. of residuals: 503

with side chains: 503

After 4 cycles of oasis-phenix

R-factor: 0.24

R-free: 0.30

No. of residuals: 597

with side chains: 588

What’s thelow resolution limit for

direct methods?

What’s thelow resolution limit for

direct methods?

SAD phasing at different resolutionsTTHA1634 Cu-Kdata, <|F|>/<F> ~ 0.55%

SAD phasing at different resolutionsTTHA1634 Cu-Kdata, <|F|>/<F> ~ 0.55%

2.1Å

3.0Å

3.5Å

4.0Å

Very good

Good

Marginally traceable

Still informative

Maps at 1 phased by a single run of OASIS + DM (Cowtan) plotted by PyMOL

dealing with low resolution SIR/SAD data

dealing with low resolution SIR/SAD data

Combining SOLVE/RESOLVE and OASIS + DM

Combining SOLVE/RESOLVE and OASIS + DM

R-phycoerythrinSIR data from the native and thep-chloromercuriphenyl sulphonic acid derivative

Space group: R3Unit cell: a = b = 189.8, c = 60.0Å;     = 120o

Number of residues in the ASU: 668 Resolution limit: 2.8ÅReplacing atoms: HgX-rays: Cu-K, λ = 1.542Å

J.Mol.Biol. 262 721-731 (1996)Chinese Physics 16, 3022-3028 (2007)

SOLVE/RESOLVE SOLVE/RESOLVE& OASIS + DM

Maps plotted by PyMOL

SOLVE/RESOLVE SOLVE/RESOLVE& OASIS + DM SOLVE/RESOLVE

SOLVE/RESOLVE &OASIS + DM

Tom70pSpace group: P21

Unit cell: a = 44.89, b = 168.8, c = 83.4Å;    β = 102.74o

Number 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%

Nature Structural & Molecular Biology 13, 589-593 (2006)Chinese Physics B 17, 1-9 (2008)

Maps plotted by PyMOL

OASIS-2006OASIS-2006Institute of Physics

Chinese Academy of SciencesBeijing 100080, P.R. China

Institute of PhysicsChinese Academy of SciencesBeijing 100080, P.R. China

http://cryst.iphy.ac.cnhttp://www.ccp4.ac.uk/prerelease

http://cryst.iphy.ac.cnhttp://www.ccp4.ac.uk/prerelease

Institute of Biophysics, Chinese Academy of Sciences, Beijing, China Institute of Biophysics, Chinese Academy of Sciences, Beijing, China

AcknowledgementsAcknowledgementsProfessor Zhengjiong LinProfessor Zhengjiong Lin

1 Beijing National Laboratory for Condensed Matter Physics,

Institute of Physics, Chinese Academy of Sciences, China2 National Laboratory of Protein Engineering and Plant Genetic

Engineering, Peking University, Beijing, China3 Institute of Biophysics, Chinese Academy of Sciences, Beijing China

1 Beijing National Laboratory for Condensed Matter Physics,

Institute of Physics, Chinese Academy of Sciences, China2 National Laboratory of Protein Engineering and Plant Genetic

Engineering, Peking University, Beijing, China3 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

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

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.

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.

Thank you!Thank you!