Electron crystallographicmethods of solving

modulated structures

Electron microscopyElectron microscopyX-ray crystallographyX-ray crystallography

Direct methods

Pseudo translationalsymmetries

Dealing withpseudo symmetries

Two-stage image processing inElectron microscopy

Translationalphase ambiguity

Ab initio solutionof superstructures

Ab initio solution ofmodulated and

composite structures

Acting as a tool ofimage processing

Pseudo centro symmetry

Enantiomorphousphase ambiguity

Protein SAD/SIR phasing

Protein model completion

电子显微学电子显微学X - 射线晶体学X - 射线晶体学直接法

赝平移对称

处理赝对称性两步法电子

显微学图像处理

超结构从头求解

用于图像处理

赝中心对称

蛋白质 SAD/SIR相位推演

蛋白质模型完整化

电子晶体学方法求解调制结构

从头测定调制结构和组合结构

Initial phasing and Model completion of Proteins

Image processing inElectron Microscopy

SoftwareModulated and Composite structures

Enantiomorphous phase ambiguityresolved by the direct method

Sample: ZCW; Space group: P21

Acta Phys. Sin. 27, 169-174 (1978)

Enantiomorphous phase ambiguityresolved by the direct method

Direct method result Final map

a c

b

c

b

cK

Before treatment After treatment

X-ray Crystallography

Objectivelens

Back focal plane

Image plane

Object

Diffractionpattern Blurred

image

Fourier transform

Fourier transform

Electron microscopy

Object

Patterson map

Diffractionpattern

Diffractionwave front

Object

Patterson map

Diffractionwave front

Diffractionpattern

X-ray Crystallography

Multiplied with F*h

Objectivelens

Back focal plane

Image plane

Object

Diffractionpattern Blurred

image

Multiplied with acontrast transfer

function

Fourier transform

Fourier transform

Electron microscopy

Structure image blurred by

convoluting withthe Fourier

transform of acontrast transfer

function

Structure image blurred by

convoluting withIt’s inverse

Object

Patterson map

Diffractionwave front

Diffractionpattern

X-ray Crystallography

Multiplied with F*h

Objectivelens

Back focal plane

Image plane

Object

Diffractionpattern Blurred

image

Multiplied with acontrast transfer

function

Fourier transform

In the derivation of X-ray diffraction phases, direct methods are acting as a tool of image processing.

They convert the blurred image Patterson map to the deblurred image electron density map.

It is reasonable to expect that direct methods can be used in high-resolu-tion electron micro-scopy as a tool of image processing.

Fourier transform

Electron microscopy

<F >F

o

A

B

F”

F’”

’

F”

F *

Phase ambiguity intrinsic in SAD

F

A

B

N

FR

FD

FN

N

D

D

Phase ambiguity intrinsic in SIR

DR

R

D

N

N

1

( ) ( ' ")exp( 2 )N

oj j j j

j

F f f i f i

h h r

( ) '( ) "( )oF F F F F h h h h

* *( ) ( ) '( ) "( )oF F F F F h h h h

* 2 "F F F

exp , 2F F i F F F

"

, – SAD phase doublet

D – derivative, R – replacing atoms, N – native

D R NF F F

;N R N D R D

,I II – SIR phase doublet

, 3

1 1tanh sin

2 2

sin sinbest bes

c

t

P

m m

h h

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

1 2

2

exp 2

1 1 2 1 cos2 cos2

2 2

m

P

2h h

h h

"

1tan( ) 2( )sin cos

2

best best

best P

h h h

h h h

Breaking SAD/SIR phase ambiguity by direct methods

' h h h

SAD/SIR data

P+(h) = 1/2

End

Calculate P+(h)

Eh ,’h , h

Calculate mh and h,best

LysozymeSpace group: P43212 Unit cell: a = 78.4, c = 37.0Å Number of residues in the ASU: 129Resolution limit: 2.01Å; Multiplicity: 47.2 Anomalous scatterer: S (10 )X-rays: Cr-K = 2.291Å, f ” = 1.14 Bijvoet ratio: <|F |>/<F > = 2.4% Data provided by Prof. Isao Tanaka and Dr. Nobuhisa Watanabe

AzurinSpace group: P4122 Unit cell: a = b = 52.65, c = 100.63ÅNumber of residues in the ASU: 129 Resolution limit: 1.9ÅMultiplicity: 10.0 Anomalous scatterer: Cu (1)X-rays: synchrotron radiation = 0.97Å f” = 2.206Bijvoet ratio: <|F|>/<F> = 1.44%Data provided by Prof. S. Hasnain

XylanaseSpace group: P21 Unit cell: a = 41.07, b = 67.14, c = 50.81Å = 113.5o Number of residues in the ASU: 303 Resolution limit: 1.75Å; Multiplicity: 15.9Anomalous scatterer: S (5 ) X-rays:synchrotron radiation= 1.488Å; f ” = 0.52Bijvoet ratio: <|F |>/<F > = 0.56% Data courtesy of Dr. Z. Dauter, National Cancer Institute, USA

Alanine racemaseSpace group: C 2 2 21 Unit cell: a = 72.68 b = 76.13, c = 136.27ÅNumber of residues in the ASU: 357 Resolution limit: 2.3ÅData collection range: 360o Anomalous scatterer: Se (8), S (6), P (1)X-rays: Cr-K, = 2.291ÅBijvoet ratio: <|F |>/<F > = 2.8% Data provided by Dr. Cheng Yang

Alanine racemaseSpace group: C 2 2 21 Unit cell: a = 72.68 b = 76.13, c = 136.27ÅNumber of residues in the ASU: 357 Resolution limit: 2.3ÅData collection range: 360o Anomalous scatterer: Se (8), S (6), P (1)X-rays: Cr-K, = 2.291ÅBijvoet ratio: <|F |>/<F > = 2.8% Data provided by Dr. Cheng Yang

SIR

SOLVE/RESOLVE + OASIS/DM

SOLVE/RESOLVE

SOLVE/RESOLVE

SAD

SOLVE/RESOLVE +OASIS/DM

SIR

SOLVE/RESOLVE SOLVE/RESOLVE+ OASIS/DM

SIR

SOLVE/RESOLVE

SAD

SOLVE/RESOLVE +OASIS/DM

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

SAD SOLVE/RESOLVE +OASIS/DM

2.1Å 3.0Å

3.5Å 4.0Å