Molecular Replacement (Alexei Vagin’s lecture) · Molecular Replacement (Alexei Vagin’s...

MolecularReplacement(AlexeiVagin’slecture)

Contents

• WhatisMolecularReplacement• FunctionsinMolecularReplacement• Weightingscheme• Informationfromdataandmodel• SomespecialtechniquesofMolecularReplacement

Molecular replacement programs and systems

Programs Systems Amore MrBump MOLREP Phenix QS BALBES PHASERManyothers EPMR CNS URO

Molecular replacement programs and systems

Programs Systems Amore MrBump MOLREP Phenix QS BALBES PHASERManyothers EPMR CNS URO

Introduction: Where MR could help?

Same protein could be crystallised in different space groupsMutants ComplexesHomologous proteinsSome structure could be derived using NMRHomology modeling

MR works best when similarity (3D similarity) between search and target molecules is high and the search model is relatively big.

4

IntroductionMolecular replacement (MR) is a phasing technique. It may help to derive initial phases. If the MR is successful then you need to do many cycles of refinement and model building. Its attractive side is that it produces initial atomic model also. However avoiding bias towards model may be difficult especially at low resolution. If there are more than one copies of the molecule in the asymmetric unit then non-crystallographic (NCS) averaging may improve phases and maps.If the resolution high enough (e.g. 2.5 or better) then automatic model building (arp/warp, solve/resolve, buccaneer) may help in model rebuilding.

5

MRSIRMIRSADMADNot specified

Diagram showing the percentage of structures in the PDB solved by different techniques

67.5% of structures are solved by Molecular Replacement (MR)

21% of structures are solved by experimental phasing

Overall resultsreportedinPDB

Molecular Replacementknown structureunknown structure

MGDKPIWEQIGSSFIQHYYQLFDNDRTQLGAIYIDASCLTWEGQQFQGKAAIVEKLSSLPFQKIQHSITAQDHQPTPDSCIISMVVGQLKADEDPIMGFHQMFLLKNINDAWVCTNDMFRLALHNFG

PSPLLVGREFVRQYYTLLNKAPEYLHRFYGRNSSYVHGGVDASGKPQEAVYGQNDIHHKVLSLNFSECHTKIRHVDAHATLSDGVVVQVMGLLSNSGQPERKFMQTFVLAPEGSVPNKFYVHNDMFRYEDE

H K L F φ0 0 1 10.4 1200 0 2 3.1 100 0 3 52.2 280

etc...

H K L F φ0 0 1 2.5 300 0 2 72.1 850 0 3 26.9 310

etc...

origin oorigin o

If we can find the rotation and translation that puts the model in the correct position in the crystal cell, THEN we can calculate phases.




H K L F φ0 0 1 10.4 1200 0 2 3.1 100 0 3 52.2 280

etc...

H K L F φ0 0 1 2.5 300 0 2 72.1 850 0 3 26.9 310

etc...

origin oorigin o





H K L F φ0 0 1 10.4 1200 0 2 3.1 100 0 3 52.2 280

etc...

H K L F φ0 0 1 2.5 300 0 2 72.1 850 0 3 26.9 310

etc...

origin oorigin o


Molecularreplacementplaceahomologousmodelintothecrystalwith

unknownstructureor

AtomicModel-->EMmap

Molecularreplacement

1)6-dimensionalsearchcheckallorientationsandpositions

placeahomologousmodelintothecrystalwithunknownstructure

orAtomicModel-->EMmap

Molecularreplacement

1)6-dimensionalsearchcheckallorientationsandpositions

2) 3-d+3-dsearchorientationspositionsConventionalMolecularReplacement

placeahomologousmodelintothecrystalwithunknownstructure

orAtomicModel-->EMmap

Functionsofmolecularreplacement

• CrossRotationfunction• SelfRotationfunction• Translationfunction• PhasedTranslationfunction• FastPackingfunction

map model

Patterson

RF(Ω)=∫Pobs(r)ℜΩ{Pmod(r)}drℜΩ-rotationoperator

PobsPmod

Ω

RF

CrossRotationFunction

map model

Patterson


PobsPmod

Ω

RF


map model

Patterson


PobsPmod

Ω

RF


map model

Patterson


PobsPmod

Ω

RF


map model

Patterson


PobsPmod

Ω

RF


map modelOptimalradiusofintegration

Diametreofthemodelandlessthansmallestcelldimension

VinterA

B

AB

BA

map

RF(Ω)=∫Pobs(r)ℜΩ{Pobs(r)}dr

Ω0 90

RF

SelfRotationFunction

map


Ω0 90

RF


map


Ω0 90

RF


map


Ω0 90

RF


a

a

a

Stereographic projection

x(a)

z(c*)

x

y y

ϕ

ϕ

θ

θ

χ

-χ

ℜ(θ,ϕ,χ)

ℜ(π-θ,π+ϕ,-χ)

Plotforrotationbyχ

SelfRotationFunctionSpacegroupP21onetetramer



TranslationFunction

TF(s)=∫Pobs(r)Pcalc(s,r)drs-vectoroftranslation

TofindrelativepositionofmoleculesagainPattersonfunctionisused.“Correctlyoriented”moleculesareshiftedtopositionr,correspondingPattersoniscalculatedanditiscomparedwithobservedPatterson.MaximumcorrespondencebetweentwoPattersonsindicatepotentiallycorrectposition.

FastPackingFunction

Κ # j

Estimationofoverlap:

Packingfunction:

Questions

• Maximumresolutionlimit?• Minimalresolutionlimit?• Weightingscheme?

HowtouseX-raydata

ShortintroductiontoFourierTransformation

ℱ

convolution product

addition addition

ℱ

Operators:

Convolution

Convolution

Functions

Realfunction Complexfunctionℱ

ℱ

ℱ

ℱ

Gaussian

Grid

Gaussian

Grid

Stepfunction Interferencefunction

A

A

1/A

A

1/A

1/A

Realspace Reciprocalspace

Fobs(s)

Product

s

Convolution

Realspace Reciprocalspaceℱ

A 1/A

Fhh

ℱ

CrystalandStructureFactors

ℱ Reciprocalspace

Mapρ(r) F(s)structurefactors

PattersonP(r) F(s)F*(s)=I(s)intensities

Realspace

productconvolution

ℱ

ℱ

ℱ

Highresolutiondata

• HighresolutionlimitfromOpticalresolution• Weightsforhighresolutiondata

res=0.356resmax2=atm2+res2

resmax

atm

res


σσ σ σ

σ

σ

σFobs(s)

Opticalresolution

Convolutionproduct


resmax

atm

res


σσ σ σ

σ

σ

σFobs(s)

Opticalresolution

Convolutionproduct


resmax

atm

res


σσ σ σ

σ

σ

σFobs(s)

Opticalresolution

Convolutionproduct


resmax

atm

res


σσ σ σ

σ

σ

σFobs(s)

Opticalresolution

Convolutionproduct


resmax

atm

res


σσ σ σ

σ

σ

σFobs(s)

Opticalresolution

Singlepeak

Optres=2σ

Convolutionproduct

Realspace Patterson

atm

patt

Optres=2atmatm2=(patt2+res2)/2

σσ

σ σ σσ

OpticalresolutionfromoriginpeakofPatterson

Optres=2

2=(atm2+res2))/2

Resolution

OpticalResolutionÅ

510

Optimalhighresolutionlimit

σσ σ σ

Å

OpticalResolution(bysfcheck)

Weightsforhighresolutiondataandsimilarity

Map

Model

Fobs(s)

2σ

1 2

1 2

Map

Model

Fobs(s)

2σ

1 2

1 2

Map

Model

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

Map

Model

PTF

Fobs(s)

2σ

1 2

1 2

1-2 2-12-21-1

notpossibletofindsolution

Map

Model

PTF

Map(blurred)

Fobs(s)

Fobs(s) Exp(-Bs2)B=1/422π σ

2σ

1 2

1 2

1-2 2-12-21-1

1 2


Map

Model

PTF

Map(blurred)

PTF

Fobs(s)

Fobs(s) Exp(-Bs2)B=1/422π σ

2σ

1 2

1 2

1-2 2-12-21-1

1 2

1-2 2-11-12-2


Clearsolution

Lowresolutiondata

Weightsforlowresolutiondataandsizeofmodel

Fobs(s)

s

Softminimalresolutioncut-offRealspace Reciprocalspaceℱ

Radmodel

Fobs(s)

Exp(-Bs2)

product:Exp(-Bs2)Fobs

s

convolution


Exp(-r2/22)σ B=1/422π

σRadmodel

=Radmodel/6σ

Fobs(s)

Exp(-Bs2)

product:Exp(-Bs2)Fobs

(1-exp(-Bs2))Fobs

s

convolution


Exp(-r2/22)σ B=1/422π

σRadmodel

=Radmodel/6σ

subtraction

WeightingschemeFused=(1-exp(-Boffs2))Fobs

1-exp(-Boffs2)

s

1

exp(-Bs2)

exp(-Bs2)

Weightingscheme

Rmin=√2Boff=2modelmodel=Radmodel/6Rmin≈Radmodel

1/Rmin

Fused=(1-exp(-Boffs2))Fobs1-exp(-Boffs2)

s

1

πσσ

exp(-Bs2)

exp(-Bs2)

Weightingscheme

Rmin=√2Boff=2modelmodel=Radmodel/6Rmin≈Radmodel

1/Rmin

Fused=(1-exp(-Boffs2))Fobs1-exp(-Boffs2)

s

1

πσσ

exp(-Bs2)

exp(-Bs2)

B=1/422πσModelsimilarity

1/Rmax

Rmax=√2B

Weightingscheme

Fused=(1-exp(-Boffs2))Fobs exp(-Bs2)

TwofiltersinImageprocessing:

GaussianhighpassfilterGaussianlowpassfilter

Wecanconsiderthisweightingschemeasanapproximationtothelikelihoodapproach

InformationinX-rayandModelmustoverlap

1/Rmin1/Rmaxs

1

1/Resmax_used(fomopt.resolution)

(fommodelsimilarity)(fommodelsize)

1/Resmin_X-ray 1/Resmax_X-ray

Canwefindsolution?Weightoflowresolutiongrows

LowhighModelSimilarity

0.10.20.30.40.5

Weightofhighresolutiongrows

Lowhigh

Modelsize

0.50.40.30.20.1

Verylikely

Veryunlikely



0.10.20.30.40.5


Lowhigh

Modelsize

0.50.40.30.20.1

Verylikely

Veryunlikely

Smallmodelwithlowsimilarity



0.10.20.30.40.5


Lowhigh

Modelsize

0.50.40.30.20.1

Verylikely

Veryunlikely

SmallmodelwithlowsimilaritySmallmodelwithhighsimilarity



0.10.20.30.40.5


Lowhigh

Modelsize

0.50.40.30.20.1

Verylikely

Veryunlikely

SmallmodelwithlowsimilaritySmallmodelwithhighsimilarity

Bigmodelwithlowsimilarity

WhatdoyouneedtodobeforeMR

1)Examinethedata2)Examinethemodel

Examinethedata(e.gbysfcheck)

• Completenessofdata• Signal-to-noise• Anisotropy(makecorrection?)• Pseudo-translation• Twinning• Resolution

Sfcheck1

Sfcheck2

Pseudo-translation

P0

0.125P0

Patterson

Pst-vector

Cell

Examinethemodel

• Lookatthemolecularshapeandflexibility• Checkthesequencesimilarity• Estimatethemodelsize• Choosethemethodofthemodelcorrection• Estimatenumberofcopies

Automaticcorrectionofthemodelusingsequencealignment

PHE VAL

Initialmodel

SequenceSearchmodel

withoutalignmentcorrectionwithalignmentcorrection

Rf Rf/sigmaRF 1 252.9 4.99RF 2 230.5 4.55 *RF 3 220.3 4.34RF 4 206.1 4.06RF 5 200.3 3.95. . . .

P 21 21 2 2 models in a.u.c. Identity 27% --- Rotation function ---

RF TF Rfac Score 1 3 0.554 0.206 2 3 0.554 0.205 6 1 0.556 0.199 3 4 0.556 0.199. . . can not find solution

Rf Rf/sigRF 1 329.2 5.27RF 2 304.9 4.88RF 3 282.6 4.52 *RF 4 249.6 3.99. . . .RF 18 205.7 3.29 *

--- Translation function ---

RF TF Rfac Score 3 2 0.556 0.197 1 4 0.559 0.19418 2 0.560 0.194 2 4 0.562 0.186with fixed model18 1 0.547 0.233 20 4 0.558 0.200 2 4 0.557 0.200

Modelimprovement

B=15

B(A2)=15(A2)+10SA(A2)

SA–surfacearea

SetatomicBvaluesaccordingtoaccessiblesurfacearea

Expectednumberofcopies

Timetohaveabreak

NMRmodel

•Translationfunction

•RotationfunctionUseassinglemodelorAveragedindividualRF⇔Averagedintensities

UseassinglemodelorAveragedindividualTF

Specialtechniquesofmolecularreplacement

• LockedRotationfunction• Multi-copysearch• UsephasesafterRefinement• SphericallyAveragePhasedTranslationfunction

SelfrotationandlockedRFPeaksselectedfromtheselfrotationfunctioncanbeusedforlockedcrossrotationfunction.LockedrotationfunctionisaveragedRFaccordingtoNCSSol_ Space group : H 3Sol_--- Rotation function --- theta phi chi Rf Rf/sigRF 1 47.90 67.54 158.59 1190 6.37RF 2 79.14 -166.90 89.47 1050 5.05RF 3 97.26 -139.11 145.11 848 4.55RF 4 137.75 -156.31 94.80 843 4.44‘ ‘ ‘ ‘Sol_--- Locked Rotation function --- theta phi chi Rf Rf/sigRF 1 127.99 139.59 122.00 2034 6.90RF 2 123.49 -52.42 122.11 1979 6.80RF 3 71.51 -171.88 105.08 1541 5.16RF 4 44.71 -107.06 154.01 1500 4.45

Multi-copysearch

Patterson

Cell Model1 Model2

F1 F2

F1F2

F2F1

*

**F1F1 F2F2*+

Realfunction

StructureFactors

Difficultcase

SpacegroupH3Resolution1.8A

Onemoleculeina.u.cIdentity35%

1.Usingcompletemodel-failed

2.Usingdomainsseparately-failed

3.Multi-copysearch-success

Initialmodel

RF&TF

complete model

RF TF Score

1 17 7 0.2082 1 1 0.2043 8 8 0.2034 14 7 0.1995 5 6 0.1966 11 2 0.1957 18 5 0.1918 16 6 0.1919 12 1 0.191. . .

domain 1

RF TF Score

1 10 2 0.2112 15 7 0.2093 12 1 0.2064 5 3 0.2025 3 1 0.2026 6 7 0.2017 7 5 0.1998 4 2 0.1989 1 2 0.197. . .

domain 2

RF TF Score

1 14 1 0.2052 8 1 0.2043 26 8 0.2034 5 6 0.2035 10 1 0.2026 1 2 0.200. . . . . .21 24 1 0.192. . . . . .

Domain1+2:Multi-copysearch multi-copy Search

R1 R2 STF TF PFmax PFmin Score

1 1 2 2 0.65 -11.55 0.209 1 2 5 1 0.98 -15.90 0.212 1 3 1 1 0.99 -12.73 0.223. . . . 7 24 3 1 0.99 -13.59 0.248 . . .

domain1 (rf7) , domain2(rf24)

InitialmodelandMRsolution

MR

initial

MRsolutionandfinalstructure

MR

final

UsePhasesafterRefinement

Search for the whole molecule using standard MR protocol failed because of domain flexibility.

Search by domains using standard MR protocol failed because of small size of the second domain.

Structure was then solved manually in three steps:

1) standard MR search for larger domain;

2) refinement of the partial model;

3) search for smaller domain in the masked map (generated from REFMAC’s FWT and PHIWT)

“unknown” structure

(1tj3)

search model with sequence identity

100%

Example: Domain motions - 1tj3

Search for the whole molecule using standard MR protocol failed because of domain flexibility.

Search by domains using standard MR protocol failed because of small size of the second domain.

Structure was then solved manually in three steps:

1) standard MR search for larger domain;

2) refinement of the partial model;

3) search for smaller domain in the masked map (generated from REFMAC’s FWT and PHIWT)

“unknown” structure

(1tj3)

search model with sequence identity

100%

Example: Domain motions - 1tj3

FittingmodelintoX-rayorEMmap

Alternativeapproach:

1.findposition2.findorientation

1.findorientation(RF)2.findposition(PTF)

SphericallyAveragedPhasedTranslationFunction(SAPTF)

SAPTF(s)=∫ρs(r)ρm(r)r2dr

s

Map

Model

radialdistribution

ρm(r)

ρ(r)



s

ρm(r)Map

Model

radialdistribution

ρm(r)

ρ(r)



s

ρs(r)ρm(r)

Map

Model

radialdistribution

ρm(r)

ρ(r)

SAPTFasFourierseriesByexpandingSAPTFintosphericalharmonicsitispossibletorepresentitasaFourierseries

SAPTF(s)=∫ρs(r)ρm(r)r2dr=

=∑hAhexp(2ihs)

Ah=∑nFhc00n(R)j0(2Ra)b00nπ

π

Algorithm

1.Findposition:Sphericallyaveragedphasedtranslationfunction

2.Findorientation:Localphasedrotationfunction

3.Checkandrefineposition:Phasedtranslationfunction

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