Weight Matrices for Sequence Similarity Scoring.docx

Weight Matrices for Sequence Similarity Scoring.docx

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WeightMatricesforSequenceSimilarityScoring

WeightMatricesforSequenceSimilarityScoring

Version2.0

May1996

DavidWheeler,Ph.D.

DepartmentofCellBiology,

BaylorCollegeofMedicine

Houston,Texas

E-mail:

wheeler@bcm.tmc.edu

TableofContents

1.Weightmatricesforsequencesimilarityscoring

2.Importanceofscoringmatrices

3.Examplesofmatrices

4.Logoddsmatrices

5.PAMmatrixconstruction

6.PropertiesofthePAMmatrix

7.AssumptionsinthePAMmodel

8.BLOSUM（BlocksSubstitutionMatrix）matrix

9.Practicalaspects

10.SelectinganoptimalPAMmatrix

11.Otherspecializedscoringmatrices

WeightMatricesforSequenceSimilarityScoring

Outline:

1.Objective:

Overviewofmethodsandtheoriesthatunderlietheconstructionofscoringmatrices.

2.Examplesofweightmatricesfornucleotideandaminoacidscoring.

3.Transitionprobabilitymatrix:

PAM

oConstruction

oProperties

oSourcesoferror

4.BLOSUMmatrix

oConstruction

oSourcesoferror

5.Practicalaspects

6.Otherrefinementstotransitionprobabilitymatrices.

Reading:

∙D.G.George,W.C.BarkerandL.T.Hunt.（1990）.MutationDataMatrixandItsUses.inMethodsinEnzymologyvol183;R.F.Doolittle,ed.pp.333-351.AcademicPress,Inc.NewYork.

∙M.O.Dayhoff（1978）AtlasofProteinSequenceandStructure（Natl.Biomed.Res.Found.,Washington）,Vol.5,Suppl.3,pp.345-352.

∙S.F.Altschul（1991）.Aminoacidsubstitutionmatricesfromaninformationtheoreticperspective.J.Mol.Biol.219555-565.

∙S.F.Altschul,M.S.Boguski,W.GishandJ.C.Wootton.（1994）.Issuesinsearchingmolecularsequencedatabases.NatureGenetics6:

119-129.

BacktoTableofContents.

Importanceofscoringmatrices

∙Scoringmatricesappearinallanalysisinvolvingsequencecomparison.

∙Thechoiceofmatrixcanstronglyinfluencetheoutcomeoftheanalysis.

∙Scoringmatricesimplicitlyrepresentaparticulartheoryofevolution.

∙Understandingtheoriesunderlyingagivenscoringmatrixcanaidinmakingproperchoice.

Similarityvs.Distance

1.Elementsofthematricesspecifytheweighttoassignagivencomparisonby:

othecostofreplacingoneresiduewithanother（distance）;or

oameasureofthesimilarityforthereplacement.

2.Distanceismorenaturallyusedforphylogenetictreereconstruction;similarityisusedfordatabasesearching.

3.Thelogicofthealgorithmdoesn'tchange:

maximizingasimilarityisfundamentallythesameasminimizingadistance.

4.Distanceandsimilaritymatricesareinter-convertiblebysomemathematicaltransformationappropriateforthegivenapplication.

BacktoTableofContents.

Examplesofmatrices

Aremarkonnotation

Whenweconsiderscoringmatrices,weencountertheconventionthatmatriceshavenumericindicescorrespondingtotherowsandcolumnsofthematrix.Thatis,

referstotheentryatthefirstrowandthefirstcolumn.Ingeneral,

referstotheentryattheithrowandthejthcolumn.Tousethisforsequencealignment,wesimplyassociateanumericvaluetoeachletterinthealphabetofthesequence.Forexample,ifthealphabetis

thenA=1,C=2,etc.Thus,onewouldfindthescoreforamatchbetweenAandCat

.Sinceweconsiderdifferentscoringmatricesinthissection,wedistinguishbetweenthembyusingdifferentlettersforthematrix,

referstotheReplacementmatrix,

tothelogoddsmatric,andsoon.

Nucleotidescoring

1.Identitymatrix（similarity）

2.ATCG

3.

4.A1000

5.

6.T0100

7.

8.C0010

9.

10.G0001

Forelementsinrowibycolumnj:

11.BLASTmatrix（similarity）

12.ATCG

13.

14.A5-4-4-4

15.

16.T-45-4-4

17.

18.C-4-45-4

19.

20.G-4-4-45

21.Transition/TransversionMatrix

22.ATCG

23.

24.A0551

25.

26.T5015

27.

28.C5105

29.

30.G1550

Nucleotidebasesfallintotwocategoriesdependingontheringstructureofthebase.Purines（AdenineandGuanine）aretworingbases,pyrimidines（CytosineandThymine）aresingleringbases.MutationsinDNAarechangesinwhichonebaseisreplacedbyanother.Amutationthatconservestheringnumberiscalledatransition（e.g.,A->GorC->T）amutationthatchangestheringnumberarecalledtransversions.（e.g.A->CorA->Tandsoon）.

Althoughtherearemorewaystocreateatransversion,thenumberoftransitionsobservedtooccurinnature（i.e.,whencomparingrelatedDNAsequences）ismuchgreater.Sincethelikelihoodoftransitionsisgreater,itissometimesdesireabletocreateaweightmatrixwhichtakesthispropensityintoaccountwhencomparingtwoDNAsequences.

UseofaTransition/TransversionMatrixreducesnoiseincomparisonsofdistantlyrelatedsequences.

Proteinscoring

1.Identitymatrix

2.GeneticCodeMatrix

oScorebasedonminimumnumberofbasechangesrequiredtoconvertoneaminoacidintoanother.

o

Distancematrix

3.Physical/chemicalcharacteristics

oAttempttoquantifysomephysicalorchemicalattributeoftheresiduesandarbitrarilyassignweightsbasedonsimilaritiesoftheresiduesinthischosenproperty.

o

Hydrophobicitymatrix

BacktoTableofContents.

Logoddsmatrices

Sisthelogoddsratiooftwoprobabilities:

theprobabilitythattworesidues,iandj,arealignedbyevolutionarydescentandtheprobabilitythattheyarealignedbychance.

∙

arethefrequenciesthatresidueiandjareobservedtoaligninsequencesknowntoberelated.Theyarederivedfroma"transitionprobabilitymatrix."

∙

and

arefrequenciesofoccurrenceofresidueiandjinthesetofsequences.

∙e.g.,PAM250,BLOSUM62etal.

PAMMatrix

Summaryofsteps:

1.

Alignsequencesthatareatleast85%identical.

ominimizeambiguityinalignments.

ominimizethenumberofcoincidentmutations.

2.

Reconstructphylogenetictreesandinferancestralsequences.71treescontaining1,572exchangeswereused.

3.

Tallyreplacements"accepted"bynaturalselection,inallpair-wisecomparisons（each

isthenumberoftimesaminoacidjwasreplacedbyaminoacidiinallcomparisons）.

4.

Computeaminoacidmutability,

i.e.,thepropensityofagivenaminoacid,j,tobereplaced.

5.

Combinedatafrom3&4toproduceaMutationProbabilityMatrixforonePAMofevolutionarydistance,accordingtothefollowingformulae:

6.

CalculateLogOddsMatrixforsimilarityscoring:

DivideeachelementoftheMutationDataMatrix,M,bythefrequencyofoccuranceofeachresidue:

RisaRelatednessOddsMatrix,

isthefrequencyofresiduei.

TheLogOddsMatrix,

iscalculatedfromtherelatednessoddsmatrix,

simplybytakingthelogofeach

.

7.

DifferentproteinfamiliesmanifestdifferentPAMrates.

BacktoTableofContents.

PropertiesofMutationProbablitiyMatrix

1.Thesumof

foranycolumn,j,isone（trivial）.Notethattheprobabilitythatanaminoacidwillchangeisontheorderof1%foreachaminoacid.Theprobabilitythatitwillstaythesameisontheorderot99%foreachaminoacid.

2.TheMutationProbabilityMatrix,M1,definesaunitofevolutionarychange:

specifically,1PAM（AcceptedPointMutationper100residues）.

othematrixcanbeusedtosimulateevolutionbyusingarandomnumbergeneratortoselectfateofeachresidueinthesequenceaccordingtotheprobabilitygiveninthetable.

oexposinga100residueproteinsequenceofaveragecompositiontotheevolutionarychangerepresentedbyM1resultsinoneaminoacidchange,onaverage.

3.SuccessiveapplicationofM1onasequenceyields2,3,4...PAMsofevolutionarychange.

4.Thefollowingoperationsareequivalent:

osuccessiveapplicationofM1onasequence.

omatrixmultiplicationofM1byitself,M1*M1,followedbyoperationonasequence.

oscalingtheelementsofM1byaconstantofproportionality,

=1,2,3...accordingtotheformulaebelow,followedbyoperationonasequence:

theaboveequationenablesthedirectcalculationofamatrixforanydesiredPAMdistance.

5.Thematrixhascompositionalinformationinit,sinceitdependsontherelativefrequenciesofaminoacidsinthepoolofsequencesfromwhichthetalliesweredrawn.Intheextremes,thefollowingobtain:

oTheelementsofthe0PAMmatrixare1for

and0for

;

oThe

PAMmatrixelementsapproachestheasymptoticaminoacidcomposition.

BacktoTableofContents.

AssumptionsinPAMmodel:

1.replacementatanysitedependsonlyontheaminoacidatthatsiteandtheprobabilitygivenbythetable（Markovmodel）.

2.sequencesthatarebeingcomparedhaveaverageaminoacidcomposition.

SourcesoferrorinPAMmodel

1.Manysequencesdepartfromaveragecomposition.

2.Rarereplacementswereobservedtooinfrequentlytoresolverelativeprobabilitiesaccurately（for36pairsnoreplacementswereobserved!

）.

3.Errorsin1PAMaremagnifiedintheextrapolationto250PAM.

4.TheMarkovprocessisanimperfectrepresentationofevolution:

Distantlyrelatedsequencesusuallyhaveislands（blocks）ofconservedresidues.Thisimpliesthatreplacementisnotequallyprobableoverentiresequence.

BacktoTableofContents.

BLOSUM（BlocksSubstitutionMatrix）Matrix

StevenHenikoffandJorjaG.Henikoff（1992）.Aminoacidsubstitutionmatricesfromproteinblocks.Proc.Natl.Acad.Sci.89:

10915-10919.

1.StartingdataisconservedblocksfromBlocksdatabase.

oaligned,ungappedsequences

owidelyvaryingsimilarity,butmeasuresaretakentoavoidbiasingthesamplewithfrequentlyoccurringhighlyrelatedsequences.

2.Talliesofreplacementsaremadebystraightforwardtallyingofallpairsofalignedresidues,

oTheobser