We stimulate the evolution of model protein sequences subject to mutations. A mutation is considered neutral if it conserves (1) the structure of the ground state, (2) its thermodynamic stability and (3) its kinetic accessibility. All other mutations are c

J.theor.Biol.(1999)200,49}64

ArticleNo.jtbi.1999.0975,availableonlineatwww.1mpi.com

NeutralEvolutionofModelProteins:

Di4usioninSequenceSpaceandOverdispersion

UGOBASTOLLA*-,H.EDUARDOROMAN?

AND

MICHELEVENDRUSCOLOA

*H¸RZ,ForschungszentrumJulich,D-52425Julich,Germany,

?DipartimentodiFisicaandINFN,;niversitadiMilano,I-20133Milano,Italy

ADepartmentofPhysicsofComplexSystems,=eizmannInstituteofScience,Rehovot76100,Israel

(Receivedon12November1998,Acceptedinrevisedformon21May1999)

Westimulatetheevolutionofmodelproteinsequencessubjecttomutations.Amutationisconsideredneutralifitconserves(1)thestructureofthegroundstate,(2)itsthermodynamicstabilityand(3)itskineticaccessibility.Allothermutationsareconsideredlethalandarerejected.Weadoptalatticemodel,amenabletoareliablesolutionoftheproteinfoldingproblem.Weprovetheexistenceofextendedneutralnetworksinsequencespace*sequencescanevolveuntiltheirsimilaritywiththestartingpointisalmostthesameasforrandomsequences.Furthermore,we"ndthattherateofneutralmutationshasabroaddistributioninsequencespace.Duetothisfact,thesubstitutionprocessisoverdispersed(theratiobetweenvarianceandmeanislargerthan1).Thisresultisincontrastwiththesimplestmodelofneutralevolution,whichassumesaPoissonprocessforsubstitutions,andinqualitativeagreementwiththebiologicaldata.

1999AcademicPress

1.Introduction

ArecentstudyontheProteinDataBank(PDB)showsthatthedistributionofpairwisesequenceidentitybetweenstructurallyhomologouspro-teinspresentsalargepeakat8.5%sequenceidentity,onlyslightlylargerthanwhatexpectedinthepurelyrandomcaseB(Rost,1998).Thisis

-Authortowhomcorrespondenceshouldbeaddressed.Presentaddress:FreieUniversitatBerlin,FBChemie,Takustr.6,D-14195Berlin,Germany.E-mail:ugo@chemie.fu-berlin.de.

BThenumberofaminoacidmatchesobtainedbypairingtworandomsequencesofthesamelengthisgivenbythebinomialdistributionwithp"ifoneassumesthatthe20

aminoacidshavethesameprobabilitytooccur.Forse-quencesoflengthNtherewillbeonaveragepNidenticalaminoacids,withavarianceNp(1!p).Forrandomse-quences,95%ofpairwisecomparisonsyieldasequenceidentitybetween1and9%.0022}5193/99/017049#16$30.00/0

aninterestingresultwhichmeansthatthestruc-turalsimilaritydoesnotimplysequencesimilarity.Anintensivecomputationalstudyonsecond-arystructuresofRNAmolecules(Schusteretal.,1994),whichisaproblemmuchsimplerthanproteinfolding,andcanbestudiedthroughe$-cientandreliablealgorithms,showedthatanexponentiallylargenumberofsequencescorres-pondsinaveragetoasinglestructure,andthedistributionofstructuresinsequencespaceisquiteinhomogeneous(itfollowsaZipflaw).Se-quencesfoldingintothemostcommonstructuresformconnected&&neutralnetworks''thatperco-latesequencespace.Theseneutralnetworksdirectlyarisefromthenon-uniquenessoftherelationbetweensequenceandstructure.

Theseresultsareimportanttounderstandhowevolutionworksatthemolecularlevel.Kimura

1999AcademicPress