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1、Quasispeciesdynamicsonanetworkofinteractinggenotypesandidiotypes:FormulationofthemodelValmirC.Barbosa,1RaulDonangelo,2,3andSergioR.Souza2,41ProgramadeEngenhariadeSistemaseComputa¸c˜ao,COPPE,UniversidadeFederaldoRiodeJaneiro,CaixaPostal68511,21941-972RiodeJaneiro-RJ,Brazil2Institutod
2、eF´ısica,UniversidadeFederaldoRiodeJaneiro,CaixaPostal68528,21941-972RiodeJaneiro-RJ,Brazil3InstitutodeF´ısica,FacultaddeIngenier´ıa,UniversidaddelaRep´ublica,JulioHerrerayReissig565,11.300Montevideo,Uruguay4InstitutodeF´ısica,UniversidadeFederaldoRioGrandedoSul,CaixaPostal15051,915
3、01-970PortoAlegre-RS,BrazilAquasispeciesisthestationarystateofasetofinterrelatedgenotypesthatevolveaccordingtotheusualprinciplesofselectionandmutation.Quasispeciesstudieshaveinvariablyconcentratedonthepossibilityoferrorsduringgenotypereplicationandtheirroleinpromotingeitherthesurviv
4、alorthedemiseofthequasispecies.Inapreviouswork[V.C.Barbosa,R.Donangelo,andS.R.Souza,J.Theor.Biol.312,114(2012)],weintroducedanetworkmodelofquasispeciesdynamics,basedonasingleprobabilityparameter(p)andcapableofaddressingseveralplausibilityissuesofpreviousmodels.Hereweextendthatmodelb
5、ypairingitsnetworkwithanotheroneaimedatmodelingthedynamicsoftheimmunesystemwhenconfrontedwiththequasispecies.Thenewnetworkisbasedontheidiotypic-networkmodelofimmunityand,togetherwiththepreviousone,constitutesanetworkmodelofinteractinggenotypesandidiotypes.Theresultingmodelrequiresfu
6、rtherparametersandasaconsequenceleadstoavastphasespace.Wehavefocusedonaparticularnicheinwhichitispossibletoobservethetrade-offsinvolvedinthequasispecies’survivalordestruction.Withinthisniche,wegivesimulationresultsthathighlightsomekeypreconditionsforquasispeciessurvival.Theseincludea
7、minimuminitialabundanceofgenotypesrelativetothatoftheidiotypesandaminimumvalueofp.Thelatter,inparticular,istobecontrastedwiththestand-alonequasispeciesnetworkofourpreviouswork,inwhicharbitrarilylowvaluesofpconstituteaguaranteeofquasispeciessurvival.PACSnumbers:87.23.Kg,89.75.Fb,02.1
8、0.Ox,02.50.-rI.INTR
