JournalofTheoreticalBiology245(2007)576–594Multi-scalemodelingofawound-healingcellmigrationassayAnnaQ.Cai,KerryA.Landman�,BarryD.HughesDepartmentofMathematicsandStatistics,UniversityofMelbourne,Vic.3010,AustraliaReceived17August2006;accepted20October2006Availableonline28October2006AbstractAcontinuummodelandadiscretemodelaredevelopedtocapturethepopulation-scaleandcell-scalebehaviorinawound-healingcellmigrationassaycreatedfromascrapewoundinaconfluentcellmonolayer.Duringwoundclosure,thecellpopulationformsasustainedtravelingwave,withclosecontactbetweencellsbehindthewavefront.Cellsexhibitcontactinhibitionofmigrationandcontact-limitedproliferation.Thecontinuummodelincludesthetwodominantmechanismsandcharacteristicsofcellmigrationandproliferation,usingacelldiffusivityfunctionthatdecreaseswithcelldensityandalogisticproliferativegrowthterm.Thediscretemodelarisesnaturallyfromthecontinuummodel.Individualcellsaresimulatedascontinuous-timerandomwalkerswithnearest-neighbortransitions,togetherwithabirth/deathprocess.Themigrationandproliferationparametersaredeterminedbyanalysingindividualmice3T3fibroblastcelltrajectoriesobtainedduringthedevelopmentofaconfluentcellmonolayerandinawoundhealingassay.Thepopulation-scalemodelsuccessfullypredictstheshapeandspeedofthetravelingwave,whilethediscretemodelisalsosuccessfulincapturingthecontactinhibitionofmigrationeffects.r2006ElsevierLtd.Allrightsreserved.Keywords:Cellmigration;Contactinhibitionofmigration;Proliferation;Simulation;Continuumanddiscretemodels1.IntroductionCellinvasioniscentraltonormalandpathologicalbiologicalphenomena.Dermalwoundhealing,angiogen-esisandtumorinvasionaretypicalexamplesofcellinvasion.Cellmigrationandproliferationarethetwokeycellfunctionsresponsibleforcellinvasion.Tissueengineer-ing,wherebyhealthytissueisculturedtorepairdamagedormissingtissue,dependsonsuccessfulinvasionofcellsonabiodegradablescaffold.Thewound-healingcellmigrationassayprovidesavaluableinvitrotoolforstudyingthecombinedprocessesofcellmigrationandpro...
