on The Effect of Heterogeneously-Distributed RyR C

ArticleNo.bulm.1999.0101Availableonlineat(1999)61,651–681TheEffectofHeterogeneously-DistributedRyRChannelsonCalciumDynamicsinCardiacMyocytesPeterA.SpiroandHansG.Othmer†DepartmentofMathematics,UniversityofUtah,SaltLakeCity,UT84112,U.S.A.Calciumplaysanessentialroleinexcitation-contractioncouplinginmuscle,andderangementsincalciumhandlingcanproduceavarietyofpotentiallyharmfulcon-ditions,especiallyincardiacmuscle.Incardiactissuespecializedinvaginationsofthesarcolemma,calledT-tubules,penetratedeepintoeachsarcomere,anddepolar-izationoftheSLleadstoaninfluxofcalciumthroughvoltage-sensitivechannelsintheT-tubulesthatinturntriggersfurthercalciumreleasefromthesarcoplas-micreticulumviaryanodine-sensitivecalciumchannels.Undercertainconditions,suchaselevatedexternalCa2C,cardiaccellscanreleasecalciumfromthesar-coplasmicreticulumspontaneously,producingacalcium‘spark’andpropagatingtravelingwavesofelevatedCa2Cconcentration,withoutdepolarizationoftheSL(WierandBlatter,1991a,CellCalcium12,241–254;Williams,1993,CellCalcium14,724–735;Chengetal.,1993a,Science262,740–744).However,undernormalrestingconditionsthesepotentiallyharmfulwavesseldomoccur.Inthispaperweinvestigatetheroleoftheperiodicdistributionofryanodine-sensitivechannelsindeterminingwhetherasparkcantriggerawave,usingamodificationoftheki-neticmodelproposedbyTangandOthmer,1994b,Biophys.J.67,2223–2235,forcalcium-inducedcalciumrelease.WeshowthatthespatiallocalizationofthesechannelsneartheT-tubuleshasasignificanteffectonbothwavepropagationandtheonsetofoscillationsinthissystem.Spatiallocalizationprovidesapossibleex-planationforthedifferingeffectsofvariousexperimentalprotocolsonthesystem’sabilitytopropagateatravelingwave.c1999SocietyforMathematicalBiology1.INTRODUCTIONCalcium(Ca2C)isaubiquitousintracellularmessengerusedtoactivateawidevarietyofcellularprocesses,includingmusclecontraction,fertilizationanddevel-opmentofdeuterostomeeggs,cellgrowth,neuromodulationandsynapticplasticity,andsensoryperception(Berridge,1993).Calciumactivatescellularprocessesbyincreasedbindingtokeysignalingproteinsfollowinganincreaseincytosoliccal-ciumconcentration([Ca2C]i).Theincreasein[Ca2C]iisusuallyinresponsetoanCurrentaddress:IncytePharmaceuticalsInc.,3174PorterDrive,PaloAlto,CA94304,U.S.A.†SupportedinpartbyNIHGrantGM29123.0092-8240/99/040651+31$30.00/0c1999SocietyforMathematicalBiology652P.A.SpiroandH.G.Othmerextracellularsignal,suchasanactionpotentialorthebindingofaligandtoatrans-membranereceptor.Inthelattercasethiscanlead,throughaseriesofchemicalsteps,totheinternalproductionofinositoltrisphosphate(IP3),whichthenbindstoIP3receptors(IP3Rs)onthemembraneoftheendoplasmicreticulum(ER),aninternalcompartmentwhichstoresCa2Catconcentrationsmuchhigherthaninthecytosol.TheIP3RsareCa2CchannelswhichareopenedbythebindingofIP3,generatingagradient-drivenfluxofCa2Cintothecytosol.ExistingmodelsofthisprocessarereviewedinTangetal.(1996).Incardiacandothermusclecells,theprimaryroleofCa2Cistomediateexcitation-contractioncoupling(ECC),theprocessbywhichanactionpotentialproducesmusclecontraction.ECCisinitiatedbytherapidpropagationofanactionpotentialalongthecellmembrane(thesarcolemma,orSL)andfromonecelltoanother.Theactionpotentialpropagatesbothalongthesurfacemembraneofthecell,aswellasalongthetransversetubules(T-tubules),whichareinvaginationsoftheSLwhichextenddeepintothecell.Incardiacmyocytestheactionpotentialopensvoltage-openedchannels(VOCs),mostlyoftheformknownasL-typechannels,intheSL.ThisresultsinaninfluxofCa2Cbecauseresting[Ca2C]iismaintainedatalowerlevel(0:1M)thantheextracellularCa2Cconcentration([Ca2C]e1mM).Therisein[Ca2C]iresultingfromtheCa2Cinfluxtriggerscalcium-inducedcalciumrelease(CICR)fromthesarcoplasmicreticulum(SR),whereCa2Cisstoredatelevatedconcentrations.[FreeCa2CconcentrationintheSR([Ca2C]sr)is,again,about1mM,andtotal[Ca2C]intheSRmaybeabouttentimeshigher,duetoheavybufferingBers(1991a)].ReleasedCa2Cthendiffusesintothemyofibrils—specializedstructurescontainingtheactinandmyosinfilaments—andinducescontraction.WhereasextracellularCa2Cprovidesthetrigger,CICRprovidesthemajorityofCa2Cusedinactivatingcontractionincardiacmuscle(Bers,1991a;SpencerandBerlin,1997).CalciumreleasefromtheSRthroughtheryanodine-sensitivechannels(RyRs),whichopeninresponsetotheinitialrisein[Ca2C]i,apparentlyalsoinvolvesself-stimulationbyreleasedCa2C.MostoftheRyRsareintheterminalcisternaeorjunctionalSR(JSR),theportionsoftheSRdirectlyabuttingtheT-tubules.TheRyRsarethuslocatedincloseappositiontotheVOCs,apropertywhichfacilitatesopeningoftheRyRsbytheCa2Ctrigger.TheproximityoftheRyRsandVOCssuggeststheexistenceofcytosolicCa2Cmicrodomains(Stern,1992),inwhich[Ca2C]iadjacenttothesechannelsmayrisesubstantiallyabovethecell-averaged[Ca2C]i.However,thereleasemechanismisnotcompletelyunderstood,andfactorsotherthancytosolCa2Cmaybeinvolved.Forinstance,Ikemotoetal.(1992),foundthatluminalCacantriggerCareleasefromtheSR.TheautocatalyticreleaseofCa2Cterminatesonce[Ca2C]ireachesasufficientlyhighlevel,probablybecauseopeni