This inter pretation is still a matter of debate its resolution is important for our understanding of the nature of quantal response In this work we explore observable consequences of the univesicular release hypothesis by studying a stochastic mode ID: 11208
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ImplicationsofAll-or-NoneSynapticTransmissionandShort-TermDepressionbeyondVesicleDepletion:AComputationalStudyVictorMatveevandXiao-JingWangVolenCenterforComplexSystems,BrandeisUniversity,Waltham,Massachusetts02454Theall-or-nonecharacteroftransmissionatcentralsynapsesiscommonlyviewedasevidencethatonlyonevesiclecanbereleasedperactionpotentialatasinglereleasesite.Thisinter-pretationisstillamatterofdebate;itsresolutionisimportantforourunderstandingofthenatureofquantalresponse.Inthisworkweexploreobservableconsequencesoftheunivesicularreleasehypothesisbystudyingastochasticmodelofsynaptictransmission.Weinvestigatedseveralalternativemechanismsfortheall-or-noneresponse:(1)theunivesicularreleasecon-straintrealizedthroughlateralinhibitionacrosspresynapticmembrane,(2)theconstraintofasinglereleasablevesicleperactivezone,and(3)thepostsynapticreceptorsaturation.Weshowthatboththeunivesicularreleaseconstraintandthepostsynapticreceptorsaturationleadtoalimitedamountofdepressionbyvesicledepletion,sothatdepletionalonecannotaccountforthestrongpaired-pulsedepressionobservedatsomecorticalsynapses.Althoughdepressioncanberapidifthereisonlyonereleasablevesicleperactivezone,thissce-narioleadstoalimitonthetransmissionprobability.Weeval-uateadditionalmechanismsbeyondvesicledepletion,andourresultssuggestthatthestrongpaired-pulsedepressionmaybearesultofactivity-dependentinactivationoftheexocytosismachinery.Furthermore,wefoundthatthestatisticalanalysisofreleaseevents,inresponsetoalongstimulustrain,mightallowonetodistinguishexperimentallybetweenunivesicularandmultive-sicularreleasescenarios.Weshowthatwithouttheunivesicularreleaseconstraint,thetemporalcorrelationbetweenreleaseeventsisalwaysnegative,whereasitistypicallypositivewithsuchaconstraintifthevesiclefusionprobabilityissuf®cientlylarge.Keywords:centralsynapse;short-termdepression;exocy-tosis;univesicularrelease;receptorsaturation;stochastic Experimentalevidencefromvariousvertebrateneuralsystemsindicatesthatatcentralsynapsestransmissionproceedsinanall-or-nonefashion(forreview,seeRedman,1990;KornandFaber,1991;Walmsleyetal.,1998).Forinstance,inexperimentsinwhichquantalanalysiswascombinedwithmorphologicalre-constructionofsynapticconnections,thenumberofpostsynapticquantalresponseswasfoundtobeeitherequaltoorlessthanthenumberofreconstructedactivezones(Kornetal.,1982;RedmanandWalmsley,1983;Somogyietal.,1998).Inotherexperiments,thedistributionofpostsynapticresponsesevokedbystimulationofsinglesynapticboutonswasfoundtobeunimodal(Edwardsetal.,1976a,b;GulyaÂsetal.,1993;Arancioetal.,1994;StevensandWang,1995;Silveretal.,1996).Theseobservationshaveledtothehypothesisthatatmostonevesiclecanbereleasedperspikeperactivezone(TrillerandKorn,1982;Stevens,1993;Kornetal.,1994).Ithasbeenproposedthatfusionofonevesicletriggersalateralinhibitionacrossthepresynapticmembrane,preventingothervesiclesfrombeingreleasedsimultaneously(TrillerandKorn,1982).Theobservationofanabsoluterefractorytimeofseveralmillisecondsafterasynapticresponse(StevensandWang,1995;Hjelmstadetal.,1997)hasbeeninterpretedasevidenceforsuchalateralinhibitionmechanism(Dobrunzetal.,1997).Asecondpossiblebasisfortheunivesicularreleaseistheconstraintthatthereisonlyasinglereleasablevesicleperactivezoneatanygiventime.Alternatively,theall-or-nonesynaptictransmissionwasproposedtoarisefromthesaturationofpostsynapticrecep-torsbyneurotransmittercontentofasinglevesicle,whichwouldimplythesamepostsynapticresponseregardlessofthenumberofvesiclesreleased(Jacketal.,1981;Edwardsetal.,1990;TongandJahr,1994;Augeretal.,1998)[forevidenceofnon-saturation,seeLiuetal.(1999)].Thesecontrastingscenariosrepresentdifferentviewsaboutthenatureofthesynapticquantalresponse.Elucida-tionofthisissueisessentialforourunderstandingofsynapticcomputationandplasticity.Thepurposeofthepresentworkistoexploreobservableimplicationsoftheall-or-nonetransmissionhypothesisbycom-putersimulationofastochasticsynapsemodelthatisconstrainedbyrecentdataoncorticalsynapsesthat,likesynapseselsewhere,oftenexhibitshort-termdepressionofresponse.Anothermoti-vationofthisstudyistotesttheproposalthatshort-termsynapticdepressioniscausedbydepletionofthereleasablevesiclepool(LileyandNorth,1952;Hubbard,1963;StevensandWang,1995).Ourresultssuggestthatwitheitherunivesicularreleaseconstraintorpostsynapticreceptorsaturation,vesicledepletionalonecan-notaccountforthestrong(morethantwofold)paired-pulsedepression(PPD)observedatcorticalsynapses(MarkramandTsodyks,1996;Thomson,1997;Varelaetal.,1997;Brenowitzetal.,1998;WangandLambert,1998).Weconsiderdepressionmechanismsbeyondvesicledepletionthatcanexplaintheob-servedPPD,includingpresynapticinhibitionviametabotropicautoreceptors(DaviesandCollingridge,1990,1993;Scanzianiet ReceivedJuly23,1999;revisedNov.8,1999;acceptedNov.29,1999.ThisworkwassupportedbytheAlfredP.SloanFoundationandNationalInstituteofMentalHealthGrantMH53717-01.WethankLarryAbbott,SachaNelson,VenkateshMurthy,andCharlesStevensforusefulcommentsandhelpfuldiscussions.CorrespondenceshouldbeaddressedtoXiao-JingWang,VolenCenterforComplexSystemsandPhysicsDepartment,BrandeisUniversity,Waltham,MA02454.E-mail:victor@ariel.ccs.brandeis.edu;xjwang@volen.brandeis.edu.Copyright2000SocietyforNeuroscience0270-6474/00/201575-14$15.00/0TheJournalofNeuroscience,February15,2000, al.,1997)andactivity-dependentinactivationofexocytosisma-chinery(Hsuetal.,1996).Moreover,wefoundthatthetemporalcorrelationbetweenstochasticresponsestoarepetitivetrainofstimulibehavesdif-ferentlydependingonwhethermultiplereleasesareallowed.Therefore,measurementofsuchtemporalcorrelationsmaypro-videanovelexperimentalwaytotesttheunivesicularreleasehypothesis.MATERIALSANDMETHODSModelofvesicleturnover.Oursynapsemodelis,inessence,asimplemodelofvesicleturnover(Fig.1).Thereareindications,bothfunctionalandmorphological,thatatleasttwodistinctpoolsofvesiclescanbeidenti®edatthepresynapticsite,arelativelysmallpoolofvesiclesimmediatelyavailableforrelease,possiblyrepresentingvesiclesdockedatthepresynapticsite,andamoredistalandmuchlargerreservepoolofvesicles(forreview,seeZucker,1996;Neher,1998).However,astraight-forwardrealizationofthetwo-poolmodelasamassactionscheme(Heinemannetal.,1993),depictedinFig.1isnotrealistic,becauseaccordingtosuchamodeltherateofre®llofthedockedpoolisproportionaltothenumberofreservepoolvesicles,.Inreality,thereshouldbeaconsiderablebottleneckinthere®llprocess,becauseatagiventimeonlythosereservevesiclesthatareclosesttothereleasesitehaveasigni®cantprobabilityforbeingdocked.Therefore,weusedanalternativescheme,wherethedockedpoolhasalimitedsize,andeachvacancycanbere®lledatarateindependentofthereservepoolsize.Inthiscaseasimplesingle-poolmodel(Fig.1)(LiuandTsien,1995;Wang,1999)provides,inourview,amoreaccuratedescriptionofvesicledynamics,aslongasthereservepoolisfarfromdepletion.Thus,ourmodelsynapseconsistsofasinglevesiclepoolofsizewithanupperlimitof,whichcanloseoneormorevesiclesinresponsetoapresynapticactionpotential.Depletionofthevesiclepoolleadstoshort-termdepression,whichrecoverswithatimeconstanttotheinverseofthevacancyre®llrate.Processesofvesiclereleaseandrecoveryaretreatedstochastically(Vere-Jones,1966;MelkonianandKostopoulos,1996;Quastel,1997;MaassandZador,1999).ReleaseofasinglevesicleduringanincomingpulseisgovernedbyaPoissonprocesswithsometime-dependentrate),whichweassumeissigni®cantonlyforthedurationofthepulse.Theintegralisthefusionrateforasinglevesicleintegratedoverthedurationofthepresynapticpulse.Thesingle-vesiclereleaseprobabilityisthenexp(),andthesingle-vesiclefailureprobabilityis1exp()(DobrunzandStevens,1997).Inouranalysisweneglectfacilitationoftransmitterrelease(Fisheretal.,1997)becausewestudypredominantlysynapsesexhibitingpro-nouncedshort-termdepression,whichgenerallyshowahighinitialre-leaseprobabilityandlittlefacilitation(KornandFaber,1987;Zucker,1989;Debanneetal.,1996;DobrunzandStevens,1997;TsodyksandMarkram,1997).Wealsoneglectactivity-dependentchangesintherecyclingkineticsthatcanin¯uencesynapticresponsetolongtrainsofstimuli(Hubbard,1963;ElmqvistandQuastel,1964;DittmanandRe-gehr,1998;StevensandWesseling,1998;WangandKaczmarek,1998),becauseinthisworkwemostlyconsidersynapticresponsetoapaired-pulsestimulus(alsoseeDiscussion).AllcalculationswereperformedusingMonte-Carlosimulationsofthemodel.Themodelingcomputerprogramwaswritteninthelanguage,compiledusingaGNUcompilerandexecutedonIntelPentium-poweredcomputersrunningundertheLinuxoperatingsystem.Becausethesim-ulationswerenotCPU-timeintensive,thousandstotensofthousandofMonte-Carloiterationswererunforeachofthegraphspresented,untilthestatisticalerrorswerenegligible.Westudytwoversionsofthesynapsemodel;onewiththeunivesicularreleaseconstraintandtheotherwithunconstrainedrelease.Univesicularreleasecase.Weimplementtheunivesicularreleasecon-straintbyassumingthatavesiclereleaseeventtransientlypreventsothervesiclesfrombeingexocytosed,assuggestedbyTrillerandKorn(1982).Then,thereleaseprobabilityperstimulusis1minusthefailureproba-bility,givenbythethpowerofsingle-vesiclereleasefailureprobability,isthenumberofvesiclesavailableforrelease(DobrunzandStevens,1997,theirEq.1.A):,(1)with.Therefore,theunivesicularreleaseconstraintimpliesanonlineardependenceofthereleaseprobabilityonthenumberofavail-ablevesicles.Forsmall(low-releaseprobability),exp(,andEquation1yieldsanapproximatelylinearrelationship:Weassumethatthereleasesitequicklyrecoversfromtheputativeinhibitionmechanismthatpreventsmultivesicularrelease.AsproposedbyDobrunzetal.(1997),suchaªlateralinhibitionºmechanismmaybeatthebasisoftheobservedbriefrefractoryperiodafterapostsynapticresponse,duringwhichtheprobabilityforanotherreleaseissmall(StevensandWang,1995;Hjelmstadetal.,1997).Experimentally,onecandistinguishbetweentherelativeandtheabsoluterefractorytimes;forhippocampalsynapsesinculture,bothvaluesarecloseto5msec(StevensandWang,1995;Hjelmstadetal.,1997).Therefore,atphysio-logical®ringrates(40Hz)weexpecttherecoveryfromrefractorinesstobecompletewithinaninterspikeinterval.Unconstrainedreleasecase.Intheabsenceoftheunivesicularreleaseconstraint,whenmultivesicularreleaseisallowed,individualvesiclesarereleasedindependentlyofeachother,withreleaseprobabilityexp().Thenumberofvesiclesreleasedinresponsetoanaction,isdeterminedbyabinomialdistributionwithparameters(sizeofavailablepool).Theaveragenumberofvesiclesreleasedisthengivenby(for®xed).Inthiscasetheamplitudeofsynapticresponsedependsonthefractionofpostsynapticreceptorsthatareboundbyneurotransmitterreleasedfromasinglevesicle,whichwedenoteby(ªoccupancyºorªsaturationºparameter).Ifthesynapticresponseproducedbyactivationofallpostsynapticre-ceptorsisgivenby,theresponseattributabletoreleaseofonevesiclewillbe,responseattributabletotwovesicleswillbebe1(12v)],andsoon;responseattributabletoreleaseof Figure1.Modelsofvesicleturn-over.Thetwo-poolsynapsemodel.Theªdockedºpooliscomposedofvesiclesimmediatelyavailableforrelease.Inresponsetoanactionpotential,adockedvesicleisreleasedwithacertainprobabilitydependenton.Thispoolisre®lledbyvesiclesfromthereservepool;thedashedarrowsigni®esthebottleneckinthere®llprocess.Single-poolsynapsemodel.ReleaseprobabilityisdescribedbyaPoissonprocesswithlateralinhibitionbetweenreleasesitesandisgivenby1minusthefailurerate,whichisequaltoexp(isthefusionrateforasinglevesicle.Vacancyinthevesiclepoolisre®lledwithatimeconstantof,whichdeterminesthedepressionrecoverydynamics.J.Neurosci.,February15,2000,(4):1575±1588MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticity isthenthen1(12v)1...1(12v)n21]5R[12(12v)n](Augeretal.,1998).Averageinitialresponseisgivenbyanaverageofoverthebinomialdistribution,),ofthenumberofvesiclesreleased, n!~N2n!!pVn~12pV!N2n5RH12On50NN! .(2)Animportantparameterofthesynapsemodelistherelease-readypoolsize,.Thesizeoftherelease-readypoolvariesacrossdifferenttypesofcentralsynapses(Zucker,1996;Neher,1998);weuseestimatesforhippocampalexcitatorysynapses,whererecordingsfromindividualboutonshavebeenachieved(BekkersandStevens,1990;Raastadetal.,1992;LiuandTsien,1995).Fortherathippocampalsynapsesinsliceandculture,Stevensandcollaborators(StevensandTsujimoto,1995;DobrunzandStevens,1997)assessedthesizeofthereleasablepoolbymeasuringthenumberofpostsynapticresponseselicitedbyashorthigh-frequencyelectricstimulationorbyabriefapplicationofahypertonicsolution(RosenmundandStevens,1996),aswellasbyopticalmonitoringoftheamountof¯uorescentdyetakenupandreleasedduringstimulation[Murthyetal.(1997);MurthyandStevens(1998);alsoseeRyanetal.(1997)].Theavailablepoolsizeestimatedinindividualexperimentsvariedbetween2and25.Ultrastruc-turalanalysisofhippocampalsynapsessuggeststhatthesenumbersareconsistentwiththenumberofvesiclesdockedatsinglesynapticactivezones(Fortietal.,1997;SchikorskiandStevens,1997).Inoursimula-3-10.Forthevesiclere®lltimeconstantwechooseavalueof2sec,whichagreeswiththetimeofrecoveryofthereadilyreleasablepoolmeasuredinhippocampalsliceexperimentsbyDobrunzandStevens(1997).Inthisform,themodelisspeci®edbythreeparameters:themaximalsizeofthevesiclepool,thedepressionrecoverytimeconstant,andthevesiclefusionrate[or,equivalently,theinitialreleaseprobabilityexp()].Forthecaseofunconstrainedrelease,thereisanadditionalsaturationparameterMetabotropicpresynapticinhibition.Presynapticmetabotropicautore-ceptorsarebelievedtoexerttheiractionprimarilythroughinhibitionofvoltage-dependentCachannels(forreview,seeWuandSaggau,1997).Let)bethedynamicalvariabledescribingthelevelofactivationofinhibitoryautoreceptors.Assumingthatthereleaseprobabilityde-pendsonapowerofthespike-triggeredCain¯ux,andthattheamountofCain¯uxisinverselyproportionalto),wereplacethevesiclefusionrateby: ,(3)wheretheconstantcontrolsthestrengthoftheinhibitoryeffect,andspeci®esCacooperativityofvesiclerelease(Zucker,1996;Neher,1998).Wechose3.Presynapticautoreceptorsareassumedtobeactivatedbyneurotransmitterreleasedbythesamesyn-apseanddiffusingawayfromthesynapticcleft;therefore,thereceptoractivityvariable)shoulddependontheprevioussynapticactivityandshowdelayedresponsetovesiclerelease,whichwemodelbysimplesecond-orderkinetics(asimilarmodelhasbeenusedinWangetal., dtax~12x!y2x tx ayOti,td~t2ti!2y .(4)arevesiclereleasetimes,coef®cientsdeterminethespeedofonsetofpresynapticinhibition,andconstantsminetherateofdecayoftheinhibitoryeffect.Wehavechosenthefollowingparametervalues:600msec,2sec,100msec,7.Theseparametervalueswerechosentoreproduceapproximatelythedependenceofpaired-pulsedepressionontheinter-pulseintervalobservedathippocampalGABAergicsynapses(seeFig10).Statisticalanalysis.Foradiscrete(point)processsuchasaspiketrain,oratrainofreleaseevents,autocorrelationfunction)characterizesthelikelihoodofobservingtwoeventsseparatedbyatimeintervalequal.Itisde®nedby:aneventinaneventin istheaverageeventrate.Inthisnormalizationtheautocorre-lationfunctionisthereforeequaltothedifferencebetweenthecondi-tionalprobabilityrateofobservinganeventat(orcloseto)timegivenaneventat(orcloseto)time,andtheaverage(unconditional)eventrate.Hereweassumethattheprocessisstationary,soneither)nordependonIntheparticularcaseofconstant-frequencystimulationofperiodtimeisdiscretizedintoequallyspacedpoints,andthevesiclereleaseeventtrainisde®nedbythequantity:1ifreleaseatthstimulus0otherwise.(6)Theexpressionfortheautocorrelationfunctionnowtakestheform:,(7)istheaveragesteady-statereleaseprobability.Anotherusefulindicatoroftemporalcorrelationsinthesynapticoutputisthecoef®cientofcorrelationbetweensuccessiveinter-releaseintervals(IRIs):,IRI ,(8)whereangledbracketsdenoteaveragevalues,andIRIisthethinter-releasetimeinterval.RESULTSShort-termdepressionattributabletovesicledepletionTimecourseofshort-termdepressionFirstweexaminetheresponseofthesynapsemodelthatincludestheunivesicularreleaseconstraint,toastimulustrainofconstantfrequency(Fig.2).ThereleaseeventsequencesandtheevolutionofreleaseprobabilitywithstimulusnumberareshowninFigurefortwodifferentstimulationtrials.Becauseonlyonereleaseisallowedperactionpotential,synapticoutputisabinaryeventsequence(release/failure).Towardtheendofthetracestherearetimeintervalsofzeroreleaseprobability;duringthoseperiodsthevesiclepooliscompletelydepleted.Thetrial-averagedreleaseprobability,whichrepresentstheaveragesynapticresponseforagivenstimulus,isshowninFigure2itdecaysmonotoni-callywithstimulationasaresultofthegradualdepletionoftheavailablevesiclepool,untilitreachesastationary-statevalue,Thecharacteristictimeofresponsedecaydependsbothontherecoverytimeconstantandtherateofstimulation.Forthelinearizedversionofthemodel(small),onecanshowthatthisdepressiontimeconstantisgivenby(seeAppendix2,Eq.17): t51 tD1r1 .(9)Therefore,istypicallymuchshorterthan;depressionisfasterwithlargervesiclefusionrateorathigherstimulation.Forexample,with0.29(and8yieldingMatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticityJ.Neurosci.,February15,2000, inFig.3)and20Hz,wehave136msecfromEquation92000msec.AscanbeseeninFigure2thenumberofavailablevesiclesisarandomquantity;consequentlythereleaseprobabilitydisplaysastochastictimeevolutionthatvariesfromtrialtotrial.Thestateofthesynapseatagiventimeisdescribedbytheprobabilitydistributionof).Evolutionof)withtimeisdemonstratedinFigure3.Plottedinthis®gurearethehisto-gramsofthevesiclepoolsizeimmediatelybeforeaspike,forseveralconsecutivestimuliina30Hztrain.Beforethearrivalofthe®rststimulus,thedistributionconsistsofasinglepeakat.Itgraduallybroadenswithstimulation,untilitsharpensagainatlowvaluesof,asthevesiclepoolgetsmoredepleted.Inthesteadystatethesynapseisnotlikelytocontainmorethanoneortworelease-readyvesicles,atphysiologicalstimulationratesmuchhigherthanthedepressionrecoveryrate1/0.5Hz.Steady-stateaverageresponse:the1/rbehaviorThesteady-statesynapticresponserateisde®nedasthesteady-statereleaseprobability,characterizingsynapticresponsepersinglestimulus,multipliedbythestimulationrate.InFiguretheresponserateisplottedasafunctionofthestimulationrate;itincreasesmonotonicallyandapproachesaplateauathighstimulationfrequencies.Synapticresponsesaturatesatalowerfrequencyifthevesiclefusionrateislarger(theinitialreleaseprobabilityishigher)oriftherecoverytimeconstantislarger(thevesiclere®llisslower)(TsodyksandMarkram,1997;Markrametal.,1998).Thesaturationoftheresponserateimpliesthatthesteady-statereleaseprobabilitydecaysas1/athighrates,becauseofvesicledepletion(LileyandNorth,1952).Aswas®rstnotedbyAbbottetal.(1997)andTsodyksandMarkram(1997),becauseofshort-termdepressiontheresponseratebecomesinsensitivetothefrequencyofsustainedpresynapticstimulationathighinputfrequencies.Thesestudiesusedlinearmodelsofsynapticdepression.Herewefoundthatthe1/behaviorholdstrueforthenonlinearmodel,whichtakesintoaccounttheuni-vesicularreleaseconstraint.Indeed,weshowinAppendix1thatforanyparametervaluesofthemodel,atsuf®cientlyhighstimu-lationfrequencies),independentofthevesiclefusionrate(Eq.14).TemporalcorrelationinthesteadystateInadditiontotheaverageresponsethatreachesaconstantinthesteadystate,variabilityandcorrelationsinthestochasticsynapticresponsecanalsobemeasuredandquanti®edexperimentally.Weanalyzedthe¯uctuationpropertiesofourmodelsynapseinthe Figure2.Responseofthesynapsemodeltoconstantfrequencystimu-Anexamplewithastimulusrateof20Hz;()thestimulustrain,)synapticresponse;twosampletrialsareshown.Blackverticalbarsrepresentreleaseevents;theheightofthethickgraybarsdenotesthereleaseprobabilityatthetimeofarrivalofaspike.Parametervalues:2sec.Trial-averagedreleaseprobabilityasafunctionoftime.Steady-statesynapticresponserate,givenbytheproductoftheaveragereleaseprobabilityandstimulationrate.Becausetheaveragereleaseprobabilitybehaveslike1/,theresponseratesaturatesathighstimulationfrequencies.Histogramfortheinter-releaseintervalsinthesteadystateisclosetoanexponentialwithtimeconstant274msec(solidline),where20Hzisthestimulationfrequency,and0.182istheaveragesteady-statereleaseprobability. Figure3.Evolutionoftheprobabilitydistribution)forthenumberofavailablevesicles.Inthetopleftcornerisindicatedthestimulusnumberina30Hztrainforwhichthehistogramiscomputed.SynapticparametersarethesameasinFigure2(2sec,0.9).Probabilitydistributioniscomputedimmediatelybeforethespike.Initialdistributionisasinglepeakat.Thelastpanelshowsthesteady-statevesiclenumberdistribution.Inthesteadystate,theaveragenumberofavailablevesiclesistypicallyoneortwo.J.Neurosci.,February15,2000,(4):1575±1588MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticity steadystate.Oneimportantcharacteristicisthedistributionofinter-releaseintervals(Fig.2).Itisveryclosetoanexponentialwithadecaytimeconstantequaltotheaverageinter-releaseinterval,givenby1/(Thetemporalautocorrelationbetweenreleaseevents)(seeEq.7forde®nition),inthesteadystate,isshowninFigure4Theautocorrelationissmallinmagnitudeandcanbeeithernegativeorpositive,respectively,forsmallandlargevaluesofthevesiclefusionrate.Itstemporalbehaviorisdescribedbyanexponentialfunctionwithatimeconstant205msecfor0.374,and535msecforTheautocorrelationfunctionofthenumberofavailablevesicleshasthesameexponentialtimecourse,butisalwayspositive,forallvalues(Fig.4ThedependenceofthetemporalcorrelationonthevesiclefusionrateisshowninFigure5.ConsistentwithFigure4thecorrelationbetweenreleaseeventsattwoconsecutivestimuli,,changessignfromnegativetopositiveasisincreased(Fig.5).Therefore,withasmallifthereisalreadyareleaseatstimulus,thereleaseprobabilityatthenextstimulus1)issmallerthantheaveragereleaseprobability,becauseofthelossofavesicle.Withalarge,however,theconditionalreleaseprobability1)becomeslargerthan,despitethevesiclereleaseatstimulus.Similarly,thecorrelationcoef®cientforthetwoconsecutiveinter-releaseintervals(Fig.5)(seeEq.8forde®nition)isnegativeforsmallvaluesandbecomespositiveforlargerThevalueofshouldbefairlylargeinthedepressioncase,becausetheinitialreleaseprobabilityexp()islarge.Therefore,forournonlinearsynapsemodelwiththeuni-vesicularreleaseconstraint,theautocorrelationfunctionofthesynapticoutputisexpectedtobepositiveingeneral.Bycontrast,forthelinearizedversionofthemodelwheredependslinearly,thecorrelationbetweensuccessiveresponsescanbefoundanalyticallyandturnsouttobealwaysnegative,regard-lessofparameterchoices(seeEq.20inAppendix2).Temporalcorrelationsarealsonegativeifmultiplereleasesareallowed(see Figure4.Temporalcorrelationsofthereleaseeventsinthesteadystate.Autocorrelationfunctionofthereleaseeventsequencefor0.95(Autocorrelationfunctionfor0.6(Parametersare2sec.Stimulationrateis15Hz.C,D,Autocorrelationfunctionforthenumberofavailablevesicles.Parametersinthesameasinrespectively.Filledcirclessimulationresults;solidcurvesareexponential®tswithcorr205msecforcorr535msecfor Figure5.Thesignofthesteady-statetemporalcorrelationdependsonthevesiclefusionrateCorrelationbetweensuccessivereleaseevents,asafunctionofCoef®cientofcorrelationbetweensucces-siveinter-releaseintervalsasafunctionof.Bothquantitiesbecomepositiveasisincreased.Parametersare2sec,15Hz.OpencirclesmarkpointscorrespondingtovaluesinFigure4.MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticityJ.Neurosci.,February15,2000, Strongpaired-pulsedepressionandtheall-or-nonehypothesisUnivesicularreleasemodelAlthoughtheresponseofthesynapsemodelshowninFigure2agreeswellwithtypicaldepressingsynapticresponsesrecordedexperimentally,theunivesicularreleasemodelcannotreproducethestrongpaired-pulsedepression(PPD50±60%,wherepaired-pulsedepressionisde®nedastheratiobetweenresponsestothesecondand®rstpulses:PPDPPDp2/p1),whichhasbeenobservedinsomeexperimentsoncorticalsynapses(Fig.6)(De-banneetal.,1996;MarkramandTsodyks,1996;Thomson,1997;Varelaetal.,1997;Brenowitzetal.,1998;WangandLambert,1998).Intuitively,ifthesynapseinitiallyhasexocytosis-readyvesicles,andifatmostonevesicleisreleasedatthe®rststimulus,therearestill(1)vesiclesavailableonthearrivalofthesecondstimulus,andPPDbyvesicledepletionalonecannotbelessthan(.Forexample,evenifisassmallas3,theresponsetothesecondstimuluscannotbe67%oftheresponsetothe®rststimulus.Moreprecisely,wecanshowthat: p1$pr~N021! pr~N0!$N021 N05121 ,(10)wherethelowerbound(canbereachedonlyontheassumptionoflineardependenceofreleaseprobabilityonthevesiclepoolsize().Thisconstraintonpaired-pulsedepressionattributabletodepletionhasbeendemonstratedear-lierbyFaber(1998).Iftheinitialreleaseprobabilityishigh(withalargevesiclefusionrate),thedifferencebetween)and1)isevensmaller,becauseofthenonlineardependence(Eq.1).Therefore,additionalfactorsarelikelytobeinvolvedinthegenerationofthestrongpaired-pulsedepression.Two-stepexocytosismodelWeconsideredthepossibilitythattheeffectivenumberofreadilyreleasablevesiclesperactivezoneislimitedtojustone.Thisnaturallyleadstotheunivesicularreleaseconstraint,withoutassumingpresynapticlateralinhibition.Supposethatthereisaheterogeneityinthefusionrateindividualvesicles.Vesicleswithhighvaluesofwouldbedepleted®rst,andsubsequentstimulicanonlyreleasevesicleswithalow,leadingtoresponsedepression.However,thestrongPPDofFigure6canbereproducedonlyifamongallavailablevesiclesonlyonevesiclehasalarge,becausePPD50%canbebarelyachievedevenwith2inthehomogeneouscase(Eq.10).Thepossibilitythatonlyonevesicleperreleasesitehasahighfusionprobabilityneedstobesubstantiatedbyabiologicalmechanismthatwouldselectasinglevesicleoutofthetotalªdockedºvesiclepool.Weimplementedsuchaconstraintthroughanassumptionthatthepoolofvesiclesdockedatthepresynapticmembraneisdividedintoseveralsubpopulationsthatareindifferentstagesofreadinessforrelease,inaccordancewiththemultistagenatureofexocytosis(NeherandZucker,1993;Èdhof,1995).Inourextendedmodel,exocytosisisrepresentedbyatwo-stageprocess;vesiclesintheintermediatestateareassumedtobedockedatthepresynapticmembranebuthavenotyetundergoneªprimingº(BittnerandHolz,1992;Xuetal.,1998)forrelease(Fig.7).Exchangebetweenthetwostagesisareversibleprocessandfollows®rst-orderkinetics,withratecon-.Nowthenumberofvesiclesimmediatelyavailableforreleaseisdeterminedbythedynamicequilibriumbetweentwostagesinvesicleskinetics.Withasuf®-cientlylowprimingrate,thenumberofvesiclesintherelease-ready(ªprimedº)statecanhaveanaverageclosetoone.Figureshowsthesimulationsresultsforthisextendedversionofthemodel.Fortheparameterschosen,averagenumberofvesiclesintheprimedstateatrestis1,whichmakespossiblea50%reductionofresponseafterasinglepulse.Wenotethatinthisscenariofortheall-or-noneresponse,althoughthereisonlyoneprimedvesicleonaverage,thereleaseprobabilitydependsnonlinearlyonthedockedvesiclepoolsize.Indeed,thenumberofprimedvesiclesisdistributedaccord-ingtoabinomialwithparametersTheprobabilityofhavingzeroprimedvesiclesis(1,whichsetsalowerboundfortheprobabilityoftransmissionfailurebecausenoreleaseispossiblewithoutaprimedvesicle.There-fore,thereleaseprobabilityisexpectedtobehavelike1,consistentwiththeexperimentaldata(DobrunzandStevens,1997).Ontheotherhand,thisscenariohasafewlimi-tations.First,evenifthenumberofvesiclesreleasedistypicallyzeroorone,morethanonevesiclecanbereleasedinindividualtrials.Thisisbecausethenumberoftheprimedvesiclesisarandomquantityand¯uctuatesintime.Second,andmoreim-portantly,inthisscenariotheinitialreleaseprobabilityislimited.Iftheprobabilityofhavingonlyonevesicleintheprimedpoolishigh,somustbetheprobabilityofhavingzeroprimedvesicles[equalto(1],leadingtoahighfailurerate.Forexample, Figure6.Examplesofshort-termdepressionatcorticalsynapses.Post-synapticresponseto20Hzstimulationinratlayer5neocorticalpyramidalneuroninslice,dual-cellularrecordingbyMarkramandTso-dyks(1996,theirFig.2Amplitudeofthe®eld-potentialresponseto5Hzstimulationoflayer4recordedinlayer2/3ofratvisualcortexinslice.FigurewasredrawnfromVarelaetal.(1997,theirFig.4J.Neurosci.,February15,2000,(4):1575±1588MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticity 1,and6,then0.17,andtheprobabilityofhavingzeroprimedvesicle(1Therefore,thefailureprobabilityisatleast0.33,andtheinitialreleaseprobabilitymustbesmallerthan1UnconstrainedreleasemodelWehaveshownabovethattheunivesicularreleaseconstraintleadstoalimitontheamountofdepressionthatcanresultfromvesicledepletion.Itcanbearguedthenthatthestrongpaired-pulsedepressionobservedexperimentallyrepresentsevidenceagainsttheunivesicularreleaseconstraintandthatthesaturationofpostsynapticreceptorsbyneurotransmitterreleasedbyasinglevesicleisapossibleexplanationoftheall-or-nonenatureofsynapticresponses(Jacketal.,1981;TongandJahr,1994;Augeretal.,1998).Hereweshowthatthisisnotthecaseandthatwithsynapticsaturation,depletion-induceddepressionislimitedaswell.Whenmultiplereleasesareallowed,themagnitudeofPPDdependscriticallyonthedegreeofsaturationofpostsynapticreceptorsbytransmittercontentofasinglevesicle.Intuitively,thehigheristhesaturation,thelessdifferencethereisbetweenthe®rstresponsecausedbythereleaseofseveralvesiclesandthesecondresponsecausedbythereleaseofasmallernumberofvesicles,andthereforethesmallershouldbethePPDeffect.Conversely,ifpostsynapticreceptorsarefarfromsaturation,synapticresponsewillbeproportionaltothenumberofreleasedvesicles,anddepressionbyvesicledepletioncanbemorepronounced.SimulationresultsareshowninFigure8.WeseethatPPDcanindeedbeverystrong,undertheconditionthatislargeandthereislittlesaturation(small).WecanderiveananalyticalexpressionforthePPDmagnitudewhentheinter-stimulusintervalismuchshorterthan,sothatthere®llbetweenstimulicanbeneglected.InthiscasePPDisgivenby(Appendix3,Eq.22): .(11)InagreementwiththesimulationresultsofFigure8,itfollowsfromthisformulathatwithunconstrainedreleasePPDcanbemadearbitrarilystrongforanybychoosingasuf®cientlylarge.Withalarge,however,thefailureprobabilitymaybecometoosmallandincompatiblewiththemeasure-mentsfromcorticalsynapses.Forexample,ifweimposearea-sonablevalueforthefailureprobability,say0.1,thenIfwerequirefurtherthatsaturationofpostsynapticreceptorsishigh(1),toreconcilewiththeputativeall-or-noneresponse,fromEquation11wehavePPD75%,i.e.,onlyamoderateamountofPPD.Evenifsynapsesareassumedtobefarfromsaturation,with0.4(Liuetal.,1999),thenPPD63%,whichisstillnotquiteasstrongasinFigure Figure7.Thetwo-stepmodelofvesiclerelease.Modelkinetics.Vesiclesundergoªprimingºbeforebecomingavailableforrelease.Prim-ingrate1/isslowerthanthereverserate1/,suchthatonaveragethereisonlyonevesicleintheimmediatelyreleasablepool.timecourseinresponsetoa30Hzstimulationforthetwo-stepsynapsemodel.Parametervaluesare2sec,1.5sec,4.6.Noticesharpdepressionofresponseafterasinglestimulus. Figure8.BehaviorofthesynapsemodelwithunconstrainedvesicleA,B,Responsetimecoursesfordifferentvaluesoftherecep-torsaturationfactor(between0and1)specifyingthedegreetowhichpostsynapticreceptorsaresaturatedbyneurotransmitterfromasinglevesicle.Responseismeasuredbytheaveragenumberofvesiclesreleasedandisnormalizedbyinitialresponse.Failurerateis5%inand1%in.Othersynapticparameterare2sec.Stimulationrateis15Hz.MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticityJ.Neurosci.,February15,2000, InFigure9isshownthecorrelationbetweensuccessivesyn-apticreleaseeventsinresponsetoaconstant-frequencyspiketrain,inthesteadystate.Incontrasttothecaseoftheunivesicularreleaseconstraint(Fig.5),temporalcorrelationisalwaysnegativewithmultivesicular(unconstrained)release.Inthiscasecorrela-tionisnegativeforallvaluesofthesingle-vesiclereleaseproba-bility()andregardlessofthemagnitudeofthepostsynapticreceptoroccupancyfactor.Thesecontrastingresultssuggestthat,inprinciple,thesignofthecorrelationbetweensuccessiveresponsesinthesteadystatecanbeusedtoassesswhetherthedependenceofthereleaseprobabilityonthenumberofavailablevesiclesislinearornonlinear,asatestoftheunivesicularreleasehypothesis.Toconclude,althoughverystrongPPDcaninprinciplebeachievedwithmultivesicularrelease,thisscenariowouldrequireaphysiologicallyimplausiblelowfailureprobability,orpostsyn-apticreceptorsmustbefarfromsaturation,whichwouldbeinconsistentwiththeall-or-nonesynapticresponse.Therefore,observationofstrongPPDatcorticalsynapsescannotbeusedasanargumentagainsttheunivesicularreleaseconstraint.DepressionbeyondvesicledepletionAboveresultssuggestthattheªfastºcomponentofsynapticdepressiondemonstratedinFigure6cannotbeexplainedbyvesicledepletionandthatadditionalmechanismsarelikelytobeinvolved.Wehavefocusedonthefollowingtwopossiblescenarios.PresynapticmetabotropicinhibitionPresynapticinhibitionbymetabotropicreceptorsrepresentsanimportantformofmodulationofsynaptictransmission.Metabo-tropicautoreceptorsareactivatedbyneurotransmitterreleasedatthesamenerveterminalandactthroughinhibitionofpresynapticcurrents(WuandSaggau,1997),leadingtoaspecialformofshort-termsynapticplasticity.SuchplasticitymechanismhasbeenobservedatGABAergicsynapsesinrathippocampusbyDaviesandCollingridge(1990,1993),whereactivationofpre-synapticGABAreceptorswasshowntoberesponsiblefortheshort-termdepressionofevokedinhibitorycurrents[alsoseeDeiszandPrince(1989)].Similareffecthasbeenobservedatglutamatergicmossy®berhippocampalsynapsesofguineapigsbyScanzianietal.(1997),withdepressionresultingfromtherecruit-mentofpresynapticmetabotropicglutamateautoreceptors[alsoseeForsytheandClements(1990);BaskysandMalenka(1991)].Westudytheeffectofmetabotropicinhibitionbyintroducingintoourmodelarelease-dependentnegativefeedbackprocess,mimickingthepresynapticinhibitionmediatedbymetabotropicautoreceptors(seeMaterialsandMethodsfordescription).Withanappropriatechoiceofparameters,theextendedmodelsuc-cessfullyreproducesthecharacteristicU-likedependenceofpaired-pulsedepressionontheinter-pulseintervaldurationob-servedexperimentallybyDaviesandCollingridge(1993)(Fig.).Maximaldepressionoccursforinter-pulseintervalsbe-tween100msecand1sec,correspondingtostimulationfrequen-ciesof1±10Hz;inthisrangemorethantwofoldreductionofresponseisobtained.Timecourseofsynapticresponsetoaperiodic5HzstimulationisdemonstratedinFigure10weassumedthatreleaseisunivesicular;resultswouldbesimilarforthemodelwithunconstrainedrelease.Interestingly,thismechanismleadstoareductionofsaturationofthepostsynapticsteady-stateresponseathighstimulationrates,therebyincreasingthedynamicrangeofthesynapse(Fig.10Thisarisesbecausemetabotropicinhibitionactsasanegativefeedbacktovesiclerelease,slowingdepletionofthevesiclepoolathighstimulationfrequencies,andthusincreasingtherangeoverwhichthepostsynapticresponsedependsonpresynaptic®ringrate.Consequently,ifasynapseshowssaturationofthesteady-stateresponseatrelativelylowstimulationfrequencies Figure9.Temporalcorrelationofsynapticresponseisnegativewithunconstrainedvesiclerelease.Correlationcoef®cientbetweenthere-sponsestotwoconsecutivestimuliofaconstantfrequencystimulationtrain,asafunctionofthesingle-vesiclereleaseprobability,fortwovalues.Unlikeinthecaseoftheunivesicularconstraint(Fig.5),herethecorrelationisalwaysnegative. Figure10.Effectofinhibitorymetabotropicautoreceptorsonsynaptictransmission.dashedlinesindicatemodelsimulationdatawithandwithoutpresynapticinhibition,respectively.Inter-pulseintervaldependenceofpaired-pulsedepression.indicateexperimentaldataobtainedbyDaviesandCollingridge(1993)byrecordinginhibitorycurrentsinpyramidalcellsinrathippocampalslicesincontrol()andinthepresenceofaGABAantagonist(opencirclesTimecourseofdepressingsynapticresponsetoa5Hzstistatereleaseprobabilityand()synapticresponserate(givenbytheproductofreleaseprobabilityandtherate),asafunctionofthestimu-lationfrequency.IncontrasttoFig.2presynapticinhibitionpreventsresponseratesaturationandextendsthesynapticdynamicrange.Synapticparametervaluesare2sec.J.Neurosci.,February15,2000,(4):1575±1588MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticity (Abbottetal.,1997;TsodyksandMarkram,1997;Markrametal.,1998),thenitspresynapticmodulationmediatedbymetabotropicreceptorsislikelysmall.Metabotropicautoinhibitionmostprob-ablyoccursatparticularclassesofsynapsesonly;insomestudiesantagonistsofmetabotropicglutamatereceptorswereshowntohavenoeffectonplasticitydynamicsofcorticalsynapses(Do-brunzandStevens,1997).InactivationofreleasemachineryStrongPPDmayalsooccurasaresultofsomeactivity-dependentinhibitionofvesiclereleasemachineryitself,forinstancethroughaCa-dependentinactivationofexocytosis.Experimentalevi-denceforsuchamechanismcomesfromtheworkofHsuetal.(1996),whofoundthattransmitterreleaseatthesquidgiantsynapsetriggeredbyintroductionofCaintotheterminaldeclinesrapidly,evenwhiletheCaconcentrationismain-tainedataconstantlevel.WhenCaconcentrationwaselevatedbycaged-Cabufferphotolysisinastepwisemanner,transmit-terreleaseoccurredonlytransientlyaftereachconcentrationincrease.Hsuetal.(1996)proposedthattheexocytosis-controllingmoleculargatesmayundergoCa-driventransitionsbetweenactivestatestriggeringvesiclereleaseandinactivecon-formationalstates.Weimplementedsuchamechanismbyintroducingintoourmodelasimplekineticschemewherethereleaseapparatusofeachvesicleiscontrolledbyagatethatcanbeinoneofthethreestates(Fig.11).Releasecanhappenonlywhenthegateisinthe(ªfusionº)state,sothevesiclefusionrateismultipliedbythefractionofgatesthatareinthestateatthetimeofarrivalofaspike.Intheabsenceofstimulation,releasegatesareinthe(ªrestº)state;transitionsbetweenthestatesandbetween(ªinactivatedº)statesoccuronlyduringanincomingactionpotential,presumablythroughbindingofaCaion.Unlesstheintervalbetweentwoconsecutivespikesismuchlargerthanthetimeconstantofrecoveryfrominactivationfractionofgatesinactivatedduringthe®rstspikewillremaininactiveatthetimeofarrivalofthesecondspike,leadingtoshort-termdepressionofresponse.AlthoughthismodelistoosimpletoreproducetheexactadaptationofresponseobservedbyHsuetal.(1996),itcapturesthebasiccharacteristicsoftheprocess.AsimilarmodelhasbeenproposedbyYamadaandZucker(1992)toexplaintheinvarianceofthetimecourseofexocytosiswithvaryingCain¯ux.Weassumedheretheuni-vesicularreleaseconstraint;resultswouldnotbesigni®cantlydifferentfortheunconstrainedcasewithhighreceptorsaturation.Withahighdegreeofthereleasemachineryinactivation,themodeldisplaysstrongpaired-pulsedepressionsimilartothedatafromcorticalsynapses(Fig.11).Notethatdepressionnowproceedsintwophases(Fig.11),thefastinitialphasebeingfollowedbyaslowerphaseofsmallermagnitude.Thisbehavioragreesbetterwiththeresponsetimecoursesobservedexperimen-tally(Fig.6).Moreover,thesteady-stateresponseratesaturatesatmoderatestimulationfrequencies(20Hz)(Fig.11Aninterestingfeatureofthismodelisthatitnaturallyincor-poratesafacilitationmechanism,inthecasewhereinactivationisweak.Forasuf®cientlysmallinactivationrate,thefractionofgatesinthestatewillincreaseduringthe®rstseveralactionpotentialsinaspiketrain.Iftherest-statemagnitudeofthevesiclefusionrateissmall,thiswouldleadtofacilitationofWehavepresentedastochasticmodelofshort-termsynapticdynamicsthatincludesavesicleturnoverprocess,withthecon-straintthatatmostonevesiclecanbereleasedperstimulus(Edwardsetal.,1976a,b;Kornetal.,1982;RedmanandWalms-ley,1983;GulyaÂsetal.,1993;Arancioetal.,1994;StevensandWang,1995;Silveretal.,1996;DobrunzandStevens,1997;Somogyietal.,1998;Walmsleyetal.,1998).Theunivesicularreleasehypothesisrepresentsacentraltenetofcorticalsynaptic Figure11.Inactivationofreleasemachinery.Kineticschemeforthemodel.Aªgateºcontrollingvesiclereleasecanbeinoneofthethreestatesshowninthe®gure.Withnostimulation,gatesarepredominantlyinthe(rest)state.Withstimulation,transitiontothe(fusion)statetakesplace,leadingtovesiclerelease.Atthesametime,quicktransitionfromthestatetotheinactivestatetakesplace,haltingexocytosis.InternalCaisassumedtobeaninstantaneousfunctionofpresynapticvoltage,soCa-driventransitionsonlyoccurduringthebrieftimeofstimulusarrival.Responsetimecourseforthereleaseinactivationmodelwith30Hzstimulation.Parametersare2sec,16.8sec333sec15sec,[Ca2msec.Notethebiphasictimecourse,thesharppaired-pulsedepressionfollowedbyaslowerdeayprocess.Steadystateresponserateasafunctionofthestimulationfrequency,reachingsaturationat20Hz.MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticityJ.Neurosci.,February15,2000, physiology,yetitsvalidityremainsamatterofdebate.Herewefoundthatthisconstrainthasseveralexperimentallyobservableimplicationsforthedynamicresponsesofsynapses.Ourmainresultsaretwofold.First,thestrongpaired-pulsedepressionobservedatsomecorticalsynapsesisunlikelytoresultfromvesicledepletionaloneandinsteadmaybecausedbyactivity-dependentinactivationoftheexocytosismachineryitself.Sec-ond,univesicularandmultivesicularreleaseleadtodifferenttemporalstatisticsofreleaseeventsinresponsetoalongtrainofstimuli,suggestinganexperimentallytestablepredictionfortheunivesicularreleasehypothesis.SynapticdepressionbeyondvesicledepletionWefoundthattheall-or-nonecharacterofsynaptictransmissionimpliesalimitationonsynapticpaired-pulsedepression.Withtheunivesicularreleaseconstraintrealizedbylateralinhibitionacrosspresynapticmembrane(Kornetal.,1994),vesicledepletionislimitedtoatmostoneperspike.Althoughvesicledepletionmaybeacceleratedbymultivesicularrelease,itseffectissmallifpostsynapticreceptorsaresaturatedbytransmittercontentofasinglevesicle(TongandJahr,1994;Augeretal.,1998);ontheotherhand,theall-or-noneresponsecannotberealizedifpostsynapticreceptorsarefarfromsaturation(Liuetal.,1999).Inbothcases,iftheall-or-noneresponseisassumed,vesicledeple-tionalonecannotexplainthestrongpaired-pulsedepressionobservedatneocorticalsynapses(Fig.6)(MarkramandTsodyks,1996;Thomson,1997;Varelaetal.,1997;Brenowitzetal.,1998;WangandLambert,1998).Wealsoanalyzedthepossibilitythatonlyoneofthedockedvesiclesisprimedandtrulyrelease-readyatanytime.Wefoundthatthisscenarioisconsistentwithexistingexperimentaldata(suchasnonlineardependenceofreleaseprobabilityonthedockedvesiclepoolsize)andcanproducestrongpaired-pulsedepressionasobservedatcorticalsynapses.However,inourimplementationbyatwo-stageexocy-tosisscheme,thisscenariohasthespecialfeatureofhavingalimitedtransmissionprobability.Itisnotknownwhethertheonereleasablevesicleconstraintcanbeimplementedinotherways,forexamplebyassumingthatasinglevesicleamongalldockedvesiclesissituatedataprivilegedpresynapticmembranelocation.However,insuchastructure-basedscenariothereleaseproba-bilitywouldbeindependentofthenumberofdockedvesicles,contrarytoexperimentalevidence(DobrunzandStevens,1997).Thus,toreconciletheall-or-nonetransmissionwiththeobser-vationsofstrongpaired-pulsedepression,onemustallowthatdepressionmechanismsbeyondvesicledepletionsigni®cantlycontributetopaired-pulsedepressionatcentralsynapses(Faber,1998).SeveralpresynapticandpostsynapticmechanismscanberuledoutaspotentialsourcesofstrongPPD.Postsynapticrecep-tordesensitizationisnotlikelytocausethedramaticdepressionofresponseforstimuliseparatedbyatimeintervalof50±200msecasinFigure6,becauseofthefastrecoveryofAMPAreceptorsfromsuchdesensitization(Colquhounetal.,1992;Trusselletal.,1993).Thisisconsistentwithstudiesinwhichshort-termplasticityatcorticalsynapseswasshowntobeunaf-fectedbydesensitization-blockingagents(Debanneetal.,1996;DobrunzandStevens,1997;Varelaetal.,1997;GalarretaandHestrin,1998;BellinghamandWalmsley,1999).Moreover,inac-tivationofpresynapticCachannelsisprobablyalsonotim-portantforPPD,becausethedegreeofinactivationcausedbyasingleactionpotentialisatmostafewpercent(Foxetal.,1987;LemosandNowycky,1989;CoxandDunlap,1994;Forsytheetal.,1998;Patiletal.,1998;Wuetal.,1998).However,inactivationofCacurrentscancontributetodepressionduringprolongedhigh-frequencystimulation(JiaandNelson,1986;Forsytheetal.,1998;Patiletal.,1998).Wehaveexploredtwofactorsthatmaycontributetopaired-pulsedepression.Wefoundthatthemodelsimulatingpresynapticinhibitionviametabotropicautoreceptorscanreproducestrongpaired-pulsedepression(Fig.10),inagreementwithexperi-mentalevidence(DaviesandCollingridge,1990,1993;Scanzianietal.,1997).Activity-dependentinactivationofreleasemachin-eryrepresentsanothermechanismthatinouropinioncanexplainthestrongPPDshowninFig.6(Hsuetal.,1996).Theversionofourmodelincorporatingsuchinactivation(Fig.11)succeedsinreproducingtwofoldpaired-pulsedepression(Fig.11)andleadstoabiphasicresponsedecay,similartoexperimentallyobservedbehavior.Ourproposedmechanismissupportedbyrecentevi-dence(BellinghamandWalmsley,1999)thatthedepressionattheendbulbofHeldiscausedbyreductionofthereleaseprob-abilitybyintracellularcalcium.Itispossiblethatsuchamecha-nismalsounderliesthestrongdepressionofresponseobservedrecentlyinterminalsofretinalbipolarcellsbyBurroneandLagnado(1998).Thetwodepressionmechanismscouldbedifferentiatedexper-imentallyinseveralways.First,presynapticinhibitionbymetabo-tropicautoreceptorsisactivatedbyreleaseofvesicles.Release-inducedreductionofsubsequentsynapticresponseisgenerallyreferredtoasrefractorinessofasynapse(Betz,1970;StevensandWang,1995;ThomsonandDeuchars,1995;Dobrunzetal.,1997;Hjelmstadetal.,1997).Bycontrast,inactivationoftheexocytosismachineryisassumedtobeinducedbystimulation-triggeredin¯ux,independentofvesiclerelease.Ifpaired-pulsede-pressionisrelease-dependent,responsestoapairofstimuliwouldbenegativelycorrelated(ThomsonandDeuchars,1995;Faber,1998).Conversely,nocorrelationisexpectedifthede-pressiondoesnotdependontheoccurrenceofvesiclerelease.Thisway,themetabotropicpresynapticinhibitionandtheinac-tivationmechanismproposedherecouldbedistinguishedexperimentally.Second,previousstudies,usinglinearmodelsofsynapticde-pression,havereproducedtheexperimentalobservationthatresponseratereachessaturationwithincreasingrateofpresyn-apticstimulation(Abbottetal.,1997;TsodyksandMarkram,1997).Here,weshowedthatthisbehaviorholdsaswellforthenonlinearmodelofvesicledepletionwiththeunivesicularreleaseconstraint,andwhentheinactivationofreleasemachineryisincluded.Bycontrast,presynapticinhibition,althoughproducingstrongtransientpaired-pulsedepression,atthesametimere-ducestheamountofsaturationinthesteady-stateresponseathighstimulationfrequencies.Thisisbecausemetabotropicauto-receptorssubserveanegativefeedbacktovesicledepletion;therebythedynamicalrangeofthesynapticresponsivenessisextended.Therefore,measurementofthesteady-stateresponserateasfunctionoftheinputfrequencycouldbeusedtodistin-guishthetwocandidatedepressionmechanisms.Finally,phar-macologicalmeanscouldbeusedtodirectlyassesstheroleofspeci®ctypesofmetabotropicautoreceptorsatagivensynapse.Univesicularreleaseversusreceptorsaturation:signofresponseautocorrelationWhetherpostsynapticreceptorsatcentralsynapsesaresaturatedbytransmittercontentofasinglevesicleremainsanissueofdebate(Tangetal.,1994;TongandJahr,1994;FrerkingandWilson,1996;Silveretal.,1996;Fortietal.,1997).RecentworkJ.Neurosci.,February15,2000,(4):1575±1588MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticity suggeststhatpostsynapticglutamatergicreceptorsatcorticalsyn-apsesaregenerallyfarfromsaturation(Liuetal.,1999;Mainenetal.,1999).Wefoundthattheunivesicularreleaseandreceptorsaturationscenariosleadtodifferentpredictionsaboutthesteady-statecorrelationbetweensynapticresponsestosuccessivespikesinaconstant-frequencytrain.Wehavedemonstratedthatforthemodelwiththeunivesicularreleaseconstraint,characterizedbynonlineardependenceofreleaseprobabilityonthenumberofavailablevesicles,thetemporalautocorrelationofthesynapticresponsetoconstant-frequencystimulationisexpectedtobepositiveifthevesiclefusionrateisreasonablylargeandisnegativeonlywithsmall(Figs.4,5).Thisisincontrastwiththebehaviorofthemodelwherethedependenceofsynapticresponseonthenumberofavailablevesiclesislinear,inwhichcasethecorrelationbetweensuccessivereleaseeventsisalwaysnegative,bothforthemodelwithunconstrained(multivesicular)release(Fig.9)andforthelinearizedversionoftheconstrainedmodel(Appendix2,Eq.20).Wenotethatsuchtemporalcorre-lationdoesnotrequirestimulationofsinglesynapticconnectionsandcouldbededucedfrommeasurementswithmultiplesynapticcontacts.Becausereleaseeventsatdifferentsynapsesarestatis-ticallyindependent,thetemporalautocorrelationofthepostsyn-apticresponsewillbeequaltothesumofcorrelationsofre-sponsesofindividualsynapses.Furthermore,theseresultsconcerningthesignofthetemporalcorrelationarestillapplicableifadditionalactivity-dependentprocessessuchassynapticfacili-tation(Fisheretal.,1997)andincreaseinthedockingrate(Hubbard,1963;ElmqvistandQuastel,1964;DittmanandRe-gehr,1998;StevensandWesseling,1998;WangandKaczmarek,1998)aretakenintoaccountbecauseinthesteadystate,param-etersaffectedbytheseprocesseswillhavereachedsomeconstantstationaryvalues.Forexample,inascenarioinwhichthesynapticvesiclefusionrateislowinitiallybutincreaseswithstimula-tionasaresultoffacilitation,thesteady-statevalueofwillbelarge,sothecorrelationbetweensuccessiveresponsesisexpectedtobenegativeinthecaseofunconstrainedreleaseandpositiveinthecaseofunivesicular(constrained)release,allowingonetodistinguishbetweenthesetwopossibilities.Inanyevent,thegeneralsuggestionisthatmeasurementofthetemporalcorrela-tionsintheresponsestoalongtrainofstimulimaybeusedtotesttheunivesicularreleasehypothesis,abasicnotionincorticalsynapticphysiology.APPENDIX1Steady-stateresponseforageneralone-poolsynapsemodelForaconstant-frequencystimulationofrate,thereisasimplerelationshipconnectingtheaveragesynapticresponseandtheaveragenumberofavailablevesiclesinthestationarystate,validforageneralsingle-poolvesiclereleasemodelwith®rst-orderrecoverykinetics.Letdenotetheaveragenum-berofavailablevesiclesimmediatelybeforearrivalofaspikeanddenotetheaveragenumberofvesiclesreleasedinthesteadystateinresponsetoasinglestimulus.Thentheaveragenumberofvesiclesthatareunavailableimmediatelyafteraspikeisequalto{2^D)}.Multiplyingthisnumberbytheprobabilityforavesiclepoolvacancytobere®lledduringoneinter-spikeinterval,re®ll weobtainanaverageforthenumberofvesiclesre®lledbetweentwospikes,whichinthesteadystatemustbeequaltotheaveragenumberofvesiclesreleased: Solvingthisequation,weobtainthefollowinglinearrelationshipbetweentheaveragenumberofvesiclesreleasedandtheaveragenumberofavailablevesicles: .(13)Thisresultisvalidbothforthemodelwiththeunivesicularreleaseconstraintandfortheunconstrainedmodelwheremul-tivesicularreleaseisallowed.Athighrateswecanexpandtheexponentintheaboveexpression;takingintoaccountthatapproacheszerowithincreasingratebecauseofdeple-tion,weget:.(14)Thus,athigh®ringratesstationarysynapticresponsedependonlyonthere®lltimeconstantandthemaximalvesiclepoolsize,anddecreasesastheinverseofrate.Inthemodelwhereonlyonereleaseperactionpotentialisallowed,averagenumberofvesiclesreleasedisequaltotheaveragereleaseprobability,andcanbereplacedwithinEquations13±14.AccordingtoEquation14,doesnotdependonvesiclefusionratehighstimulationfrequencies.Thisresultisnotspeci®ctoconstant-frequencystimulationandholdsinthecaseofarbitrarystationarystimulationpatternofaveragerateAPPENDIX2Linearizedone-poolmodel:temporalcorrelationIfoneassumeslineardependenceofreleaseprobabilityonthenumberofvesicles,then(theconstraintofatmostonereleaseperactionpotentialismaintained),andthislinear-izedmodelcanbeobtainedasalimitingcasefromtheinitialnonlinearmodel(exp())for1.Inthatcase,certainstatisticalcharacteristicsofthemodel'sre-sponsetoconstant-frequencypresynapticstimulationcanbecal-culatedanalytically,usingmathematicaltheoryofstochasticpro-cesses(vanKampen,1981).Forinputstimulationrateof,theaveragenumberofavailablevesiclesinthesteadystate(measuredimmediatelybeforeeachofthepulses)isgivenby: .(15)Thecorrespondingsteady-statereleaseprobabilityisequalto.Theaboveexpressioncanbefound(indifferentnotations)inAbbottetal.(1997)andTsodyksandMarkramThetimecourseofresponseisexponentialandisgivenby:,(16))denotesthenumberofvesiclesimmediatelybeforethspike,andtheresponsedecaytimeconstantis: t521 Dtb~12aV1 tD11 Dt1 .(17)MatveevandWangUnivesicularReleaseandShort-TermSynapticPlasticityJ.Neurosci.,February15,2000, Equation16isequivalenttotheexpressionfoundinTsodyksandMarkram(1997),withthesubstitutionsThetimeconstantgivenbyEquation17alsodeterminesthedecayofthetemporalautocorrelationforthenumbersofavail-ablevesiclesinthestationarystate: ,(18)wherethesteady-statevarianceofthenumberofavailablevesiclesisequalto: .(19)However,thecorrelationcharacteristicthatcanbemeasuredexperimentallyisthecorrelationbetweenreleaseevents(seede®nition,Eq.7): tGG0;2^pr&11N021 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