Prolonged Intracellular Na+ Dynamics Govern Electrical Activity in Accessory Olfactory Bulb Mitral

25 Pages·2015·2.69 MB·English

RESEARCHARTICLE
+
Prolonged Intracellular Na Dynamics Govern
Electrical Activity in Accessory Olfactory Bulb
Mitral Cells
AsaphZylbertal1*,AnatKahan2,YoramBen-Shaul2,YosefYarom1,ShlomoWagner3
1 DepartmentofNeurobiology,InstituteofLifeSciences,HebrewUniversityandtheEdmondandLilySafra
CenterforBrainSciences,Jerusalem,Israel,2 SchoolofMedicine,DepartmentofMedicalNeurobiology,
HebrewUniversity,Jerusalem,Israel,3 SagolDepartmentofNeurobiology,UniversityofHaifa,Haifa,Israel
*[email protected]
a11111
Abstract
Persistentactivityhasbeenreportedinmanybrainareasandishypothesizedtomediate
workingmemoryandemotionalbrainstatesandtorelyuponnetworkorbiophysicalfeed-
OPENACCESS back.Here,wedemonstrateanovelmechanismbywhichpersistentneuronalactivitycan
begeneratedwithoutfeedback,relyinginsteadontheslowremovalofNa+fromneuronsfol-
Citation:ZylbertalA,KahanA,Ben-ShaulY,Yarom
Y,WagnerS(2015)ProlongedIntracellularNa+ lowingburstsofactivity.Weshowthatmitralcellsintheaccessoryolfactorybulb(AOB),
DynamicsGovernElectricalActivityinAccessory whichplaysamajorroleinmammaliansocialbehavior,mayrespondtoabriefsensory
OlfactoryBulbMitralCells.PLoSBiol13(12): stimulationwithpersistentfiring.Bycombiningelectricalrecordings,Ca2+andNa+imaging,
e1002319.doi:10.1371/journal.pbio.1002319
andrealisticcomputationalmodeling,weexploredthemechanismsunderlyingthepersis-
AcademicEditor:NaoshigeUchida,Harvard
tentactivityinAOBmitralcells.Wefoundthattheexceptionallyslowinwardcurrentthat
University,UNITEDSTATES
underliesthisactivityisgovernedbyprolongeddynamicsofintracellularNa+([Na+]),which
i
Received:September7,2015
affectsneuronalelectricalactivityviaseveralpathways.Specifically,elevateddendritic
Accepted:November5,2015 [Na+] reversestheNa+-Ca2+exchangeractivity,thusmodifyingthe[Ca2+] set-point.This
i i
Published:December16,2015 process,whichreliesonubiquitousmembranemechanisms,islikelytoplayaroleinother
neuronaltypesinvariousbrainregions.
Copyright:©2015Zylbertaletal.Thisisanopen
accessarticledistributedunderthetermsofthe
CreativeCommonsAttributionLicense,whichpermits
unrestricteduse,distribution,andreproductioninany
medium,providedtheoriginalauthorandsourceare
AuthorSummary
credited.
Theaccessoryolfactorysystemisessentialforchemicalcommunicationinanimalsduring
DataAvailabilityStatement:Alldatafilesusedfor
generationofthearticlefigures,alongwiththecode socialinteractions.Duringthisprocess,theprinciplecellsoftheaccessoryolfactorybulb
toreproducethefigures,areavailableintheGerman (AOB)mayrespondtotransientstimulationwithprolongedactivity,sometimeslasting
NeuroinformaticsNode(g-node)portal:http://dx.doi. forminutes—apropertyknownaspersistentactivity.Thisproperty,whichhasbeen
org/10.12751/g-node.vd9c21.
observedinotherbrainareas,isusuallyattributedtopositivefeedbackmechanismseither
Funding:ThisworkwassupportedbytheIsrael atthecellularorthenetworklevel.Here,weshowhowpersistentactivitycanemergewith-
ScienceFoundation(http://www.isf.org.il/)grant outfeedback,relyingonslowchangesininternalionicconcentrations,whichkeepa
#1350/12,receivedbyShlomoWagnerandthe
recordofpastneuronalactivityforlongperiodsoftime.Weusedacombinedcomputa-
GatsbyCharitableFoundation(http://www.gatsby.org.
tionalandexperimentalapproachtoshowthatthecomplexinteractionbetweenvarious
uk/).Thefundershadnoroleinstudydesign,data
ions,theirextrusionmechanisms,andthemembranepotentialleadstostimulus-
collectionandanalysis,decisiontopublish,or
preparationofthemanuscript.
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ProlongedActivityand[Na+] inAOBMitralCells
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CompetingInterests:Theauthorshavedeclared
thatnocompetinginterestsexist. dependentpersistentactivityintheAOB.Thesamemechanismmayapplytootherneuro-
naltypesinvariousbrainregions.
Abbreviations:AIS,axoninitialsegment;AOB,
accessoryolfactorybulb;CAN,calcium-activated
non-selective;EPSC,excitatorypost-synaptic
current;PSTH,peristimulustimehistogram;SBFI,
sodium-bindingbenzofuranisophthalate;TTX, Introduction
tetrodotoxin;VNO,vomeronasalorgan;VSN,
Theaccessoryolfactorysystem,alsoknownasthevomeronasalsystem,mediateschemical
vomeronasalsensoryneuron.
communicationbetweenconspecificsofmostmammalianandreptilianspeciesduringsocial
interactions[1].Inputstothischemosensorysystemoriginatefromthesensoryneuronsofthe
vomeronasalorgan(VNO)thatsynapseonthemitralcellsoftheaccessoryolfactorybulb
(AOB),whichprovidetheoutputofthebulb[2].Previously,wehaveshownthatAOBmitral
cellsinvitrorespondtobriefafferentnervestimulationwithpersistentfiringactivitylasting
severalminutes[3].
Persistentactivity,definedastheabilityofneuronstoremainactiveintheabsenceofexter-
nalinputs,wasdocumentedinmanybrainareas.Suchactivityenablesthebraintomaintain
aninternalstatewithoutcontinuousexternalinput.Ithasbeensuggestedthatpersistentactiv-
ityisaneuronalcorrelateofworkingmemory[4],andthatitcanmediateneuronalintegration
overlongtimescales[5].
Thetimescaleofpersistentactivity(>1min)ismuchlongerthanthatofmostbiophysical
mechanisms(typically0.5–100ms).Mostattemptstoexplainhowtheextremelyprolonged
timescalesofpersistentactivityemergefromsuchrapidbiophysicalprocesseshaveinvolved
feedbackmechanisms[6].Suchfeedbackcanbeimplementedwithrecurrentexcitationatthe
networklevel[7–9],oralternatively,bybiochemicalpathwaysatthecellularlevel.Anexample
ofthelatteristhemechanismproposedtounderliepersistentactivityintheentorhinalcortex
[10,11]andhippocampalCA1pyramidalneurons[12,13].Themechanisminvolvesaninterac-
tionbetweenCa2+influxduringspikingandacalcium-activatednon-selective(CAN)cation
conductancethatdepolarizesthecell.However,theoreticalmodelsofprolongedspikingbased
onfeedbackmechanismsarehardtoconstructinawaythatisrobusttosmallparameter
changes,immunetonoiseandcontinuouslygraded[10,14–16].
PersistentactivityinAOBmitralcellswasshowntodependuponCa2+influxandCAN
conductance.However,thisintrinsiccellularmechanismdoesnotdependonafeedbackcycle
involvingongoingneuralactivity,aspersistentfiringreadilyresumesafteratemporalfiring
cessation[3].
Inthepresentstudywecombinedelectrophysiological,imaging,andcomputational
approachestoexplorethemechanismsunderlyingpersistentfiringinAOBmitralcells.We
describeanovelmechanisminvolvinginterplaybetweenhomeostaticprocessescontrolling
intracellularNa+andCa2+concentrations.Thisnovelmechanism,whichdoesnotrelyupon
feedback,isbothresistanttonoiseandallowsmultiplestablefiringstates.
Results
AOBMitralCellsAreCapableofRespondingtoTransientStimuliwith
PersistentFiring,BothInVitroAndInVivo
ProlongedfiringactivityofAOBmitralcellswasdemonstratedinbehavingmiceduringsocial
investigationofconspecifics[17].Ithasremainedunclearwhetherthissustainedactivity
reflectsthecontinuousdetectionofthestimulusornetworkproperties.Inordertoexplorethis
issue,weexaminedAOBresponsesinanesthetizedmicefollowingwell-controlledchemosen-
sorystimulusapplicationtotheVNO(Fig1Aand1B,S1Fig)[18].
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Fig1.AOBmitralcellsarecapableofrespondingwithpersistentfiringtotransientstimulibothinvivoandinvitro.(A)Top:rasterplotsshowinga
singleunitresponsetotenrepetitionsofVNOstimulationbyfemalesaliva(red),urine(green),andvaginalsecretion(blue).Bottom:Peristimulustime
histogram(PSTH)ofthechangesinfiringfrequency.Verticalblacklinesdenotethetimesofapplicationofthesolutionstothenasalcavityandtheactivation
ofthesympatheticnerve.(B)Changeinthemeanfiringfrequency,measuredduring20sfollowingstimulusflush(highlightedintervalinA)comparedwiththe
initialfiringrateforthesameunitandstimulus.Errorbarsdenotestandarderrorofthemean(SEM).(C)Top:invivoresponseofasingleunitintheAOBtoa
brieftrainofelectricalstimulideliveredtothevomeronasalnervefibers(redbar).Bottom:PSTHshowingthemeanchangeinfiringfrequencyoverseven
repetitionsofthesamestimulationprotocol.(D)Top:theresponseofanAOBmitralcell(upperpanel),recordedinvitrousingwholecellpatchtechnique,
followinga30Hzspiketrainevokedbypulsecurrentinjections(lowerpanel).Spikesaretruncated(at−10mV)toshowtheunderlyingplateaupotential.
Bottom:aPSTHshowingthemeanchangeinfiringfrequencyofthreecells(tenrepetitionsineach,sametimescaleandstimulusasinthetoppanel).Thick
blackline:meanPSTHofthethreecells.Redbardenotes4sof30Hzstimulation.ShadedareasdenoteSEM.SeealsoS1Fig.
doi:10.1371/journal.pbio.1002319.g001
Whileresponsedynamicsoftenmatchedthoseattributedtothevomeronasalpump[18,19],
inothercases,elevatedfiringratesremainedhighwellbeyondthistimescale,sometimeseven
afterthestimuluswasflushedfromthenasalcavityandtheVNO.Underahighlystrictstatisti-
calcriterion(seeDataAnalysisinMaterialsandMethods),reliablecasesofpersistentactivity
werefoundinaboutonepercent(n=7)oftherecordedunits,andwereassociatedwitha
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particularstimulus,whileotherstimulielicitedonlytransientresponseinthesamecells(Fig
1Aand1B).Thisstimulusselectivityisconsistentwitharequirementforahighlevelofactiva-
tiontotriggertheprolongedfiring(seebelow).
Similarly,prolongedsingleunitAOBspikingactivitycouldbereadilyelicitedinanesthe-
tizedmicebydirectstimulationofthevomeronasalnervewithametalelectrode(Fig1C),fur-
therconfirmingthatthesustainedresponsesareindependentofVNOdynamics.Finally,In
agreementwithourpreviousstudy[3],persistentfiringcouldbeelicitedinAOBmitralcellsin
brainslices.AnexampleisshowninFig1D(top),wherea4strainofactionpotentialsisfol-
lowedbyaprolongedperiodofpersistentspikingatarateof1–3Hzlastingforoveraminute.
Thereproducibilityofthisfiringepochisdemonstratedbythemeanrateresponseforthe
threerecordedcells(Fig1D,bottom).Altogether,theseresultsandtheresultsofourprevious
studies[3,20]provethatAOBmitralcellsarecapableofpersistentfiringresponses,bothin
vitroandinvivotoeitherelectricalorchemicalsensorystimulation.
PersistentFiringActivityinAOBMitralCellsInvolvesaProlonged
DepolarizingCurrentwithComplexDynamics
Conductingtheinvitroprotocoldescribedabovewhileshiftingthemembranepotentialto−60
mV(Fig2A)blockedthepersistentfiringandunmaskedaprolongeddepolarizationwitha
similartimecourseasthefiringactivity(comparetoFig1D).Toanalyzethecurrentsunderly-
ingtheprolongeddepolarization,thehybrid-clampmethodologywasused(seeMaterialsand
Methods).Cellswerevoltage-clampedto−80mVandtrainsofactionpotentialsatvariousfre-
quenciesweredeliveredduringa4slongcurrent-clampperiod.Theevokedinwardcurrent
(Fig2B)comprisedaninitial,rapidlydecayingphase(transientphase,enlargedinFig2C),fol-
lowedbyasecond,prolongedphase(persistentphase),thatpeakedafter>10s(Fig2B,arrows)
andslowlydecayedwithamoreprolongedtimecourse(>30s).Notably,thechargetransfer
duringeachofthephasesmonotonicallyincreasedwiththestimulusfrequency(Fig2D).Thus,
theprolongedinwardcurrentunderlyingpersistentfiringinAOBmitralcellsseemstoinvolve
transientandpersistentcomponentsthatareproportionaltothefiringfrequencyduringthe
stimulation.
TheProlongedInwardCurrentIstheSumofaNa+-K+Pump-Mediated
OutwardCurrentandaCa2+-DependentInwardCurrent(I )
CAN
Thecomplexdynamicsoftheprolongedinwardcurrentsuggestthatmultiplebiophysical
mechanismsareinvolved.Toisolatetheparticipatingprocesses,weabolishedtheinwardcur-
rent,previouslyshowntobemediatedbyCa2+-dependent,CANconductance[3].Removalof
Ca2+fromtheextracellularsolution,aswellasblockingtheincreasein[Ca2+] byadding5mM
i
BAPTAtothepipettesolution(S2Fig),abolishedtheprolongedinwardcurrent.Underthese
conditions,thestimulatingtrainwasfollowedbyanoutwardcurrentof18±3pAthatmono-
tonicallydecayedwithasingletimeconstant(τ=5±1s,n=11cells,Fig2E,greentrace).Sub-
tractingtheoutwardcurrentfromthecontrolconditioncurrent(Fig2E,bluetrace)yieldsanet
inwardcurrent(Fig2E,blacktrace),whichislikelyduetotheCANconductance.Similar
resultswerepreviouslyobtainedbyblockingN/Rtypevoltage-sensitiveCa2+channels[3].
AsshowninFig2F,theoutwardcurrentmeasuredintheabsenceofCa2+ionswasindepen-
dentofmembranepotential,suggestingthatitisnotmediatedbyionicconductance.Themost
likelycandidateforavoltage-insensitiveoutwardcurrentisanionicpumpcurrent,suchasthe
oneproducedbytheplasmamembraneNa+-K+pump(Na+-K+ATPase)[21].AsshowninFig
2G(green),blockingtheNa+-K+pumpusingouabainunmasksastrongnetinwardcurrent
peakingimmediatelyafterthespiketrain.Thedifferencebetweenthecurrentsbeforeandafter
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Fig2.ThecomplexcurrentresponsefollowingaspiketrainiscomprisedofaNa+-dependentoutward
currentandaprolongedCa2+-dependentinwardcurrent.(A)Meanvoltageresponse(n=4cells)toa30
Hzspiketrain.Ahyperpolarizingcurrentwasinjectedthroughouttherecordingtopreventfiringbeforeand
afterthestimulustrain.(B)Meancurrentresponses(n=6–10cellspertrace)followinga4slongspiketrain
atmultiplefrequencies(denotedbydifferentshades).Arrowspointtothepeakofthefilteredsignals.(C)
Magnifiedviewoftheinitial3softhecurrentsshownin(B),revealingtheinitialtransientphase.(D)The
chargetransferred(current-timeintegral)asafunctionofstimulusfrequency.Graycurve:thechargetransfer
betweent=0.25sandt=1.5spoststimulation(transientphase,uptotheverticaldashedlineinB).Black
curve:thechargetransferredbetweent=1.5sandt=42spoststimulation(persistentphase).Errorbars
denoteSEM.(E)Themeancurrent(n=11cells)followinganevoked4slongspiketrainat30Hzbefore
(blue)andafterremovalofCa2+fromthebathsolution(green).Thedifferencebetweenthetwotracesis
showninblack,presumablyreflectingtheprolongedCa2+-dependentcurrentperse.Shadedareasdenote
SEM.(F)TheoutwardcurrentrecordedafterCa2+removalataholdingvoltageof−80mV(darkgreen)and
−50mV(lightgreen).(G)Themeaninwardcurrent(n=5cells)followinganevoked4slongspiketrainat30
Hzbefore(blue)andafterapplicationoftheNa+-K+pumpblockerouabain(green).Thedifferencebetween
thetwotracesisshowninblack.Lowopacitytracesshowtheaverageresponsesofindividualcells.
doi:10.1371/journal.pbio.1002319.g002
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ouabainapplicationisanetoutwardcurrentresemblingtheonemeasuredintheabsenceof
Ca2+ions(Fig2G,black).Thus,theoutwardcurrentismostlikelymediatedbytheNa+-K+
pump.
Overall,thesedatasuggestthatthecomplexdynamicsoftheprolongedinwardcurrent
reflectthesumoftwoopposingcurrents—avoltage-independentoutwardcurrent(Na+-K+
pump)decayingoverafewsecondsandaprolongedCa2+-dependentinwardcurrent(I )
CAN
thatremainsactiveforminutes.
TheMagnitudeoftheInwardCurrentIsCorrelatedwith[Ca2+] atthe
i
DendriticTuft
Tostudythespatio-temporalrelationshipbetween[Ca2+] andI ,wecorrelated[Ca2+]
i CAN i
indicatorfluorescenceinvariouscellularcompartmentswiththesimultaneouslyrecorded
somaticinwardcurrent.Tothatend,AOBmitralcellswerefilledwithaCa2+indicatorusing
thepatchpipette(insetinFig3).Then,tuftfluorescence(Fig3A)andthecorresponding
inwardcurrents(Fig3B)weresimultaneouslymonitoredastrainsofactionpotentialsatvari-
ousfrequenciesweredeliveredviathepatchpipettetoactivatetheneurons.Thetransient
increasein[Ca2+] inthedendritictuftwasfollowedbyanextremelyprolongeddecaylasting
i
longerthantheintervalbetweenstimuli,resultinginsummationof[Ca2+] levelsoverconsecu-
i
tivetrains(Fig3A).Similarly,theprolongedinwardcurrentalsopersistedlongerthanthe
intervalbetweenstimuli,resultinginprogressiveincreaseininwardcurrentaswell(Fig3B).
Toanalyzetherelationshipbetweendendritic[Ca2+] andtheinwardcurrent,thecurrent
i
amplitudeateachtimepointwasplottedagainstthesimultaneouslymeasuredfluorescence
level.Fig3Cshowsthisanalysis,appliedtothedatashowninFig3Aand3B.Asapparent,the
inwardcurrentshowsaclearsigmoidaldependenceonthefluorescencesignal,suggestingthat
the[Ca2+] inthedendritictufttightlycorrelateswiththeslowdynamicsofinwardcurrent(see
i
S3EandS3FFigformoreexamples).Incontrasttotuftfluorescence,somaticfluorescence
doesnotcorrelatewiththemagnitudeoftheinwardcurrent(Fig3D,S3AandS3DFig).The
closerelationshipbetweentuft[Ca2+] andthemagnitudeoftheinwardcurrentsuggeststhat
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theprolongedcurrentreflectstheextendedelevationoftuft[Ca2+].Indeed,closeexamination
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oftuftfluorescencelevels(Fig3E)revealedthatthedecayof[Ca2+] inthetuftfollowedtwo
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distincttimescales:fastinitialdecay(τ=1.9s,meanofthreecells)followedbyveryslowdecay
(τ=47.0s).Thisslowprocesssuggeststhat[Ca2+] isinaquasi-stablestate,thelevelofwhich
i
isdeterminedbythestimulusfrequency.Consistentwiththis,increasingthestimulationfre-
quencyfrom15Hzto30Hzalmostdoubledthequasi-stablestatelevel(Fig3E,blueandgreen
traces).
Overall,theseresultssuggestthattheinwardcurrentunderlyingpersistentfiringofAOB
mitralcellsismediatedbydendriticCa2+-dependentionicconductance(CAN)andthatits
slowdynamicslikelyreflectacomplexinteractionbetweenseveralionicextrusion
mechanisms.
AHypotheticalMechanismInvolvingtheNa+-K+Pump,thePlasma
MembraneCa2+Pump,andtheNa+-Ca2+ExchangerCanExplainthe
ObservedSlowCurrentDynamics
Theresultdescribedabove,inwhichthetuft[Ca2+] decaystoaquasi-stablestatedetermined
i
bythestimulationfrequency,suggeststhatthequasi-stablestateisgeneratedbyslowlychang-
ing,activity-dependentquantity.Onesuchquantitymaybethetuft[Na+],whichaffectsthe
i
Ca2+dynamicsbyinteractingwithionictransportmechanismssuchastheNa+-Ca2+
exchanger.Thisexchanger,whichisthemajormechanismforcontroloflargeexcessCa2+
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Fig3.ThedynamicsoftheprolongedinwardcurrentisdirectlyrelatedtotheCa2+concentrationinthedendritictuft,enablingstimulusintegration
overextendedtimescales.(A)Fluorescencesignalrecordedfromthedendritictuftduringrepeatedstimulationbyspiketrains(4slongat5,10,15,and20
Hz,redbars).Inset:fluorescencemicroscopeimageofthemitralcellfilledwithOGB-1,showingthedendritictuftfromwhichthesignalswererecorded(red
circle).Scalebaris50μm.Thefluorescencelevelrecordedbeforethefirsttrain(dashedline)wasusedasF tocalculatedF/Fvalues([F-F ]/F ).(B)
min min min
Currenttracesrecordedsimultaneouslyalongwiththefluorescencesignalsshownin(A).(C)Ascatterplotoftherecordedcurrent(B),calculatedrelativeto
thecurrentrecordedbeforethefirsttrain,versusthesimultaneouslyrecordeddendritictuftfluorescentsignal(A),colorcodedasin(A)and(B).Thedataof
thefirst7sfollowingeachspiketrainwerediscarded.Asigmoidcurvewasfittedtothedata(dashedline).(D)Sameas(C),withsomaticfluorescence
signals.(E)Themeanfluorescencesignalinthedendritictuftduringresponsesto15Hz(blue)and30Hzspiketrains(green).Bothsignalscanbemodeled
asasumoftwoexponentialfunctions(graylines),onehavingashorttimeconstant(~2s)andtheotheraverylongone(~200s).SeealsoS3Fig.
doi:10.1371/journal.pbio.1002319.g003
[22],usestheNa+electrochemicalgradienttoextrudeCa2+.Thus,increasein[Na+] which
i
leadstoadecreasedNa+gradient,reduceorevenreversetheCa2+fluxthroughtheexchanger
[23].Weexaminedthispossibilityinasimpleabstractdynamicalmodel,withaminimalnum-
berofparameters(Fig4A;seeS1Textforadescriptionofthemodelequations).Inthismodel,
[Ca2+] and[Na+] increaseatarateproportionaltoanabstract“voltage”quantity,giventhat
i i
the“voltage”isaboveacertainthreshold.[Na+] decaysexponentiallytozeroovertime,while
i
[Ca2+] decaystoalevellinearlydeterminedby[Na+] (thequasi-stablestate).The“voltage”is
i i
asumofthreecomponents:externallyappliedcurrent,inwardCa2+-dependentcurrent,and
outward(negative)Na+-dependent“pump”current.
Fig4Band4Dshowstheresultsofrunningthismodelwithapulseofexternallyapplied
current(blackbar).Asapparent,the“voltage”(Fig4B)behaviorqualitativelyresemblesthe
experimentalobservations(comparetoFigs1Dand2A).Thisvoltagetrajectoryisduetothe
changesin[Na+] and[Ca2+] (Fig4C)andthecorrespondingcurrents(Fig4D).Thus,thefea-
i i
sibilityofthemechanismsuggestedaboveisconfirmedbythissimpleabstractmodel.Inorder
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Fig4.Asimpleabstractmodel,basedontheinteractionsbetweenionicextrusionmechanisms,reproducesthelong-termvoltagebehavior
observedinmitralcells.(A)Aschematicdescriptionoftheabstractmodel—the“voltage”isthesumofanexternalstimulation,inward[Ca2+]-dependent
i
current(I )andoutward[Na+]-dependentcurrent(I ).[Ca2+] and[Na+] influxratesaredeterminedlinearlybythe“voltage”onceitcrossesathreshold.
CAN i pump i i
[Na+] exponentiallydecaystozero,while[Ca2+] decaystoalevelsetby[Na+].I and[Ca2+] haveasigmoidalrelationship,whileI and[Na+] havea
i i i CAN i pump i
logarithmicone.(B)–(D),thedynamicsof:(B)“voltage;”(C)[Ca2+] (orange)and[Na+] (red);(D)I (orange)andI (red)whenrunningthemodelwith
i i CAN pump
transientexternalstimulation(blackbar).Alltimeandquantityunitsarearbitrary.(E)Adescriptionofthedetailedconductance-basedmodel,showingthe
compartmentaldistributionofthechannels,pumps,andexchangersoverlaidonthereconstructionofthemitralcellusedforthemodel.g :leak
leak
conductance,composedfromseparatepassiveNa+andK+conductances;g :transientvoltage-gatedNa+conductance;g /g :fastandslow
nat k-fast k-slow
voltage-gatedK+channels;g :voltage-gatedCa2+conductance;g :Ca2+-dependentnon-specificcationconductance.
Ca CAN
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tofurthertestthishypotheticalmechanismandproducequantitativepredictions,weincorpo-
ratedtheprinciplesofthismechanismintoarealisticconductance-basedmodel.
AConductance-BasedModelReproducestheDynamicsoftheCa2+-
DependentFluorescenceandtheMembraneCurrents
Arealisticconductance-basedmodel(seeMaterialsandMethods),wasconstructedusingthe
detailedmorphologyofasingletypicalmitralcell(Fig4EandS4Fig)forwhichthe
electrophysiologicalpropertieswerecharacterized.Themodelassumesthatactiveconduc-
tancesresideintheapicaldendritesanddendritictufts,aswellasinthesomaandaxoninitial
segment[24],sothat[Na+] increaseinthesecompartmentsfollowingfiring.Anovelfeatureof
i
ourmodelistheincorporationofcompartmental[Na+] asstatevariablesalongwithlongitudi-
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nalionicdiffusion.Accordingly,[Na+] notonlysetsthelocalNa+reversalpotentialbutalso
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affectslocalizedionicextrusionmechanisms(Na+-K+pumps,Na+-Ca2+exchangers).TheCa2+
influx,bufferingandextrusionmechanisms(includingasimulatedCa2+indicator),aswellasa
Ca2+dependentconductance,wereintroducedinthedendritictufts.Thespatialdistributionof
membranalmechanismsinthemodelisshowninFig4E(SeeMaterialsandMethodsforalink
tothemodelsourcecodeandS1Textforafulldescriptionofthemodelequationsandparame-
ters).Usingsuchamodel,onecancalculatethetemporaldynamicsof[Na+] and[Ca2+] in
i I
variouscellularcompartments.
Anevolutionarymulti-objectivealgorithm[25,26]wasusedtofindthebiophysicalparame-
tersthatbestfitourelectrophysiologicalobservations.Aninitialevolutionaryprocesswas
employedtofindthebestfittothefollowingmeasuredparameters:theresponsetoahyperpo-
larizingcurrentpulse(Fig5A),theshapeoftheactionpotential(Fig5B),themodulationofthe
spikeamplitudeduringastrong(350pA)currentinjection(Fig5G),andtheI-fcurve(Fig
5H).Asshown,themodelaccuratelyreproducesthebehavioroftherealcellwithrespectto
theseobjectives.Notably,thespikeamplitudemodulationduringdepolarizingcurrentinjec-
tionsimulatedbythemodelpreciselyfittedtheexperimentalobservations,despitethefactthat
onlya350pAcurrentinjectionwasusedasanobjective(Fig5E–5G).Importantly,thespike
amplitudemodulationinthemodelwastheresultof[Na+] accumulationduringthespike
i
trainandwouldnotbereproducedwhen[Na+] accumulationwasprevented(S5Fig).
i
Thegoalofthenextevolutionaryprocesswastofindtheparametersthatreproducethetuft
Ca2+indicatorfluorescenceandtheprolongedsomaticinwardcurrent(seeMaterialsand
Methods).Trainsofactionpotentialswithfrequenciesof1,15,and30Hzwereusedtoactivate
themodelneuron.Thesimulateddendritictuftfluorescenceandtheaccompanyingprolonged
inwardcurrentwerethencomparedtotheexperimentalobservations.Atafrequencyof1Hz
(Fig6A),thesimulation(redline)perfectlyreproducedtheobservedfluorescencesignal(blue
line).Athigherfrequencies(15Hzand30Hz,Fig6B),bothmeasured(blueandgreenlines)
andsimulated(orangeandredlines)fluorescencelevels,rapidlyincreasedtosaturationlevels
duringthestimulation(Fig6B,topgreenbar).Therapidincreasewasfollowedbyanequally
rapiddeclinetoalowquasi-stablelevelthatstronglydependedonthestimulationfrequency
(Fig6B).Moreover,thesimulatedprolongedinwardcurrentalsocloselyfittheexperimentally
measuredcurrent(Fig6C).
Inordertoassessthesensitivityofthemodeltochangesinitsparameters,wecreatedapop-
ulationof1,200modelneurons.Ineachmodel,eachparameter(exceptthechannels'half-acti-
vationvoltageparameters)wasrandomlyselectedfromauniformdistributionthatspanned
between-10%and+10%relativetotheoriginalvalue.Wethenexamined,ineachofthemod-
els,thepredictedprolongedinwardcurrentsevokedby30Hzspiketrain.Thepropertiesofthe
resultingcurrentsdistributenormally(seeexamplehistogramsforthemaximumcurrentin
PLOSBiology|DOI:10.1371/journal.pbio.1002319 December16,2015 9/25
ProlongedActivityand[Na+] inAOBMitralCells
i
Fig5.ThepassiveandfiringpropertiesofanAOBmitralcellarereproducedbyaconductance-basedmodelofareconstructedcell.(A)–(G)
Comparisonbetweentheexperimentalobservation(blue)andthemodelprediction(orange)ofthe:(A)Meanvoltageresponsetoahyperpolarizingcurrent
steps(30and60pA).(B)Meanspiketrajectory.(C)–(G)Firingresponsestostepcurrentinjectionsof30,100,150,200,and350pA,respectively.(H)I-f
curveofthereal(blue)andmodel(orange)cells.SeealsoS4andS5Figs.
doi:10.1371/journal.pbio.1002319.g005
S6AFigandtheresidualcurrentafter1minforthetrainendinS6BFig).Asapparentfromthe
80%boundsofthedistribution(S6CFig),thischangeinparametersdidnotcausealargedevi-
ationfromthefitofthemodeltotheexperimentaldata.
Acriticalvalidationofthemodelisitsabilitytoreproducethepersistentfiringrecordedin
AOBmitralcells.Indeed,atrainofsimulatedspikesevokedlonglastingpersistentactivity(Fig
6D)whichresembledtheexperimentalobservations(Fig1D).AddingGaussiancurrentnoise
introducedvariabilitytotheresponsesthatuponaveragingreproducedthePSTHobservedin
vitro(compareFigs6Eto1D).
Anothercriticalvalidationistheabilityofthemodeltopredictthetimecourseofdendritic
[Na+],andparticularlyitsriseduringstimulationandveryslowsubsequentdecaythatmain-
i
tainsaquasi-stablestateforthetuft[Ca2+].Tothatend,weusedtwofluorescentNa+indica-
i
tors,sodium-bindingbenzofuranisophthalate(SBFI)andSodiumGreen,toimagethe
PLOSBiology|DOI:10.1371/journal.pbio.1002319 December16,2015 10/25