introduction membrane potential as a jump diffusion process Poisson spike trains information transmission in large systems of neurons statistical inference model verification references

De
Publié par

introduction membrane potential as a (jump) diffusion process Poisson spike trains information transmission in large systems of neurons statistical inference, model verification references Modelization of membrane potentials and information transmission in large systems of neurons Reinhard Hopfner Johannes Gutenberg Universitat Mainz Marseille 2010

  • poisson spike

  • universitat mainz www

  • statistical inference

  • introduction membrane potential

  • pyramidal neuron

  • mainz

  • theorem proof


Publié le : mardi 19 juin 2012
Lecture(s) : 39
Source : univ-orleans.fr
Nombre de pages : 28
Voir plus Voir moins
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssoinnialgreystsmesfoenModelizationofmembranepotentialsandruoinformationtransmissioninlargesystemsofneuronsReinhardHo¨pfnerJohannesGutenbergUniversita¨tMainzwww.mathematik.uni-mainz.de/hoepfnerMarseille2010sntstasiitaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoi123456nembmarenptoneitlasaintroductionaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssmembranepotentialasa(jump)diffusionprocessPoissonspiketrainsoinniinformationtransmissioninlargesystemsofneuronstheoremfoorpinterpretationstatisticalinference,modelverificationcommentsonlevel10inexample2commentsonexample1referencesalgreystsmesfoenrunoststasiitaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenpointroductionettnailsaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssoinnialgreystsmesfoexample1:membranepotentialinapyramidalneuronemittingspikesdata:KilbandLuhmann,InstituteofPhysiology,Mainz(in:Jahn09)enrunoststasiitaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssoinnialgreystsmesfoenruoexample2:pyramidalneuronunderdifferentexperimentalconditionsnetworkactivitystimulatedbyincreasingconcentrationofpotassium(K)data:KilbandLuhmann,InstituteofPhysiology,Mainz(in:Ho¨pfner07)sntstasiitaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssoinnialgreystsmesfoenrunoststasiitspikesaregeneratedwhenthemembranpotentialVtinthesomaishighenoughaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnmviewthemembranepotentialbetweensuccessivespikesasastochasticprocessof(jump)diffusiontype:siisnonialgreystsmesfosynapses,dendrites,soma:additivityandexponentialdecayoneneuronhasO(104)synapses,90%excitatory,10%inhibitorycontributionofincomingspikestothemembranepotential:left:singleexcitingsynapsis;middle:singleinhibitorysynapsis;right:2excitingand1inhibitorysynapsescombinedenrunoststasiitaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssoinnialgreystsmesfoenrunoexample3:spiketrainsrecordedinthevisualcortex210iidexperiments-identicalvisualstimulus(Shadlen-Newsome98)hence:viewthespiketrainµemittedbyoneneuronasarandompointmeasureon[0,)withstochasticintensitysuchthatmeanvalueofintensityattimetcorrespondstostimulusattimetststasiitaclniefercn,eomedlevircationerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiejumpdiffusionprocessmodelizationrtanisniofmrtaoinrtasnimssoinnialgrforthemembranepotentialbetweensuccessivespikeseystsmesfoenrunostsamanymodelsaretimehomogeneous,e.g.mean-revertingOrnstein-Uhlenbeck(Lansky-Lanska87,Tuckwell89,Lansky-Sato99,Lansky-Sacerdote01,Ditlevsen-Lansky05,...)orCox-Ingersoll-Ross(Lansky-Lanska87,Giorny-Lansky-Nobile-Ricciardi88,Lansky-Sacerdote-Tomassetti95,Ditlevsen-Lansky06,Brodda-Ho¨pfner06,...)stage1(timehomogeneousandstationary):CIRtypemodel(Vt)t0foraneuronbelongingtoanactiveneuronalnetworkpdVt=([KR+f]Vt)τdt+σ(VtK0)+τdWtwithconstantsσ,τ>0,referencelevelsK0<KR<KEK0:lowerboundforpossiblevaluesofthemembranepotentialKR:meanvalueofmembranepotentialforneuron’atrest’KE:excitationthresholdandsomequantitymeasuringthedegreeofactivityofthenetworkf0:cnotsnaterrpseneitgntsergnhtfoxeetnrlatsmilusuittscilaniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinewmllmerbnaeptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssoinnialgreystsmesfoenruknown:shiftingmembranepotentialVbyK0,process(VtK0)t0´`isergodicwithinvariantlawΓσ22(KRK0+f),σ22on[0,)2has(stationary)meanKRK0+fandvarianceσ2(KRK0+f)notdependingonthetimeconstantτ(Cox-Ingersoll-Ross85,Ikeda-Watanabe89,...)timehomogeneousCIRmodelgivesconvincingfitforthemembranepotentialdataofexample1(newelectronicstabilizationdevicewasusedbyKilb)(Jahn09)noreasonablefitforsomeofthemembranepotentialdatainexample2(atleastinlevels8,9,10whereneuronisabletogeneratespikes)(Ho¨pfner07)butinmanydatasetswhichseemCIRcompatibleevidencefortimedependenceconcerningtermf0inthedriftssomeindicationforpresenceofjumpsopenquestion;PRO:biologicalreasons;CONTRA:sophisticatedsemimartingaletools(Jacod09,AitSahalia-Jacod09)donotworkasastheyshouldforsure,neuronscanbehavedifferently:OU,othertypesofdiffusions,nodiffusionatall,...,but:CIRseemssuitableforslowlyspikingneuronsbelongingtoanactivenetworktstasiitaclniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)pidusionrpoecssoPsiosnpskiertmorerealistic:betweensuccessivespikesanisniofmrtaoinrtasnimssoinnialgreystsmesfoenrunousedeterministicfcttf(t)oftime(strengthofexternalstimulus)introducePoissonjumps,positiveandsummable:PRMµ(dt,dy)on(0,M)×(0,)withintensityτfe(t)dtν(dy)sindependentofBMW,forsomedeterministicfunRctiontfe(t)andsomeσ-finitemeasureν(dy)on(0,M)suchthat(0,M)yν(dy)<stage2:timeinhomogeneousmodelwithjumps:ZpdVt=([KR+f(t)]Vt)τdt+y|µ(d{t,zdy})+σ(VtK0)+τdWt-fe(t)tsapathwiseuniqueness,uniquestrongsolution(Yamada-Watanabe71,Dawson-Li06,Fu-Li08,...)explicitLaplacetransformsfortransitionprobabilities(Kawazu-Watanabe71,...)ittscilaniefercn,eomedlevirctaoinerefercnse
nirtoudtcoinembmarenptoneitlasaaj(mu)piduisnorpoecssoPsiosnpskiertanisniofmrtaoinrtasnimssionnialgreyssproposition:shiftingthemembranepotentialbyK0,theprocesshasexplicitLT(VtK0)t0λ−→Eeλ(VtK0)|(VsK0)=xfortransitionprobabilities,offormetsmfoenrunosZtno«expxΨs,t(λ)[KRK0+f(v)v,t(λ)+fe(v)Ψev,t(λ)τdvsτ(tv)ZΨv,t(λ)=eλ,Ψev,t(λ)=[1eyΨv,t(λ)]ν(dy)1+λσ22(1eτ(tv))LTanalogoustoresultsofKawazu-Watanabefortime-homogeneouscase(Kawazu-Watanabe71,Ho¨pfner09)tstasiitaclniefercn,eomedlevirctaoinerefercnse
Soyez le premier à déposer un commentaire !

17/1000 caractères maximum.