混合尖峰發(fā)放模型-神經(jīng)科學(xué)課件

混合尖峰發(fā)放模型

Tounderstandhowthebrainworks,weneedtocombineexperimentalstudiesofanimalandhumannervoussystemswithnumericalsimulationoflarge-scalebrainmodels.

——E.M.Izhikevich神經(jīng)元是生物體中信息傳遞的基本單元。文章解讀（Hybridspikingmodels）——severalkindsofmodelssimulationmethodsofsimplemodelofspiking neurons問題探究——重現(xiàn)圖2中不同神經(jīng)元的活動模式，并指出 相應(yīng)活動模式的參數(shù)統(tǒng)計各種模式下發(fā)放率與輸入刺激的強度之 間的關(guān)系輸入均值為符合泊松分布的隨機電脈沖， 考察均值與發(fā)放率之間關(guān)系Theleakyintegrate-and-firemodelv:membranepotentialC:memberanecapacitancegleak:leakyohmicconductanceEleak:leakyreversepotentialI:inputcurrentItlacksanintrinsicspike-generationmechanism,andhenceisjusta‘threshold’model.Thequadraticintegrate-and-firemodelv:membranepotentialC:memberanecapacitanceI:inputcurrentK:apositiveparameterVrest:restingpotentialsVthresh:instantaneous thresholdpotentialsAhybridspikingmodel—asitcombinesasmoothspike-generationmechanismwithautocatalyticupstrokeofthespikeandahard‘a(chǎn)fter-spike’reset.SimplemodelofspikingneuronsU:arecoveryvariablea:thetimescaleofub:thesensitivityofuc:theafter-spikeresetvalueofvd:theafter-spikeresetofuSimplemodelofspikingneuronsU:arecoveryvariablea:thetimescaleofub:thesensitivityofuc:theafter-spikeresetvalueofvd:theafter-spikeresetofuOtherhybridspikingmodelsAllafter-spikingresettingarethesame.U：aconductanceE:thereversepotentialofuSimplemodelofspikingneuronsSimulationmethods1)HowtodetectVpeakcrossing?2)Strongsynapticconductancescausenumericalinstability.Howtoavoidnumericalinstability?SimplemodelofspikingneuronsSimulationmethodsDetectingVpeakcrossing:linearinterpolationAvoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodstime-varyingconductancethereversepotentialforaparticularsynapticcurrentie.g.i=NMDA,AMPA,GABAAandGABABAvoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsThetotalconductanceThetotalreversepotentialAvoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsIndeed,positivevaluesofg(t)pushthemembranevoltagetowardsthereversepotentialE(t).However,wheng(t)islarge,thetermtg(t)[E(t)?v(t)]becomeslarge,resultinginovershootanddivergencefromE(t).Noticethat,nomatterhowsmallthesimulationsteptis,theconductancevariablecouldalwaysbecomesolargeastocreatetheinstability.Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsFinally，Sincethenumericalinstabilityiscausedbythelinearterm,onecanusethehybridnumericalmethodthatcombinesthesimplicityandefficiencyofexplicitmethodsandthenumericalstabilityofimplicitmethods.Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsLeft:Right:問題探究一

重現(xiàn)圖2中不同神經(jīng)元的活動模式，并指出相應(yīng)活動模式的參數(shù)——form“Simplemodelofspikingneurons”

問題探究一:程序示例subplot(5,4,1)a=0.02;b=0.2;c=-65;d=6;V=-70;u=b*V;VV=[];uu=[];tau=0.25;tspan=0:tau:100;T1=tspan(end)/10;fort=tspanif(t>T1)I=14;elseI=0;end;V=V+tau*(0.04*V^2+5*V+140-u+I);u=u+tau*a*(b*V-u);ifV>30VV(end+1)=30;V=c;u=u+d;elseVV(end+1)=V;end;uu(end+1)=u;end;plot(tspan,VV,[0T1T1max(tspan)],-90+[001010]);axis([0max(tspan)-9030])axisoff;title('(A)tonicspiking');問題探究一:figure1問題探究一:figure2問題探究一:參數(shù)問題探究一:參數(shù)問題探究二統(tǒng)計各種模式下發(fā)放率和輸入刺激的強度之間的關(guān)系1）在不同模式下，改變輸入刺激電流I的大小，并統(tǒng)計不同的輸入電流I對應(yīng)的發(fā)放率r，利用plot函數(shù)繪制不同模式下的“r-I”關(guān)系圖2）對A模式（tonicspiking）的“r-I”關(guān)系圖進行擬合，得出其對應(yīng)表達式注：統(tǒng)計發(fā)放率方法眾多，此處采用較為簡便的“時間平均法”問題探究二：程序示例V=V+tau*(0.04*V^2+5*V+140-u+I);u=u+tau*a*(b*V-u);ifV>30VV(end+1)=30;V=c;u=u+d;elseVV(end+1)=V;end;uu(end+1)=u;end;ffl(i)=histc(VV,30)/100;endfigureplot(dl,ffl,'-o')title('(A)tonicspiking');subplot(5,4,1)a=0.02;b=0.2;c=-65;d=6;V=-70;u=b*V;VV=[];uu=[];tau=0.25;tspan=0:tau:100;T1=tspan(end)/10;dl=1:50;ffl=zeros(1,length(dl));fori=1:length(dl)fort=tspanif(t>T1)I=dl(i);elseI=0;end;問題探究二：“r-I”關(guān)系圖問題探究二對A模式（tonicspiking）的“r-I”關(guān)系圖進行擬合LinearmodelPoly2:f(x)=p1*x^2+p2*x+p3Coefficients(with95%confidencebounds):p1=0.001364(0.001358,0.001369)p2=6.425e-005(-0.0002163,0.0003448)p3=-0.007935(-0.01104,-0.004833)即：問題探究三輸入均值為