混合尖峰发放模型-神经科学课件

混合尖峰发放模型

混合尖峰发放模型

1Tounderstandhowthebrainworks,weneedtocombineexperimentalstudiesofanimalandhumannervoussystemswithnumericalsimulationoflarge-scalebrainmodels.

——E.M.IzhikevichTounderstandhowthebra2神经元是生物体中信息传递的基本单元。神经元是生物体中信息传递的基本单元。3文章解读（Hybridspikingmodels）——severalkindsofmodelssimulationmethodsofsimplemodelofspiking neurons问题探究——重现图2中不同神经元的活动模式，并指出 相应活动模式的参数统计各种模式下发放率与输入刺激的强度之 间的关系输入均值为符合泊松分布的随机电脉冲， 考察均值与发放率之间关系文章解读（Hybridspikingmodels）4Theleakyintegrate-and-firemodelv:membranepotentialC:memberanecapacitancegleak:leakyohmicconductanceEleak:leakyreversepotentialI:inputcurrentItlacksanintrinsicspike-generationmechanism,andhenceisjusta‘threshold’model.Theleakyintegrate-and-firem5Thequadraticintegrate-and-firemodelv:membranepotentialC:memberanecapacitanceI:inputcurrentK:apositiveparameterVrest:restingpotentialsVthresh:instantaneous thresholdpotentialsAhybridspikingmodel—asitcombinesasmoothspike-generationmechanismwithautocatalyticupstrokeofthespikeandahard‘after-spike’reset.Thequadraticintegrate-and-fi6SimplemodelofspikingneuronsU:arecoveryvariablea:thetimescaleofub:thesensitivityofuc:theafter-spikeresetvalueofvd:theafter-spikeresetofuSimplemodelofspikingneuron7SimplemodelofspikingneuronsU:arecoveryvariablea:thetimescaleofub:thesensitivityofuc:theafter-spikeresetvalueofvd:theafter-spikeresetofuSimplemodelofspikingneuron8OtherhybridspikingmodelsAllafter-spikingresettingarethesame.U：aconductanceE:thereversepotentialofuOtherhybridspikingmodelsAl9SimplemodelofspikingneuronsSimulationmethods1)HowtodetectVpeakcrossing?2)Strongsynapticconductancescausenumericalinstability.Howtoavoidnumericalinstability?Simplemodelofspikingneuron10SimplemodelofspikingneuronsSimulationmethodsDetectingVpeakcrossing:linearinterpolationSimplemodelofspikingneuron11Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodstime-varyingconductancethereversepotentialforaparticularsynapticcurrentie.g.i=NMDA,AMPA,GABAAandGABABAvoidingnumericalinstability12Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsThetotalconductanceThetotalreversepotentialAvoidingnumericalinstability13Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsIndeed,positivevaluesofg(t)pushthemembranevoltagetowardsthereversepotentialE(t).However,wheng(t)islarge,thetermtg(t)[E(t)−v(t)]becomeslarge,resultinginovershootanddivergencefromE(t).Noticethat,nomatterhowsmallthesimulationsteptis,theconductancevariablecouldalwaysbecomesolargeastocreatetheinstability.Avoidingnumericalinstability14Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsFinally，Sincethenumericalinstabilityiscausedbythelinearterm,onecanusethehybridnumericalmethodthatcombinesthesimplicityandefficiencyofexplicitmethodsandthenumericalstabilityofimplicitmethods.Avoidingnumericalinstability15Avoidingnumericalinstability:SimplemodelofspikingneuronsSimulationmethodsLeft:Right:Avoidingnumericalinstability16问题探究一

重现图2中不同神经元的活动模式，并指出相应活动模式的参数——form“Simplemodelofspikingneurons”

问题探究一重现图2中不同神经元的活动模式，并指出相应17问题探究一: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');问题探究一:程序示例subplot(5,4,1)ifV18问题探究一:figure1问题探究一:figure119问题探究一:figure2问题探究一:figure220问题探究一:参数问题探究一:参数21问题探究一:参数问题探究一:参数22问题探究二统计各种模式下发放率和输入刺激的强度之间的关系1）在不同模式下，改变输入刺激电流I的大小，并统计不同的输入电流I对应的发放率r，利用plot函数绘制不同模式下的“r-I”关系图2）对A模式（tonicspiking）的“r-I”关系图进行拟合，得出其对应表达式注：统计发放率方法众多，此处采用较为简便的“时间平均法”问题探究二统计各种模式下发放率和输入刺激的强度之间的关系1）23问题探究二：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;问题探究二：程序示例V=V+tau*(0.04*V^24问题探究二：“r-I”关系图问题探究二：“r-I”关系图25问题探究二对A模式（tonicspiking）的“r-I”关系图进行拟合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：问题探究二对A模式（tonicspiking）的“r-I”26问题探究三输入均值为符合泊松分布的随机电脉冲，考察均值和发放率之间的关系(1)选择“tonicspiking”的脉冲为基本脉冲单元，在一个单位的时间内有n