计算神经科学

©Copyright2010CenterforBioinformatics,PekingUniversityAnIntroductiontotheMathematicalModelingofPrimaryVisualCortexLouisTao陶乐天北京大学生命科学学院生物信息中心CenterforBioinformatics,CollegeofLifeSciencesPekingUniversityCollaboratorsDavidCai蔡申瓯(SJTU,CIMSNYU),GregorKovacic(RPI),DaveMcLaughlin(CIMSNYU),AdiRangan(CIMSNYU),RobertShapley(CNSNYU),MichaelShelley(CIMSNYU)交大致远学院计算神经科学夏季短期班24May2010©Copyright2010CenterforBioinformatics,PekingUniversityNeuronalNetworksAreComplex~1011neurons&1015connections104cells&1kmwiringin1mm3ofcortex©Copyright2010CenterforBioinformatics,PekingUniversityNeurons神经元•Informationprocessingunits信息处理加工单元•1010-1013neuronsinmammalianbrains哺乳动物大脑•104cellbodiesandroughly1kmof‘wiring’permm3•Differentshapes,sizes,functions,…不同形状、大小、功能•Spikingvs.Analogneurons锋电位（动作电位）(“analogneurons,”e.g.,bipolarandamacrinecellsinretina,sensory-motorneuronsofinvertebrates,…视网膜里的双极细胞与无长突细胞，无脊椎动物的感觉-运动神经元，等)•Manyothercells(e.g.,gliacells胶质细胞)incortex:tosupplyenergy,toprovidestructuralstability,…,andnotdirectlyinvolvedininformationprocessing©Copyright2010CenterforBioinformatics,PekingUniversityComputationalNeuroscience•What“computations”areperformedbyneurons&neuronalnetworks?•Howarethesecomputationsdone?•What?–Featuredetection(visualsystems,olfactorysystem,…)–Coincidence/timing(auditorysystem)–Memory(hippocampus)–Sensory-motor(eyesaccades,…)–NeuralCode:firingrate,spiketiming•How?–Celllevel:molecularandbiophysical–Network&systemslevel•What&HowtoStudy?–Cellular:membranepotential,ionchannels,synapticmechanisms–Extracellular:firingrates,spiketimes,statisticsofspiketrains,…–Systems:fMRI,opticalimaging,…©Copyright2010CenterforBioinformatics,PekingUniversitySystemsNeuroscience1.Neuronalactivityandbehavior(correlations)2.Coding:actionpotentialfrequency(ratecoding)actionpotentialtiming(temporalcoding)populationcoding(e.g.,V1)attractor/transientcoding(e.g.,olfaction)3.Modeling:neuronalnetworkasdynamicalsystem4.Today’sexample:visualcortex©Copyright2010CenterforBioinformatics,PekingUniversityNeuronalandNetworkDynamics•Individualneurons–Hodgkin-Huxleyequation–Actionpotentialgeneration(ionicchannel,…)–Synapticcurrents•NetworkActivity–Wilson-Cowantypemodels–Neuronalnetworks:integrate-and-fireneuronalnetworks,HHneuronalnetworks,…©Copyright2010CenterforBioinformatics,PekingUniversityTheNeuralSignal信号动作电位ActionPotentials:asequenceofshort,electricalpulsesinthemembranepotentialofaneuron•V~100mvin1-2msec•Actionpotentialpropagatesatconstantspeedalongaxons–velocity~1cmin1msec•Actionpotentialdoesnotchangeshapeasitpropagates•Stereotypedshape:eachactionpotentialhasthesameshapeandform-thereforetheformoftheactionpotentialdoesnotcarryinformation•SpikeTrains:SequenceofactionpotentialcanberegularorirregularISI:Inter-SpikeInterval•Informationcarriedbyspiketrains~100mV©Copyright2010CenterforBioinformatics,PekingUniversityActionPotentials动作电位•Actionpotential(spikes):voltagepulsesrespondingto‘strong’input•All-or-Noneelectricalevents,initiatednearthecellbody,propagatesalongaxons(atroughlyconstantvelocityandamplitude)•Hodgkin&Huxley(1950s)studiedvariousioniccurrentsindividually(usingpharmacologicalblocks);usedsquidgiantaxon(1/2mmdiameter)•ActionPotentialgenerationinvolves2major,voltage-dependentcurrents:sodiumandpotassium;individualioniccurrentobeysOhm’slaw,,1lnioninsideionionionsynionionionoutsidecRTIGVVGVRzFc©Copyright2010CenterforBioinformatics,PekingUniversity22mmmNaKLeaksyninjVVdCIIIIItRxHodgkinHuxleyNeuronModel1963NobelPrizeSquidGiantAxon©Copyright2010CenterforBioinformatics,PekingUniversity22mmmNaKLeaksyninjVVdCIIIIItRx34NaNaNaKKKIgmhVVIgnVVHodgkinHuxleyNeuronModel222255mV,115mS/cm90mV,36mS/cm65mV,0.1mS/cm,1F/cm/10msecNaNaKKLeakLeakmmmLeakVgVgVgCCgsynsynmsynIGtVVleakleakmrestIGVVSynapticcurrent:inducedbyactionpotentialsofotherneuronsLeakcurrent:©Copyright2010CenterforBioinformatics,PekingUniversity22mmmNaKLeaksyninjVVdCIIIIItRxHodgkinHuxleyNeuronModelVoltageClampDelcomyn(1997)DevicetomeasurethecurrentnecessarytokeepthedesiredV©Copyright2010CenterforBioinformatics,PekingUniversity22mmmNaKLeaksyninjVVdCIIIIItRxHodgkinHuxleyNeuronModel+25mVVrestvoltagestepcommandKKKIgVEnndtdnnggnKK4Estimatenandnfromtimecourse©Copyright2010CenterforBioinformatics,PekingUniversityHodgkinHuxleyNeuronModelVrestEstimaten(V)andn(V)fordifferentvoltagestepsn01VModelingtheK-current©Copyright2010CenterforBioinformatics,PekingUniversity22mmmNaKLeaksyninjVVdCIIIIItRxHodgkinHuxleyNeuronModel3NaNamhggmhdmmmdtdhhhdtEstimatem(V),m(V),h(V),h(V)fordifferentvoltagestepsVModelingtheNa-current©Copyright2010CenterforBioinformatics,PekingUniversity22mmmNaKLeaksyninjVVdCIIIIItRxHodgkinHuxleyNeuronModel3NaNamhggmhdmmmdtdhhhdtEstimatem(V),m(V),h(V),h(V)fordifferentvoltagestepsVmhVV0101ModelingtheNa-current©Copyright2010CenterforBioinformatics,PekingUniversity0.125exp0.12514exp18mmVVVVV0.07exp201.0exp0.1301hhVVVV