Table Of ContentC
OMPUTATIONAL
N
EUROSCIENCE
A COMPREHENSIVE APPROACH
CHAPMAN & HALL/CRC
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C
OMPUTATIONAL
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EUROSCIENCE
A COMPREHENSIVE APPROACH
EDITED BY
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IANFENG ENG
CHAPMAN & HALL/CRC
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C3626_Disc.fm Page 1 Thursday, August 28, 2003 9:23 AM
Library of Congress Cataloging-in-Publication Data
Computational neuroscience : comprehensive approach / edited by Jianfeng Feng.
p. cm.(cid:151)(Chapman & Hall/CRC mathematical biology and medicine series)
Includes bibliographical references and index.
ISBN 1-58488-362-6 (alk. paper)
1. Computational neuroscience. I. Feng, Jianfeng. II. Series.
QP357.5.C633 2003
573.81(cid:151)dc21 2003051578
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Contents
1 ATheoreticalOverview
HenryCTuckwell1,andJianfengFeng2 1Epidemiologyand
InformationScience,FacultyofMedicineStAntoine,UniversityofParis6,
27rueChaligny,75012Paris,France,2DepartmentofInformatics,
UniversityofSussex,BrightonBN19QH,U.K.
1.1Introduction
1.2Deterministicdynamicalsystems
1.2.1Basicnotationandtechniques
1.2.2Singleneuronmodelling
1.2.3Phasemodel
1.3Stochasticdynamicalsystems
1.3.1Jumpprocesses
1.3.2Diffusionprocesses
1.3.3Jump-diffusionmodels
1.3.4Perturbationofdeterministicdynamicalsystems
1.4Informationtheory
1.4.1Shannoninformation
1.4.2Mutualinformation
1.4.3Fisherinformation
1.4.4 Relationshipbetweenthevariousmeasurementsofinforma-
tion
1.5Optimalcontrol
1.5.1Optimalcontrolofmovement
1.5.2Optimalcontrolofsingleneuron
2 AtomisticSimulationsofIonChannels
PeterD.TielemanDept.ofBiologicalSciences,UniversityofCalgary,
Alberta,CanadaT2N1N4
2.1Introduction
2.1.1Scopeofthischapter
2.1.2Ionchannels
2.2Simulationmethods
2.2.1Moleculardynamics
2.2.2Continuumelectrostatics
2.2.3Browniandynamics
2.2.4Othermethods
2.3 Selectedapplications
2.3.1Simpli (cid:222)edsystems
2.3.2GramicidinA
2.3.3Alamethicin
2.3.4OmpF
2.3.5ThepotassiumchannelKcsA
2.4 Outlook
3 ModellingNeuronalCalciumDynamics
SaleetM.Jafri1,andKeun-HangYang2 1PrograminBioinformatics
andComputationalBiology,SchoolofComputationalSciences,George
MasonUniversity,10900UniversityBlvd.,Manassas,VA20110,U.S.,
2DepartmentofNeurology,TheJohnsHopkinsUniversity,Schoolof
Medicine,600NorthWolfeStreet,Meyer2-147Baltimore,MD21287,
U.S.
3.1Introduction
3.2 Basicprinciples
3.2.1Intracellularcalciumstores
3.2.2Calciumchannels
3.2.3Calciumpumpsandexchangers
3.2.4Mitochondrialcalcium
3.3Specialcalciumsignalingforneurons
3.3.1Localdomaincalcium
3.3.2Cross-talkbetweenchannels
3.3.3Controlofgeneexpression
3.4Conclusions
4 Structure-BasedModelsofNODiffusionintheNervousSystem
AndrewPhilippides1,PhilHusbands2,TomSmith1,andMichael
O(cid:146)Shea1 CentreforComputationalNeuroscienceandRobotics(CCNR),
1DepartmentofBiology,2DepartmentofInformatics,UniversityofSussex,
Brighton,U.K.
4.1Introduction
4.2Methods
4.2.1EquationsgoverningNOdiffusioninthebrain
4.2.2Analyticsolutionstothediffusionequation
4.2.3ModellingdiffusionofNOfromanirregular3Dstructure
4.2.4Parametervalues
4.3 Results
4.3.1Diffusionfromatypicalneuron
4.3.2Effectofneuronsize
4.3.3Smallsources
4.4Exploringfunctionalroleswithmoreabstractmodels
4.4.1TheGasNetmodel
4.4.2Gasdiffusioninthenetworks
4.4.3Modulation
4.5Conclusions
5 StochasticModellingofSingleIonChannels
AlanG.Hawkes EuropeanBusinessManagementSchool,Universityof
Wales,Swansea,SA28PP,U.K.
5.1Introduction
5.2Somebasicprobability
5.3 Singlechannelmodels
5.3.1Athree-statemechanism
5.3.2Asimplechannel-blockmechanism
5.3.3A (cid:222)ve-statemodel
5.4Transitionprobabilities,macroscopiccurrentsandnoise
5.4.1Transitionprobabilities
5.4.2Macroscopiccurrentsandnoise
5.5Behaviourofsinglechannelsunderequilibriumconditions
5.5.1Thedurationofstayinanindividualstate
5.5.2Thedistributionofopentimesandshuttimes
5.5.3Jointdistributions
5.5.4Correlationsbetweenintervals
5.5.5Burstingbehaviour
5.6 Timeintervalomission
5.7 Somemiscellaneoustopics
5.7.1Multiplelevels
5.7.2HiddenMarkovMethodsofanalysis
6 TheBiophysicalBasisofFiringVariabilityinCorticalNeurons
HughP.C.Robinson DepartmentofPhysiology,Universityof
Cambridge,DowningStreet,Cambridge,CB23EG,U.K.
6.1Introduction
6.2Typicalinputiscorrelatedandirregular
6.3Synapticunreliability
6.4 Postsynapticionchannelnoise
6.5Integrationofatransientinputbycorticalneurons
6.6Noisyspikegenerationdynamics
6.7DynamicsofNMDAreceptors
6.8Class1andclass2neuronsshowdifferentnoisesensitivities
6.9Corticalcelldynamicalclasses
6.10Implicationsforsynchronous (cid:222)ring
6.11Conclusions
7 GeneratingQuantitativelyAccurate,butComputationallyConcise,Models
ofSingleNeurons
GarethLeng,ArletaReiff-Marganiec,MikeLudwig,andNancy
Sabatier CollegeofMedicalandVeterinarySciences,Universityof
Edinburgh,EH98XD,U.K.
7.1Introduction
7.1.1Thescaleoftheproblem
7.1.2Strategiesfordevelopingcomputationallyconcisemodels
7.2Thehypothalamo-hypophysialsystem
7.2.1Firingpatternsofvasopressinneurons
7.2.2 Implications of membrane bistability for responsiveness to
afferentinput
7.2.3Firingpatternsofoxytocincells
7.2.4Intrinsicproperties
7.2.5IntracellularCa 2+concentration
7.2.6Implications
7.3 Statisticalmethodstoinvestigatetheintrinsicmechanismsunderly-
ingspikepatterning
7.3.1Selectingrecordingsforanalysis
7.3.2Interspikeintervaldistributions
7.3.3Modelling
7.3.4Simulatingoxytocincellactivity
7.3.5Experimentaltestingofthemodel
7.3.6Firingrateanalysis
7.3.7Indexofdispersion
7.3.8Autocorrelationanalysis
7.4 Summaryandconclusions
8 BurstingActivityinWeaklyElectricFish
Ru¤digerKrahe1 andFabrizioGabbiani2 1BeckmanInstitutefor
AdvancedScienceandTechnology,DepartmentofMolecularand
IntegrativePhysiology,UniversityofIllinoisatUrbana/Champaign,405N.
MathewsAve.Urbana,IL61801,U.S.2DivisionofNeuroscience,Baylor
CollegeofMedicine,OneBaylorPlaza,Houston,TX77030,U.S.
8.1Introduction
8.1.1Whatisaburst?
8.1.2Whybursts?
8.2 Overviewoftheelectrosensorysystem
8.2.1Behavioralsigni (cid:222)canceofelectrosensation
8.2.2Neuroanatomyoftheelectrosensorysystem
8.2.3Electrophysiologyandencodingofamplitudemodulations
8.3 Featureextractionbyspikebursts
8.3.1Burstsreliablyindicaterelevantstimulusfeatures
8.3.2Featureextractionanalysis
8.4Factorsshapingburst (cid:222)ringinvivo
8.5 Conditionalactionpotentialbackpropagationcontrolsburst(cid:222)ringin
vitro
8.5.1Experimentalevidenceforconditionalbackpropagation
8.5.2Multicompartmentalmodelofpyramidalcellbursts
8.5.3Reducedmodelsofburst (cid:222)ring
8.6Comparisonwithotherburstingneurons
8.6.1Ping-pongbetweensomaanddendrite
8.6.2Dynamicalpropertiesofburstoscillations
8.6.3Intra-burstISIsequences
8.7Conclusions
9 LikelihoodMethodsforNeuralSpikeTrainDataAnalysis
EmeryN.Brown,RiccardoBarbieri,UriT.Eden,andLorenM.
Frank NeuroscienceStatisticsResearchLaboratory,Departmentof
AnesthesiaandCriticalCare,MassachusettsGeneralHospital,U.S.,
DivisionofHealthSciencesandTechnology,HarvardMedicalSchool,
MassachusettsInstituteofTechnology,U.S.
9.1Introduction
9.2 Theory
9.2.1 Theconditionalintensityfunctionandinterspikeintervalprob-
abilitydensity
9.2.2Thelikelihoodfunctionofapointprocessmodel
9.2.3 Summarizing the likelihood function: maximum likelihood
estimationandFisherinformation
9.2.4Propertiesofmaximumlikelihoodestimates
9.2.5Modelselectionandmodelgoodness-of- (cid:222)t
9.3 Applications
9.3.1Ananalysisofthespikingactivityofaretinalneuron
9.3.2Ananalysisofhippocampalplace-speci (cid:222)c(cid:222)ringactivity
9.3.3 Ananalysisofthespatialreceptive(cid:222)elddynamicsofahip-
pocampalneuron
9.4Conclusion
9.5 Appendix
10Biologically-DetailedNetworkModelling
AndrewDavisonYaleUniversitySchoolofMedicine,Sectionof
Neurobiology,P.O.Box208001,NewHaven,CT06520-8001,U.S.
10.1Introduction
10.2Cells
10.2.1Modellingolfactorybulbneurons
10.2.2Modellingcerebellumneurons
10.3Synapses
10.4Connections
10.4.1Networktopology
10.4.2Numberofconnections
10.4.3Distributionofconnections
10.5Inputs
10.5.1Spatiotemporalpatternofinputs
10.5.2Inputstoindividualcells
10.6Implementation
10.7Validation
10.8Conclusions
11HebbianLearningandSpike-Timing-DependentPlasticity
SenSongFreemanBuilding,ColdSpringHarborLaboratory,1Bungtown
Rd.,ColdSpringHarbor,NY22734,U.S.
11.1Hebbianmodelsofplasticity
11.2Spike-timingdependentplasticity
11.3RoleofconstraintsinHebbianlearning
11.3.1Covariancerule
11.3.2Constraintsbasedonpostsynapticrate
11.3.3Constraintsontotalsynapticweights
11.4CompetitiveHebbianlearningthroughSTDP
11.4.1STDPisstableandcompetitivebyitself
11.4.2Temporalcorrelationbetweeninputsandoutputneuron
11.4.3Meanrateofchangeinsynapticstrength
11.4.4Equilibriumsynapticstrengths
11.4.5Threecommonscenariosandcomparisontosimulations
11.5TemporalaspectsofSTDP
11.6STDPinanetwork
11.6.1Hebbianmodelsofmapdevelopmentandplasticity
11.6.2Distributedsynchronyinarecurrentnetwork
11.7Conclusion
12CorrelatedNeuronalActivity:High-andLow-LevelViews
EmilioSalinas1,andTerrenceJ.Sejnowski2,31Departmentof
NeurobiologyandAnatomy,WakeForestUniversitySchoolofMedicine,
MedicalCenterBoulevard,Winston-Salem,NC27157-1010,U.S.,
2ComputationalNeurobiologyLaboratory,HowardHughesMedical
Institute,TheSalkInstituteforBiologicalStudies,10010NorthTorrey
PinesRoad,LaJolla,CA92037,U.S.,3DepartmentofBiology,University
ofCaliforniaatSanDiego,LaJolla,CA92093,U.S.
12.1Introduction:thetiminggame
12.2Functionalrolesforspiketiming
12.2.1Stimulusrepresentation
12.2.2Information (cid:223)ow
12.3Correlationsarisingfromcommoninput
12.4Correlationsarisingfromlocalnetworkinteractions
12.5Whenareneuronssensitivetocorrelatedinput?
12.5.1Coincidencedetection
