Analysis of Parallel Spike Trains PDF
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SPRINGER SERIES IN COMPUTATIONAL NEUROSCIENCE G r ü n • R o t Analysis of t e r E d i t o r Parallel s Spike Trains A n a l y s i s o f P a r a l l e l S p i k e T r a i n s Sonja Grün Stefan Rotter Editors Springer Series in Computational Neuroscience Volume 7 SeriesEditors AlainDestexhe CNRS Gif-sur-Yvette France RomainBrette ÉcoleNormaleSupérieure Paris France Forfurthervolumes: http://www.springer.com/series/8164 Sonja Grün (cid:2) Stefan Rotter Editors Analysis of Parallel Spike Trains Editors SonjaGrün StefanRotter LaboratoryforStatisticalNeuroscience BernsteinCenterFreiburg RIKENBrainScienceInstitute &FacultyofBiology 2-1Hirosawa Albert-LudwigUniversity Wakoshi Hansastrasse9a Saitama351-0198 79104Freiburg Japan Germany [email protected] [email protected] ISBN978-1-4419-5674-3 e-ISBN978-1-4419-5675-0 DOI10.1007/978-1-4419-5675-0 SpringerNewYorkDordrechtHeidelbergLondon LibraryofCongressControlNumber:2010933856 ©SpringerScience+BusinessMedia,LLC2010 Allrightsreserved.Thisworkmaynotbetranslatedorcopiedinwholeorinpartwithoutthewritten permission of the publisher (Springer Science+Business Media, LLC, 233 Spring Street, New York, NY10013,USA),exceptforbriefexcerptsinconnectionwithreviewsorscholarlyanalysis.Usein connectionwithanyformofinformationstorageandretrieval,electronicadaptation,computersoftware, orbysimilarordissimilarmethodologynowknownorhereafterdevelopedisforbidden. Theuseinthispublicationoftradenames,trademarks,servicemarks,andsimilarterms,eveniftheyare notidentifiedassuch,isnottobetakenasanexpressionofopinionastowhetherornottheyaresubject toproprietaryrights. Coverdesign:Thecoverartwork(originalinoilpastelandacrylic)wasdesignedandcreatedbyAdrián PonceAlvarez. Printedonacid-freepaper SpringerispartofSpringerScience+BusinessMedia(www.springer.com) Foreword Closetofiftyyearsago,whentwogenerationsofneuroscientistscontributingtothis bookhadnotyetbeenbornandIwasstillhappyinhighschool,GeorgeGerstein, DonaldPerkel,andcolleagues,inaseriesofpapers,laidthefoundationsforwhat wastobecomethequantitativeanalysisofthedynamicsofneuronalspikingactiv- ity and the interactions within and across neuronal networks. In the context of the presenttextbook,itisinstructivetorereadsomeofthesepapers. Thefullabstractofthe1960Sciencepaper(Gerstein1960)reads: Theuseofahigh-speeddigitalcomputerforinvestigationofneuralfiringpatternsisde- scribed.Thehighsensitivityofthemethodpermitsdetectionofstimulus-responserelations buriedinabackgroundofspontaneousactivity. Theabstractofthe1964Sciencepaper(GersteinandClark1964)continues: Atungstenmicroelectrodewithseveralsmallholesburntinthevinylinsulationenablesthe actionpotentialsfromseveraladjacentneuronstobeobservedsimultaneously.Adigital computer is used to separate the contributions of each neuron by examining and classi- fyingthewaveformsoftheactionpotentials.Thesemethodsallowstudiestobemadeof interactionsbetweenneuronsthatlieclosetogether. Such studies were indeed made, albeit that their numbers increased only very slowly initially, mostly due to rather formidable problems with the experimental technology involved. With regard to the analysis of data resulting from such ex- periments,theabstractsofthetwocompanionpapersinBiophysicalJournal1967 (Perkel et al. 1967a, 1967b) are strikingly explicit and, even in 2010, scaringly timely. In fact, taken together, they read as an ambitious programme manifesto, aimed at establishing a novel, theory-driven data analysis paradigm for network physiology,which,aswenowknow,itindeeddid. First,onthespikingactivityofsingleneurons: Inagrowingclassofneurophysiologicalexperiments,thetrainofimpulses(“spikes”)pro- ducedbyanervecellissubjectedtostatisticaltreatmentinvolvingthetimeintervalsbe- tweenspikes.Thestatisticaltechniquesavailablefortheanalysisofsinglespiketrainsare describedandrelatedtotheunderlyingmathematicaltheory,thatofstochasticpointpro- cesses,i.e.,ofstochasticprocesseswhoserealizationsmaybedescribedasseriesofpoint eventsoccurringintime,separatedbyrandomintervals.Forsinglestationaryspiketrains, v vi Foreword several orders of complexity of statistical treatment are described; the major distinction is that between statistical measures that depend in an essential way on the serial order ofinterspikeintervalsandthosethatareorder-independent.Theinterrelationsamongthe severaltypesofcalculationsareshown,andanattemptismadetoamelioratethecurrent nomenclaturalconfusioninthisfield.Applications,interpretations,andpotentialdifficul- tiesofthestatisticaltechniquesarediscussed,withspecialreferencetotypesofspiketrains encountered experimentally. Next, the related types of analysis are described for experi- mentswhichinvolverepeatedpresentationsofabrief,isolatedstimulus.Finally,theeffects ofnonstationarity,e.g.long-termchangesinfiringrate,onthevariousstatisticalmeasures arediscussed.Severalcommonlyobservedpatternsofspikeactivityareshowntobediffer- entiallysensitivetosuchchanges. Then,ontheactivityofpairsofneuronsandtheirinteractions: The statistical analysis of two simultaneously observed trains of neuronal spikes is de- scribed,usingasaconceptualframeworkthetheoryofstochasticpointprocesses.Thefirst statisticalquestionthatarisesiswhethertheobservedtrainsareindependent;statistical techniquesfortestingindependencearedevelopedaroundthenotionthat,underthenull hypothesis, the times of spike occurrence in one train represent random instants in time withrespecttotheother.Ifthenullhypothesisisrejected—ifdependenceisattributedto thetrains—theproblemthenbecomesthatofcharacterizingthenatureandsourceoftheob- serveddependencies.Statisticalsignsofvariousclassesofdependencies,includingdirect interactionandsharedinput,arediscussedandillustratedthroughcomputersimulationsof interactingneurons.Theeffectsofnonstationaritiesonthestatisticalmeasuresforsimulta- neousspiketrainsarealsodiscussed.Fortwo-traincomparisonsofirregularlydischarging nervecells,moderatenonstationaritiesareshowntohavelittleeffectonthedetectionof interactions.Combiningrepetitivestimulationandsimultaneousrecordingofspiketrains from two (or more) neurons yields additional clues as to possible modes of interaction amongthemonitoredneurons;thetheorypresentedisillustratedbyanapplicationtoex- perimentallyobtaineddatafromauditoryneurons. Rereadingtheseabstractsleavesuswondering,whatthepresentbookisallabout and why, in the year 2010, we would still need it. Indeed, these early studies in the 1960s already formulated the fundamental questions that are still very much with us: How can neuronal interactions be segregated from ongoing background activity?Howcantheconceptsofactivitydynamicsandcorrelationsberefinedand reconciled?And,mostofall:Whatistheirroleinbrainfunction?Itis,therefore,a reassuringthoughttohavethesameGeorgeGersteincontributingachapteronthese issuesinthisnewtextbook. In the 1980s, Computational Neuroscience established itself as a new research field in the neurosciences (Sejnowski et al. 1988; Schwartz 1990; Rumelhart et al. 1986). As Valentino Braitenberg so aptly put it (Braitenberg 1992): “We are convinced that ultimately a satisfactory explanation of thought and behavior will be given in a language akin to that of physics, i.e. in mathematical terms.” In- deed, the theory of neuronal networks explaining basic features of single neu- rons and simple networks made rapid progress, and many theoreticians were at- tracted to the field. Thus, over the next decade, many papers, dedicated confer- ences(e.g.,PalmandAertsen1987;AertsenandBraitenberg1992;Aertsen1993; Aertsen and Braitenberg 1996), and monographs (e.g., Abeles 1982; Amit 1992; Braitenberg1984;Palm1982)exploredthefoundationsofafuturetheoryofbrain function. Soon, text books suitable for advanced courses, followed (e.g., Abeles Foreword vii 1991; Dayan and Abbot 2001; Gerstner and Kistler 2002; Hertz et al. 1991; Koch1998). Comparedtothisrapidprogressinthedevelopmentofcomputationalmodelsand theory,progressintheanalysisofexperimentalspiketrainrecordingssoonlagged behind. The nonstationarity and irregularity of spiking activity recorded from the braininaction,itsconsiderablevariabilityacrossrepetitionsofatask,andthecom- plex interplay of multiple time scales, all taken together constituted very severe problems—and continue to do so—for the adequate handling of the experimental data. As a result, an unambiguous interpretation of the various quantitative mea- suresandthesearchformeaningfulstructureintherecordeddataalltoooftenre- mainedillusive.Irecallthatonenight,manyyearsago,IawokeinfrontoftheTV screen after the program had ended. After studying the nonprogram on the screen forawhile,Iconcludedthatitwasevidentlypackedwithhighlyinterestingspatio- temporal patterns—in any case, I saw them occurring and recurring virtually any- where,almostatwill.Needlesstosay,though,thatitprovedabithardtoestablish theirstatisticalandfunctionalsignificance.Thus,despitesomeearlygroundbreak- ingoverviewsonadvanceddataanalysismethodsforspecificareas(e.g.,Eggermont 1990;Riekeetal.1997),itshouldtakeanother20yearsbeforethisfirstcomprehen- sivetextbookonthestateoftheartintheanalysisofparallelspiketrainrecordings couldbeproduced. Important techniques are now available for routine usage in the laboratory, and theirlimitsareinmostcaseswellunderstood.Thus,itistimelytobringthisknowl- edgetotheclassroomnow.Consequently,thepresentbookluckilyavoidstherep- etitionoflengthyconceptualdiscussionsfromearliertimesand,instead,hurriesto present the material in a format suitable for the practitioner and the student. The scopeofthecontributionsrangesfromthemathematicalframeworkunderlyingthe variousmethodstopracticalquestionslikethegenerationofrandomnumbers.Clos- ingthecycle,onechapterinthebookreturnstotheearliercitedquestiononTheuse of a high-speed digital computer for investigation of neural firing patterns. It ex- plainshow,withthehelpofmoderncomputerclustersandhigh-levelparallelpro- gramming,wecannowcomputestatisticaltestscapturingbiologicalconstraintsto aprecisioninaccessiblebyanalyticalapproachesofthepast. However, this book in no way presents an end point to the quest. The authors canonlyhintatthechallengesposedbytheadventofmassivelyparallelrecording technology.Manysuchsystemsarealreadyinstalledworldwide.Yet,presentlythey arestillmostlyusedtoincreasethespeedofdatacollection,ratherthanutilizingthe qualitativelynewopportunitytoassessthehigher-orderstructureofneuronalassem- bliesinaction.Iamconfidentthatintheyearstocome,theauthorswillcontinuein theirendeavorandwillsurpriseuswithmanyfascinatingnewinsightsintothefunc- tioningofthebrain.Arewardingprospect,indeed,sincethealternativeofstudying aTVscreenoutsidebroadcastingtimehasmeanwhileceasedtobeanoption. BernsteinCenterFreiburg AdAertsen viii Foreword References AbelesM(1982)Localcorticalcircuits.Springer,Berlin AbelesM(1991)Corticonics.CambridgeUniversityPress,Cambridge AertsenA(ed)(1993)Braintheory:spatio-temporalaspectsofbrainfunction.ElsevierScience Publ.,Amsterdam AertsenA,BraitenbergV(eds)(1992)Informationprocessinginthecortex:experimentsandthe- ory.Springer,Berlin AertsenA,BraitenbergV(eds)(1996)Braintheory:biologicalbasisandcomputationalprinciples. ElsevierSciencePubl.,Amsterdam AmitD(1992)Modelingbrainfunction:theworldofattractorneuralnetworks.CambridgeUni- versityPress,Cambridge BraitenbergV(1984)Vehicles:experimentsinsyntheticpsychology.MITPress,Cambridge BraitenbergV(1992)Manifestoofbrainscience.In:AertsenA,BraitenbergV(eds)Information processinginthecortex.Springer,Berlin DayanP,AbbotLF(2001)Theoreticalneuroscience.MITPress,Cambridge EggermontJJ(1990)Thecorrelativebrain.Springer,Berlin GersteinGL(1960)Analysisoffiringpatternsinsingleneurons.Science131:1811–1812 GersteinGL,ClarkWA(1964)Simultaneousstudiesoffiringpatternsinseveralneurons.Science 143:1325–1327 GerstnerW,KistlerWM(2002)Spikingneuronmodels.CambridgeUniversityPress,Cambridge HertzJA,KroghA,PalmerRG(1991)Introductiontothetheoryofneuralcomputation.Perseus Publishing,Cambridge KochC(1998)Biophysicsofcomputation:informationprocessinginsingleneurons.OxfordUni- versityPress,NewYork Palm G (1982) Neural assembilies – an alternative approach to artificial intelligence. Springer, Berlin PalmG,AertsenA(eds)(1987)Braintheory.Springer,Berlin PerkelDH,GersteinGL,MooreGP(1967a)Neuronalspiketrainsandstochasticpointprocesses. I.Thesinglespiketrain.BiophysicalJ7:391–418 PerkelDH,GersteinGL,MooreGP(1967b)Neuronalspiketrainsandstochasticpointprocesses. II.Simultaneousspiketrains.BiophysicalJ7:419–440 RiekeF,WarlandD,deRuytervanSteveninckR,BialekW(1997)Spikes:exploringtheneural code.MITPress,Cambridge RumelhartDE,McClellandJL,thePDPResearchGroup(1986)Paralleldistributedprocessing, explorationsinthemicrostructureofcognition.MITPress,Cambridge SchwartzE(ed)(1990)Computationalneuroscience.MITPress,Cambridge SejnowskiTJ,KochC,ChurchlandPC(1988)Computationalneuroscience.Science241:1299– 1306 Preface WhyDataAnalysisof ParallelSpikeTrainsisNeeded Thebrainiscomposedofbillionsofneurons,theelementaryunitsofneuronalinfor- mationprocessing.Theneocortex,whichiscriticaltomosthigherbrainfunctions, isahighlycomplexnetworkofneuronseachofwhichreceivessignalsfromthou- sands of other neurons and projects its own spikes to thousands of other neurons. Inordertoobserveneuronalactivityintheactivebrain,alargevarietyofrecording techniquesarebeingemployed:intra-cellularrecordingsofthemembranepotentials of individual neurons, extra-cellular spike recordings from one or more individual neurons,andrecordingsofsignalsthatmeasuretheactivityofpopulationsofneu- rons either locally as the local field potential, or from larger brain regions via the EEG,MEG,orfMRI.Anyparticularchoiceoftherecordingtechniquereflectsthe hypothesistheresearcherhasinmindaboutthemechanismsofneuronalprocessing. The focus on spike recordings from individual neurons imposed on this book impliesthatonestrivestounderstandtheelementaryunitsofneuronalprocessing. Earlyelectro-physiologicalexperimentswereboundtorecordfromsingleneurons only. The resulting insights are now the basis for the “classical” view of sensory coding:firingratesaremodulatedinafeed-forwardhierarchyofprocessingsteps. Signalsfromsensoryepitheliaareassumedtoeventuallyconvergetocorticaldetec- tors for certain combinations of stimulus features. Highly specific percepts would berepresentedbytheelevatedfiringofasinglenervecellorasmallgroupofneu- rons.Duetoanumberofconceptualshortcomings,however,ithasbeenseriously questionedwhethersuchaschemequalifiesasauniversalmethodforrepresentation inthebrain. It was Donald Hebb (1949) who first demonstrated the conceptual power of a braintheorybasedoncellassemblies.InspiredbyHebb’sinfluentialwritings,and driven by more recent physiological and anatomical evidence in favor of a dis- tributednetworkhypothesis,braintheoristsconstructedmodelsthatrelyongroups ofneurons,ratherthansinglenervecells,asthefunctionalbuildingblocksforrepre- sentationandprocessingofinformation.Despiteconceptualsimilarities,suchcon- cepts of neuronal cooperativitydiffer in their detailed assumptions with respect to thespatio-temporalorganizationoftheneuronalactivity. ix x Preface To understand the principles of coordinated neuronal activity and its spatio- temporalscales,itisobligatorytoobservetheactivityofmultiplesingle-neuronssi- multaneously.Duetorecenttechnologicaldevelopmentsinrecordingmethodology, thiscaneasilyandregularlybedone.Coordinatedactivityofneuronsisonlyvisible in(wide-sense)correlationsoftheirrespectivespiketrains,whichtypicallyadmitno simpleinterpretationintermsoffixedsynapticwiringdiagrams.Rather,itbecame evident that the correlation dynamics apparent in time-resolved multiple-channel measurementsreflectvariableandcontext-dependentcoalitionsamongneuronsand groupsofneurons.Thus,theanalysisofsimultaneouslyrecordedspiketrainsallows us to relate concerted activity of ensembles of neurons to behavior and cognition. Different analysis approaches are thereby relevant to distinguish different or even complementaryspatio-temporalscales.Analysisofparallelspiketrainsisthelogi- calnextsteptoimproveourunderstandingoftheneuronalmechanismsunderlying informationprocessinginthebrain. Purpose oftheBook Solid data analysis is the most important basis for the meaningful evaluation and reliable interpretation of experiments. Although the technology of parallel spike train recording using multielectrode arrangements has been available for decades now,itonlyrecentlygainedwidepopularityamongelectro-physiologists.However, the relevant literature for the analysis of cooperative phenomena in parallel spike trainsisunfortunatelyscatteredacrossmanyjournalpublications,andweknowof thepaintocompileausefulreaderforourstudents.Reinforcedbytheconsiderable interest in courses and schools on data analysis on these issues (offered by us and othercolleagues),theideacameuptocollecttheknowledgeonspiketrainanalysis thatisavailableintheliteratureinasinglebook. This first textbook on spike train analysis concentrates on the analysis of par- allel spike trains. The focus is on concepts and methods of correlation analysis (synchrony,patterns,ratecovariance),combinedwithasolidintroductionintoap- proachesforsinglespiketrains,thatrepresentthebasisofcorrelationanalysis.Any specificmethodof analysismustmakeassumptionsaboutthenatureof thedatait operateson.Ithappensthatthosewhoapplyanyparticularanalysisprocedureare notwellinformedabouttheunderlyingassumptions,becausetheyareonlyimplicit ornotdiscussedatallintheliterature.Manytraditionalanalysismethodsarebased on firing rates obtained by trial-averaging, and some of the assumptions for such procedurestoworkcanindeedbeignoredwithoutseriousconsequences. The situation is different for correlation analysis, the result of which may be considerablydistortedifcertaincriticalassumptionsforthemethodtoworkarevi- olatedbythedata.Therefore,wehaveputeffortsinstatingexplicitlytheunderlying assumptions of the various methods, and giving methods at hand allowing to test iftheassumptionsareindeedfulfilled.In addition,wesupplythereaderalsowith stochasticmodelingtoolsandnumericalmethodstotestiftheanalysismethodcho- senservestheintendedpurpose.Inthestillongoingdiscussionontherelevanceof
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