Dynamicsand Representationinthe Primary Visual Cortex

vorgelegt vonDiplom-Informatiker

Péter Adorj án

Vom Fachbereich13 - InformatikderTechnischeUniversiẗatBerlin

zur ErlangungdesakademischenGradesDoktorderNaturwissenschaften

- Dr. rer. nat.-

genehmigteDissertation

Promotionsausschuß:Vorsitzender:Prof. Dr. GünterHommelBerichter:Prof. Dr. KlausObermayerBerichter:Prof. Dr. AndreasV. M. HerzBerichter:Prof. Dr. JackD. Cowan

TagderwissenschaftlichenAussprache:14.12.2000

Berlin 2000

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Copyright PéterAdorján,2000

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Grau,teurer Freund,ist alle Theorie,Undgrün desLebensgoldnerBaum.

(JohannWolfgangvonGoethe)

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Acknowledgments

I would like to expressmy greatestgratitudeto Prof. Klaus Obermayer, the supervisorof this re-searchwork. Prof.Obermayerhassetupanexcellentlaboratory, theNeuralInformationProcessingGroupatTechnicalUniversityBerlin with anenormouswork andattention.This freeandintellectu-ally moving scientificenvironmentwashighly inspiringfor my studies.Thenumerousdiscussions,seminars,invited guests,workshops,andmeetingswith our collaboratorswereessentialsourcesofmotivatingnew ideas.

Amongour collaboratorsI would like expressspecialthanksto Prof. Jenny Lund. Her crystalclearexplanationsprovideddeepinsight into theanatomyof thevisualcortex. Constructive discussionswith Prof.JackD. Cowanandwith Prof.JonathanLevitt weresimilarly highly motivating.

I am greatly indebtedto all my colleaguesat the Neural Information ProcessingGroup. It wasgreatfun to work togetherin a closeandfruitful collaborationwith ChristianPiepenbrockandLarsSchwabe. It was importantsynergic drive to changeideaswith CorneliusWeber. The excitingconversationswith ThoreGraepelareunforgettable.I enjoyedseveraldiscussionswith Drs. MartinStetter, UteBauerandMichaelScholz.

I would like to alsothankto all thosepeoplewhohavehelpedin building thefoundationsof my sci-entificwork. I rememberwith agreatpleasurethelife andstudyin thehighly pluralisticatmosphereof the Trefort ÁgostonHigh Schoolin Budapest.I have gainedessentialamountof knowledgeofbiologicallydetailedmathematicaldescriptionof neuralsystemsin PéterÉrdi’s laboratory(Dept.ofBiophysics,HungarianAcademyof Sciences),whereI couldwork togetherwith Drs. GyörgyBarnaandTamásGrőbler.

I amverygratefulto my grandparentsandparentsfor their invaluablesupportthroughoutmy course.

I would like to dedicatethiswork with all my loveto Erika.

This work wassupportedby theGermanScienceFoundation(Ob 102/2-1.;Gratuiertenkolleg “Sig-nalkettenin LebendenSystems”GK 120-2),by MRC G9408137,by HFSPORG-98/94,by VipromBiomed2EC grant,by WellcomeTrust050080/Z/97andby theVW FoundationI/71945.

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Abstract

We investigatetheprocessingandrepresentationof staticvisualpatternsin theearlyvisualsystemof mammals(especiallycatsandprimates).We demonstratethatneurophysiologicalandanatomi-cal findingscanmotivatetheoreticalconsiderationsabouttheneuralprocessingandvice versa.Weexplore“How?” and“Why?” questionsin a closeconnectionto eachother. Methodologicallythismeansusingbiologicallydetailed“bottom-up”computationalmodelsandabstract“top-down” mod-els in parallelor in combination.Specifically, we focuson thecontrast-andorientation-processingin the primary visual cortex (V1) with a strongemphasison the dynamicsof the neuralactivityandsynapses.We considerneuraldynamicson threedifferenttime scales:(i) the fasttime evolu-tion of the cortical activity with a time constantof 16 � 20 msec; (ii) the intermediatemodulationof the recurrentcortical competitionstrengthwith a time constantin the orderof 100 � 200msec(theapproximatelengthof a fixation period);(iii) contrastadaptationby theslow modulationof thedynamicnatureof thesynaptictransmissionwith a timeconstantof 5 � 10sec.Firstly, we explorehow orientationselectivity couldbegeneratedin theprimaryvisualcortex (V1)(chapters2, 3). Orientationselectivity is a remarkableandwell-exploredfeatureof thesimplecellsin V1. However, thereis still considerabledebateabouttheneurophysiologicalandanatomicalori-gin of thehighly featureselective responseof thesecells. The majorquestionconcernsthe extentto which thesimplecell propertiesaredeterminedby thestructureof their feed-forward connectiv-ity versusthe recurrentprojections.In contrastto previousmodels,in which the initial orientationbiasis generatedby convergentgeniculate(feed-forward)input to thesimplecells,andsubsequentlysharpenedby the lateralcircuits,our approachis basedon anisotropicintracorticalexcitatorycon-nections.Westudythehypothesisthattheserecurrentprojectionsprovideboththeinitial orientationbiasandits subsequentamplificationandthereforeorientationselectivity is generatedpurely intra-cortically. Our computationalstudyshows that indeedthe “intracortical hypothesis”is a plausiblealternative to theotherexisting hypotheses.Themodelpredictsthatthedynamicsof theorientationtuningcouldbe indicative of theunderlyingneuralmechanism.Thereforewe investigaterecurrentdynamicsin acorticalorientationhypercolumnin amorebiologicallydetailedstatisticalneuralfieldmodel(chapter3).

Secondly, we studywhy the recurrentcortical re-processingof the feed-forwardinput is importantfor therepresentationof theimageprojectedon theretina(chapter4). We proposethattherecurrentlateralconnectionsimplementcompetitionbetweenorientationselective simplecellswith overlap-pingreceptivefields.Then,weintroducetheconceptof “dynamiccoding”, andinvestigatetheshortterm dynamicsof the recurrentcompetitionin the primary visual cortex in termsof informationprocessing.We find thatinformationtransferis optimal in any increasingtime window afterstimu-lus onsetif therecurrentcorticalamplificationdecreases.In themodel,the initially strongcorticalcompetitiondecreases,andtherole of thegeniculateorigin feed-forwardprojectionsbecomesmoreimportant.Thesegeniculo-corticalprojectionscarrya topographicrepresentationof theimagepro-jectedto the retina. Motivatedby informationtheory, our resultsoffer a compromisebetweenthe“feed-forward” andthe“recurrent”hypothesesfor orientationselectivity. We suggestthatbotharevalid, however, in differentphasesof thecorticalprocessingduringa fixation period. In the initialphaseof processing,the recurrentcompetitionis strong,andthe salientorientationis signaledina winner-take-all fashion.In thesecondphase, corticalcompetitionbecomesweaker, allowing thedetectionof multipleorientations.A detailedcomputationalmodelprovidesexperimentallytestable

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predictionsaboutthedynamicsof corticalresponseto multiple orientations.

Thirdly, we study how and why contrastadaptationoccursin V1 (chapter5). We find that theadaptationof the transmitterreleaseprobability accountswell for all the puzzling experimentaldatathat is availableaboutthe neurophysiologyof contrastadaptation.The goodmatchbetweenour simulationresultsand the experimentaldataoriginatesfrom the fact that the dynamicnatureof the synaptictransmissiondependson the transmitterreleaseprobability. The adaptationrulefor the transmitterreleaseprobability is derived from the assumedfunctionalobjective of contrastadaptation.We proposethatcontrastadaptationreducestheredundancy in thecorticalresponsebymatchingtheactivationfunctionof singlecorticalneuronsto thesecond-ordersignalstatistics.Wealsoshow that increasingthe releaseprobability in a low-contrastenvironmenthasthe functionaladvantagethat it inducesa corticalneuronto detectsynchrony in its presynapticspike trains,ratherthanthepresynapticfiring rates. This synchrony detectionmodemaybeproperfor noisefilteringif thecontrastlevel is decreasedbecausesynchronousgeniculatefiring eventsaremorelikely to bestimulusrelated.

Contents

1 Intr oduction 11.1 Why theprimaryvisualcortex? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11.2 Informationtheorymeetssensoryprocessing?. . . . . . . . . . . . . . . . . . . . . 41.3 Structureof thethesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9

2 Generatingorientation selectivity intracortically—a rate model 112.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 112.2 Methods. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

2.2.1 Overview . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 142.2.2 Stimuli . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.3 Themagnocellularlayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152.2.4 Thegeniculo-corticalconnectivity . . . . . . . . . . . . . . . . . . . . . . . 182.2.5 Thecorticallayer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182.2.6 Implementation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

2.3 Results. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202.3.1 Orientationbiasandorientationtuning. . . . . . . . . . . . . . . . . . . . . 202.3.2 Theroleof lateralinhibition . . . . . . . . . . . . . . . . . . . . . . . . . . 212.3.3 Spatialfrequency tuningandspatialreceptive-fields. . . . . . . . . . . . . . 25

2.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.1 Modelassumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312.4.2 Intracorticalvs.afferentorigin of theorientationbias . . . . . . . . . . . . . 312.4.3 Sidestepconnectionsandorientationbias . . . . . . . . . . . . . . . . . . . 33

3 Generatingorientation selectivity intracortically—a statistical neural field approach 353.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 353.2 Thestatisticalmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

3.2.1 Neurons. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 373.2.2 Spikes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 393.2.3 Recurrentconnectivity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 403.2.4 Synapses. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2.5 Discretization. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.2.6 Interpretationof thepopulationalactivity . . . . . . . . . . . . . . . . . . . 41

3.3 Computationalresults. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 413.3.1 Emergentorientationselectivity . . . . . . . . . . . . . . . . . . . . . . . . 42

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3.3.2 Orientationtuningdynamics . . . . . . . . . . . . . . . . . . . . . . . . . . 433.4 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4 Dynamic coding: fr om the salient towards the details 474.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 484.2 Dynamiccorticalamplifier . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 49

4.2.1 Themodelsetup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 494.2.2 Computationalresults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.3 Dynamiccode. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 544.3.1 Theabstractmodel . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 564.3.2 Optimizingtherecurrentcompetitiondynamics. . . . . . . . . . . . . . . . 584.3.3 Informationtransferin time—Results . . . . . . . . . . . . . . . . . . . . . 60

4.4 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 624.4.1 Modelconclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634.4.2 Modelassumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 644.4.3 Modelpredictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

5 Contrast adaptation and infomax in visual cortical neurons 675.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685.2 Model setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.2.1 Theneuralnetwork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705.2.2 Singlecell andsynapticmodel . . . . . . . . . . . . . . . . . . . . . . . . . 70

5.3 Slow dynamicsandcontrastadaptation—theoreticalresults . . . . . . . . . . . . . . 725.3.1 Adaptationrule—infomax . . . . . . . . . . . . . . . . . . . . . . . . . . . 725.3.2 Redistributionof synapticresources—transients. . . . . . . . . . . . . . . . 74

5.4 Simulationsof contrastresponseandcontrastadaptation—numericalresults . . . . . 765.4.1 Simulationprotocol,dataanalysis . . . . . . . . . . . . . . . . . . . . . . . 775.4.2 Thecontrastresponsefunction . . . . . . . . . . . . . . . . . . . . . . . . . 775.4.3 Adaptationof thegeniculo-corticalsynapses . . . . . . . . . . . . . . . . . 795.4.4 Recurrentexcitationandcontrastadaptation. . . . . . . . . . . . . . . . . . 815.4.5 Modifying thereleaseprobabilityof therecurrentexcitatorysynapses. . . . 81

5.5 Possiblephysiologicalindicationsof thetransmitterreleaseprobabilityadaptation. . 855.5.1 Determiningtherecoverytime constantτrec . . . . . . . . . . . . . . . . . . 875.5.2 Determiningthetransmitterreleaseprobability p . . . . . . . . . . . . . . . 87

5.6 Discussion. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 885.6.1 Modelpredictions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 895.6.2 Modelassumptions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 905.6.3 Contrastadaptationandthereceptivefield profile . . . . . . . . . . . . . . . 90

A Parametersfor the feed-forward model in chapter 2 93A.1 Receptive-fieldparametersof theLGN M cellsin themodel . . . . . . . . . . . . . 93A.2 Parametersof theGeniculateTransferFunction . . . . . . . . . . . . . . . . . . . . 93

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B Empirical entropy manipulation—derivations for chapter 4 95B.1 Estimatingthemutualinformation . . . . . . . . . . . . . . . . . . . . . . . . . . . 95B.2 Empiricalentropy manipulation—Additivenoise . . . . . . . . . . . . . . . . . . . 96

B.2.1 Parzenestimatefor theempiricalentropy . . . . . . . . . . . . . . . . . . . 97B.2.2 Estimationof theoptimalcompetitionparameter . . . . . . . . . . . . . . . 98

B.3 Empiricalentropy manipulation—Poissonspiking . . . . . . . . . . . . . . . . . . . 99

C Derivations for the contrast adaptation model in chapter 5 101C.1 Effective transferfunction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101C.2 Mean-fieldderivationfor thesynaptictransmitter . . . . . . . . . . . . . . . . . . . 102

Chapter 1

Intr oduction

1.1 Why the primary visual cortex?

Theprimaryvisualcortex (abbreviatedasV1, andalsoreferredto asarea17 or striatecortex) is thefirst cortical areathatprocessesthevisualsignalsarriving from theretina. Thefeed-forwardinputto V1 is preprocessedby the retinal ganglionandthe relay cells of the lateralgeniculatenucleus(LGN). Thesubcorticalpreprocessingin theretinaandin theLGN includesdetectionof shortscalespatialandtemporalchangesin theilluminationpattern,detectionof color, andadaptationto simplestatisticalpropertiesof thevisualworld, like themeanluminancelevel.1

Retinalganglionandgeniculatecellshave localizedreceptivefieldswith a shapesimilar to aMexicanhat. Two typesof retinalganglionandgeniculatecellscanbedistinguishedbasedon theirreceptivefield profiles.TheON-centercellscanbeexcitedby illuminating thecenterpart,andcanbesuppressedby illuminating theannulussurroundingtheir receptive field center. TheOFF-centercellsexhibit theoppositebehavior. As a consequenceof this center-opponentorganizationof theirreceptive field profiles,thesecellsaremainly sensitive to local changesin the illumination pattern.Diffuseillumination evokesalmostno response.Theactivity patternof theretinalganglioncells ismappedtopographicallyto theprimaryvisualcortex via therelaycellsof theLGN.

Thesubcorticalpreprocessingof thevisualsignalshardlyinvolvesfeatureextraction.Informa-tion theoreticalstudiesproposethatretinalganglioncellseliminatesimpleandirrelevant—firstandsecondorder—spatialandtemporalredundanciesfrom the sensorysignalto obtaina compactbutsufficiently informationrich representationof thevisualinput(Shapley andEnroth-Cugell,1984;At-ick andRedlich,1990;Atick andRedlich,1992).By lowerorderredundancieswemeantheaverageintensity level (e.g., lightness),variance(e.g.,contrast)or correlationsbetweentwo points in thevisualfield (reflectedin anunequalpower spectrum).2 In otherwords,thetaskof thesesubcorticalpreprocessingregionsis to transmitmaximal(or a minimally required)amountof informationviatheir limited channelbandwidth. Transmittingmaximal informationon an informationbottleneckenforcesan efficient neuralcodethatdoesnot containirrelevantor “boring” messages.This codeforms the basisfor the extractionof the relevant and“interesting” contentin the sensoryinput at

1For a detaileddescriptionof theanatomicalstructureandthephysiologyof thesubcorticalvisualpathwaysseeKandeletal. (1991).

2For furtherdiscussionof redundancy reductionseesection1.2and,e.g.,Atick andRedlich(1992).

2 Intr oduction

latercorticalprocessingstages.As a resultof thesubcorticalpreprocessing,the primaryvisualcortex receivesa faithful and

ecologicalrepresentationof theimagepattern. Theimagepatternhelpsto recognizeobjects,shapesandthereforeit carriesrelevantinformation.Thepatternis formedby thehigher-ordercorrelations,i.e. constellationsof differentmodalitiesbetweenseveralpointsin the visual field or in time. Theword “ecological” hererefersto thevery importantconceptthatthesensoryprocessingsystemsarenotgenerallyoptimal,but they areadaptedto oursurroundingworld andthey alsofit to our internalneeds.It is alsosuggestedthat the cortical representationis faithful: in contrastto the precedingsubcorticalprocessingstages,thecorticalprocessingdoesnot reducethedimensionalityof thesig-nalanymore,it is probablynotcompact(Field,1994).Insteadof removing furtherredundancies,thevisualcortex is morelikely to extractanddescribetheremaininghigherorderredundancies,becausethey constitutetherelevantinformation.Note,however, thatorientationselectivity, themostpromi-nentfeatureof the primary visual cortex, canbe very well explainedby the redundancy reductionprinciple(Dimitrov andCowan,1998).

It is highly challengingto find generalprinciplesor optimalitycriteriafor thecorticalrepresen-tation. Onecodingstrategy couldbeto extracthiddeninterdependenciesbetweenpictureelements(like pixels)andobtaina transparentrepresentation,in which therepresentingunitsor neuronsarehighly specializedto certainfeaturesor objectsin thevisualenvironment.Entitieslike theseobjectsarelikely to appearindependentlyfrom eachother, thereforethis representationcanbe learnedonthebasisof statisticalindependence(seenext sectionfor furtherdiscussion).This is calledfactorialcode.

The decompositionof the visual input into different submodalitiesand features—basedonthesehigher-ordercorrelations—essentiallystartsin the primary visual cortex (V1). Specializedgroupsof cellsextract informationaboutthe differentaspectsof the visualscenes.Form, motion,or depth(andtheir combinations)at eachlocationof thevisualfield areprocessedby highly inter-connectedparallelpathways. Thesepathwaysarespecializedto the differentmodalities,but theystronglymodulateeachothervia theextensive interconnectivity. Furthermore,neuronsarespecial-ized to features,suchasorientation,cornersor morecompoundpatterns.The decompositionintodifferentmodalitiesandfeaturesresultsin anovercompleterepresentationin thecortex. Thedimen-sionalityof therepresentationin V1 increasesby severalfactorscomparedto theretinalor geniculaterepresentation:260million neuronsprocessthefeed-forwardinput from 2 million LGN fibers.Thecomplexity of theextractedfeaturesincreasesfrom V1 towardshighervisualareas(likeMT), whereonecanfind the prototypeof “grandmacells”, the faceselective neurons. As a consequence,inhigherareasfewerneuronsrepresenta givensensorysignal.

The cortical representationis a surrealmosaicof knowledgepiecesat differentcomplexitylevels. Thedecompositioninto “mosaicpieces”decreasesthecomplexity of theneuralrepresenta-tion andit is conducive to building new associationsthatmayhelp to interpretthesensorysignals.A patternof light intensitiesis transformedinto neuralactivity patterns,wherethe activity of theindividual neuronsor neuronalpopulationsaccountfor thepresenceof meaningfulobjectsor com-plex features.This representationreflectssemanticaspectsof the input. Naturally, thereis a needto combineor bind theselittle mosaicpiecesinto thecoherentimagewe perceive. Theanatomicalstructuresor corenetworksthatarespecializedto certainfeaturesor submodalitiesarestronglyin-terconnected.The binding of differentfeaturesis establishedvia recurrentinterconnectivity. Dueto this interconnectivity, perceptionof a coherentimageemerges. Furthermore,visual cuesfromdifferentsubmodalitiescansupportthe interpretationof others. (Several illusions arisefrom thiseffect,e.g.,whentheluminancegradientindicatesanillusionarythree-dimensionalstructure.)

1.1Why the primary visual cortex? 3

Summarizingthis brief introduction,the visual systemdecomposesand integratesthe visualscenesin parallel. The integrative processesmaintainthe illusion of perceiving coherentimages,while asa resultof thedecompositionprinciple,we arealsoableto analyzevisualscenesat severallevels of complexity: we canidentify objects,colors,motion, forms, or faces. The neuralmech-anismsof the imagedecompositionand integrationarewell hiddenby our own nervoussystem.Normally thesemechanismscannotbeapproachedconsciously. Introspectionis usuallya hopelessmethodfor understandingthem. However, in certainsituations,whenthereis an obviousdiscrep-ancy betweentheactualreality asweknow it andourperception,we canseebehindthecurtain.Asour referencesystemis the realworld andnot our neurophysiologicalreality, we call theseeffectsillusions. Illusionsrevealsomeneuralprocessingprinciplesor connectivity structuresthatareother-wisewell hiddenfrom our “eyes”. It is interestingto notethat thevisualsystemcanbemosteasilytrickedwith thehelpof weird, artificial stimuli. This indicatesthat thevisualsystemis specificallyprepared(throughevolution andlearning)to interpretour naturalenvironment(seealsoin section1.2andchapter4).

Visualsciencesarenot evenscratchingthesurfaceof theprinciplesunderlyingtheintegrativeprocessesinvolvedin perception.However, thedecompositionstrategy of thevisualsystem,is quitewell described,althoughnot too well understood.Therepresentationin V1 andalsoin otherearlyvisualcorticalareasis relatively transparentin thesensethatactivity of singlecellscorrelateswellwith thepresenceof simplefeaturesin thevisualstimulus.For instance,orientationselectivity, firstdescribedby HubelandWiesel(1962),is a prominentpropertyof severalcells in V1. Orientationselectivecellsrespondstronglyto edgesor gratingswith a certainorientation,but they remaininac-tive if theorthogonalorientationis presented.Eventhoughthediscovery of orientationselectivitywasa revolutionarystepto approachcodingstrategiesin the neocortex, sincethenmostof the re-searchhasbeendescriptive ratherthaninterpretive. Substantialknowledgehasbeengainedabouttheanatomicalstructuresandneurophysiologicalmechanismsthatareresponsiblefor thegenerationof orientationselectivity (seechapter2 andDas(1996);Vidyasagaret al. (1996);Sompolinsky andShapley (1997)for reviews), but therehave beenvery few studiesaimingto understandthereasonfor thepresenceof orientationor otherfeatureselectivity in thevisualcortex in termsof signalpro-cessing.In somesense,theexperimentaldescriptionof thevisualcortical functionis well aheadofour theoreticalunderstandingof it. Motivatedby andbasedon thehugeamountof availableexperi-mentaldata,several“bottom-up”computationalmodelshavebeenproposed.Thesemodelsprovidea betterunderstandingof theneural“wetware” by deducinghigher-orderfunctionfrom anatomicalandneurophysiologicalobservations.However, someof thebasicquestionsarestill open,includingthe origin of orientationselectivity. Therefore,we exploreda computationalmodelto highlight anew alternative hypothesisaboutthe intracorticalgenerationof orientationselectivity (chapters2and3).

Certainly, researchcannotcontinuewithout gainingsomeunderstandingof the principlesofcortical representationandwithout providing a quantitative descriptionof the neuralresponsesinconnectionto the representedworld. RecentexperimentalstudiesdescribingneuralresponsesinV1 have madethis needeven clearer. Thesemeasurementsdemonstratedthat the responseof theorientationselective cells in V1 doesnot solely dependon the orientationof an edgewithin the“classicalreceptivefield”3, but it canbestronglymodulatedby patternsplacedseveraldegreesout-side(e.g., Sillito et al., 1995;Zipseret al., 1996;Levitt andLund,1997;Polatet al., 1998).These

3Theclassicalreceptive field is theareafrom whereneuralfiring canbeevokedby localizedvisualstimulation.

4 Intr oduction

reports,however, contradicteachotheratseveralpoints.Thediscrepanciesaremainly4 dueto slightdifferencesin theinterpretationof theneuralresponsesandthestimulussetupin the individual ex-periments.Stimulussetupis asensitiveissuebecausetheparameterspaceexplodesusingcompoundstimuli assembledfrom gratingsor barswith differentcontrast,orientation,or spatialfrequency. Un-fortunately, thereis no generaltheorythat couldguideandmotivatecertainsetupsandsystematicexplorationof theneuralresponseto thevisual input. Thereis a strongneedto point out “interest-ing” directionsin this largeparameterspacebecausethenumberof availablerecordingsis stronglylimited by technicalconstraints.

Onepossibleway to addresstheabovequestionsanddetermine“interesting”directionsin thestimulusspacefor thevisualcortex is acarefulandquantitativestatisticalor informationtheoretical(seenext section)analysisof the recordedneuralresponsesto statisticallycharacterizedstimulussets. This approachhasbeensuccessfullyappliedespeciallyin the examinationof the sensorysystemsof insects(see,e.g., Laughlin, 1994;Rieke et al., 1997),but interestingnew researchisconductedin mammaliancortex too (e.g., RichmondandOptican,1990;Sugaseet al., 1999).Theotherpossibleway is to reveal codingprinciples(suchasthe abovementionedfactorialcode)em-ployedby the neocortex thatmay be optimal for sensoryprocessing(for moredetaileddiscussionseenext sectionand,e.g., Barlow, 1961;Linsker, 1989;OlshausenandField,1996).Following thelatterdirectionof researchstrategy, in thepresentthesiswe deduceneurophysiologicalpredictionsstartingfrom optimality requirementsfor thecorticalencoding.Fromhigh orderfunctionwe pro-ceedtowardsthebiological reality. This approachis referredto as“top-down” modeling. In closeconnectionwith our investigationinto the origin of orientationselectivity (chapters2 and3), firstwe explore the role of feed-forwardandrecurrentlateralconnectionsin obtaininganefficient cor-tical representationin time (chapter4). Secondly, we studycontrastadaptation(chapter5) andwederive a learningrule for thetransmitterreleaseprobabilityat thegeniculo-corticalsynapses.Bothapproachesarebasedon theprincipleof maximizingthemutualinformationbetweencorticalinputandoutput.

1.2 Inf ormation theory meetssensoryprocessing?

In the following we shortlydiscusswhy classicalinformationtheory(ShannonandWeaver, 1949)couldprovide a useful“toolbox” for investigatingneuralrepresentation.In parallel, the basicter-minology is introduced. More comprehensive reviews canbe found in (e.g., Atick, 1992;Riekeetal., 1997).

The word “information” hasa fairly complicated,multilayeredmeaning.What do we asso-ciatewith theword “information”? Excitement,novelty, learning,structure,semantics...To besure,it is scarcelya trivial task to give a mathematicallyexact andusefuldefinition for “information”thatalsofits our commonsenseinterpretation.Thereforethemostwidely usedformal measureofinformationis not intendedto be a formalizationof our subjective conceptof information. Shan-nonandWeaver (1949)introducedinformationtheoryfor solving problemsof telecommunicationsystems.This informationmeasureis calledShannoninformation. Surprisingasit maysound,in-formationtheoryhasrecentlyprovento bea powerful tool of investigationinto theneuralcodeandtherepresentationof sensorysignals.

Let us put asidefor a momentthe promotionof Shannoninformationand imaginea phone

4Technicaldifficultiescouldalsocausediscrepanciesin theresults,but thesearenot in thescopeof thecurrentdiscussion.

1.2Inf ormation theory meetssensoryprocessing? 5

cable. Beyonddoubt,thereareseveral differencesbetweena phonecableandthe centralnervoussystem,but let uspoint out only oneof them: thephonecabledoesnot “care” whetherwe transmittheUlyssesby JamesJoyce,theBerlin phonebook,or this thesisthroughit. Clearly, somehumanobserverswouldfind all of thesethreeinformationstreamsabsolutelyboringor irrelevant,but somemay not. Shannonand Weaver (1949) introducedan objective measureof information from theperspectiveof thephonecable.Themeasureignoressemanticaspects.Givena stochasticinforma-tion source(denotedhereasa randomvariableS) with theprobabilitystructureP(S)andthesetofpossiblesignalsor alphabet

�, theShannoninformationof asignals � � is

I � s��� � log2 P � s��� (1.1)In thefollowing discussiontheterm“signal” shalldesignateany typeof representationof amessage.Thiscouldbeanimage,text, sound,or neuralactivity pattern.Shannoninformationindicatesthere-ductionof uncertaintyby communicatingmessages. Theunit of informationaccordingto theabovedefinitionis bit becausethelogarithmhasa baseof 2. For instance,telling thegenderof somebodywehavemethasaninformationcontentof 1 bit becausethenumberof possiblepeopleis reducedtothehalf (assumingthatthemale-femaleratio in thesetof thepossiblepeopleis 1:1). Following ourexample,telling thenameof thepersonhasa high informationcontent,assumingthateachindivid-ualhasa relatively low likelihood.Shannoninformationis themeasureof unexpectedness.Thelesslikely or moresurprisinganeventor a message,thelargerits informationcontent.

Theaverageinformationcontentof thepossiblesignalsis calledentropy

H � S�� � ∑s�� P � s� log2P � s��� (1.2)

Theentropy of a signalsourceis thenumberof bits thatareon theaveragenecessaryto encodethesignal.Thesignaltransmissionof theinformationis mostefficient if it usesthesameamountof bitsontheaverageastheentropy of thesignal.If morebitsareusedfor theencodingthanit is necessary,thentherepresentationis redundant.

Entropy measurestheaveragereductionin uncertaintyby makingoneobservation. If on theaverageoneobservationreducesthepossiblesetof signalsto thehalf, thenits entropy is 1 bit. Theentropy is maximalif everysignalis equallylikely. If someof thesignalsoccurfrequently, but othersonly rarely, theobservercouldexpectthefrequenteventwith agoodchanceevenbeforemakingtheobservation.In thiscasetheentropy is lower, andtheefficacy of thecommunicationbetweensignalsourceandtheobserver is suboptimal.

Now considerthe casein which the signals is a combinationof n symbols( s � s1 � ����� � sn).Images,e.g.,arecomposedof individual but usuallynot independentpixels. In this casethesignalis avectorof thecomponents,andits entropy satisfies

H � S��� n∑i � 1H � Si ��� (1.3)

Theequalityholdsif andonly if the individual componentsarestatisticallyindependent.Correla-tionsbetweenthe components(e.g.,pixels)decreasethe entropy andthereforethe codingefficacybecauseby observingonepixel onecouldinfer thevalueof theother.

To sumup, the signalsourcecantransferinformationwith thehighestrateto theobserver ifeachsignalis equallylikely andthesignalcomponentsarestatisticallyindependentfrom eachother.

6 Intr oduction

If thenumberof bits availablefor transmittinga signalstream(e.g.,a phoneconversion)is limited,thenit is essentialto obtainan optimal encodingof the given signalset(e.g.,the humanspeech).Themaximalentropy thatcanbetheoreticallyreachedin an informationchannelis calledchannelcapacity

C � maxP ���s� � H � S����� maxP � si � � n∑i � 1H � Si ����� nlog2N � (1.4)

whereN is the numberof different symbolsat eachcomponentof s. Basedon this, one couldcalculate,e.g.,thecapacityof 100by 100imagematrixesif 256differentgraylevelsareavailable.Similarly thecapacityof written text thatconsistsof N letterscanbedetermined.Determiningthecapacityof a codingschemeis essentialto characterizetheefficiency of theinformationtransfer. Itturnsout, e.g.,that naturallanguagesdo not usethe full capacityprovidedby the setof availableletters. If the randomvariableis discrete,thenthechannelcapacityis constrainedby theavailablecomponentsandsignals.Shannoninformation,andentropy canbeextendedfor continuousrandomvariables. In the continuouscase,the capacityis constrainedby the maximalavailablesignal-to-noiseratioon thechannel.

If the full channelcapacityis not used,thenthecodingis redundant,lessefficient. Giventhechannelcapacity, theredundancyof a signalsourceS is

R � 1 � H � S�C

� (1.5)Redundancy gives a measurefor the inefficacy of the signal transmission. One can distinguishbetweentwo typesof redundancy sourcesby reformulatingtheabovedefinition

R � 1C

�C � n∑

i � 1H � Si � � !#" $first% order & 1C

�n

∑i � 1H � Si � � H � S� � !#" $

higher% order � (1.6)The first term increasesif the different symbolsin the available alphabetare usedwith unequalprobability. This is referredto asfirst order redundancy. The secondterm increasesif thereareinterdependenciesbetweenthesignalcomponents(e.g.,betweenpixels).Thisis referredto ashigherorder redundancy. Natural languagesare redundantboth becauseof too frequentuseof certainletters,like “e”, andinterdependenciesbetweenlettersin a sequence(e.g.,consonantsarelikely tobefollowedby vowels).

What is the goal of neural coding?

Having introducedthe basictermsof information theory, let us returnto our original problemofapplyinginformationtheoryin thecontext of neuralrepresentation.As it wasemphasizedbefore,Shannoninformationignoressemanticaspectsof thesignals.Instead,it considersastochasticsignalsourcewith a givenstatisticalstructureP � S� andaninformationchannel.Transmittinginformationis problematicif thechannelcapacityis limited. Thisis calledthe“informationbottleneckproblem”.Suchlimitation canarisefrom noise,constrainednumberof representationalunitsandlimited dy-namicrangeof theactivity (limited alphabet).Smallsubsystemsof thenervoussystemcouldbealso

1.2Inf ormation theory meetssensoryprocessing? 7

consideredasunitsthatare“blind” to semanticsof thesignal,andtheironly taskis to transmitinfor-mationto eachotherin aneffective manner(Atick, 1992). Basedon this paradigm,Barlow (1961)proposedthat thegoal of sensorycodingis to completelyreducethe redundancy that is presentinthestimulus.This is calledminimalredundancycode.

Alternatively, Field haspointedout (Field, 1987; Field, 1994) that the goal of the corticalencodingis to minimize the statisticaldependency betweenneurons(the secondterm in Eq. 1.6)in suchway that the outputentropy H � S� nonethelessremainsconstant.This codeis calledmini-mumentropyor factorial code. If theneuronsarestatisticallyindependent,decodingcanbebasedon looking at theactivity of the individual neurons,without consideringcomplex interdependencypatternsof firing.

Minimal entropy codealonedoesnot reduceredundancy, and thereforeit is not motivatedby an informationbottleneckasthe minimal redundancy code. Minimal entropy or factorialcodetransfersthehigherorderinterdependenciesinto first orderredundancies.Thismeansthatthefiringhistogramsof singleneuronsareredundant,neuronsaremorelikely to fire with a certainfrequency.In thiscodetheentropy of thesinglecomponentsH � Si � is minimized(thatis why it is called“mini-malentropy code”).Severalstudiesindicatethattheorientationselectivesimplecellsform asparseandfactorialrepresentationof thenaturalworld (Field, 1987;OlshausenandField, 1996;Bell andSejnowski, 1997;OlshausenandMillman, 2000).In otherwords,minimalentropy codeis obtainedin theprimaryvisualcortex by theorientationselectivecells.

Statisticallyindependentcomponentsof naturalscenescouldberelatedto independentobjects,causesor semanticunits.Therefore,a factorialrepresentationcouldalsobeadvantageousfor higherordercognitive function. Furthermore,after obtaininga factorialcode,a subsequentsimplegaincontrolmechanismcanmaptheneuraloutputsuchthat it obtainsmaximalentropy givena limiteddynamicrangeof activity. If the interdependency betweencodingunits is minimal, a smallerdy-namicrangeis enoughto gaina givenamountof informationaboutthesignal.Combiningfactorialcodewith a propergaincontrolminimizestheredundancy in theneuralcode.

Theobservationthatfactorialcodeallowsto reducethedynamicrangeof theneuronswhile theinformationtransferis keptconstantisusedby Atick andRedlich(1990).They demonstratedthatthereceptivefield shapesof retinalganglioncellscanbeexplainedby theminimalredundancy principle.They suggestthatredundancy canbereducedby reducingthechannelcapacity(thedynamicrangeofneuralresponse)subjectto theconstraintthattheinformationgainedaboutthesensoryinput is equalto a given minimal requiredinformation. In otherwords, they proposethat the neuronalchannelcapacityshouldnot be wastedfor encodingthe input noise. The optimal solution is a receptivefield, which decorrelatesthesensorysignal.Atick andRedlich(1990)have shown thatconsideringonly second-ordercorrelationsis enoughto explain receptivefield propertiesof theretinalganglioncells. If outputnoiseis alsopresent,thenthe systemincreasescorrelationsin the signalbecausecorrelationsdistinguishsignalfrom noise(thenoisewasassumedto beuncorrelatedonthedifferentunits).

Neural codeand the (interactions with the) representedworld

It is essentialthat the optimal coding strategy dependson the actuala priori distribution of theencodedstimulus. Natural imagesarenot random,they have an inherentstructure. They form averysmallsubsetof all possibleimages,in otherwords,they areredundant(comparedto whatcouldbe communicatedby photon-beams).It hasbeenarguedthat the neuralrepresentationis matchedto this statisticalstructure(e.g.Field, 1987;Laughlin, 1981;Atick andRedlich,1990;Atick and

8 Intr oduction

Redlich,1992;Field,1994;vanderSchaafandvanHateren,1996).If thevisualsystemisspecializedto our visual environment,understandingthe structureof the visual world could guide us in theunderstandingof thevisualsystem(Gibson,1966).Redundancy in theneuralcodecanbeminimizedby eliminatingthe redundancy in the sensoryinput. As first- andsecond-ordercorrelationsdo notcarryrelevantinformationit is anefficient codingstrategy to remove them. However, higher-ordercorrelationsmake a visual scene,text, musicmeaningfulfor us. Extractinganddescribingthesecorrelations,for exampleby obtaininga factorialcode,is thereforea betterstrategy thenremovingthem(Field,1994).

In order to reduceor extract redundanciesfrom naturalstimuli, it is necessaryto learn theenvironment’s statisticalstructure. This continuouslyobserved structureor redundancy becomespartof our knowledge abouttheworld. Here,we usetheword “knowledge”with a wider meaningthat includesthe hard-wired,geneticallydeterminedstructures(obtainedthroughthe evolution) aswell asthe theknowledgeaccumulatedfrom personalexperiencesandlearning.Our expectations,ourknowledgeaboutthecorrelationsin theoutsideworld arecrutchesin theprocessof interpreting,learningand detectingnovelty. Even thoughwhite noisehasthe highestinformation contentinShannonsense,it is meaninglessfor ahumanobserverbecauseourneuralsystemis notableto copewith suchhigh informationrate.

We would like to remindthe readerthat the mainassumptionin thepreviousdiscussionwasthat neuralsubsystemsneedto communicatewith eachother in an efficient way, given a limitedchannelbandwidth.To reachthis goalonestrategy is to removetheredundanciesfrom theoriginalsignalandobtainacompactcodewith minimalredundancy. Severalstudiesindicatethatsubcorticalsystemsdo remove low-orderredundancies.Thecodingstrategy for corticalprocessingis likely tobe different. It tries to transferthe complex interdependenciesin the signalinto simplefirst-orderredundancies.As aconsequence,singlecodingunitsrepresentindependentobjectsthatarelikely tobemeaningful.Notethatoncethehigherorderinterdependenciesareextracted,it is easyto reducethe first orderredundancy in singleneurons’activity. This canbe doneby a properinput-outputmappingthatmatchestheprior probabilitydistributionof therepresentedobject.

To sumup, we have shortly illustratedthatconsideringtheone-way chainof signal-channel-receiver, informationtheorycanexplain someimportantaspectsof neuralfunctionin earlysensorysystems.However, this framework is likely to be too restrictedto approachthe high level corticalprocessing.It may be insufficient to analyzethe high dimensionalinput spacealone. Insteadofconsideringthestatisticalstructuresolelyof thesignal(i.e. theoutsideworld), onemayinvestigatethestructureof the interactionswith the outsideworld. This extendedframework couldprovide adescriptionof codingin a semanticspacethatis definedbasedon behavioral relevancy.

Our researchpresentedin this thesisfocuseson two aspectsof optimalcodingin theprimaryvisual cortex. Firstly, in the context of contrastadaptationwe arguethat the visual systemadaptscontinuouslyto the slowly changingenvironment. We proposethat the functionalrole of contrastadaptationis to eliminatethedependenceof corticalactivity ontherootmeansquare(r.m.s.)contrastthatsoonaftera changebecomesa sourceof redundancy. In parallel,we investigatethe low-levelneuralmechanismthatcouldberesponsiblefor “implementing”contrastadaptation.Thesebottom-up andtop-down approachesmeetat the learningrule for the transmitterreleaseprobability. Sec-ondly, we investigatetheshorttermdynamicsof therecurrentcompetitionandneuralactivity in theprimaryvisualcortex in termsof informationprocessingandin thecontext of orientationselectivity.We considera free-viewing scenariowheretheenvironmentis exploredby fixating subsequentlyatdifferentpositions.This studyis basedon two key observations.(i) Thecodingstrategy thatmax-imizesinformationtransferdependson thesignal-to-noiseratio (SNR)of theoutput. (ii) TheSNR

1.3Structur eof the thesis 9

changeswith timewithin thedurationof afixationperiodbecausewith increasingtimewindow, thenumberof spikesavailablefor encodingincreases.It follows that theneuralcodingstrategy shouldbe modulatedon a fasttime scaleto fit to the decreasednoiselevel. We refer to this principle as“dynamic coding”. In the context of orientationselectivity in V1, we suggestthat it is optimal todecreaserecurrentcompetitionamongdifferentedgedetectorstunedto differentorientationsafterstimulusonset(afterthebeginningof a fixation period).This resultsin a complexity based,hierar-chical featureextraction.Thehierarchicallevelsaredistributedin time. Themodelpredictsthat inthefirst phaseof a fixation period,salientandtypical featuresareprocessed.In the secondphase,lesstypical,detailedstructuresarerepresented.

1.3 Structure of the thesis

Eachchapteris self-containedwith anextensive review of thepreviouswork andanintroductiontothediscussedsubject.' In chapters2 and3, we explore a new hypothesisaboutthe origin of orientationselectivity

in V1. Accordingto our “intracortical hypothesis”anisotropicrecurrentprojectionsprovideboth the initial orientationbiasandits subsequentamplification.In chapter2 we setupa ratemodelfor an orientationhypercolumnandstudythe emergentreceptive fields andthe aver-ageresponsedynamics.Our studyshows that the emerging responsepropertiesaresimilarto theresponsepropertiesthatareobservedexperimentally, hencethehypothesisof anintra-corticalgenerationof orientationbiasandsharporientationtuningis a sensiblealternativetothe notion of a feed-forwardbiasby convergentgeniculo-corticalprojectionpatternsthat issubsequentlysharpenedby therecurrentconnections.' In chapter3, the intracorticalhypothesisis further explored. Using a statisticalneuralfieldapproachwe studytherecurrentconnectivity patternandresponsedynamicsin a greaterbio-logical detailness.We find that theanisotropy in therecurrentconnectionsthatis capableforgeneratingtheorientationbiasdoesnotneedto beextremestrong,andthereforeit maynotbeobviously reflectedin therecurrentcorticalpatterns.Furthermore,we canaccountfor theex-perimentalobservationthatorientationtuningof themembranepotentialsharpensgradually,while thespikingactivity showsanimmediatesharplytunedresponse.' In chapter4, theroleof recurrentcorticalamplificationandits short-termdynamicsis studiedin termsof informationprocessing.We proposethattherecurrentcorticalcompetitionshoulddecreaseafterstimulusonsetto obtainoptimalamountof informationaboutthefeed-forwardsignalin any increasingtime window. Themainmotivationfor thechangingcorticalcompe-tition comesfrom theobservationthatwith increasingtime window thesignal-to-noiseratioin thecorticalneuralactivity increasesbecausemoresamplesareavailablefor representationandestimation.In thefirst phaseof processing,only themostsalientorientationis extractedby thestrongrecurrentcompetition.In thesecond,lesscompetitivephase,therepresentationdetailedstructuresand,therefore,multiple orientationsbecomespossible. Our informationtheoretichypothesisis studiedin anabstractmodelfor a recurrentnetwork. A moredetailedmodel is alsoexploredin orderto give experimentalpredictionsfor the cortical responsetomultiple bars.

10 Intr oduction' In chapter5, contrastadaptation,thus cortical dynamicson a longer time scaleis studied.Firstly, we proposethat a novel form of synapticplasticity may be responsiblefor contrastadaptation. In contrastto the classicalparadigmof modulatingthe synapticstrengththatscalestheamplitudeof thesynaptictransmission,we suggestthatadaptationof thedynamicsof synaptictransmissionis theneuralmechanismthatexplainsall theavailableexperimentaldata. In our modelthe synapticdynamicsis changedvia the transmitterreleaseprobability.Wefurtherproposethatswitchingbetweendifferentmodesof synaptictransmissionhasfunc-tionaladvantagesin thecontext of contrastadaptation.Secondly, wederiveanadaptationrulethe transmitterreleaseprobability basedon the hypothesisthat contrastadaptationservestoachieve the mostefficient cortical representationof the feed-forward input arriving from thelateralgeniculaterelaycells.

Chapter 2

Generatingorientation selectivityintracortically—a rate model

Abstract

We report resultsof numericalsimulationsfor a modelof generationof orientationselectivity inmacaquestriatecortex. In contrastto previousmodels,wheretheinitial orientationbiasis generatedby convergentgeniculateinput to simplecells andsubsequentlysharpenedby lateralcircuits, ourapproachis basedon anisotropicintracorticalexcitatoryconnectionswhich provide both the initialorientationbiasandits subsequentamplification.Ourstudyshows thattheemergingresponseprop-ertiesaresimilar to the responsepropertiesthatareobservedexperimentally, hencethehypothesisof anintracorticalgenerationof orientationbiasis a sensiblealternativeto thenotionof anafferentbiasby convergentgeniculo-corticalprojectionpatterns.In contrastto modelsbasedon anafferentorientationbias,however, the “intracortical hypothesis”predictsthat orientationtuning graduallyevolvesfrom an initially nonorientedresponseanda completelossof orientationtuning whentherecurrentexcitation is blocked, but new experimentsmust be designedto unambiguouslydecidebetweenbothhypotheses.1

2.1 Intr oduction

Theemergenceof orientationselectivity in theprimaryvisualcortex of highermammalshasbeenoneof themostactive areasof researchduring thepastdecades(for recentreviews seeDas,1996;Sompolinsky and Shapley, 1997). Currently favored modelsassumeconvergent thalamic feed-forward projectionsfrom elongatedregionsof the thalamicvisual field representationwhich arecomplementedby strongintracorticalrecurrentconnections.Accordingto thoseideas,theafferentprojectiongeneratesan orientationbias which is subsequentlyamplifiedby intracorticalcircuits.While the role of intracolumnarrecurrentexcitation and inhibition in the generationof tunedre-sponseshasbeenclarifiedat leastto someextent,theorigin of theinitial orientationbias,suggestedto bea propertyof thegeniculo-corticalprojection,is debatable.

1This chapteris basedon (Adorján,Levitt, Lund andObermayer, 1999).

12 Generatingorientation selectivity intracortically—a rate model

The ideaof anafferentorientationbiasgoesbackto HubelandWiesel(1962)who proposedthatsimplecells in cat striatecortex areorientationselective becausethey receive segregatedON-andOFF-inputfrom appropriatelyelongatedareasof theLGN retinotopicmap.Accordingto theirhypothesis,theaxisof elongationof theafferentprojectiondeterminesorientationpreferencewhilethe aspectratio of the receptive-field determinesthe specificityof the response.Estimatesof theaspectratio of thecorticalcells’ anatomicalreceptive-fields,however, arein conflict with thesharptuningof simplecells(Chapmanet al., 1991;Peiet al., 1994;ReidandAlonso,1995;SompolinskyandShapley, 1997)and- asa purely feed-forward model - Hubel andWiesel’s hypothesiscouldnot accountfor responsepropertiessuchasthe contrastinvarianceof the tuning width (SclarandFreeman,1982)or thesensitivity of theorientationtuningcurveto changesin thestrengthof lateralinhibition (Tsumotoet al., 1979; Sillito et al., 1980;Eysel et al., 1990; Satoet al., 1996;Crooketal., 1997;Crook,KisvárdayandEysel,1998).

The fact that the lateralintracorticalexcitatorycontribution to a cortical cell’s synapticinputin layer4 is muchbigger(80% � 95%)thantheafferentLGN input (see,e.g.Petersetal.,1994),theresultsof experimentsblockinginhibition,andevidencefor cross-orientationsuppressionfrom phys-iological studies(Hataet al., 1988;Bonds,1989;DeAngeliset al., 1992)motivatedthe extensionof Hubel andWiesel’s hypothesisto includelateralinhibition betweencortical cells. In particularcross-orientationinhibitionwasthoughttobeagoodcandidatefor sharpeningorientationtuning,andmodelstudies(see,e.g.Wehmeieret al., 1989;WörgötterandKoch,1991;Sabatini,1996)demon-stratedthataninitially weakorientationbiascanindeedevolveintoasharplytunedresponseby thesekindsof interactions.A numberof studieshave reportedfinding crossorientationinhibition (Hataetal.,1988;Bonds,1989;Douglasetal.,1991;DeAngelisetal.,1992;Peietal.,1994)andblockadeof crossorientationinhibition reducesorientationselectivity (Eyselet al., 1990;WörgötterandEy-sel,1991;Crooket al.,1997;Crook,KisvárdayandEysel,1998).Ontheotherhand,Ferster(1986)reportedthelackof any cross-orientationhyperpolarization,andshowedthatIPSPsevokedby visualstimulationwereactuallystrongestat thepreferredorientation.Furthermore,theabsenceof cross-orientationshuntinginhibition wasalsoshown (Douglaset al., 1988;FersterandJagadeesh,1992).WhenBermanet al. (1992)suggestedthat the measuredsmall changesin membraneconductanceandthemeasuredsmallhyperpolarizationarenot sufficient to cancelstrongmonosynapticafferentinputsandNelsonet al. (1994)reportedthatblockinginhibition within a singlecell doesnot affectits orientationtuning,it becameclearthatanessentialingredientwasmissingfrom thesemodelsofgenerationorientationspecificity.

Thesefindings led to the currentset of hypothesesconcerningthe origin of orientationse-lectivity, which includestrongrecurrentlateralexcitation in additionto iso- andcross-orientationinhibition (DouglasandMartin, 1991;Ben-Yishaiet al., 1995;Douglaset al., 1995;Somerset al.,1995;Mundelet al., 1997;CarandiniandRingach,1997).Accordingto thesehypotheses,recurrentiso-orientationexcitation selectively amplifiesthe weak afferent signal while iso-orientationandcross-orientationinhibition arerequiredfor thecontrolof the amplificationandfor the sharpeningof theinitial orientationbiasrespectively. Thesemodelswere,finally, ableto reconcilea largebodyof dataandleadto aconsensusabouttherole of local lateralinteractionsin orientationtuning.

Returningto the evidencefor an afferentvs. a cortical origin of the initial orientationbias,experimentalresultsfor catandferret(Chapmanet al., 1991;ReidandAlonso,1995;Fersteret al.,1996)seemto supporttheideaof thalamicfeed-forwardgenerationof anorientationbias.Peiet al.(1994),Volgushev et al. (1995),andRingachet al. (1997a), on theotherhand,describemany cellswith an initially nonspecificresponsewhich evolvesto a sharplyorientationtunedresponseafterapproximately10 msec,contradictingobservationsof immediate,strongly tunedafferent EPSPs

2.1Intr oduction 13

Figure2.1: Hypothesesaboutorientationselectivity: (i) convergenceof the feed-forwardconnec-tionsfrom anelongatedregionin theLGN is solelyresponsiblefor orientationselectivity; (ii) recur-rent inhibition sharpensthe feed-forwardorientationbias; (iii) corticalamplifiermodels,recurrentexcitationandinhibition sharpensthefeed-forwardorientationbias;(iv) the“intracorticalhypothe-sis”, theinitial orientationbiasis generatedandsharpenedby theanisotropicrecurrentconnections.

(Fersteret al., 1996). Also, inhibitory blockadeexperimentsindicatecircularratherthanelongatedexcitatoryreceptive-fields(Tsumotoetal.,1979;Sillito etal.,1980).Indirectevidencefor acorticalcomponentof theorientationbias,alsocomesfrom recentdevelopmentalstudies(Kim andBonho-effer, 1994;Bonhoeffer andGoedecke,1996).Reversesutureexperimentsperformedin kittensandyoungferretsleft thevisualcorticalorientationmapunchanged,evenwhentheeyesneverhadcom-monvisualexperience.If monoculardeprivationresultsin acompletereorganizationof theafferentprojectionashasbeenreportedby (Antonini andStryker, 1993)thenit is difficult to explain(but seeWolf et al. (1996)for anattempt)that “connecting”or “reconnecting”of fibersafterreversesuturecanleadto the restorationof the samebiasesin the afferentprojectionsandto virtually identicalcorticalorientationmaps.

Given the abovementionedcontradictoryevidence,the fact thatorientationselectivity in pri-mateshasnot yet beenextensively addressed,and the fact that nearlyall previous modelstudiesconsideronly an afferentorigin of the orientationbiasmotivatedus to explore an alternativehy-pothesis, namelythatboththeinitial orientationbiasandthesubsequentamplificationaregeneratedby the samespecificlateralexcitatory recurrentconnections.Thuswe focus on the mechanismsunderlyingthe initial symmetrybreakingin the orientationdomainwhich may—in principle—besmall (Ben-Yishai et al., 1995)but which in reality hasto be large enoughto robustly overcomenoise. The goal of this study is twofold. Firstly, the predictionsof the “intracortical hypothesis”areexploredandthereceptive-fieldproperties—orientationselectivity, spatialfrequency tuning,and

14 Generatingorientation selectivity intracortically—a rate model

spatialreceptive-fields—arederived. Secondly, we look for experimentsto testour “intracorticalhypothesis”.Thegoalof our studyis thento show that—giventhecurrentevidence—intracorticalgenerationof orientationselectivity is a viablealternative to the“afferent” hypothesisandneedstobeexploredseriously.

In thefollowing sectionwedescribethestructureof ourmodelandprovidethemodelparame-ters.Section2.3containstheresultsof ournumericalsimulationswith respectto thecontrastdepen-denceof orientationtuning,thedynamicsof theresponse,theroleof lateralexcitationandinhibitionin orientationselectivity, andwith respectto thespatialfrequency tuningandspatialstructureof thereceptive-fields. Section2.4 containsa critical discussionof modelassumptions,a comparisonofmodelpredictionswith experimentaldata,a comparisonwith othermodelsof orientationselectiv-ity, in particularwith modelswhich assumean afferentorientationbias,anda discussionof someexperimentallytestablemodelpredictions.The model is basedon the tuning propertiesof simplecellsin layer4Cα of macaquestriatecortex, for whichananatomicalsubstratefor thegenerationoforientationselectivity hasrecentlybeensuggested(Yoshiokaet al., 1994). A preliminarystudyonthe“intracorticalhypothesis”waspublishedin (Baueretal., 1997).

2.2 Methods

2.2.1 Overview

Asabasisof ourmodelingstudywechoseorientationselectivecellsin layer4Cα of thestriatecortexin themacaquemonkey. Thisseemsanappropriatechoicefor threereasons.(i) Orientationselectivecellsarefoundfor thefirst time in mid andupperlayer4C (BlasdelandFitzpatrick,1984;HawkenandParker, 1984)and they coincidewith the emergenceof lateralaxonprojectionsfrom the ex-citatory spiny stellateneuronsreachingup to 500 to 1500µm alongoneaxis from the cell bodies(Lund,1987;Andersonet al., 1993;Yoshiokaet al., 1994),which mayactuallyserveasananatom-ical substratefor generationof orientationselectivity. (ii) A recentreport suggeststhat orienta-tion tuningfor somecells in primatelayer4Cα is not establishedimmediatelyafterresponseonsetbut graduallydevelopsafter an initial nonorientedresponsewithin the first 10-15msec(Ringachet al., 1997a, andpersonalcommunication).This phenomenonhasalsobeenobservedin catstriatecortex (Dinseet al., 1991). In contrastCelebriniet al. (1993) reportsimmediatelytunedcorticalresponse,but amoredetailedmodelingstudy(Adorjánetal., 1998)gaveapossiblesolutionfor thiscontradiction.(iii) No attempthasyetbeenmadeto explain theemergenceof orientationselectivityin macaquestriatecortex, althoughits architecturediffers in several importantwaysfrom the pri-maryvisualareasof catsandferrets.It is possiblethatthemechanismsunderlyingtheemergenceofreceptive-fieldpropertiesdiffer betweenspecies.

Our computationalmodelconsistsof threelayers: the visual field layer, the magnocellularlayer of the LGN, anda cortical layer which correspondsto the upperregion of 4Cα of primaryvisual cortex (Fig. 2.2). We choseto consideronly monocularON-cells,andhave neglectedON-OFFinteractionsto simplify our model.We havedonesobecauseit hasalreadybeendemonstratedthatblockingtheON pathwaydoesnotalterorientationor directionselectivity of V1 cells(Schiller,1982;SherkandHorton, 1984). Furthermore,cross-correlationstudies(Tanaka,1983;Reid andAlonso,1995)provide strongevidencethat inputsfrom the LGN to the individual subfieldsof V1simplecellsareessentiallysegregatedto thesametype(i.e.ON to ON andOFFto OFF).Thus,ON-OFF interactionsseemunlikely to berequiredfor generationof orientationselectivity. Parameters

2.2Methods 15

Convolution,transfer function

Grid of connectionistneurons

Stimuli

} Upper 4CαSpiny−stellatecells(exc.)Basket−cells(inh.)

} LGNM−cells

Visual Field}Gratings, bars

∼ 500µm ∼ 0.2ο

Figure2.2: Thestructureof theconnectionistmodelfor generatingorientationselectivity intracorti-cally.

aretakenfrom measurementsat5( eccentricityin thevisualfield representation.Tosimplify notationwe will identify modelneuronsof the samekind by the locationof their receptive-field centerinvisualspace,andnot by their anatomicallocationsin eachlayer.

2.2.2 Stimuli

Stimuli arestationaryspotsor gratingswhich arepresentedto thevisualfield layer. Theluminancevaluesls for aspotstimulusaregivenby

ls �)x�*� 1 & c + exp� � � x1 � u1 � 2 , s21 � exp � � � x2 � u2 � 2 , s22 � � (2.1)where u �-� u1 � u2 � is thepositionof thespot’s centerin visualfield, c its Webercontrast( � Lmax �Lmin � , Lmin � ), and x �.� x1 � x2 � arevisualfield coordinates.A stationarysinusoidalgratinglg is givenby

lg �)x�� 1 & c + cos� 2π f + d �)x � α ��� � (2.2)wherec �0/ 0 �1� 12 denotesMichelsoncontrast( � Lmax � Lmin � , � Lmax & Lmin � ), α theorientation,f thespatialfrequency, andd �3x � α ��� x1sinα � x2cosα. If not mentionedotherwise,all thesimulationswith sinusoidalgratingsweremadeat theoptimalspatialfrequency of thegeniculateM-cells.2.2.3 The magnocellular layer

Thereceptive-fieldprofilesS of thegeniculateM-cells aredescribedby a Differenceof Gaussians(DoG) model (Rodieck,1965)and the afferent input R�4u� to a geniculateM-cell at location u inthe magnocellularlayer is given by the convolution of the stimulus ls5 g in the visual field layer

16 Generatingorientation selectivity intracortically—a rate model

with thereceptive-fieldprofilesS. Parametersof thereceptive-fieldprofilesweretakenfrom (Spearetal.,1994)andwerecorrectedfor 5( eccentricity(seeAppendixA.1). They arelistedin Table2.1.

Propertiesof geniculateM-cells (Spearet al., 1994)Peakcentersensitivity kc in [inpa (% c) % 1 deg % 2] 2077.64Centerradiusrc in [deg] 0.103Peaksurroundsensitivity ks in [inp (% c) % 1 deg% 2] 14.75Surroundradiusrs in [deg] 1.16Optimalspatialfrequency fopt in [cycl/deg] 0.59Maximal responseMmax in [spikessec% 1] 43.00ContrastgainG in [spikessec% 1 (% c)% 1] 1.82Activity gain1, b [inp % 1] 0.064ContrastthresholdcminM in [% ] 1.36Activity thresholdTM [inp] 7.77

Geniculo-cortical connectivityRadiusof thegeniculateaxonalarborrax in [µm](Freundet al., 1989;BlasdelandLund,1983) 400Radiusof thedendriticarborof corticalcellsrdend in [µm] (Lund,1980) 100

Ar chitectureof upper 4CαMagnificationfactor(HubelandWiesel,1974)in [deg/mm] 0.4Numberratioof excitatoryto inhibitory cells(Lund,1987) 8:2Numberratioof excitatoryto inhibitory synapses(Beaulieuetal., 1992) 83:17Numberratioof afferentto lateralexcitatorysynapses(Peterset al., 1994) 6:94Numberratioof synapsesterminatingonexcitatoryto synapsesterminatingon inhibitory cells(Freundetal., 1989;Andersonet al., 1994) 9:1Activity gainβ 0.13Activity thresholdTC 0.003ExcitatoryconnectionstrengthWC � e��6 e� i 78� 3.73Inhibitory connectionstrengthWC � i ��6 e� i 78� -24.5Specificityof excitatoryconnectivity (seeFig. 1b) in [ %deg] -1.6

Specificityof inhibitory connectivity (seeFig. 1b) in [ %deg] -0.06

aArbitrary scalableunit indicatingtheafferentinputonapostsynapticgeniculateM-cell

Table2.1: Summaryof modelparametersusedin thisstudy.

Becausetheemergenceof theorientationselective responseis muchfasterthanthe temporalmodulationof the usuallyusedstimuli, the outputO of the magnocellularlayer is assumedto be

2.2Methods 17

instantaneous,andit is calculatedvia a transferfunctiongM,

O � gM � R�*�-9 0 if R � TMR% TMR% TM : b otherwise � (2.3)

whoseparametersTM andb weredeterminedaccordingto AppendixA.2.

18 Generatingorientation selectivity intracortically—a rate model

2.2.4 The geniculo-cortical connectivity

The total afferent input A into a cortical cell is given by the convolution of the outputsO of thegeniculateM-cellswith a circularly symmetricconeshapedweightkernelwith radiusrA ,

WA � d ���?> rdend, we obtainrA � rax � rdend � 300µm in cortical coordinatesand— givena corticalmagnificationfactorof 0 � 4( , mm — rA � 0 � 12( in visualfield coordinates.Notethatthereis noafferentorientationbiasto anindividualcorticalcell becauseits receptive-fieldis circularsymmetric.

2.2.5 The cortical layer

Our model of a cortical orientationcycle (orientationhypercolumn)consistsof 300 neuronsofwhich 80% areexcitatory and20% are inhibitory (Fitzpatricket al., 1987;Lund, 1987;Beaulieuet al., 1992).Thediameterof thehypercolumnis approximately500µmwhich leadsto a maximumdistancebetweenreceptive-field centersin visual spaceof approximately0 � 2( for cells locatedinthesameorientationhypercolumn.Thediameterof a corticalcell’s receptive-fieldis approximately0 � 2( � 0 � 3( , thusreceptive-fieldsof cellswithin oneorientationhypercolumnoverlapheavily.

For the purposeof the modelwe assumethat cells whosereceptive-fieldslie alongoneaxisin visualspacebelongto one“orientationcolumn” (Fig. 2.3a)andarelaterallyconnectedby strongexcitatory interactions. Inhibitory connectionsfollow the sametendency in a lessspecificway.Thestrengthof interactionbetweenunitsfrom differentorientationcolumnsfalls off with theanglebetweentheiraxes(Fig.2.3b).Aswill beseenlater, theorientationof theaxisin Fig.2.3adeterminesthepreferredorientationof its cells,andtheinteractionsshown in Fig. 2.3bthencorrespondto iso-orientationexcitation,iso-orientationinhibition, andweakcross-orientationinhibition. This choiceof corticalconnectivity in theorientationdomainis reasonablegiventhephysiologicalexperimentswhich indicatehighly specificiso-orientationexcitationaswell asstrongiso-orientationinhibition(Ferster, 1986;Douglaset al., 1991),andthe experimentsshowing the importanceof inhibition intheemergenceof theorientationselective response(Tsumotoet al., 1979;Sillito et al., 1980;Satoet al., 1996) or the presenceof lateral inhibition arriving from oblique or orthogonallyorientedcells (Hata et al., 1988;Bonds,1989; Eyselet al., 1990; Wörgötter andEysel,1991; DeAngeliset al., 1992;Peiet al., 1994;Crooket al., 1997;Crook,KisvárdayandEysel,1998). We will showin section2.3 that themodelwith this setof parametersfits to availableexperimentaldataandthattheseresultsarerobust to changesin the specificchoiceof theseparameters(cf., Figs. 2.7, 2.8).Theoverall distribution of differenttypesof synapsestargetingdifferentcells is listed in Table2.1.Excitatoryconnectionsoriginateeither from the magnocellularLGN layer or from othercortical

26 %of thetotal numberof synapses,whichwasarbitrarily setto 1000.

2.2Methods 19

(a)

∆θ

(b)−90 −45 0 45 90

0

30

60

e

i

∆Θ in [°]

Per

cent

age

of C

onn.

Figure2.3: (a) Cartoonof anorientationhypercolumn.Filled andemptycirclesdenotethecentersof receptive-fieldsin visual spaceof cells from two orientationcolumnswith a difference∆Θ inpreferredorientation.Themaximumdistancebetweenfield centersis = 0 � 2( andcorrespondsto thehypercolumndiameterat 5( eccentricity. receptive-field (dottedanddashedcircles)diametersareapproximately0 � 3( . (b) PercentageP � p � ∆Θ � (Eq. 2.8) of excitatory, e @ e ande @ i, (solid line)andinhibitory, i @ e andi @ i, (dottedline) lateralconnectionsasa functionof thedifference∆Θof orientationpreference,asusedin mostof thenumericalsimulations.Theparticularchoiceof thelateralconnectivity patternwasmotivatedby the availableexperimentaldata(seetext) aswell asby thenumericalsimulationswhich areshown later. Thesynapticloadis calculatedby multiplyingthe numberof synapsesat the given differencein the preferredorientations∆Θ with the weightof a single synapsemaking contactwith an excitatory or an inhibitory neuron. A typical set ofparametersis: synapticweightsWC: e @ 6 e, i 7 =3.73,i @ 6 e, i 7 = -24.5,slopeof the percentageof the lateralexcitatoryandinhibitory connectionsP � p 5 0�A% P � p 5 15BC�15B asa functionof thedifferenceinpreferredorientation:e @ 6 e, i 7 -1.6 %deg andi @ 6 e,i 7 -0.06 %deg.cells,while inhibitory synapsesaremadeonly betweencorticalcells.All threetypesof connectionsmayterminateonexcitatoryor inhibitory cells.

Cortical neuronsare modeledascontinuous-valuedunits, whosestatem is interpretedas a“membranepotential”.Let θ denotethepreferredorientationof a cell asgivenby theorientationoftheaxesin Fig. 2.3a,index i thepositionof its receptive-fieldcenteralongeachaxis,p � 6 exc � inh7thetypeof thecell, andt thetime. Thenweobtainfor themembranepotentialm:

ddt

m� p�Θ 5 i � t �*� � m� p�Θ 5 i � t � & I � (2.5)wherethesynapticinputI � A & L (2.6)is thesumof theafferentinputA (section2.2.4),andthelateralinput

L � Θ � q � t �� ∑p 5 j 5Θ D NC � p � q ��EΘ � Θ F E � WC � p � q� gC � m� Θ F � p � j � t ���G� (2.7)

20 Generatingorientation selectivity intracortically—a rate model

NC � p � q ��EΘ � Θ F E � is the numberof synapsesfrom a cortical cell of type p targetinga cortical cellof type q whosedifferenceof preferredorientationis EΘ � Θ F E . WC � p � q� is the strengthof a sin-gle connectionbetweencells of type p andtype q. The percentageof the excitatory or inhibitoryconnectionsasa functionof differencein preferredorientations∆Θ (Fig. 1b) is

P � p � ∆Θ �� NC � p ��6 e� i 7 � ∆Θ �∑∆Θ NC � p �46 e� i 7 � ∆Θ � � (2.8)Thecorticaltransferfunction

gC � x�*�IHJ K 0 if x � TCβ � x � TC � if TC L x L TC & β % 11 otherwise (2.9)describesthetransformationbetweenthemembranepotentialandtheoutputfiring frequency. ThestrengthNCWCβ of the recurrentamplification is being changedin section2.3.2 by varying thestrengthof thedifferentsynapsesWC (cf., Figs.2.7,2.9) at a fixednumberof connectionsNC (seeTable2.1)andafixedβ (β � 0 � 13)3. ThethresholdTC wassetto thegeniculateinputwhichacorticalcell in upper4Cα receivesat thresholdcontrast(cminC � 2%)(HawkenandParker, 1984),TC � 0 � 003.Themaximalactivity of thecorticalcellsis 1.

2.2.6 Implementation

The modelwasimplementedin C on a standardUnix workstation. The afferent input to a singlecortical cell was integratedin spaceusing the extendedSimpson’s rule (Presset al., 1994). Thesystemof ordinarydifferentialequations,Eq. 2.5, wasintegratedusing fourth-order Runge-Kuttamethod(Presset al., 1994)with a timestepof 0 � 5 (in arbitraryunit).2.3 Results

2.3.1 Orientation biasand orientation tuning

In ourmodel,all corticalcellsreceivegeniculateinput from acircularsymmetricregionof themag-nocellularlayer, hencethegeniculateinputto individualcorticalcellsdoesnotprovideanorientationbias. The orientationbiasis generatedby the anisotropiclateral interactions.The excitatory cou-pling is strongestbetweencellswhosefieldsarelocatedon a particularaxis in thevisualfield (cf.Fig. 2.3) suchthat the sumof the total geniculateinput arriving to all suchcoupledcells dependson theorientationof thestimulus(columnarorientationbias). In themodelthesestronglycoupledcellshave thesamepreferredorientationandform one“orientationcolumn”. Theorientationbiasof the summedgeniculateinput to suchan orientationcolumnis determinedby the orientationoftheaxison which thecells’ receptive-fieldslie. This columnarorientationbias is sharpenedby thesamerecurrentconnections,thusthegenerationof theinitial orientationbiasandthesharpeningoftheorientationtuningareinseparableprocesses.

3β was chosensmall enoughsuchthat the steadystateactivity of the network assuminga transferfunction with nosaturationis alwayslessthan1 for all possiblevaluesof I (Eq.2.6)

2.3Results 21

(a)0 90 180

0

0.15

0.3

Orientation α in [°]

Ste

ady

Sta

te R

espo

nse

100%40% 6%

(b)0 50 100

0

1

2

Contrast c in [%]

Am

plifi

catio

n

90°75°60°

Figure2.4: (a) Orientationtuningcurvesof excitatory(solid line) andinhibitory (dottedline) cellsfor threedifferentvaluesof stimuluscontrast.The tuning width (half width at half height) is ap-proximately23( for bothcell typesandis independentof contrast.(b) Corticalamplificationfactor(steadystateactivity dividedby theafferentgeniculateinput) asa functionof contrastfor threedif-ferentstimulusorientations.Stimuli weregratingswith optimalspatialfrequency. Parametersweretakenfrom Table2.1andFig. 2.3.

Fig. 2.4ashows orientationtuning curvesof a cortical cell for a gratingstimulusof optimalspatialfrequency but varyingcontrast.Tuningwidth is independentof contrast(cf. SclarandFree-man,1982)andis approximatelyequalfor excitatoryandinhibitory cells,aslong asthespecificityof theexcitatory(e @ e ande @ i) andinhibitory (i @ e andi @ i) connectionsin theorientationdomainis independentof the type of the target cell. Tuning widths (half width at half height)areapproximately23( for the parameterschosenbut mayvary with theconnectionspecificityandthestrengthof the lateralinteractions(seesection2.3.2). If the recurrentexcitation is strongenough,the tuning width is to a large extent determinedby the specificityof the lateral interactions.Thetuningwidth no longerdependson thestrengthof theorientationbias,i.e. , thenetwork operatesinits “marginal phase”(Ben-Yishaiet al., 1995). If thestrengthof the lateralexcitationfalls below acritical value,thetuningwidth becomesbiasdependent(cf. Fig. 2.9).

Fig. 2.4bshows that the cortical amplificationfactor, definedas the steadystatecortical re-sponsedividedby the afferentgeniculateinput, remainsconstantwith respectto stimuluscontrastfor strongenoughrecurrentexcitation. This resultindicatesthata recurrentnetwork exhibits eithercontrastinvariantorientationtuning or saturationin the contrastresponsefunction,but not both iflinear summationof the synapticinputsanda piecewise linear transferfunction is assumed.Thisresulthasbeenconfirmedanalyticallyby Bartschet al. (1997).Henceadditionalmechanismshaveto be invokedto explain thesaturationof thecontrastresponsecurves,a finding which contradictsclaimsput forwardin previousmodelingstudies(Todorov, SiapasandSomers,1997).

2.3.2 The role of lateral inhibition

A largenumberof experimentsin the pasthave suggestedthat lateralinhibition playsat leasttworolesin theemergenceof orientationselectivecells: it controlsrunawayexcitationandit leadsto thesharpeningof theorientationtuning.

Blocking inhibition on a largecortical site with the GABAA antagonistbicucullinebroadens

22 Generatingorientation selectivity intracortically—a rate model

0 90 180 0

0.5

1

Orientation α in [°]

Ste

ady

Sta

te R

espo

nse

0 −10.2−16.9−20.3−25.4

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0.15

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Orientation α in [°]

Ste

ady

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te R

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0 −3.4 −6.8 −8.5 −25.4

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Orientation α in [°]

Ste

ady

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te R

espo

nse

−25.4−18.6−10.20

−24 −12 0 0

45

90

HW

HH

in [°

]

Strength of Inhibition WC(i,p)

−24 −12 0 0

45

90 H

WH

H in

[°]

Strength of Inhibition WC(i,p)

−24 −12 0 0

45

90

HW

HH

in [°

]

Strength of Inhibition WC(i,p)

(a) (b) (c)

Figure2.5: Orientationtuningcurvesandhalf width at half heightasa functionof (a) thestrengthWC of all inhibitory connections,(b) thestrengthWC of inhibitory connectionsfor ∆Θ > 30( , withall otherWC setto -24.5,and(c) thestrengthWC of inhibitory connectionstargetingon asinglecell,with all otherWC setto -24.5. The dottedvertical line in (a, bottom)indicatesthe strengthabovewhich thecortical responsebegins to saturate.The tuningcurves(top) areplottedat five differentparametervalues,as indicatedin the insets. Stimuli weregratingswith optimal spatialfrequencyandc � 60% contrast.Parametersweretakenfrom Table2.1andFig. 2.3.or diminishesthe orientationselective cortical response,dependingon its concentration(Tsumotoet al., 1979;Sillito et al., 1980;Satoet al., 1996). We simulatedtheeffect of theseexperimentsbyreducingthestrengthWC of all inhibitory connections.Themodelthenpredictsa broadeningof thetuningcurve if the strengthof inhibition is reducedto 70%orless(Fig. 2.5a(top)), but in contrastto experimentalfindings,the broadeningof the tuning curve is mainly dueto the fact that corticalcellssaturatebecausethey aredriveninto theflat regionof their transferfunction.Sincerealcorticalcells saturateway below their maximumfiring rate - with (Sillito et al., 1980)andwithout (see,e.g.Ohzawa et al., 1985)thepresenceof bicuculline- theremustbeadditionalmechanismsfor thecontrolof runawayexcitation.

Inactivationof smallcorticalsitesby micro-iontophoresisof GABA broadensorientationtun-ing when inactivation andrecordingsiteshave differentpreferredorientation(Eyselet al., 1990;Crook et al., 1997;Crook, KisvárdayandEysel,1998). To emulatethe local inactivation experi-mentswe changedthestrengthWC of inhibition betweencellswhosedifferencein preferredorien-tationwaslarger than30( . Thestrengthof inhibition is changedsequentiallycorrespondingto thedifferent levels of inhibitory blockadein the real experimentalsetup. The numericalsimulationsshowed that the selective blockadeof cross-orientationinhibition leadsto an increasedresponseat the null-orientationand/orto a decreasedresponseat the optimal orientation.The tuning curvebroadenssignificantly if the strengthof inhibition is reducedto 30%orless(Fig. 2.5b),andactiv-

2.3Results 23

ity now remainsbelow the saturationlevel of the cortical cells. Iso-orientationinhibition, whichremainsactive, is still sufficient to controlrunawayexcitation.

Intracellularblockadeof inhibitionelevatestheactivity ateveryorientationby thesameamount,but doesnot affect orientationtuningat simplecells(Nelsonet al., 1994).We simulatedthis exper-imentby changingthestrengthWC of theinhibitory connectionsafferentto a singleexcitatorycell.Thesimulationresults(Fig. 2.5c)indeedshow a smallelevationof theactivity level, but thetuningwidth remainedconstant,becausethe cell is drivenby sharplytunedrecurrentexcitation from theunaffectedcells.

0 25 50 75 100 −0.6

0

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Tot

al In

put

e; opt.e; nulli; opt.i; null

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put e; opt.

e; nulli; opt.i; null

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0

0.6

1.2 4 8

Time in [arbitrary unit]

Tot

al In

put / e; opt.

e; nulli; opt.i; null

Figure2.6: Total excitatory andtotal inhibitory input to a simulatedcortical cell asa function oftime for gratingstimuli of null andoptimal stimulusorientationandfor differentstrengthsof theexcitatoryconnections:WC � 3 � 4 (left); WC � 3 � 73(middle);WC � 3 � 9 (right). Gratingshadoptimalspatialfrequency andc � 60% contrast.Parametersweretakenfrom Table2.1andFig. 2.3.

Fig. 2.6 centershows thetime courseof thetotal excitatoryandthetotal inhibitory input to acorticalcell for optimalandfor null stimuli at therecurrentexcitatorystrengthWC � 3 � 73generallyusedin our simulations.A fastunspecificrise of excitation is followedby the onsetof inhibition.As inhibition rises,the activity of excitatory cells tunedto the null orientationdecayswhile theactivity of cellstunedto theoptimalorientationgrows. Finally, a tunedresponseemerges.Thusthemodelpredictsanon-orientedinitial responseandagradualsharpeningof orientationtuning,similarto what hasbeenreportedby Peiet al. (1994)andVolgushev et al. (1995)for catarea17, andformacaqueV1, layer4Cα (Ringachetal.,1997a, andpersonalcommunication).Thispredictiondiffersfrom the predictionsof modelsassuminga Hubel andWieselstyleafferentorientationbiaswhichprovidestunedinput immediately(cf. Somerset al., 1995). Figs.2.6 left andright show how thetime-courseof excitationandinhibition changesif thestrengthof thelateralexcitatoryconnectionsdecreasedfrom WC � 3 � 73 to WC � 3 � 4 or increasedto WC � 3 � 9. If the lateralexcitation is weak(Fig. 2.6 left) thentheafferentnonspecificinput becomesdominantandit invokeslong nonspecificresponse.The emergenceof the tunedresponseis delayedand the tuning width decreases.Incontrast,at strongerlateralexcitation (Fig. 2.6 right) the initial nonspecificresponseis very short.Tuning is establishedfaster, but becausethe steadystateactivity is higher, the time to reachthesteadystateincreases,asthetuningbecomessharper.

SincethestrengthsWC andthelocalprojectionpatternof theexcitatoryandinhibitory connec-tionsarefreeparameters,weexploredthesharpnessof orientationtuning(half width at half height)andthe maximalsteadystateactivity asa function of the strengthof the excitatoryandinhibitoryconnections(Fig. 2.7) andfor differentlateralconnectivity schemes(Fig. 2.8). NCWCβ is approxi-matelytheslopeof thepostsynapticmembranepotentialasa functionof thepresynapticfiring rate

24 Generatingorientation selectivity intracortically—a rate model

2 4 6 −50

−25

0 . . . . . . . . .. . . . . . . . .. . . . . . . .. . . . . . .. . . . . . .. . . . . .. . . . . .. . . . . .. . . . .. . . . .. . . .. . . .

→→

Strength of Excitation

Str

engt

h of

Inhi

bitio

n

HWHH in [°]

20 30 40

2 4 6Strength of Excitation

Max. Steady State Activity

0 0.5 1

(a) (b)

Figure2.7: (a) Orientationtuningwidth (half width athalf height)asa functionof thestrengthsWCof excitatoryandinhibitory connections.Grayvaluesindicatetuningwidthsbetween15( and45( .Thedotsmarktheareain parameterspacewheretheresponsesof thecellssaturate(theblackregionin b), at leastat theoptimalorientation.Thewhite arrow markstheconnectionstrengthswhich aretypicallyusedfor thenumericalsimulationspresentedthroughoutthispaper. (b) Themaximalsteadystatecorticalactivity asa functionof thestrengthsWC of excitatoryandinhibitory connections.Thegrayvaluesindicatethe maximalsteadystatecortical activity. Stimuli weregratingswith optimalspatialfrequency andc � 60% contrast.Theparametersweretakenfrom Table2.1andFig. 2.3.if the postsynapticmembranepotentialis closeto the reversalpotential(seeSection2.5). In bothfiguresthetuningwidth andthecorticalactivity is codedby brightnessvalues.In Figs.2.7aand2.8adotsindicatetheregion in parameterspacefor which theresponseof thecellssaturates(equivalentto theblackregionwherethemaximalsteadystateactivity is 1 in Figs.2.7band2.8b).

Thephasediagramshows threeregimesfor themodel(cf. Sompolinsky andShapley, 1997).If therecurrentexcitationis not strongenoughthenthecorticalresponseis not orientationselectiveandveryweak.Towardsstrongerrecurrentexcitation,whenthenetwork amplifiestheafferentinputtunedresponseemerges(cf. Douglasetal.,1995).Thetuningissharpestif thedepolarizingload(thegeniculateandthelateralexcitatoryinput) is justat thelimit whenit still canbebalancedby thehy-perpolarizingeffects(lateralinhibition andtheleakage)(cf. TsodyksandSejnowski,1995).In otherwords,givenacertainlateralinhibition strength,sharpesttuningemergesat thestrongestlateralex-citationwhenthecorticalresponsestill convergesto asteadystate.Notethatbecausethenumberofexcitatoryconnectionsis muchlargerthaninhibitory ones(seeTable1), andtheexcitatoryconnec-tionsarelessdistributedamongtheorientationcolumns(they aremorespecific),balancedexcitationandinhibition requiresstrongerinhibitory connections.Sharplytunedresponsesemergewhentheeffectivestrengthof thesingleexcitatoryconnectionsfulfill WC � e��6 e� i 78� = 3 � 1 & 0 � 03 + WC � i �46 e� i 7M� ,

2.3Results 25

a linearrelationship.Thusthemodelpredictsthatsharporientationtuningis robustagainstchangesin thelateralactivity aslongasexcitationandinhibition remainapproximatelybalanced.If thevisualcortex operatesat high recurrentlateralexcitatoryandinhibitory load(cf., e.g. Peterset al., 1994)then the modelpredicts,that at a high, but not completereductionof lateralactivity, orientationtuningremainssharp.As a consequence,thecoolingexperimentby Fersteret al. (1996)is not nec-essarilydecisiveevidencefor theafferentorigin of theorientationtuning,assumingthatinactivationof cortical activity waseffective but not complete. Increasingthe excitatory connectionstrengthleadsto saturationat optimalorientation,henceto broadertuning 4. For reasonsmentionedin thepreviousparagraph,closeto theoptimal tuningwidth thetime to reachthesteadystategrows withthespecificityof theresponse(datanotshown). Thephasediagramremainssimilar if iso-orientationinhibition is increasedandcross-orientationinhibition is decreased(datanot shown), but strongerexcitationis neededto establisha tunedresponseandtheregion in parameterspacefor which cellsdonot saturateshrinks.

Figs. 2.8ashows the orientationtuning width as a function of different lateral connectivitypatterns.Theslopesof theexcitatoryandinhibitory connectionpercentagesasafunctionof angulardifferenceweretaken asfree parameters.The connectivity patternsare indicatedin Fig. 2.8c forninerepresentativeexampleswhichcovertherangeof slopesshown in Figs.2.8ab. Sharplyselectiveresponseemergesin awideregimewheretheslopeof thepercentageof connectionsasafunctionofangulardifferencefor theexcitatoryconnectionsis changedfrom � 6 � 6 %deg to � 0 � 2 %deg andtheslopefor theinhibitory connectionsis changedfrom � 0 � 2 %deg to & 0 � 4 %deg. In a relatively largepartof thisregimetheresponsesaturates(dottedarea)which againhintsat thenecessityto consideradditionalmechanismsto control runaway excitation for theselateralconnectivity schemes.Sharpesttuningis achieved for fairly specificexcitatory connectivity patternsanda slight dominanceof iso- vs.cross-orientationinhibition. If thespecificityof excitatoryconnectionsis decreased,strongercross-orientationinhibition is requiredfor a tunedresponse.If excitatorycellsareconnectedin a highlyspecificpattern,then strongeriso-orientationinhibition is neededto control runaway excitation.If the excitation is too localizedin the orientationdomainthen cell groupswith closepreferredorientationmutuallysuppresseachother, andno tunedresponseemerges.Furthermore,extremelyspecificlateral inhibitory andexcitatory couplingsseparatethe differentorientationcolumnsandgiverisetomultimodal,periodicresponsepatternsin theorientationdomain(CarandiniandRingach,1997)(datanot shown).

2.3.3 Spatial fr equencytuning and spatial receptive-fields

Fig. 2.9ashows plotsof thehalf width at half heightof theorientationtuningcurvesasa functionof spatialfrequency of thegratingstimuli. Figs.2.9b,c, d show thespatialfrequency tuningcurvesfor theafferentgeniculateinput to a singlecell (thick line) andfor theoutputat differentstimulusorientations(∆α � 15( , top to bottom). Orientationandspatialfrequency tuningwereinvestigatedfor four differentlateralpatternsof excitatoryconnections:highly specific(h) andstrong(s)connec-tions coveringa distanceof 500µm, lessspecific(l) but strong(s) excitatoryconnectionscoveringa distanceof 500µm, highly specific(h) but weak(w) connectionscoveringa distanceof 500µm,

4Sincecells have not beenobserved to saturateat their maximumfiring frequency, mechanismsother than recurrentexcitation andinhibition mustbe presentto control runaway excitation if excitatory connectionsaretoo strong. The prob-lem is connectedto the problemof how to explain the saturationof the cortical neurons’contrast-responsefunction (see,e.g. Albrecht andHamilton,1982). Candidatemechanismsincludeadaptationeffectsat the synapticsummationor spikegeneration,but they arestill amatterof controversy.

26 Generatingorientation selectivity intracortically—a rate model

(a)

....................

....................

.............................................................................

....................................................

.............................

.................. →→

Exc. specificity

Inh.

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ityHWHH in [°]

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Max. Steady State Activity

0 0.5 1

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0

100

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ctio

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0 90 0

100

0 90∆Θ in [°]

0 90

Figure2.8: (a) Orientationtuning (half width at half height)asa functionof the specificityof thelateralexcitatoryandinhibitory connections.ThefreeparametersweretheslopesP � p 5 0�N% P � p 5 15B �15B ofthepercentagesof excitatoryandinhibitory lateralconnectionsasa functionof angulardifference.Gray valuesindicatetuning widths between15( and 45( , similar to Fig. 2.7. The arrow in (a)indicatestheconnectivity patternwhich wastypically usedfor thenumericalsimulationspresentedthroughoutthis paper;dots mark the region in parameterspacefor which cells begin to saturate(t