STIMULUS ENCODING BY MUL TIDIMENSIONAL RECEPTIVE FIELDS IN SINGLE CELLS AND CELL POPULATIONS IN VI OF A WAKE MONKEY

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1 STIMULUS ENCODING BY MUL TIDIMENSIONAL RECEPTIVE FIELDS IN SINGLE CELLS AND CELL POPULATIONS IN VI OF A WAKE MONKEY Edward Stern Center fr Neural Cmputatin and Department f Neurbilgy Life Sciences Institute Hebrew University Jerusalem, Israel Ad Aertsen Institut fur Neurinfnnatik Ruhr-Universitat-Bchum Bchum, Gennany Eiln Vaadia Center fr Neural Cmputatin and Physilgy Department Hadassah Medical Schl Hebrew University Jerusalem, Israel Shaul Hchstein Center fr Neural Cmputatin and Department f Neurbilgy, Life Sciences Institute Hebrew University Jerusalem, Israel ABSTRACT Multiple single neurn respnses were recrded frm a single electrde in VI f alert, behaving mnkeys. Drifting sinusidal gratings were presented in the cells' verlapping receptive fields, and the stimulus was varied alng several visual dimensins. The degree f dimensinal separability was calculated fr a large ppulatin f neurns, and fund t be a cntinuum. Several cells shwed different tempral respnse dependencies t variatin f different stimulus dimensins, i.e. the tuning f the mdulated firing was nt necessarily the same as that f the mean firing rate. We describe a multidimensinal receptive field, and use simultaneusly recrded respnses t cmpute a multi-neurn receptive field, describing the infrmatin prcessing capabilities f a grup f cells. Using dynamic crrelatin analysis, we prpse several cmputatinal schemes fr multidimensinal spatitempral tuning fr grups f cells. The implicatins fr neurnal cding f stimuli are discussed. 377

2 378 Stern, Aensen, Vaadia, and Hchstein INTRODUCTION The receptive field is perhaps the mst useful cncept fr understanding neurnal infrmatin prcessing. The ideal definitin f the receptive field is that set f stimuli which cause a change in the neurn's firing prperties. Hwever, as with many such cncepts, the use f the receptive field in describing the behavir f sensry neurns falls shrt f the ideal. The classical methd fr describing the receptive field has been t measure the "tuning curve" i.e. the respnse f the neurn as a functin f the value f ne dimensin f the stimulus. This presents a prblem because the sensry wrld is multidimensinal; Fr example, even a simple visual stimulus, such as a patch f a sinusidal grating, may vary in lcatin, rientatin, spatial frequency, tempral frequency, mvement directin and speed, phase, cntrast, clr, etc. Des the tuning t ne dimensin remain cnstant when ther dimensins are varied? i.e. are the dimensins linearly separable? It is nt unreasnable t expect inseparability: Cnsider an riented, spatially discrete receptive field. The excitatin generated by passing a bar thrugh the receptive field will f curse change with rientatin. Hwever, the shape f this tuning curve will depend upn the bar width, related t the spatial frequency. This effect has nt been studied quantitatively, hwever. If interactins amng dimensins exist, d they accunt fr a large prtin f the cell's respnse variance? Are there discrete ppulatins f cells, with sme cells shwing interactins amng dimensins and thers nt? These questin have clear implicatins fr the prblem f neural cding. Related t the questin f dimensinal separability is that f stimulus encding: Given that the receptive field is multidimensinal in nature, hw can the cell maximize the amunt f stimulus infrmatin it encdes? Des the neurn use a single cde t represent all the stimulus dimensins? It is pssible that interactins lead t greater uncertainty in stimulus identificatin. Des the small number f visual crtical cells encde all the pssible cmbinatins f stimuli using nly spike rate as the dependent variable? We present data indicating that mre infrmatin is indeed present in the neurnal respnse, and prpse a new apprach fr its utilizatin. The final prblem that we address is the fllwing: Clearly, many cells participate in the stimulus encding prcess. Arriving at a valid cncept f a multidimensinal receptive field, can we generalize this cncept t mre than ne cell intrducing the ntin f a multi-cellular receptive field? METHODS Drifting sinusidal gratings were presented fr 500 msec t the central 10 degrees f the visual field f mnkeys perfrming a fixatin task. The gratings were varied in rientatin, spatial frequency,tempral frequency, and mvement directin. We recrded frm up t 3 cells simultaneusly with a single electrde in the mnkey's primary visual crtex (VI). The cells described in this study were well separated, using a templatematching prcedure. The respnses f the neurns were pltted as Peri-Stimulus Time Histgrams (PSTHs) and their parameters quantified (Abeles, 1982), and ffline Furier analysis and time-dependent crsscrrelatin analysis (Aertsen et ai, 1989) were perfrmed.

3 Stimulus Encding by Multidimensinal Receptive Fields in Single Cells and Cell Ppulatins 379 RESULTS Recrding the respnses f visual crtical neurns t stimuli varied ver a number f dimensins, we fund that in sme cases, the tuning curve t ne dimensin depended n the value f anther dimensin. Figure la shws the spatial-frequency tuning curve f a single cell measured at 2 different stimulus rientatins. When the rientatin f the stimulus is 72 degrees, the peak respnse is at a spatial frequency f 4.5 cycles/degree (cpd), while at an rientatin f216 degrees, the spatial frequency f peak respnse is 2.3 cpd. If the respnses t different visual dimensins were truly linearly separable, the tuning curve t any single dimensin wuld have the same shape and, in particular, psitin f peak, despite any variatins in ther dimensins. If the tuning curves are nt parallel, then interactins must exist between dimensins. Clearly, this is an example f a cell whse respnses are nt linearly separable. In rder t quantify the inseparability phenmenn, analyses f variance were perfrmed, using spike rate as the dependent variable, and the visual dimensins f the stimuli as the independent variables. We then measured the amunt f interactin as a percentage f the ttal between-cnditins <1) 0.9 ~ 0.8 bo O.7 s:: 'C 0.6 u:: "0 0.5 ~ 0.4 E 0.3 a 0.2 s:: 0.1 A. Spatial Frequency Tuning Dependence upn Orientatin O~--~~~~n---P-~~~ Spatial Frequency (cpd) B. Interactin effects between stimulus dimensins: Percentage r ttal variance 30' _ N f""i ~ \I"') , I ' 1,, _ -N -1""'11 -"'" -It/')! 1I11~ 1I11~ II ~ % f nn-residual variance ORl=72-6- ORl=216 nfac=34 nfac=45 Figure 1: Dimensinal Inseparability r Visual Crtical Neurns. A: An example r dimensinsinal inseparability in the respnse r a single cell; B: Histgram r dimensinal inseparability as a percentage r ttal respnse variance.

4 380 Stern, Aertsen, Vaadia, and Hchstein variance divided by the residuals. The resulting histgram fr 69 cells is shwn in Figure lb. Althugh there are several cells with nn-significant interactins, i.e. linearly separable dimensins, this is nt the majrity f cells. The amunt f dimensinal inseparability seems t be a cntinuum. We suggest that separability is a significant variable in the cding capability f the neurns, which must be taken int accunt when mdeling the representatin f sensry infrmatin by crtical neural netwrks. We fund that the time curse f the respnse was nt always cnstant, but varied with stimulus parameters. Crtical cell respnses may have cmpnents which are sustained (cnstant ver time), transient (with a peak near stimulus nset and/r ffset), r mdulated (varying with the stimulus perid). Fr example, Figure 2 shws the respnses f a single neurn in VI t 50 stimuli, varying in rientatin and spatial frequency. Each respnse is pltted as a PSTH, and the stippled bar under the PSTH indicates the time f Orientatin D DD~DD [:j Eaij tj D D~EJijjG5D 23DG!5~GjD D~[MjE5E:5 lim! f.ll!!u D.I 11m., f Iq lip B.' Ill.' f 1.'1 1.5 G:J [;J CiIIJ ~ c:::j Ej~~~E:::J... t I 1.1 I Ft.2! U.. t p.i! u.s li!.t! I.t J I!.'! i.4 J O.8D~~~D DG5~tJD 04EJt5DCj II '! U I flu t f.4 I f.1 I 11'"! 1.0 I p.i : u! Figure 2: Spatial Frequency/Orientatin Tuning f Respnses f VI Cell

5 Stimulus Encding by Multidimensinal Receptive Fields in Single Cells and Cell Ppulatins 381 the stimulus presentatin (500 msec). The numbers beneath each PSTH are the firing rate averaged ver the respnse time. and the standard deviatins f the respnse ver repetitins f the stimulus (in this case 40). Clearly. the cell is rientatin selective, and the neurnal respnse is als tuned t spatial frequency. The stimulus eliciting the highest firing rate is ORI=252 degrees; SF=3.2 cycles/degree (cpd). Hwever, when lking at the respnses t lwer spatial frequencies, we see a mdulatin in the PSTH. The mdulatin, when present, has 2 peaks, crrespnding t the tempral frequency f the stimulus grating (4 cycles/secnd). Therefre, althugh the respnse rate f the cell is lwer at lw spatial frequencies than fr ther stimuli, the spike train carries additinal infrmatin abut anther stimulus dimensin. If the visual neurn is cnsidered as a linear system, the predicted respnse t a drifting sinusidal grating wuld be a (rectified) sinusid f the same (tempral) frequency as that f the stimulus, i.e. a mdulated respnse (Enrth-Cugell & Rbsn, 1966; Hchstein & Shapley, 1976; Spitzer & Hchstein. 1988). Hwever, as seen in Figure 2, in sme stimulus regimes the cell's respnse deviates frm linearity. We cnclude that the linearity r nnlinearity f the respnse is dependent upn the stimulus cnditins (Spitzer & Hchstein, 1985). A mdulated respnse is ne that wuld be expected frm simple cells, while the sustained respnse seen at higher spatial frequencies is that expected frm cmplex cells. Our data therefre suggest that the simple/cmplex cell categrizatin is nt cmplete. A further example f respnse time-curse dependence n stimulus parameters is seen in Figure 3A. In this case, the stimulus was varied in spatial frequency and tempral frequency, while ther dimensins were held cnstant. Again, as spatial frequency is raised. the mdulatin f the PSTH gives way t a mre sustained respnse. Funhennre, as tempral frequency is raised. bth the sustained and the mdulated respnses are replaced by a single transient respnse. When present, the frequency f the mdulatin fllws that f the tempral frequency f the stimulus. Furier analysis f the respnse histgrams (Figure 3B) reveals that the DC and fundamental cmpnent (FC) are nt tuned t the same stimulus values (arrws indicating peaks). We prpse that this infrmatin may be available t the cell readut, enabling the single cell t encde multiple stimulus dimensins simultaneusly. Thus, a cmplete descriptin f the receptive field must be multidimensinal in nature. Furthermre, in light f the evidence that the spike train is nt cnstant, ne f the dimensins which must be used t display the receptive field must be time. Figure 4 shws ne methd f displaying a multidimensinal respnse map, with time alng the abscissa (in 10 msec bins) and rientatin alng the rdinate. In the tp tw figures, the z axis, represented in gray-scale, is the number f cunts (spikes) per bin. Therefre, each line is a PSTH, with cunts (bin height) cded by shading. In this example. cell 2 (upper picture) is tuned t rientatin, with peaks at 90 and 270 degrees. The cell is nly slightly directin selective, as represented by the fact that the 2 areas f high activity are similarly shaded. Hwever, there is a transient peak at270 degrees which

6 382 Stern, Aertsen, Vaadia, and Hchstein A. Spatial Frequency (cpd) lb DG:J~G:J~ ,.0! 4.21 p..!'" 1 III"! I.e 1 p.l! I.S ! 1.11 RCJ~~~~ ".4 : 1.51 pi.,! m.s /II.!. liz.'! n.i Fi.S! is.1 C:W~~CitJ~ I III"! "'I ~i.i! tl.s pu! 14.1 p.1! IU ".S! 14.1 ~ 2 UJ~CWJ[MJ~ pi D.C [ft.'! 1M FO.I! IS! tl.o! 1.1 IA.'! 1M B. nnnalized values TF (cycles/secnd) SF (cpd) 1 Figure 3: A. TF/SF Tuning f respnse f VI cell. B. Tuning f DC and FC f respnse t stimulus parameters. is absent at 90 degrees. The middle picture. representing a simultaneusly recrded cell shws a different pattern f activity. The rientatin tuning f this cell is similar t that f cell 2, but it has slinger directinal selectivity. (twards 90 degrees). In this case, the liansient is als at 90 degrees. The bttm picture shws the jint activity f these 2 cells. Rather than each line being a PSTH, each line is a Jint PSTH (JPSTH; Aertsen et al. 1989). This histgram represents the time-dependent crrelated activity f a pair f cells. It is equivalent t sliding a windw acrss a spike liain f ne neurn and

7 Stimulus Encding by Multidimensinal Receptive Fields in Single Cells and Cell Ppulatins cell 2 cunts/bin \ cell 3 t ~ 216 Q,I :s III -S I:.~ 0... => cell 2,3 cincidence time (msec) SF=4.S cpd Figure 4: Respnse Maps. Tp, Middle: Single-cell Multidimensinal Receptive Fields; Bttm: Multi-Cell Multidimensinal Receptive Field asking when a spike frm anther neurn falls within the windw. The size f the windw can be varied; here we used 2 msec. Therefre, we are asking when these cells fire within 2 msec f each ther, and hw this is cnnected t the stimulus. The z axis is nw cincidences per bin. We may cnsider this the lgical AND activity f these cells; if there is a cell receiving infnnatin frm bth f these neurns, this is the receptive field which wuld describe its input. Clearly. it is different frm the each f the 2 individual cells. In ur results. it is mre narrwly tuned. and the tuning can nt be predicted frm the individual cmpnents. We emphasize that this is the "raw" JPSTH. which is nt crrected fr stimulus effects. cmmn input. r nrmalized. This is because we want a measure cmparable t the PSTHs themselves, t cmpare a multi-unit

8 384 Stern, Aertsen, Vaadia, and Hchstein receptive field t its single unit cmpnents. In this case, hwever, a significant (p<o.01; Palm et ai, 1988) "mn-directinal" interactin is present. Fr a mre cmplete descriptin f the receptive field, this type f figure, shwn here fr ne spatial frequency nly, can be shwn fr all spatial frequencies as "slices" alng a furth axis. Hwever, space limitatins prevent us frm presenting this multidimensinal aspect f the multicellular receptive field. CONCLUSIONS We have shwn that interactins amng stimulus dimensins accunt fr a significant prpnin f the respnse variance f V 1 cells. The variance f the interactins itself may be a useful parameter when cnsidering a ppulatin respnse, as the amunt and lcatin f the dimensinal inseparability varies amng cells. We have als shwn that different tempral characteristics f the spike trains can be tuned t different dimensins, and add t the encding capabilities f the cell in a neurbiigically realistic manner. Finally, we use these results t generate multidimensinal receptive fields, fr single cells and small grups f cells. We emphasize that this can be generalized t larger ppulatins f cells, and t cmpute the ppulatin respnses f cells that may be meaningful fr the cne x as a bilgical neurnal netwrk. Acknwledgements We thank Israel Nelken, Hagai Bergman, Vldya Yakvlev, Mshe Abeles, Peter Hillman, Rben Shapley and Valentin Braitenberg fr helpful discussins. This study was suppned by grants frm the U.S.-Israel Bi-Natinal Science Fundatin (BSF) and the Israel Academy f Sciences. References 1. Abeles, M. Quantificatin, Smthing, and Cnfidence Limits fr Single Units' Histgrams 1. Neursci. Melhds 5, , Aertsen, A.M.H.J., Gerstein, G. L., Habib, M.K., and Palm, G. Dynamics f Neurnal Firing Crrelatin: Mdulatin f "Effective Cnnectivity" 1. Neurphysi151 (5), , Enrth-CugeU, C. and Rbsn, J.G. The Cntrast Sensitivity f Retinal Ganglin Cells f the Call Physil. Lnd 187, , Hchstein, S. and Shapley, R. M. Linear and Nnlinear Spatial Subunits in Y Cat Retinal Ganglin Cells 1 Physil. Lnd 262, , Palm, G., Aensen, A.M.H.J. and Gerstein, G.L. On the Significance f Crrelatins Amng Neurnal Spike Trains Bii. Cybern. 59, 1-11, Spitzer, H. and Hchstein, S. Simple and Cmplex-Cell Respnse Dependencies n Stimulatin Parameters 1.Neurphysil 53, , Spitzer, H. and Hchstein, S. Cmplex Cell Receptive Field Mdels Prg. in Neurbilgy, 31, , 1988.