{"title": "Stimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations in V1 of Awake Monkey", "book": "Advances in Neural Information Processing Systems", "page_first": 377, "page_last": 384, "abstract": null, "full_text": "STIMULUS ENCODING BY \n\nMUL TIDIMENSIONAL RECEPTIVE FIELDS \nIN SINGLE CELLS AND CELL POPULATIONS \n\nIN VI OF A WAKE MONKEY \n\nEdward Stern \n\nCenter for Neural Computation \nand Department of Neurobiology \n\nLife Sciences Institute \nHebrew University \nJerusalem, Israel \n\nEilon Vaadia \n\nCenter for Neural Computation \n\nand Physiology Department \nHadassah Medical School \n\nHebrew University \nJerusalem, Israel \n\nABSTRACT \n\nAd Aertsen \n\nInstitut fur Neuroinfonnatik \nRuhr-Universitat-Bochum \n\nBochum, Gennany \n\nShaul Hochstein \n\nCenter for Neural Computation \nand Department of Neurobiology, \n\nLife Sciences Institute \nHebrew University \nJerusalem, Israel \n\nin \n\ntemporal \n\nshowed different \n\nMultiple single neuron responses were recorded \nfrom a single electrode in VI of alert, behaving \nmonkeys. Drifting sinusoidal gratings were \npresented \nthe cells' overlapping receptive \nfields, and the stimulus was varied along several \nvisual dimensions. The degree of dimensional \nseparability was calculated for a large population \nof neurons, and found to be a continuum. Several \ncells \nresponse \ndependencies to variation of different stimulus \ndimensions, \ntuning of the modulated \nfiring was not necessarily the same as that of the \nmean firing rate. We describe a multidimensional \nreceptive field, and use simultaneously recorded \nresponses to compute a multi-neuron receptive \nfield, describing \ninformation processing \ncapabilities of a group of cells. Using dynamic \ncorrelation \nseveral \nfor multidimensional \ncomputational schemes \nspatiotemporal tuning for groups of cells. The \nimplications for neuronal coding of stimuli are \ndiscussed. \n\nanalysis, we propose \n\ni.e. \n\nthe \n\nthe \n\n377 \n\n\f378 \n\nStern, Aensen, Vaadia, and Hochstein \n\nINTRODUCTION \n\nThe receptive field is perhaps the most useful concept for understanding neuronal \ninformation processing. The ideal definition of the receptive field is that set of stimuli \nwhich cause a change in the neuron's firing properties. However, as with many such \nconcepts, the use of the receptive field in describing the behavior of sensory neurons falls \nshort of the ideal. The classical method for describing the receptive field has been to \nmeasure the \"tuning curve\" i.e. the response of the neuron as a function of the value of \none dimension of the stimulus. This presents a problem because the sensory world is \nmultidimensional; For example, even a simple visual stimulus, such as a patch of a \nsinusoidal grating, may vary in location, orientation, spatial frequency, temporal \nfrequency, movement direction and speed, phase, contrast, color, etc. Does the tuning to \none dimension remain constant when other dimensions are varied? i.e. are the dimensions \nlinearly separable? It is not unreasonable to expect inseparability: Consider an oriented, \nspatially discrete receptive field. The excitation generated by passing a bar through the \nreceptive field will of course change with orientation. However, the shape of this tuning \ncurve will depend upon the bar width, related to the spatial frequency. This effect has not \nbeen studied quantitatively, however. If interactions among dimensions exist, do they \naccount for a large portion of the cell's response variance? Are there discrete populations \nof cells, with some cells showing interactions among dimensions and others not? These \nquestion have clear implications for the problem of neural coding. \n\nRelated to the question of dimensional separability is that of stimulus encoding: Given \nthat the receptive field is multidimensional in nature, how can the cell maximize the \namount of stimulus information it encodes? Does the neuron use a single code to \nrepresent all the stimulus dimensions? It is possible that interactions lead to greater \nuncertainty in stimulus identification. Does the small number of visual cortical cells \nencode all the possible combinations of stimuli using only spike rate as the dependent \nvariable? We present data indicating that more information is indeed present in the \nneuronal response, and propose a new approach for its utilization. \n\nThe final problem that we address is the following: Clearly, many cells participate in the \nstimulus encoding process. Arriving at a valid concept of a multidimensional receptive \nfield, can we generalize this concept to more than one cell introducing the notion of a \nmulti-cellular receptive field? \n\nMETHODS \n\nDrifting sinusoidal gratings were presented for 500 msec to the central 10 degrees of the \nvisual field of monkeys performing a fixation task. The gratings were varied in \norientation, spatial frequency,temporal frequency, and movement direction. We recorded \nfrom up to 3 cells simultaneously with a single electrode in the monkey's primary visual \ncortex (VI). The cells described in this study were well separated, using a template(cid:173)\nmatching procedure. The responses of the neurons were plotted as Peri-Stimulus Time \nHistograms (PSTHs) and their parameters quantified (Abeles, 1982), and offline Fourier \nanalysis and time-dependent crosscorrelation analysis (Aertsen et ai, 1989) were \nperformed. \n\n\fStimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations \n\n379 \n\nRESULTS \n\nRecording the responses of visual cortical neurons to stimuli varied over a number of \ndimensions, we found that in some cases, the tuning curve to one dimension depended on \nthe value of another dimension. Figure lA shows the spatial-frequency tuning curve of a \nsingle cell measured at 2 different stimulus orientations. When the orientation of the \nstimulus is 72 degrees, the peak response is at a spatial frequency of 4.5 cycles/degree \n(cpd), while at an orientation of216 degrees, the spatial frequency of peak response is 2.3 \ncpd. If the responses to different visual dimensions were truly linearly separable, the \ntuning curve to any single dimension would have the same shape and, in particular, \nposition of peak, despite any variations in other dimensions. If the tuning curves are not \nparallel, then interactions must exist between dimensions. Clearly, this is an example of \na cell whose responses are not linearly separable. In order to quantify the inseparability \nphenomenon, analyses of variance were performed, using spike rate as the dependent \nvariable, and the visual dimensions of the stimuli as the independent variables. We then \nmeasured the amount of interaction as a percentage of the total between-conditions \n\nA. \nSpatial Frequency \nTuning Dependence upon \nOrientation \n\nB. Interaction effects between \nstimulus dimensions: \nPercentage or total variance \n\n30'.....-------------. \n\n25 \n\n<1) 0.9 \n~ 0.8 \nbO O.7 \ns:: \n'C 0.6 \nu:: \n\"0 0.5 \n~ 0.4 \nE 0.3 a 0.2 \n\ns:: 0.1 \n\nO~--~~~~n---P-~~~ \n0.1 \n10 \n\n1 \n\nSpatial Frequency (cpd) \n\n!\u00a31I11~ 1I11~ II \n\noooooo~ \n_ \n, \n\n- - - - - -\n\n~ \\I\"') \n, \n\"'\" \n\n1 \n1\"\"'11 \n\n% of non-residual variance \n\nN \nI \n_ \n\nf\"\"I \n' \nN \n\n110 \n, \n\nIt/') \n\n__ ORl=72 -6- ORl=216 \nnfac=45 \nnfac=34 \n\nFigure 1: Dimensional Inseparability or Visual Cortical Neurons. A: \nAn example or dimensionsional inseparability in the response or a single \ncell; B: Histogram or dimensional inseparability as a percentage or \n\ntotal response variance. \n\n\f380 \n\nStern, Aertsen, Vaadia, and Hochstein \n\nvariance divided by the residuals. The resulting histogram for 69 cells is shown in Figure \nlB. Although there are several cells with non-significant interactions, i.e. linearly \nseparable dimensions, this is not the majority of cells. The amount of dimensional \ninseparability seems to be a continuum. We suggest that separability is a significant \nvariable in the coding capability of the neurons, which must be taken into account when \nmodeling the representation of sensory information by cortical neural networks. \n\nWe found that the time course of the response was not always constant, but varied with \nstimulus parameters. Cortical cell responses may have components which are sustained \n(constant over time), transient (with a peak near stimulus onset and/or offset), or \nmodulated (varying with the stimulus period). For example, Figure 2 shows the responses \nof a single neuron in VI to 50 stimuli, varying in orientation and spatial frequency. Each \nresponse is plotted as a PSTH, and the stippled bar under the PSTH indicates the time of \n\nOrientation \n\n-\n\nliM ! f.ll !!u \u2022 D.I \n\nDD~DD \n4.5 D [:j Eaij tJ D \nD~EJijjG5D \n23DG!5~GjD \nD~[MjE5E:5 \n1.5 G:J [;J CiIIJ ~ c:::J \nEj~~~E:::J \nO.8D~~~D \nDG5~tJD \n04oEJt5DCj \n\n! U .. t p.i ! u .s lI!.t ! I.t J I!.' ! i.4 J \n\n11m., f Iq lip \u2022 B.' Ill.' f 1.'1 \n\n.... t \n\nI 1.1 I Ft.2 \n\n! 1.0 I p.i \n\n: u! \n\nII \u00b7' \n\n! U \n\nI flU t f.4 I 117.1 \u2022 f .1 I 11'\" \n\nFigure 2: Spatial Frequency/Orientation Tuning of Responses \n\nof VI Cell \n\n\fStimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations \n\n381 \n\nthe stimulus presentation (500 msec). The numbers beneath each PSTH are the firing rate \naveraged over the response time. and the standard deviations of the response over \nrepetitions of the stimulus (in this case 40). Clearly. the cell is orientation selective, and \nthe neuronal response is also tuned to spatial frequency. The stimulus eliciting the \nhighest firing rate is ORI=252 degrees; SF=3.2 cycles/degree (cpd). However, when \nlooking at the responses to lower spatial frequencies, we see a modulation in the PSTH. \nThe modulation, when present, has 2 peaks, corresponding to the temporal frequency of \nthe stimulus grating (4 cycles/second). Therefore, although the response rate of the cell is \nlower at low spatial frequencies than for other stimuli, the spike train carries additional \ninformation about another stimulus dimension. \n\nIf the visual neuron is considered as a linear system, the predicted response to a drifting \nsinusoidal grating would be a (rectified) sinusoid of the same (temporal) frequency as that \nof the stimulus, i.e. a modulated response (Enroth-Cugell & Robson, 1966; Hochstein & \nShapley, 1976; Spitzer & Hochstein. 1988). However, as seen in Figure 2, in some \nstimulus regimes the cell's response deviates from linearity. We conclude that the \nlinearity or nonlinearity of the response is dependent upon the stimulus conditions \n(Spitzer & Hochstein, 1985). A modulated response is one that would be expected from \nsimple cells, while the sustained response seen at higher spatial frequencies is that \nexpected from complex cells. Our data therefore suggest that the simple/complex cell \ncategorization is not complete. \n\nA further example of response time-course dependence on stimulus parameters is seen in \nFigure 3A. In this case, the stimulus was varied in spatial frequency and temporal \nfrequency, while other dimensions were held constant. Again, as spatial frequency is \nraised. the modulation of the PSTH gives way to a more sustained response. Funhennore, \nas temporal frequency is raised. both the sustained and the modulated responses are \nreplaced by a single transient response. When present, the frequency of the modulation \nfollows that of the temporal frequency of the stimulus. Fourier analysis of the response \nhistograms (Figure 3B) reveals that the DC and fundamental component (FC) are not \ntuned to the same stimulus values (arrows indicating peaks). We propose that this \ninformation may be available to the cell readout, enabling the single cell to encode \nmultiple stimulus dimensions simultaneously. \n\nThus, a complete description of the receptive field must be multidimensional in nature. \nFurthermore, in light of the evidence that the spike train is not constant, one of the \ndimensions which must be used to display the receptive field must be time. \n\nFigure 4 shows one method of displaying a multidimensional response map, with time \nalong the abscissa (in 10 msec bins) and orientation along the ordinate. In the top two \nfigures, the z axis, represented in gray-scale, is the number of counts (spikes) per bin. \nTherefore, each line is a PSTH, with counts (bin height) coded by shading. In this \nexample. cell 2 (upper picture) is tuned to orientation, with peaks at 90 and 270 degrees. \nThe cell is only slightly direction selective, as represented by the fact that the 2 areas of \nhigh activity are similarly shaded. However, there is a transient peak at270 degrees which \n\n\f382 \n\nStern, Aertsen, Vaadia, and Hochstein \n\nSpatial Frequency (cpd) \n\n0.6 \n\n0.11 \n\n1.1 \n\n1.5 \n\n2.1 \n\n,.0 ! 4.21 p.. !'\" 1 III\" ! I.e 1 p.l ! I.S 1 111.1 ! 1.11 \n\nlb DG:J~G:J~ \nRCJ~~~~ \n\" .4 : 1.51 pi., ! m.s /II.! \u2022\u2022.\u2022 lIZ.' ! n.I Fi.S ! is.1 \nC:W~~CitJ~ \nI \n~ 2 UJ~CWJ[MJ~ \n\nIII\"! \"'I ~i.I ! tl.S pu ! 14.1 p.1 ! IU \".S ! 14.1 \n\npi \u2022\u2022 \u2022 D.C [fT.' ! 1M FO.I ! IS! tl.O ! 1 .1 IA.' ! 1M \n\nA. \n\nB. \n\n2 \n\nnonnalized values \n\n1 \n\no \n\n1 \n\n1.1 \n\n0.8 \n\n0.6 \n\nSF (cpd) \n\n16 \n\nTF (cycles/second) \n\nFigure 3: A. TF/SF Tuning of response of VI cell. \n\nB. Tuning of DC and FC of response to stimulus parameters. \n\nis absent at 90 degrees. The middle picture. representing a simultaneously recorded cell \nshows a different pattern of activity. The orientation tuning of this cell is similar to that \nof cell 2, but it has slIonger directional selectivity. (towards 90 degrees). In this case, the \nlIansient is also at 90 degrees. The bottom picture shows the joint activity of these 2 \ncells. Rather than each line being a PSTH, each line is a Joint PSTH (JPSTH; Aertsen et \nal. 1989). This histogram represents the time-dependent correlated activity of a pair of \ncells. It is equivalent to sliding a window across a spike lIain of one neuron and \n\n\f250 \n200 \n150 \n\\00 \n50 \no \n\n60 \n50 \n40 \n30 \n20 \n10 \no \n\ncell 3 \n\n324 \n\n-III t \n.\u00a7 108 -S \n\n~ 216 \nQ,I :s \n\n0 \n\nI: \n... \n.~ \n=> \n\ncell 2,3 coincidence \n\n324 \n\n216 \n\n108 \n\no \n\no \n\n250 \n\n500 \n\nStimulus Encoding by Multidimensional Receptive Fields in Single Cells and Cell Populations \n\n383 \n\ncell 2 \n\ncounts/bin \n\n324 \n\n216 \n\n108 \n\no \n\n750 \n\n1000 \nSF=4.S cpd \n\ntime (msec) \nFigure 4: Response Maps. \nTop, Middle: Single-cell Multidimensional Receptive Fields; \nBottom: Multi-Cell Multidimensional Receptive Field \n\nasking when a spike from another neuron falls within the window. The size of the \nwindow can be varied; here we used 2 msec. Therefore, we are asking when these cells \nfire within 2 msec of each other, and how this is connected to the stimulus. The z axis is \nnow coincidences per bin. We may consider this the logical AND activity of these cells; \nif there is a cell receiving infonnation from both of these neurons, this is the receptive \nfield which would describe its input. Clearly. it is different from the each of the 2 \nindividual cells. In our results. it is more narrowly tuned. and the tuning can not be \npredicted from the individual components. We emphasize that this is the \"raw\" JPSTH. \nwhich is not corrected for stimulus effects. common input. or normalized. This is because \nwe want a measure comparable to the PSTHs themselves, to compare a multi-unit \n\n\f384 \n\nStern, Aertsen, Vaadia, and Hochstein \n\nreceptive field to its single unit components. In this case, however, a significant (p