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The two-dimensional spatial structure of nonlinear subunits in the receptive fields of complex cells
VisionRes.Vol. 30, No. 2, pp. 249-254, 1990 printedin Great Britain. All rights rcsawd
0042.6989/90S3.00+ 0.00 CopyrightQ 1990PergamonRess pk
RESEARCH
NOTE
THE TWO-DIMENSIONAL SPATIAL STRUCTURE OF NONLINEAR SUBUNITS IN THE RECEPTIVE FIELDS OF COMPLEX CELLS ROBERT G. SZULBORSKI+ and LARRYA. PALMER? Department of Anatomy and David Mahoney Institute of Neurological Sciences, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, U.S.A. (Received 4 January 1989; in revised form 12 June 1989) Abstract-We have estimated the second-order response properties of complex cells in two spatial dimensions by cross-correlating their spike trains with a binary approximation of a Gaussian white noise stimulus ensemble. Wiener-like kernels were computed and geuemlly consisted of two or three parallel, elongated subregions alternating between augmented and suppmssed response. These subunits were scattered across ‘he receptive fields of complex cells and their axes of elongation agreed with the optimal orientation determined with drifting gratings. Complex cells
Subunits
Striate cortex
Cat
INTRODUCTION
demonstrated that while CCs clearly display It is well known that the first-order response uniform tlrst-order behavior, they exhibit properties of complex cells are, to a large degree, nonuniform spatial structure when examined spatially homogeneous; that is, that there exists with pairs of bars (1978). As expected, a CC’s extensive or even complete overlap of bright and response to the simultaneous presentation of dark subregions in complex cells’ receptive two bars differed from the simple sum of the fields. Such spatial homogeneity makes it im- responses to the two bars presented individupossible to accurately predict a complex cell’s ally; however, this difference varied in a systemresponse to a composite stimulus consisting of atic fashion depending upon the relative simpler stimuli, stimuli for which the cell’s positions of the two bars. A distinct secondindividual responses are known. For example, order spatial substructure was observed for all complex cells exhibit both orientation and 10 CCs studied and was termed a subunit. This spatial frequency tuning despite their uniform subunit consisted of a central region where the first-order spatial receptive fields (RFs). Thus, response exceeded that predicted by linear CCs behave nonlinearly, failing to follow the superposition (augmented response) and flanking reglons where the response was less than principle of spatial superposition. One way to characterize nonlinearities of that predicted by superposition (suppressed respatial summation is to determine higher-order sponse). Later studies by Heggelund (1981) and responses, the simplest being those of second- by Emerson, Citron, Vaughn and Klein (1987) order, i.e. the responses to pairs of stimuli. have provided further evidence for the existence For example, Rybicki, Tracy and Pollen of subunits in CC RFs. The significance of these subunits is not showed that the response of complex cells clearly known. Movshon et al. (1978) have to pairs of slits depended on the inter-slit shown that one-dimensional (1D) subunit strucspacing. Movshon, Thompson and Tolhurst ture is well matched by the inverse Fourier transform of the spatial frequency tuning curve. *Present address: Department of Ophthalmology. Barnes They speculated that subunits may correspond Hospital, Washington University Medical Center, St to the neurons supplying the primary afferent Louis, MO 63110, U.S.A. tTo whom correspondence should be addressed. input to CCs. Subunit spatial structure would 249
Research Note
2so
then reflect the RF structure of the afferent neuron. Emerson et al. (1987) took a different view and interpreted the subunit as a functional entity not perforce equivalent to a single afferent neuron. Knowledge of subunit structure in the second spatial dimension might clarify the meaning of subunits and might also account for the orientation selectivity of CCs. One general method for characterizing nonlinear interactions is the Gaussian white noise (GWN) technique (Marmarelis & Marmarelis, 1978; Wiener, 1958). Full two-dimensional (2D) GWN consists of a stimulus ensemble in which every unit area of a set defined over two spatial dimensions varies independently in contrast over time. The output of a cell driven by such a stimulus ensemble may be used to calculate Wiener kernels which completely describe nonlinear interactions of any order (e.g. Lee & Schetzen, 1965). Other white noise type stimuli may be used to calculate similar kernels. The relationships between ditierent sets of kernels have been examined by Klein and Yasui (1979) and Klein (1987) and utilized by Emerson et al. (1987) for measuring nonlinear spatiotemporal interactions in visual cortical cells. The experiments described briefly in this report utilized a modified white noise technique to measure second-order nonlinear summation over two spatial dimensions. By applying this method to a population of CCs in cat striate cortex, we have determined the 2D spatial structure of their subunits and found a good correlation between this structure and the orientation preference of these cells. METHODS
The general methods used in performing extracellular, single unit recordings in cat area i7 are described in detail elsewhere (Jones & Palmer, 1987). In brief, adult cats were initially anesthetized with an intraperitoneal injection of sodium thiopental (4Omg/kg). Two venous catheters and a tracheal tube wem insorted. The animal was paralyzed with an injection of 60 mg of gallamine triethiodide and then maintained on a positive pressure respirator. End-tidal CO2 was monitored and kept between 4 and 5% via adjustments in tidal volume and respiratory rate. Anesthesia and paralysis were maintained with appropriate infusions (2.5 mg/hr of sodium thiopental and 2 mg/hr of tubocurarine chloride with 15 mg/hr of gallamine triethiodide, respectively). The pupils were dilated with I % atropine
sulfate and the nictitating membranes were retracted with phenylephrine hydrochloride. Plano contact lenses were inserted to prevent cornea1 dessication while corrective lenses were used to focus stimuli at 57 cm onto the retina. A craniotomy and durotomy were performed to expose area 17. A tungsten-in-glass electrode (Levick, 1972) was inserted into the cortex and a 4% agar-saline solution was applied to minimize respiratory pulsations and cortical drying. Complex cells were identified by their characteristic response to drifting sinusoidal gratings. As shown by many investigators. This consists of an elevation of the mean firing rate (d.c.) with very little modulation at the temporal frequency of the grating (DeValois, Albrecht & Thorell, 1982; Maffei 8c Fiorentini, 1973; Movshon et al., 1978; Pollen & Ronner, 1982). In addition, the RFs of these cells exhibited extensive overlap of regions excited by bright and dark stimuli, as quantitatively measured using single stimulus techniques described recently in connection with simple cells (Jones & Palmer, 1987). A 16 x 16 cartesian grid, one axis of which was aligned with the cell’s preferred orientation, was used to completely encompass the cell’s responsive region and to define 256 stimulus locations. The stimulus consisted of simultaneously presented pairs of individual stimuli whose positions could vary over this 2D region of space. A computer-controlled Picasso CRT image generator was used for generating small square or rectangular bright or dark stimuli (mean iuminance 22cd/m* with stimulus contrast being f 32% of the mean) on a Tektronix 608 monitor. Stimulus duration was generally 50 msec, however stimuli lasting 100 msec were occasionally employed. (In reality, it is impossible to simultaneously present two distinct spatial stimuli with the Picasso image generator. Instead, two spatial stimuli were interleaved at a rate of 200 Hz; that is, each element of a pair was alternately presented for 5 msec throughout the temporal duration of the stimulus pair, usually a total of 50 msec. Since this rate far exceeds the flicker fusion frequency measured at several locations in the cat’s visual system, it effectively produces the percept of a simultaneous pair of stimuli.) Interactions between pairs of temporally asynchronous stimuli were not examined in this study. The set of stimuli utilized was a carefully chosen subset of all possible pairs of individual stimuli, which, given 512 distinct, individual
Research Note
stimuli (256 locations and 2 contrasts), numbered greater than 130,000 arid,,,,,, 50 msec per pair, would require almost ‘2 hr for a single presentation of the entire set. One element of every pair of stimuli was a fixed, reference stimulus while the other element occupied one of the 256 defined locations. A complete set of stimuli consisted of the fixed stimulus paired with all possible single stimuli, including itself. Both stimuli in any one pair can have either contrast, thus a total of 1024 pairs (256 x 4) of individual stimuli comprise the complete set of stimuli given a single fixed location. Two different stimulus paradigms were employed utilizing either one or five fixed stimuli. The five locations consisted of four cardinal points around a fifth point centered within the RF. When one fixed stimulus was used, it was located at one of these five sites. The elements of the stimulus set were randomly presented. All elements were presented once before a new random sequence was begun (Palmer, Gottschalk & Jones, 1987). The temporal offset of every spike (relative to the stimulus frame) and information about the concurrent stimulus comprised the raw data. The reverse correlation technique developed in this laboratory (Jones & Palmer, 1987) was adapted and combined with the kernel formulations of Emerson et al. (1987) to calculate second-order Wiener-like kernels. These kernels depict the 2D spatial distribution of second-order nonlinear interactions. RESULTS AND DISCUSSION
A total of 160 cells, 100 of which were identified as complex, were examined in area 17 of 26 adult cats. A total of 407 sets of interaction profiles (IPs) were obtained from these complex cells. The RFs of all CCs examined were within 13 deg of the area centralis. An investigation of the 2D spatial structure of the first-order RF of CCs was performed but will be presented elsewhere. Approximately three quarters of the complex cells studied (73 out of 100) yielded Wienerlike kernels with definite, nonrandom structure. Figure 1 shows 4 representative examples of these kernels in which the fixed reference stimulus was located at the center of the cell’s receptive field (indicated by the intersection of the horizontal and vertical lines on the plot). The time intervals used for calculating the reverse correlations are indicated along with the dimensions of the region examined. The results are
251
drawn as contour plots in which solid lines indicate. regions of etive, augmented response (i.e. response in excess of linear superposition) while dashed lines indicate regions of negative, suppressed response (less than superposition). Contours are drawn at f 10,30,50,70 and 90% of the peak response. The f50% contours are dotted. The detailed 2D spatial organization of these kernels varied from cell to cell but several general properties were found. In almost all cases, there is a central, or nearly central, region of augmented response. In addition, the great majority of kernels contain neighboring regions of suppressed response. This usually consists of two flanking suppressed zones, however, several kernels contain only one suppressed subregion while a few contain either none or more than two such subregions. The subregions, both augmented and suppressed, in almost all of the kernels are elongated, as evident in Fig. 1 A-C. The average length-to-width ratio of the central regions is greater than 3.0. The flanking troughs were often broader in width than the central peak; nonetheless, the flanking subregions were still distinctly elongated. Three of the 100 cells had kernels with approximately circular, central, augmented subregions, with length-to-width ratios near 1.0. The kernel of such as cell is seen in Fig. 1D. However, cells with this kernel structure comprise a very small minority of all the cells studied. In general, kernels consist of two or three parallel, elongated subregions of alternating sign. Variations in the spatial arrangement of the subregions are also evident in Fig. 1. The subregions in most kernels are staggered along their long axes. In other words, if a line were drawn connecting the extrema of the individual subregions it would not be perpendicular to the long axis of the subregion. In addition, this imaginary line would not always be straight, but would instead consist of line segments with differing spatial orientations. Thus subregions are often staggered but apparently in no uniform fashion. Another feature of kernei structure exhibited in Fig. 1 is the variation in magnitude of individual subregions. In any one kernel, the amplitude of an augmented subregion may be approximately equal to or may be larger or smaller than the amplitude of neighboring sup pressed subregions. No particular preference in this relationship has been discerned. This
Research Note
252
6.3’
4
:
D
61 mrrc I
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46
-
mr4c
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A
7.6.
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____c
-
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Fig. 1. Second-order Wiener-like kernela for four complex cells. JMa were obtained using a reverse correlation method. Kern& arc drawn as contour plots with solid lines denoting subregions of augmented response and da&cd lines showing regions of suppremed response (details in text). Contours are drnwn at f 10,30.50 (drawn as dotted lines). 70 and 90% of the maximum. The fixed reference stimulus used in computing kernels was located at the intcmeetion of the horizontal and vertical lines on the plots. The dimensions of the region studied and time interval, T, used in calculating the reverse correlation are indicated.
variation in relative amplitudes coupled with the frequent spatial staggering of subregions is reflected in the lack of spatial symmetry in many kernels. The effect of changing the position of the tied, reference stimulus is illustrated in Fig. 2. The Wiener-like kernels in Fig. 2 were calculated from the response of the same cell whose center-&d-stimulus kernel is shown in Fig. 1A. The positions of the ilxed stimuli used in computing the kernels are indicated by the intersection of the horizontal and vertical lines on each plot. In this figure, the maximum amplitude across all five kernels was determined and the contours are drawn in relation to this “global” maximum. Thus, each kernel need not have contours at all levels.
The basic structure of the kernel, an elongated central subregion with augmented response flanked by elongated subregions of suppressed response, is apparent the position of the fixed stimulus. subregions in different kernels for a are not identical in structure. The positions and amplitudes of the subtqions in relation to the location of the fixed stimulus can vary. The spatial dimensions of individual subrqions and their detaikd structure can also cw~ with fixed stimulus position. In addition, the spatial orientation of the elongated subregions may vary with the position of the fixed stimulus. A general design of the second-order spatial substructure of complex cells has emeqted from the preliminary analysis of the data from these
253
Fig. 2. Second-o~er Wiener-like kernels for one complex cell with the fixed referencestimulus at five differentlocations indicated by the intemections of the horixontal and vertical lines on each plot. These data are from the same cell shown in Fig. 1A. Kernels are presentedas contour plots using the same conventions as in Fig. I except that a single maximum was determinedover all the grids. AI1contours are drawn relative to this single maximum.
studies. Following the terminology of Movshon et al. (1978), we refer to the organized structure of any one second-order kernel as a subunit. While there are many variations, an average subunit consists of two or three parallel, elongated subregions-a central peak and &king troughs-usually staggered in position along their long axes and often with no particular spatial symmetry. Similar, but not identical, subunits are scattered across that region of space wherein single bright and dark stimuli produce a response. This general org~~tion
is consistent with the 1D spatial structure of subunits described in previous studies (Movshon et al., 1978; Baker & Cynader, 1986; Emerson et al., 1987). Movshon et al. (1978) speculated that CC subunits might be dim&y identified with either lateral geniculate nucleus (LGN) or simple cell inputs.. The 2D spatial structures of the subunits described in this report certainly differ from the RFs of LGN cells. But, the elongated nature of the subregions comprising a subunit strongly resembles the 2D spatial structure of simple cells
254
ResearchNote
(Jones & Palmer, 1987) and evokes a temptation to equate the two. If this were the case, the 2D spatial structure of a subunit would arise from and be identical to the RF of a single afferent simple cell. While simple cells may provide the primary input to complex cells (Hubel & Wiesel, 1962) it does not necessarily follow that the structure of any individual complex cell subunit directly reflects the RF structure of a particular afferent simple cell. All models of complex cell input utilize multiple afferents with spatially overlapping RFs (Hubel & Wiesel, 1962; Pollen & Ronner, 1982; Spitzer & Hochstein, 1985). Any single stimulus influences more than one afferent; thus pairs of stimuli would drive even mole inputs. The second-order kernels we measured depict the distribution of nonlinear summation, however it may arise, over two dimensions of space. Thus, they do not directly delineate the RF structure of any one afferent neuron, rather, they are a product of the nonlinear combination of precursor component cells. This is not to say that subunit structure is not influenced by the RF organization of afferents; rather, subunits structure more likely represents some type of average of the RFs of all the inputs and their interactions. Unlike simple cells, whose linearity mandates that a complete description of their behavior is supplied by their first-order response properties, or impulse response function, complex cells are not fully described by their first-order responses. Higher-order terms are needed to more fully describe their behavior. Movshon et al.‘s IPs as well as our 2D subunits are types of higherorder terms, having been collected with pairs of stimuli. That the 2D spatial subunits presented here provide a more complete description of CCs is evident from their overall organization within their respective grids. Recall that these grids were initially aligned with the orientation producing the cell’s maximal response. The elongation of subunit subregions parallel to an axis of the grid indicates that subunit spatial structure is consistent with the overall orientation preference of the cell. Whether this 2D subunit structure represents the initial expression of orientation selectivity in the neural chain from retina to complex cells or whether it merely reflects the passive propogation of a property generated in precursor cells, is not known. Whether the bandwidth of CC orientation tuning is also consistent with subunit structure is currently being studied. Nonetheless, the 2D
structure of these subunits suggests that they may be involved in producing CC orientation tuning as well as spatial frequency tuning as previously suggested (Movshon et al., 1978). Thus, for the first time a measure of complex cells’ spatial response properties reflects the spectral property of orientation tuning. REFERENCES Baker, C. L. & Cynader, M. S. (1986). Spatial receptive-field properties of direction-sclecective neurons in cat striate cortex. Journal of Neurophysiology, 55, 1136-l 152. DeValois, R. L., Albrecht, D. G. 8 Thorell, L. G. (1982). Spatial frequency selectivity of cells in macaque visual cortex. Vision Research, 22, 545-559. Emerson, R. C., Citron, M. C., Vaughn, W. J. & Klein S. A. (1987) Nonlinear directionally selective subunits in wmplex cells of cat striate cortex. Journal of Neurophysiology, 58, 33-65.
Heggclund, P. (1981). Receptive field or8anixation of complex cells in cat striate cortex. Experimental Brarir Research, 42 99-107.
Hubel, D. H. & Wiwl, T. N. (1962). Receptive fieids, binocular interaction and functional architecture in the cat’s visual cortex. Journal of Physiology, London Ido, 106-154. Jones, J. P. & Palmer, L. A. (1987). The two-dimensional spatial structure of simple receptive fields in cat striate cortex. Journal of Neurophysiology, 58, 1212-1232. Klein, S. A. (1987). Relationships between kernels measund with different stimuli. In Marmarelis, V. 2. (Ed.), Adoanced methods of physidogical system modeling (pp. 278-288). Los Angeles: Biomedical Simulations Resource.
Klein, S. & Yasui, S. (1979). Nonlinear systems analysis with non-Gaussian white stimuli: General basis function&s and kernels. IEEE Transactions on Information Theory, 25, 495 -500. Lee, Y. W. & Schetzen,
M. (1965). Measurement of the Wiener kernels of a non-linear system by crosscorrelation. International Journal qf Control, 2, 237-254. Levick, W. R. (1972). Another tun@en microelectrode. Medicine and Biological Engineering,
10, 510-515.
Maffei, L. & Fiorentini, A. (1973). The visual cortex as a spatial frequency analyzer. Vision Research. 13, 1255-1267. Manmuelis, P. 2. & Marmarelis, V. 2. (1978). AM@S of physiological
systems:
The white-noise approach.
New
York: Plenum Press. Movshon. J. A., Thompson, I. D. & Tolhurst, D. J. (1978). Receptive field or&z&on of complex cells in the c&s striate cortex. J-1 of PhystiIogy, L,on&n, 283,79-99. Palmer, L. A., Gottschalk A. & forms, 3. P. (1987). Constraints on the estimation of spatial receptive Be!d prow of simple cells in visual cortex. In Marmar& V. Z (Ed.), Advanced methods of pl?ysiological system mu&&g (pp. 205-216). Los Angeles BkmcdW SWtloao Rorouroe. Pollen, D. A. & Ronner, S. F. (1982). Spatial wmpu?ation performed by simple and camp!! all8 in the viawfcortex of the cat. Vision Research, 22, 101-118. Spitzer. H. & Ho&stein, S. (1985). A wmpkxall reesptivcfield model. Journal of Neurophysioiogy, 53, 12664286. Wiener, N. (1958). No&near problems in run& theory. Cambridge, MA: MIT Press.
0042.6989/90S3.00+ 0.00 CopyrightQ 1990PergamonRess pk
RESEARCH
NOTE
THE TWO-DIMENSIONAL SPATIAL STRUCTURE OF NONLINEAR SUBUNITS IN THE RECEPTIVE FIELDS OF COMPLEX CELLS ROBERT G. SZULBORSKI+ and LARRYA. PALMER? Department of Anatomy and David Mahoney Institute of Neurological Sciences, School of Medicine, University of Pennsylvania, Philadelphia, PA 19104, U.S.A. (Received 4 January 1989; in revised form 12 June 1989) Abstract-We have estimated the second-order response properties of complex cells in two spatial dimensions by cross-correlating their spike trains with a binary approximation of a Gaussian white noise stimulus ensemble. Wiener-like kernels were computed and geuemlly consisted of two or three parallel, elongated subregions alternating between augmented and suppmssed response. These subunits were scattered across ‘he receptive fields of complex cells and their axes of elongation agreed with the optimal orientation determined with drifting gratings. Complex cells
Subunits
Striate cortex
Cat
INTRODUCTION
demonstrated that while CCs clearly display It is well known that the first-order response uniform tlrst-order behavior, they exhibit properties of complex cells are, to a large degree, nonuniform spatial structure when examined spatially homogeneous; that is, that there exists with pairs of bars (1978). As expected, a CC’s extensive or even complete overlap of bright and response to the simultaneous presentation of dark subregions in complex cells’ receptive two bars differed from the simple sum of the fields. Such spatial homogeneity makes it im- responses to the two bars presented individupossible to accurately predict a complex cell’s ally; however, this difference varied in a systemresponse to a composite stimulus consisting of atic fashion depending upon the relative simpler stimuli, stimuli for which the cell’s positions of the two bars. A distinct secondindividual responses are known. For example, order spatial substructure was observed for all complex cells exhibit both orientation and 10 CCs studied and was termed a subunit. This spatial frequency tuning despite their uniform subunit consisted of a central region where the first-order spatial receptive fields (RFs). Thus, response exceeded that predicted by linear CCs behave nonlinearly, failing to follow the superposition (augmented response) and flanking reglons where the response was less than principle of spatial superposition. One way to characterize nonlinearities of that predicted by superposition (suppressed respatial summation is to determine higher-order sponse). Later studies by Heggelund (1981) and responses, the simplest being those of second- by Emerson, Citron, Vaughn and Klein (1987) order, i.e. the responses to pairs of stimuli. have provided further evidence for the existence For example, Rybicki, Tracy and Pollen of subunits in CC RFs. The significance of these subunits is not showed that the response of complex cells clearly known. Movshon et al. (1978) have to pairs of slits depended on the inter-slit shown that one-dimensional (1D) subunit strucspacing. Movshon, Thompson and Tolhurst ture is well matched by the inverse Fourier transform of the spatial frequency tuning curve. *Present address: Department of Ophthalmology. Barnes They speculated that subunits may correspond Hospital, Washington University Medical Center, St to the neurons supplying the primary afferent Louis, MO 63110, U.S.A. tTo whom correspondence should be addressed. input to CCs. Subunit spatial structure would 249
Research Note
2so
then reflect the RF structure of the afferent neuron. Emerson et al. (1987) took a different view and interpreted the subunit as a functional entity not perforce equivalent to a single afferent neuron. Knowledge of subunit structure in the second spatial dimension might clarify the meaning of subunits and might also account for the orientation selectivity of CCs. One general method for characterizing nonlinear interactions is the Gaussian white noise (GWN) technique (Marmarelis & Marmarelis, 1978; Wiener, 1958). Full two-dimensional (2D) GWN consists of a stimulus ensemble in which every unit area of a set defined over two spatial dimensions varies independently in contrast over time. The output of a cell driven by such a stimulus ensemble may be used to calculate Wiener kernels which completely describe nonlinear interactions of any order (e.g. Lee & Schetzen, 1965). Other white noise type stimuli may be used to calculate similar kernels. The relationships between ditierent sets of kernels have been examined by Klein and Yasui (1979) and Klein (1987) and utilized by Emerson et al. (1987) for measuring nonlinear spatiotemporal interactions in visual cortical cells. The experiments described briefly in this report utilized a modified white noise technique to measure second-order nonlinear summation over two spatial dimensions. By applying this method to a population of CCs in cat striate cortex, we have determined the 2D spatial structure of their subunits and found a good correlation between this structure and the orientation preference of these cells. METHODS
The general methods used in performing extracellular, single unit recordings in cat area i7 are described in detail elsewhere (Jones & Palmer, 1987). In brief, adult cats were initially anesthetized with an intraperitoneal injection of sodium thiopental (4Omg/kg). Two venous catheters and a tracheal tube wem insorted. The animal was paralyzed with an injection of 60 mg of gallamine triethiodide and then maintained on a positive pressure respirator. End-tidal CO2 was monitored and kept between 4 and 5% via adjustments in tidal volume and respiratory rate. Anesthesia and paralysis were maintained with appropriate infusions (2.5 mg/hr of sodium thiopental and 2 mg/hr of tubocurarine chloride with 15 mg/hr of gallamine triethiodide, respectively). The pupils were dilated with I % atropine
sulfate and the nictitating membranes were retracted with phenylephrine hydrochloride. Plano contact lenses were inserted to prevent cornea1 dessication while corrective lenses were used to focus stimuli at 57 cm onto the retina. A craniotomy and durotomy were performed to expose area 17. A tungsten-in-glass electrode (Levick, 1972) was inserted into the cortex and a 4% agar-saline solution was applied to minimize respiratory pulsations and cortical drying. Complex cells were identified by their characteristic response to drifting sinusoidal gratings. As shown by many investigators. This consists of an elevation of the mean firing rate (d.c.) with very little modulation at the temporal frequency of the grating (DeValois, Albrecht & Thorell, 1982; Maffei 8c Fiorentini, 1973; Movshon et al., 1978; Pollen & Ronner, 1982). In addition, the RFs of these cells exhibited extensive overlap of regions excited by bright and dark stimuli, as quantitatively measured using single stimulus techniques described recently in connection with simple cells (Jones & Palmer, 1987). A 16 x 16 cartesian grid, one axis of which was aligned with the cell’s preferred orientation, was used to completely encompass the cell’s responsive region and to define 256 stimulus locations. The stimulus consisted of simultaneously presented pairs of individual stimuli whose positions could vary over this 2D region of space. A computer-controlled Picasso CRT image generator was used for generating small square or rectangular bright or dark stimuli (mean iuminance 22cd/m* with stimulus contrast being f 32% of the mean) on a Tektronix 608 monitor. Stimulus duration was generally 50 msec, however stimuli lasting 100 msec were occasionally employed. (In reality, it is impossible to simultaneously present two distinct spatial stimuli with the Picasso image generator. Instead, two spatial stimuli were interleaved at a rate of 200 Hz; that is, each element of a pair was alternately presented for 5 msec throughout the temporal duration of the stimulus pair, usually a total of 50 msec. Since this rate far exceeds the flicker fusion frequency measured at several locations in the cat’s visual system, it effectively produces the percept of a simultaneous pair of stimuli.) Interactions between pairs of temporally asynchronous stimuli were not examined in this study. The set of stimuli utilized was a carefully chosen subset of all possible pairs of individual stimuli, which, given 512 distinct, individual
Research Note
stimuli (256 locations and 2 contrasts), numbered greater than 130,000 arid,,,,,, 50 msec per pair, would require almost ‘2 hr for a single presentation of the entire set. One element of every pair of stimuli was a fixed, reference stimulus while the other element occupied one of the 256 defined locations. A complete set of stimuli consisted of the fixed stimulus paired with all possible single stimuli, including itself. Both stimuli in any one pair can have either contrast, thus a total of 1024 pairs (256 x 4) of individual stimuli comprise the complete set of stimuli given a single fixed location. Two different stimulus paradigms were employed utilizing either one or five fixed stimuli. The five locations consisted of four cardinal points around a fifth point centered within the RF. When one fixed stimulus was used, it was located at one of these five sites. The elements of the stimulus set were randomly presented. All elements were presented once before a new random sequence was begun (Palmer, Gottschalk & Jones, 1987). The temporal offset of every spike (relative to the stimulus frame) and information about the concurrent stimulus comprised the raw data. The reverse correlation technique developed in this laboratory (Jones & Palmer, 1987) was adapted and combined with the kernel formulations of Emerson et al. (1987) to calculate second-order Wiener-like kernels. These kernels depict the 2D spatial distribution of second-order nonlinear interactions. RESULTS AND DISCUSSION
A total of 160 cells, 100 of which were identified as complex, were examined in area 17 of 26 adult cats. A total of 407 sets of interaction profiles (IPs) were obtained from these complex cells. The RFs of all CCs examined were within 13 deg of the area centralis. An investigation of the 2D spatial structure of the first-order RF of CCs was performed but will be presented elsewhere. Approximately three quarters of the complex cells studied (73 out of 100) yielded Wienerlike kernels with definite, nonrandom structure. Figure 1 shows 4 representative examples of these kernels in which the fixed reference stimulus was located at the center of the cell’s receptive field (indicated by the intersection of the horizontal and vertical lines on the plot). The time intervals used for calculating the reverse correlations are indicated along with the dimensions of the region examined. The results are
251
drawn as contour plots in which solid lines indicate. regions of etive, augmented response (i.e. response in excess of linear superposition) while dashed lines indicate regions of negative, suppressed response (less than superposition). Contours are drawn at f 10,30,50,70 and 90% of the peak response. The f50% contours are dotted. The detailed 2D spatial organization of these kernels varied from cell to cell but several general properties were found. In almost all cases, there is a central, or nearly central, region of augmented response. In addition, the great majority of kernels contain neighboring regions of suppressed response. This usually consists of two flanking suppressed zones, however, several kernels contain only one suppressed subregion while a few contain either none or more than two such subregions. The subregions, both augmented and suppressed, in almost all of the kernels are elongated, as evident in Fig. 1 A-C. The average length-to-width ratio of the central regions is greater than 3.0. The flanking troughs were often broader in width than the central peak; nonetheless, the flanking subregions were still distinctly elongated. Three of the 100 cells had kernels with approximately circular, central, augmented subregions, with length-to-width ratios near 1.0. The kernel of such as cell is seen in Fig. 1D. However, cells with this kernel structure comprise a very small minority of all the cells studied. In general, kernels consist of two or three parallel, elongated subregions of alternating sign. Variations in the spatial arrangement of the subregions are also evident in Fig. 1. The subregions in most kernels are staggered along their long axes. In other words, if a line were drawn connecting the extrema of the individual subregions it would not be perpendicular to the long axis of the subregion. In addition, this imaginary line would not always be straight, but would instead consist of line segments with differing spatial orientations. Thus subregions are often staggered but apparently in no uniform fashion. Another feature of kernei structure exhibited in Fig. 1 is the variation in magnitude of individual subregions. In any one kernel, the amplitude of an augmented subregion may be approximately equal to or may be larger or smaller than the amplitude of neighboring sup pressed subregions. No particular preference in this relationship has been discerned. This
Research Note
252
6.3’
4
:
D
61 mrrc I
/\
46
-
mr4c
1
A
7.6.
5.6
1 c---
1.3’
____c
-
5.2.
*
Fig. 1. Second-order Wiener-like kernela for four complex cells. JMa were obtained using a reverse correlation method. Kern& arc drawn as contour plots with solid lines denoting subregions of augmented response and da&cd lines showing regions of suppremed response (details in text). Contours are drnwn at f 10,30.50 (drawn as dotted lines). 70 and 90% of the maximum. The fixed reference stimulus used in computing kernels was located at the intcmeetion of the horizontal and vertical lines on the plots. The dimensions of the region studied and time interval, T, used in calculating the reverse correlation are indicated.
variation in relative amplitudes coupled with the frequent spatial staggering of subregions is reflected in the lack of spatial symmetry in many kernels. The effect of changing the position of the tied, reference stimulus is illustrated in Fig. 2. The Wiener-like kernels in Fig. 2 were calculated from the response of the same cell whose center-&d-stimulus kernel is shown in Fig. 1A. The positions of the ilxed stimuli used in computing the kernels are indicated by the intersection of the horizontal and vertical lines on each plot. In this figure, the maximum amplitude across all five kernels was determined and the contours are drawn in relation to this “global” maximum. Thus, each kernel need not have contours at all levels.
The basic structure of the kernel, an elongated central subregion with augmented response flanked by elongated subregions of suppressed response, is apparent the position of the fixed stimulus. subregions in different kernels for a are not identical in structure. The positions and amplitudes of the subtqions in relation to the location of the fixed stimulus can vary. The spatial dimensions of individual subrqions and their detaikd structure can also cw~ with fixed stimulus position. In addition, the spatial orientation of the elongated subregions may vary with the position of the fixed stimulus. A general design of the second-order spatial substructure of complex cells has emeqted from the preliminary analysis of the data from these
253
Fig. 2. Second-o~er Wiener-like kernels for one complex cell with the fixed referencestimulus at five differentlocations indicated by the intemections of the horixontal and vertical lines on each plot. These data are from the same cell shown in Fig. 1A. Kernels are presentedas contour plots using the same conventions as in Fig. I except that a single maximum was determinedover all the grids. AI1contours are drawn relative to this single maximum.
studies. Following the terminology of Movshon et al. (1978), we refer to the organized structure of any one second-order kernel as a subunit. While there are many variations, an average subunit consists of two or three parallel, elongated subregions-a central peak and &king troughs-usually staggered in position along their long axes and often with no particular spatial symmetry. Similar, but not identical, subunits are scattered across that region of space wherein single bright and dark stimuli produce a response. This general org~~tion
is consistent with the 1D spatial structure of subunits described in previous studies (Movshon et al., 1978; Baker & Cynader, 1986; Emerson et al., 1987). Movshon et al. (1978) speculated that CC subunits might be dim&y identified with either lateral geniculate nucleus (LGN) or simple cell inputs.. The 2D spatial structures of the subunits described in this report certainly differ from the RFs of LGN cells. But, the elongated nature of the subregions comprising a subunit strongly resembles the 2D spatial structure of simple cells
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ResearchNote
(Jones & Palmer, 1987) and evokes a temptation to equate the two. If this were the case, the 2D spatial structure of a subunit would arise from and be identical to the RF of a single afferent simple cell. While simple cells may provide the primary input to complex cells (Hubel & Wiesel, 1962) it does not necessarily follow that the structure of any individual complex cell subunit directly reflects the RF structure of a particular afferent simple cell. All models of complex cell input utilize multiple afferents with spatially overlapping RFs (Hubel & Wiesel, 1962; Pollen & Ronner, 1982; Spitzer & Hochstein, 1985). Any single stimulus influences more than one afferent; thus pairs of stimuli would drive even mole inputs. The second-order kernels we measured depict the distribution of nonlinear summation, however it may arise, over two dimensions of space. Thus, they do not directly delineate the RF structure of any one afferent neuron, rather, they are a product of the nonlinear combination of precursor component cells. This is not to say that subunit structure is not influenced by the RF organization of afferents; rather, subunits structure more likely represents some type of average of the RFs of all the inputs and their interactions. Unlike simple cells, whose linearity mandates that a complete description of their behavior is supplied by their first-order response properties, or impulse response function, complex cells are not fully described by their first-order responses. Higher-order terms are needed to more fully describe their behavior. Movshon et al.‘s IPs as well as our 2D subunits are types of higherorder terms, having been collected with pairs of stimuli. That the 2D spatial subunits presented here provide a more complete description of CCs is evident from their overall organization within their respective grids. Recall that these grids were initially aligned with the orientation producing the cell’s maximal response. The elongation of subunit subregions parallel to an axis of the grid indicates that subunit spatial structure is consistent with the overall orientation preference of the cell. Whether this 2D subunit structure represents the initial expression of orientation selectivity in the neural chain from retina to complex cells or whether it merely reflects the passive propogation of a property generated in precursor cells, is not known. Whether the bandwidth of CC orientation tuning is also consistent with subunit structure is currently being studied. Nonetheless, the 2D
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