The Journal of Neurophysiology Vol. 78 No. 4 October 1997, pp. 2018-2033
Copyright ©1997 by the American Physiological Society

Processing of Color- and Noncolor-Coded Signals in the Gourami Retina. II. Amacrine Cells

Hiroko M. Sakai¹, Hildred Machuca¹, and Ken-Ichi Naka^{1, 2}

¹ Departments of Ophthalmology and ² Physiology and Neuroscience, New York University Medical Center, New York, New York 10016

	ABSTRACT

Abstract Introduction Methods Results Discussion References

Sakai, Hiroko M., Hildred Machuca, and Ken-Ichi Naka. Processing of color- and noncolor-coded signals in the gourami retina. II. Amacrine cells. J. Neurophysiol. 78: 2018-2033, 1997. The same set of stimuli and analytic methods that was used to study the dynamics of horizontal cells (Sakai et al. 1997a) was applied to a study of the response dynamics and signal processing in amacrine cells in the retina of the kissing gourami, Helostoma rudolfi. The retina contains two major classes of amacrine cells that could be identified from their morphology: C and N amacrine cells. C amacrine cells had a two-layered dendritic field, whereas N cells had a monolayered dendritic field. Both types of amacrine cell were tracer-coupled but coupling was more extensive in the N amacrine cells. Responses from C amacrine cells lacked a DC component and had a small linear component that was <10% in terms of mean square error (MSE); the second-order component often accounted for >50% of the modulation response. The C amacrine cells did not show any characteristic color coding under any stimulus condition. Most responses of N cells to a pulsatile stimulus consisted of a series of depolarizing transient potentials and steady illumination did not generate any DC potential in these cells. The response to a white-noise modulated input was composed of well-defined first- and second-order components and, possibly, higher-order components. The response evoked by a red or green white-noise-modulated stimulus given alone was not color coded. Modulated red illumination in the presence of a green illumination elicited a color-coded response from >70% of N amacrine cells. Color information was carried not only by the polarity but also by the dynamics of the first-order component. No convincing evidence was obtained to indicate that the second-order component might be involved in color processing. Some N amacrine cells produced a well-defined (second-order) interaction kernel to show that the temporal sequence of red and green stimuli was a parameter to be considered. In a complex cell such as an amacrine cell, responses evoked by a pulsatile stimulus given in darkness and by modulation of a mean luminance could be very different in terms of their characteristics. It was not always possible to predict the response evoked by one stimulus from observing the cell's response to another stimulus. This is because, in N cells, a flash-evoked (nonsteady state) response is composed largely of nonlinear components whereas a modulation (steady state) response is composed of linear as well as nonlinear components.

	INTRODUCTION

Abstract Introduction Methods Results Discussion References

Amacrine cells are interposed between the neurons that form the outer retina, the horizontal and bipolar cells, and the neurons of the output stage of the retina, the ganglion cells. The strategic location of amacrine cells suggests that their function is to modify the signals that originate in the outer retina and to transmit the modified signals to the ganglion cells. Many past studies have produced correlations between the morphology of amacrine cells and their light-evoked responses (Ammermüller and Kolb 1995; Bloomfield 1992; Chino and Hashimoto 1986; Dacheux and Raviola 1986, 1995; Djamgoz et al. 1989; Freed et al. 1966; Kolb and Nelson 1996; Peters and Masland 1996; Taylor 1996; Teranishi et al. 1987; Zhou and Fain 1996). A mosaic of amacrine cells (Vaney 1990), their immunochemical activity (Marc 1992; Sherry and Yazulla 1993), and their extensive tracer coupling (Vaney 1991, 1994) also have been examined. Current injection study on the amacrine cells' model network also has been reported (Smith and Vardi 1995). Although some amacrine cells are known to perform specific functions (Bloomfield 1991), the more general role of these cells in the retinal neuron network remains to be defined. For example, the role of amacrine cells in the formation of a concentric receptive field is still unknown (Morgan 1992). One possible exception is the functional role of amacrine cells in the catfish (Sakai and Naka 1992). The frequently used term "sustained amacrine cells" illustrates the fact that past studies have been confined to describe the statics of responses evoked by flashes given in darkness. This is because the response from any amacrine cell is expected to be dynamic. In the catfish, a white-noise stimulus evokes vigorous depolarizing transient responses from the so-called sustained amacrine cells, showing that modulation of a mean luminance is most appropriate for studies of the response dynamics of these cells. Few studies have examined the responses evoked in these cells by modulation of a mean luminance, with the exception of the study by Werblin (1977) with a whirling windmill. No systems approach has been applied in attempts to define response dynamics, apart from a series of studies on the amacrine cells of the catfish, as summarized by Sakai and Naka (1988).

The role of amacrine cells in color processing is also unclear, but there are many reports in which the spectral sensitivity of amacrine cells has been discussed (e.g., Teranishi et al. 1987). Some studies have demonstrated that color-coded responses are associated with the sustained component but detailed evidence is lacking (Ammermüller and Weiler 1988; Chino and Hashimoto 1986; Djamgoz et al. 1990; Mitarai et al. 1978; Teranishi et al. 1987).

In this study, we examined the response dynamics of the amacrine cells of the gourami using the same set of light stimuli and analytic routines as was used in our study of the response dynamics of horizonal cells (Sakai et al. 1997a) and of ganglion cells (Sakai et al. 1997b). Thus processing of color- and noncolor-coded signals in amacrine cells is discussed here in the context of similar processing that occurs in horizontal and ganglion cells. The canonical nature of the kernel allows us to compare temporal dynamics as well as color processing in horizontal, amacrine, and ganglion cells, including spike discharges. Such comparisons are based on the frequency characteristics of the first-order kernel, the waveform of the kernel, and signatures of second-order kernel.

The main conclusions drawn from this study are as follows. 1) There are two types of amacrine cells: C cells the first-order component of which accounts for <10%, in terms of mean-square-error (MSE), of the total modulation response and N cells the first-order component of which accounts for nearly 60% of the modulation response. 2) C cells have a bistratified dendritic field whereas all N cells have a monostratified dendritic field and both types of cell are extensively tracer-coupled. 3) Characteristic nonlinearity is generated in both C cells and N cells and the nonlinearity is similar to that found in the catfish (Sakai and Naka 1987a). 4) Information on color is carried mainly by the first-order component and not by the second-order component. 5) The polarity, as well as the frequency characteristics, of linear components is associated with the processing of color information. 6) Some N cells generated a well-defined cross-kernel to show that these cells were detecting a specific time sequence of red and green stimuli.

	METHODS

Abstract Introduction Methods Results Discussion References

The studies were performed with an eye-cup preparation of the kissing gourami, Helostoma rudolfi. Methods for recording intracellular responses, methods of light stimulation, procedures for morphological analysis, and methods for the acquisition and analysis of data were identical to those described in Sakai et al. (1997a). To simplify our analysis, as in the two accompanying papers (Sakai et al. 1997a,b), we used a large field of light that covered the entire surface of the retina. Light stimuli were derived from a red light- or a green light-emitting diode (LED) and covered the entire retinal surface. Use of this simple spatial configuration can be justified by our finding that, in catfish amacrine cells, a large field of light evoked a response similar to that generated by the receptive-field center (Sakai et al. 1995). Our experiments on the discharges from ganglion cells of the gourami with a spatio-temporal white-noise stimulus combined with classical spot-annular stimulation showed that, as in the catfish retina, a large field of light produced a response similar to that evoked by a spot of light(J. L. Wang, V. Bhanot, and K.-I. Naka, unpublished data).

Representation of kernels

The first-order kernel is two-dimensional; the kernel's amplitude on an incremental or contrast-sensitivity scale is plotted against time. The second-order and cross-kernels are a three-dimensional structure with two time axes that correspond to ₁ and ₂ in Eqs.2-5 in Sakai et al. (1997a). The second-order kernels are symmetric functions of their arguments, whereas the cross-kernel is, in general, an asymmetric function of its arguments. This kernel describes the nonlinear interaction of red and green inputs as it affects the output. In this report, as in previous ones, the second-order and cross-kernels are displayed as a contour map in which a three-dimensional structure is collapsed onto a two-dimensional plane. The depolarizing peaks are depicted by solid lines and the hyperpolarizing valleys by dashed lines. Our experience has shown that this method is optimal for representing second-order kernels, although most authors display kernels as three-dimensional solids.

Depth of modulation

In most of our experiments, we adjusted the depth of modulation so that the modulation responses generated by the red and green inputs were similar. Sakai, Wang, and Naka (1995) showed, however, that a change in the depth of modulation did not affect the dynamics of the response, as revealed by the waveform of the first- and second-order kernels, but affected only the amplitude of the kernels (cf. Shapley and Victor 1978). In this series of experiments, we focused on the dynamics of a response. With ±3( = SD) taken as the limit of Gaussian white-noise modulation, the depth of modulation was between 20 and 80%.

Morphological classification

The morphology of a large number of cells was studied by injection of Lucifer yellow dye and neurobiotin, as described by Sakai et al. (1997a). Stained cells were viewed as flat mounts and selected preparations were reimbedded in Epon and sectioned for studies of the layering of the dendritic fields of stained cells. Two types of amacrine cells, C and N cells, were easily distinguishable in terms of morphology. We stained 65 C cells and 85 N cells. All these cells were tracer-coupled. The dendritic fields of C amacrine cells always were bistratified, and those of N amacrine cells always were monostratified. Results of a detailed morphological study, as well as morphometric measurements of tracer-coupled cells, are being analyzed (V. Bhanot and K.-I. Naka, unpublished results).

Functional classification

Responses evoked by a pulsatile stimulus can be used to classify cells in an arbitrary fashion as red- or green-ON or -OFF cells. However, we found that the waveform of the first-order kernel, the signature of the second-order kernels, and the MSEs of the first- and second-order models were all convenient parameters for classifying amacrine cells. Accordingly, we classified amacrine cells as N or C based on the MSEs of the first- and second-order components (Table 2). This classification, as in the catfish, conformed with the morphological classification. N cells also are classified as red-ON and -OFF cells based on the polarity of the red first-order kernel because this kernel is robust in the sense that the waveform of the red first-order kernel is unchanged whether or not there is a green input. N cells are also classified into color- and noncolor-coded cells. The complexity of this classification is inevitable because retinae that process color information also must be complex. Table 1 shows the detailed classification of amacrinecells based on the polarity and waveform of the first-order kernels. Classification is relative, not absolute, and there can be as many classification schemes as the number of parameters or experimenters.

	RESULTS

Abstract Introduction Methods Results Discussion References

C amacrine cells

One class of amacrine cell in the retina of the gourami has morphological and physiological features similar to those of both the C amacrine cells in the catfish retina (Sakai and Naka 1988) and the transient amacrine cells in other retinae (Djamgoz et al. 1990; Kaneko 1970; Teranishi et al. 1987). The catfish C amacrine cell has a bistratified dendritic field, with one field in the proximal part and the other in the distal part of the inner plexiform layer (Naka and Ohtsuka 1975). Functionally, the major part of the cell's response is accounted for by the second-order component (Naka et al. 1975). The similarity in morphology and physiology of the two types of cell, those in the catfish and those in the gourami, leads us to refer to this class of amacrine cells in the retina of the gourami as C amacrine cells. Figure 1, A and B, shows flat-mount views of a neurobiotin-stained C amacrine cell. Neurobiotin was injected into a cell, and this fact was confirmed by the observation that Lucifer yellow staining showed a single brightly stained C cell surrounded by a few faintly stained neighboring C cells as reported by Teranishi et al. (1987). Figure 1A shows a view of the distal dendritic field that includes three cell bodies, which are marked by asterisks, and Fig. 1B depicts the proximal dendritic field. Morphologically, the C amacrine cell is characterized by: a small cell body in the inner nuclear layer; a bistratified dendritic field; and the tracer coupling of both dendritic fields. The three densely stained cells shown in this figure were situated at the border of a cluster of stained C cells, and some tracer-stained dendrites can be seen to end abruptly. There seems to be a physical barrier between two dendrites that impedes the spread of the tracer. Figure 3C shows a cross-sectional view of one of the neurobiotin-stained C amacrine cells shown in Fig. 1, A and B. The location of the cell body and the characteristic stratification of two dendritic fields are apparent, and, in this picture, two primary dendrites can be seen to connect the two dendritic fields, distal and proximal.

View larger version (83K): [in this window] [in a new window]   FIG. 1. C amacrine cells stained with neurobiotin. A: distal dendritic field. *, 3 cell bodies. B: proximal dendritic field. Both dendritic fields are tracer-coupled. C: a cross-section showing the distal and proximal dendritic fields and 2 principal dendrites that connect the fields. One stained cell body is seen in the distal layer, from which 2 descending dendrites are seen. In A and B, the other dendritic fields are seen as out-of-focus-image. This picture is from the edge of a cluster of tracer-coupled cells (n = 30) at a site where the strength of tracer coupling decreased abruptly. Bar is 10 µm.

View larger version (36K): [in this window] [in a new window]   FIG. 3. White-noise analysis of the C cell whose pulsatile-stimulus-evoked responses are shown in Fig. 2. A: 2 noisy first-order kernels evoked by a red and a green white-noise stimulus, respectively. Mean square errors (MSEs) of the first-order models were >90%. B: 2 second-order kernels generated by the red and green inputs. Red kernel has the characteristic feature (signature) of a 4-eye kernel, in which 2 peaks and 2 valleys occupy the 4 corners of a square whose bases are parallel to 2 time axes (cf. Figs. 16 and 17 in Sakai and Naka 1987). Green second-order kernel also has a 4-eye signature, but the peaks and valleys are elongated along the diagonal. This arrangement shows that a second low-pass filter was involved in the generation of the green kernel. C: reconstruction of a C cell's response evoked by a 10-Hz sinusoidal red input, marked input. Stimulus was given in the presence of a steady green illumination. Modulation response is marked response. Two traces, indicated by models, are the first- and second-order predictions. First-order model is a 10-Hz sinusoid, and the second-order component is frequency doubling. Second-order prediction includes the first-order component. MSE for this model response was 40%, a typical value for a C cell in the gourami retina (Table 2). Records are shownas poststimulus-time histograms. Units for second-order kernels are mV·mm4·photons2·s2.

The typical responses of a C amacrine cell are shown in Fig. 2A. In this case, a series of responses was evoked by various combinations of red and green stimuli given as a pulsatile stimulus and as steady illumination. Although each response is slightly different from others with respect to the details of the waveform, both red and green stimuli produced transient depolarization at both the ON and OFF sets of the pulsatile stimulus and of the steady illumination. The C amacrine cell responded only to increments or decrements of a stimulus and not to steady illumination, as shown originally by Kaneko and Hashimoto (1969). Figure 2, B and C, shows, on an expanded time scale, two responses evoked by a red or a green flash given in the presence of steady green or red illumination. The spontaneous oscillations (63 Hz) and the transient nature of the responses are evident. Sakai and Naka (1990b) presented evidence that, in the catfish, similar spontaneous oscillations in C cells were the result of an interaction between C and N amacrine cells. Djamgoz et al. (1990) observed similar oscillations in transient amacrine cells in the goldfish retina.

View larger version (24K): [in this window] [in a new window]   FIG. 2. Flash-evoked responses from a C amacrine cell. A: a series of responses evoked by various combinations of pulsatile stimuli and steady illumination. Cell's response to any combinations of stimuli was a transient depolarization at the ON or OFF set of the stimulus. Both ON and OFF sets of a steady illumination also produced transient depolarization. Thick baseline shows spontaneous oscillations. Note the absence of the cell's response to steady illumination. B and C: responses evoked by single red and green pulsatile stimuli shown on an expanded time scale. Green or red steady illumination was present. Spontaneous 63-Hz oscillation is evident. Mean luminance was 9 × 1011 photons·mm2·s1 for the red input and9 × 1010 photons·mm2·s1 for the green input. In this and in the following figure, there are 2 stimulus traces, 1 to indicate the timing of pulsatile stimulus and the other steady illumination.

The results are shown in Fig. 3 of the white-noise analysis of the C amacrine cell whose step-evoked responses are shown in Fig. 2. The two first-order kernels, generated by either a red or a green white-noise stimulus (Fig. 3A), are noisy and indicate that the cell produced only small linear components. In this particular cell, the MSE of the first-order model was 93%, showing that the linear component constituted 7% of the total modulation response in terms of MSE (Table 2). Figure 3B shows the second-order kernels generated by a red and a green stimulus. The red second-order kernel shows the characteristic signature of a class of second-order kernels that are referred to as four-eye kernels (Sakai and Naka 1987b) with two peaks and two valleys positioned at the four corners of a square whose axes are parallel to two time axes. This signature suggests that the generation of the nonlinearity can be approximated by a cascade of the Wiener type, a LN cascade, in which a dynamic linearity is followed by a static nonlinearity equivalent to a squaring device (Fig. 16 in Sakai and Naka 1987b). The green second-order kernel also has a four-eye signature. However, the green kernel differs from the red kernel in two respects: the kernel has a longer transport delay (or peak response time) and the kernel's peaks and valleys are elongated along the diagonal. Two second-order kernels can be superposed on top of each other by shifting one kernel by 5 ms along the diagonal. These two observations indicate that the generation of the green kernel involves an extra stage of low-pass filtering. The generation of the green kernel can be modeled by a cascade of LNL structure, in which a static nonlinearity is sandwiched between two dynamic linear filters (Victor and Shapley 1979). Modeling of this LNL cascade will be illustrated in our next paper (Fig. 13 in Sakai et al. 1997b). The second linear filtering appears to occur before the generation of nonlinearity. A similar difference in the four-eye kernels generated by the center and surround inputs or by the red and green inputs has been consistently seen in both C amacrine cells and in some ganglion cells in the catfish and gourami retina (Fig. 3 in Sakai and Naka 1995; Fig. 3C, 1 and 2, in Sakai et al. 1997b). Figure 3C shows the results of a model experiment where a response was evoked by a red stimulus, a 10-Hz sinusoidal signal, and a green input that was kept at a steady level. The first- and second-order models were computed by convolution of the original sinusoidal stimulus by the first- and second-order kernels. The figure shows the input stimulus, marked input, which was a 10-Hz sinusoid; the cellular response evoked by the sinusoid input, marked response; and the first- and second-order components, marked models that were predicted by the first- and second-order kernels. The model shows the frequency doubling that is characteristic of the C amacrine cell; it is due to the fact that the cell's response largely was composed of the second-order component, and the contribution from the first-order component was very small. In the cell for which results are shown here, the MSEs of the first- and second-order model are 93 and 30%, respectively, i.e., the second-order component accounts for ~60%, in terms of MSE, of the total modulation response, whereas the MSE of first-order component is <10%. The main function of C amacrine cells in the retina of the gourami, as in the catfish, appears to be the generation of a second-order nonlinearity that serves to detect changes around a mean luminance, regardless of the color of the input. Here we note that the function dictated by a four-eye kernel is more complex than a simple frequency doubling. We will comment on this later. We do not know whether the extra filter stage in the process of generation of the green second-order kernel can be referred to as color processing or not. We analyzed white-noise-evoked responses from 46 cells out of 65 neurobiotin-stained C cells. All 46 cells showed functional traits similar to those shown in Figs. 2 and 3. Nineteen stained cells, which showed a bistratified dendritic field, produced ON-OFF transient responses but white-noise records were not long enough to fully analyze their modulation responses.

View larger version (35K): [in this window] [in a new window]   FIG. 13. Interaction kernels from experiments in which red and green inputs were modulated by 2 independent white noises. This kernel is h2xu(1,2) in Eq. 4 in Sakai et al. 1997a. Red input is x and green input is u. A and B were from N cells and C and D were from luminosity and chromaticity horizontal cells. Noisy signature of horizontal-cell kernels shows that there was no dynamic interaction component in the cells' modulation response. For details, see text.

N amacrine cells

In the retina of the gourami, there is another class of amacrine cells that we will refer to as N amacrine cells. This type of cell is characterized morphologically by a small cell body and the abrupt ending of its monolayered dendrites in Lucifer yellow-stained preparations (Fig. 5). Functionally, it is characterized by the presence of well defined first- and second-order components (Figs. 8, 10, and 12 and Table 2). This class of cells is analogous to a class of similar cells in the catfish retina, the N amacrine cells, which correspond to the sustained amacrine cells in the retinae of other lower vertebrates (Djamgoz et al. 1990; Kaneko 1970; Teranishi et al. 1984, 1985).

View larger version (67K): [in this window] [in a new window]   FIG. 5. Morphology of the cell whose responses are shown in Fig. 4. Image was obtained after injection of Lucifer yellow. Note the abrupt endings of dendrites. Several neighboring cells also are stained faintly, as reported originally by Teranishi et al. (1987). Bar, 10 µM.

View larger version (22K): [in this window] [in a new window]   FIG. 8. Noncolor-coded ON- and OFF-N amacrine cells. A1: a response was evoked by a red pulsatile stimulus given in the presence of steady green illumination. B1: a response was evoked by a green pulsatile stimulus given in the presence of steady red illumination. Two responses are characterized by a series of depolarizing transients followed by a large hyperpolarization at the OFF set of the pulsatile stimulus. C1: 2 first-order kernels evoked by a red () or green (- - -) white-noise input in the presence of steady green or red illumination. Depolarizing first-order kernels show that this cell was an ON cell. A2: response evoked by a red pulsatile stimulus given in the presence of steady green illumination. B2: a response evoked by a green pulsatile stimulus in the presence of steady red illumination. Pulsatile-stimulus-evoked depolarization is transient and oscillation is evident. Depolarizing transient seen at the OFF set of stimulus is larger than that seen at the ON set; this cell was an OFF cell. C2: 2 first-order kernels generated by red () or green (- - -) white-noise inputs in the presence of steady green or red illumination. Both kernels are hyperpolarized, indicating that this cell can be classified as an OFF cell. D1: 2 sets of kernels shown in C1 and C2 are superposed to show that waveforms of kernels from ON and OFF cells are identical. Polarity of the kernels shown in C2 is reversed to facilitate the comparison of 2 sets of kernels. Kernels depicted by a dashed line were generated by a green input. Mean luminance was 9 × 1011 photons·mm2·s1 for the red input and 9 × 1010 photons·mm2·s1 for the green input. Units are mV·photons1·mm2·s1 for the red kernels. Kernel units are 1.1 × 107 and 0.9 × 107 mV·photons1·mm2·s1 for the red and green kernels, respectively. Green kernels were normalized, with respect to amplitude, to the red kernels to facilitate comparisons of waveforms of red and green kernels.

View larger version (27K): [in this window] [in a new window]   FIG. 10. Responses from a color-coded N amacrine cell. A and B: responses to a red or a green pulsatile stimulus in the presence of steady green or red illumination. Responses are composed of a series of transient depolarizing peaks, and there is no apparent sign of color coding with the exception that the red ON response is weaker. C: 2 first-order kernels evoked by a red or green white-noise stimulus given alone. Two kernels are identical in waveform, showing that the modulation response evoked by a single input was not color coded. D: 2 first-order kernels from 2 input stimuli, in which both the red and the green inputs were modulated by 2 independent white-noise signals, and the resulting response (single output), was decomposed into its red and green components. Red kernel is similar to that generated in the 1-input experiment shown in C, but the green kernel has become triphasic (+TRI) with a depolarizing principal peak. E and F: second-order kernels generated by the red and green inputs measured from the same set of records that generated kernels shown in D. Red kernel has a typical 4-eye signature whereas the green kernel shows indications of oscillation. This is a 9-eye second-order kernel with 2 smaller that are not apparent. Mean luminance of the red and green inputs was similar to those in Fig. 2. Kernel units are 1.4 × 107 and 0.9 × 107 mV·photons1·mm2·s1 for the red and green kernels, respectively. Green kernel in D is plotted on a scale similar to that for the green kernel in C. Units for second-order kernels are mV·mm4·photons2·s2.

View larger version (28K): [in this window] [in a new window]   FIG. 12. Responses from a color-coded N amacrine cell. A and B: responses evoked by a red or green pulsatile stimulus given in the presence of steady green or red illumination. These responses are a series of depolarizing transients. ON and OFF set of illumination triggered a series of transients. There are no apparent features that suggest the color-coded nature of the cell. C: red and green first-order kernels obtained in the presence of steady green or red illumination. Both kernels have complex waveforms. Red and green inputs produced first-order kernels of different waveforms. D: red and green first-order kernels obtained by simultaneous modulation of the 2 inputs, red and green. Amplitude of the red kernel is somewhat larger than that in C, but the amplitude of the green kernel is much smaller, showing that there is an interaction between the responses evoked by the 2 inputs, i.e., the sensitivity of the green component was reduced greatly in the presence of modulating red input. E and F: red and green second-order kernels obtained in the presence of steady green or red illumination. These kernels were measured from records that generated first-order kernels shown in C. Signatures of both kernels are similar to that of the catfish N amacrine cells in that their peaks and valleys are elongated orthogonal to the diagonal. Mean luminance of red and green inputs were similar to those in Fig. 2. Kernel units are 1.3 × 107 and 0.4 × 107 mV·photons1·mm2·s1 for the red and green kernels respectively. Green kernel in D is plotted on a scale similar to that for the green kernel in C. Units for second-order kernels are mV·mm4·photons2·s2.

Figure 4 shows a series of responses from a N amacrine cell. Responses evoked by red and green pulsatile stimuli in the presence of steady green or red illumination are characterized by the presence of sharp depolarizing transients. The response evoked by a flash of green light was a series of depolarizing peaks with no apparent OFF response, whereas the red-evoked responses displayed a large depolarizing peak at the OFF set of the flash, suggesting that this cell might have been a red-OFF and green-ON cell. In most N amacrine cells of the gourami retina, including the cell shown here, steady illumination did not produce any change in membrane potential. Gourami N amacrine cells responded mainly to a change around a mean luminance, in contrast to the catfish's N amacrine cells, which generate a large DC component in response to steady illumination (Fig. 2 in Sakai and Naka 1992). A series of brief spike-like depolarizing peaks that followed the OFF set of the stimulus was also a characteristic of some N cells of the gourami. The responses evoked by a series of pulsatile stimuli that are shown in Fig. 4 were different from the responses of sustained amacrine cells in other species in that the former responses were composed entirely of depolarizing transients. Most sustained amacrine cells observed in the lower vertebrate retina contained a well-defined sustained component (Ammermüler and Kolb 1995; Ammermüler and Weiler 1988; Djamgoz et al. 1990; Teranishi et al. 1987). Figure 5 shows the morphology of the cell that produced the responses shown in Fig. 4, as revealed by injection of Lucifer yellow. The cell is characterized by a small cell body with thick principal dendrites, which do not taper into fine processes but end abruptly, as already shown by Teranishi et al. (1987) and by Negishi and Teranishi (1990). The abrupt ending of dendrites is characteristic of N amacrine cells of the gourami, and it is at such sites that the strong tracer coupling probably occurs. In the Lucifer yellow-stained preparation, faint staining of several neighboring cells also reveals the remnants of cell coupling (Teranishi et al. 1987).

View larger version (24K): [in this window] [in a new window]   FIG. 4. Responses from a N cell evoked by a series of pulsatile stimuli given in the presence of a steady illumination of the opposing color. This cell appears to be a red-OFF and green-ON cell, as judged from the waveforms of flash-evoked responses. Note the absence of both a hyperpolarizing component at the OFF set of the stimulus and of a DC component in the response. Note also the series of spike-like depolarization after the OFF set of the red pulsatile stimulus. Termination of the steady red illumination and ON set of the steady green illumination produced a transient depolarization. Luminance was 9 × 1011 photons·mm2·s1 for the red input and 9 × 1010 photons·mm2·s1 for the green input.

In Fig. 6 we compare the responses elicited by a pulsatile stimulus and the sinusoidal modulation of a mean luminance. Figure 6, A and B, shows the responses evoked by a green pulsatile stimulus in the presence of steady red illumination and by a red pulsatile stimulus in the presence of steady green illumination, respectively. These responses consist of several components: transient depolarization seen at the ON and OFF sets of a flash stimulus and spike-like oscillatory wavelets superimposed on the depolarizing phase. There is no apparent difference between the responses evoked by the red and green flashes to suggest that the cell's response might be color coded. The ON-OFF nature of these two-step responses suggests that this cell could have been a C or transient amacrine cell with frequency-doubling characteristics. Figure 6C shows the green or red input modulated by a sinusoidal signal of 11 Hz in the presence of a steady green or red illumination. Contrary to the step-evoked responses shown in Fig. 6, A and B, the responses evoked by modulation inputs, Fig. 6C, are much simpler in waveform. The modulation responses do not show any sign of frequency doubling. The two modulation responses are clearly out of phase; this cell is a green-ON and red-OFF cell. An 11-Hz sinusoid input generated a depolarizing response with an11-Hz basic frequency. The 80-Hz oscillation also is seen in the depolarizing phase of the response. This 80-Hz oscillation is similar to the 72-Hz oscillation observed in C cells. In N cells, oscillations were seen during the light-evoked depolarizing phase, whereas in C cells, oscillations were seen in darkness. In spite of the transient nature of the flash-evoked response of this cell, we classify this cell as a N amacrine cell because the cell produced a clearly defined linear component; the cell's morphology, as seen in Lucifer yellow-stained preparations, had a monolayered dendritic field characteristic of a N cell; and the cell's modulation response was not frequency doubling.

View larger version (22K): [in this window] [in a new window]   FIG. 6. Responses from a N amacrine cell of the gourami evoked either by a pulsatile stimulus or by modulation of a mean luminance by an11-Hz sinusoid. A and B: responses generated by a green and a red pulsatile stimulus in the presence of a steady red and a steady green illumination, respectively. Principal feature of these responses is the transient depolarization seen at the ON and OFF sets of the pulsatile stimuli. Spike-like wavelets in the depolarizing phase correspond to the 80-Hz oscillation that is seen more clearly in C. C: responses were evoked by modulation of green or red mean illuminance by an 11-Hz sinusoidal signal in the presence of steady red or steady green illumination. Records are displaced laterally so that 2 stimuli, red and green, traces are superimposed and illustrate the phase difference between the red and green responses. For this particular input, a green depolarizing response, top, was generated during the brightening phase, and a red depolarizing response, bottom, was generated during the dimming phase of the sinusoidal inputs. This cell can be classified as green-ON and red-OFF cell. Pulsatile stimulus evoked a transient ON-OFF depolarization whereas the 11-Hz stimulus evoked an 11-Hz response. There was no frequency doubling in the modulation response to justify our classification of this cell as a N amacrine cell. Often, as illustrated here, we found no direct correlation between waveforms of the responses evoked by a pulsatile stimulus and by modulation of a mean luminance. Mean luminance was 9 × 1011 photons·mm2·s1 for the red input and 9 × 1010 photons·mm2·s1 for the green input. Depth of modulation of the sinusoidal inputs was 38%.

First- and second-order kernels were obtained from a cell (the responses of which are shown in Fig. 6) and used to predict the cell's response to two types of modulation signal, a red stimulus modulated by a white-noise signal (Fig. 7A1) and a 9-Hz sinusoid (Fig. 7B1) in the presence of a steady green illumination. The predictions from the first-order kernels, first-order models, are shown in Fig. 7, A2 and B2. The first-order model predicted by the sinusoidal stimulus is a 9-Hz sinusoid. The second-order models predicted by the second-order kernels are shown in Fig. 7 A3 and B3. The sinusoidal response shows that the second-order component is frequency doubling. In Fig. 7, A4 and B4, the cellular responses are shown as solid lines, and the predictions, the sum of the first- and second-order predictions, are shown as dashed lines. These two traces, the actual response and the prediction, match quite well, although, as shown in the case of the sinusoidal response, the kernels fail to predict the 80-Hz oscillation. Second-order kernels from amacrine cells of the gourami often show alternating peaks and valleys on the diagonal, indicating the oscillatory nature of these amacrine cells (Figs. 10F and 12, E and F). Similarly, catfish amacrine cells, in particular N amacrine cells, show prominent oscillations, and the N amacrine cell is the source of the 35-Hz oscillation (Hosokawa and Naka 1985). Although the responses evoked by a pulsatile stimulus from a N amacrine cell were very complex, the results in Figs. 6 and 7 show that the modulation response was simple in waveform and could be approximated, to a reasonable degree of accuracy, by its first- and second-order components. The apparent absence of clearly defined frequency doubling in the responses evoked by a sinusoidal input was due to the smaller contribution to the response of the second-order component, as well as the phase relationship between the first- and second-order components. The second-order component appeared as a hump on the falling phase of the model response (Fig. 7B4). In this particular cell, the MSEs of the first- and second-order models were 65 and 45%, respectively. Teranishi et al. (1987) reported that a cell that produced an ON-OFF transient depolarizing response, similar to those shown in Fig. 6, had a monolayered dendritic field. These authors could have obtained useful information if they used a sinusoidally modulated stimulus in addition to flash stimulus.

View larger version (39K): [in this window] [in a new window]   FIG. 7. Analysis of the white-noise-evoked responses obtained from the N cell whose pulsatile responses were shown in Fig. 6. Prediction of modulation responses by the first- and second-order kernels are shown. A1 and B1: inputs, which were a white-noise or a 9-Hz sinusoidal modulation of a mean luminance. Dark levels are indicated. A2 and B2: predictions made by the first-order kernel (first-order model). A3 and B3: predictions by the second-order kernel (second-order model). A4 and B4: cellular responses () and the model response (- - -), which is the sum of the first- and second-order models. Model response represented by the dashed lines closely matches the cellular responses. First- and second-order kernels predict the response with a fair degree of accuracy apart from the oscillation seen in the depolarizing phase. In the case of white-noise evoked responses, MSEs of the first- and second-order models were 65 and 45%, respectively. Responses evoked by each sinusoidal cycle exhibit some variability, whereas the prediction is identical for every cycle of sinusoidal input. Modulating input was red and there was a steady green illumination.

N amacrine cells in the retina of the gourami can be further classified into noncolor- and color-coded on the basis of their responses to a modulation input. Figure 8 shows two examples of noncolor-coded cells, one is an ON cell (Fig. 8, A1-C1) and the other an OFF cell Fig. 8, A2-C2). Responses evoked by a red and a green pulsatile stimulus in the presence of steady green or red illumination are shown in Fig. 8, A1 and B1. This is a ON cell. These responses are characterized by a series of fast depolarizing transients during flash illumination and by a large hyperpolarization at the OFF set of a red or a green flash. Oscillatory components are also prominent. This cell's response was exceptional in two aspects: a small but well-defined DC component in the response and a large hyperpolarizing phase seen at the OFF set of the stimulus. Responses shown in Fig. 8, A1 and B1, are somewhat similar to the responses from sustained cells in other retinas (cf. Djamgoz et al. 1990). Figure 8C1 shows two first-order kernels evoked by a red and by a green white-noise stimulus given in the presence of a steady green or red illumination. These kernels have a biphasic waveform, with a large initial depolarizing phase. This cell was an ON cell. The two kernels have an almost identical waveform. In Table 1, these kernels are referred to as +BI kernels. Both the red and the green stimulus also generated second-order kernels with a similar signature.

Figure 8, A2 and B2, shows the flash-evoked responses of another noncolor-coded cell. The responses shown in A2 and B2 were generated by a red or green pulsatile stimulus given in the presence of a steady green or red illumination and were almost identical. The responses were characterized by many sharp transient depolarization and oscillations that were triggered by the stimulus. The large depolarization seen at the OFF set of the flash stimulus suggests that the cell was an OFF cell. The absence of a hyperpolarizing component in the response is conspicuous, as it was in most N-amacrine cells examined in this study, with the exception of the cell the results for which are shown in Fig. 8, A1 and B1. As shown for another N cell in Fig. 4, the flash-evoked response was followed by a series of oscillatory transient peaks. The two first-order kernels, shown in Fig. 8C2, evoked by a red or green white-noise stimulus given in the presence of steady green or red illumination are biphasic with a large initial hyperpolarizing phase, indicating that this cell was an OFF cell. These two kernels, with an identical waveform, are classified as BI kernels in Table 1. Note that there was no initial hyperpolarizing phase in the responses evoked by the pulsatile stimulus. As the MSE of the first-order model was 55% in this cell, there was a large linear component in the modulation response. It was not possible to predict the polarity or the nature of the linear component of a modulation response from observations of the response evoked by a pulsatile stimulus. Responses evoked by a modulation stimulus and a pulsatile stimulus could be very different. This was because a sudden appearance of a flash in darkness produced a large nonlinear response whereas the steady state modulation response had a large proportion of linear component. Apparently, the flash-evoked response largely was composed of nonlinear components. The first-order kernels shown in Fig. 8C, 1 and 2, have an identical waveform but they differ in terms of polarity, as shown in Fig. 8D1, in which four kernels are superimposed for a comparison of their waveform. The polarity of kernels from the OFF cell shown in Fig. 8C2 is reversed. The two sets of kernels match exactly in terms of waveform, implying that the dynamics of ON and OFF noncolor-coded cells shown in Fig. 8 were almost identical. As with the noncolor coded C cell inFig. 3B, the second-order kernels generated by red andgreen stimuli for the cell in Fig. 8 were similar in terms of signature.

The morphology of the cell, as revealed by injection of neurobiotin, that generated the responses shown in Fig. 8, A2 and B2, is shown in Fig. 9. This cell is characterized by a small cell body and extensive tracer coupling of its monostratified dendritic field (Fig. 9). Such a small cell body is usually not distinguishable from the large principal dendrites that emerge to make contact with neighboring cells (Fig. 9). Smaller processes with somewhat larger endings also are seen emerging from secondary dendrites, which do not make any contacts. In this particular case, a single injection of neurobiotin stained >50 cells. Lucifer yellow staining yielded a single well-stained cell surrounded by a few faintly stained cells similar to that in Fig. 5.

View larger version (152K): [in this window] [in a new window]   FIG. 9. Tracer-coupled noncolor-coded N amacrine cells. One of these cells produced the response shown in Fig. 8. These cells have small cell bodies and 2 or 3 principal dendrites, whose diameters do not differ very much from other cell bodies. Demarcation between these 2 parts of the cell is not easy. Small processes with an enlarged ending can be seen emerging from dendrites. All dendrites are in focus, demonstrating that they form a flat monolayer. Bar, 5 µM.

Figure 10 shows an example of a color-coded N amacrine cell. Responses evoked by a red or green pulsatile stimulus given in the presence of steady green or red illumination yielded a series of transient depolarizing peaks (Fig. 10, A and B). These responses evoked by a pulsatile stimulus had no apparent features that indicated the cell's color-coding function. The relative strength of the depolarizing peaks in the red and green responses does, however, suggest that this cell might have been a red-OFF and green-ON cell. The two first-order kernels in Fig. 10C were determined from responses evoked by a red or green white-noise stimulus given alone, namely, without any steady background illumination. The waveforms of the two kernels are almost identical except during the rebound phase. Both kernels have a biphasic waveform, in other words, the linear component produced an initial hyperpolarization followed by a depolarization(-BI). Because the second-order kernels generated either by the red or the green input had a similar signature, the cell's response to a single modulation input was not color coded. Again, the responses shown in Fig. 10, A and B, have no features that suggest a hyperpolarizing phase of the modulation response. Figure 10D shows two kernels evoked by a red and a green stimulus modulated by two independent white-noise signals. The red kernel is identical to that obtained with the red input alone (Fig. 10C). The green kernel, by contrast, is now triphasic with a depolarizing peak, showing that the green stimulus given in the presence of steady or modulated red illumination produced mainly an ON response (Fig. 10D). Note that the amplitude of the green kernel was reduced greatly. The presence of modulating red input decreased the cell's sensitivity to a green input. In Table 1, the triphasic kernel is referred to as a +TRI kernel. The two second-order kernels shown in Fig. 10, E and F, were obtained from the same set of records as those that generated the first-order kernels shown in Fig. 10D. The red second-order kernel shown in Fig. 3B has the four-eye signature characteristic of the C amacrine cells. The green second-order kernel is depicted by a series of peaks and valleys, which indicate the oscillatory nature of the second-order component. In both the red and green second-order kernels, the peaks and valleys are almost circular, and in the case of red kernels, the peaks and valleys occupy four corners of a square the bases of which are parallel to two time axes. Thus unlike those in the catfish retina, some N amacrine cells of the gourami generated second-order kernels with a four-eye (Fig. 10E) or a nine-eye (Fig. 10F) signature. In the latter case, two depolarizing peaks were very small and are not shown in the figure. Both four- and nine-eye kernels can be modeled by a Wiener structure in which a linear dynamic filter is followed by a squaring device. If the linear filter is biphasic as the red first-order kernel in Fig. 10C, the second-order kernel of the resulting model has a four-eye signature. If the filter is triphasic, as the green first-order kernel in Fig. 10D, the second-order kernel of the resulting model has a nine-eye signature. This cell is classified as a N cell because, morphologically, the cell's dendritic field was monostratified (Fig. 11) and, functionally, this cell generated a well defined first-order kernel (Fig. 10, C and D). First-order kernels shown in this figure predicted the cell's modulation response with MSEs of 55-60%. The linear component comprised 40-45% of the total modulation response in terms of MSEs. With regard to the site of generation of four- or nine-eye kernels, there are two possibilities: the second-order kernel might be generated in the N amacrine cell itself by a process similar to that identified in the C amacrine cells or the second-order nonlinearity generated in the C amacrine cells might be transmitted to the N amacrine cells without any further filtering. In this case, there must be a class of C amacrine cells that generate second-order kernels with a nine-eye signature. We have not encountered such C cells so far. We do not have any evidence in favor of either of these possibilities, but current-injection experiments performed on a pair of C and N amacrine cells should provide some clues as to how a four-eye kernel is generated by a N cell. The cell that produced the responses in Fig. 10 is shown in Fig. 11. The asterisk indicates the site of injection of the tracer. The injected cell was identified in Lucifer yellow-stained preparations, but was lost in neurobiotin-stained preparations. The loss of the injected cell occurred quite frequently in our preparations from the gourami (V. Bhanot and K.-I. Naka, unpublished data). However, when the image of the Lucifer yellow-stained cell was superimposed on the injection site, the cell's dendrites matched those of the surrounding cells, confirming our hypothesis that the injected cell was lost during histochemical procedures. The small cell bodies share the characteristics of those shown in Fig. 9. The dendritic fields of these cells are arrayed horizontally relative to the field of vision of the fish, as seen also in the case of some N amacrine cells in the catfish (Naka 1980). This figure shows that the density of N amacrine cell was ~1,500 cells/mm². Often, but not always, we found an array of radiating fibers that originated from the site of injection of the tracer. This array might correspond to the stellate OFF amacrine cell reported by Ammermüler and Weiler (1988) or the A32b amacrine cell of Ammermüler and Kolb (1995). Such radiating fibers were not observed in Lucifer yellow-stained preparations, indicating that the primary site of injection was a N amacrine cell. Another example of the response form a color-coded N amacrine cell is seen in Fig. 12, in which A and B show responses evoked by pulsatile stimuli in the presence of steady illumination with the opposite color. The two responses are almost identical and consist of a series of transient depolarizations. As in most N cells of the gourami, there is no DC component or afterhyperpolarization. Two first-order kernels (Fig. 12C), generated by a red or a green stimulus in the presence of steady green or red illumination are not opposite in polarity, but they differ in terms of waveform, i.e., the response dynamics are different. This observation, together with the similar results in Fig. 10, shows that color-coded signals are processed by a difference in the polarity of the response, as well as by a difference in the dynamics of the response. We will expand on this subject of color coding by means of different response dynamics in our next paper (Sakai et al. 1997b). Figure 12D shows two first-order kernels obtained under similar conditions to those under which the two kernels in Fig. 12C were generated. However, in the experiment for which results are shown in Fig. 12D, both stimuli were modulated by two independent white-noise signals, and the two kernels were measured from a single output response. Compared with the two kernels in Fig. 12C, the red kernel has a larger amplitude and the green kernel is very small. The waveform, as well as the amplitude, of the green first-order kernel changed with the different mode of illumination by the red input. The red input, when it was modulated, reduced greatly the amplitude of the green kernel as we have already shown in Fig. 10D. The horizontal cells displayed no differences in the kernels obtained in two-input white-noise experiments in which one input was held at a steady level or modulated, in other words, there was no cross-talk (dynamic interaction) between the red and green modulation responses in the horizontal cells (Fig. 9 in Sakai et al. 1997a). In the horizontal cells, interaction between the red and green inputs occurs through changes in response parameter. However, in the N amacrine cells, the presence of a modulating response often interfered with the response evoked by the other input. We recall here that a kernel is a measure of incremental sensitivity. Thus the presence of the red modulating input markedly decreased the sensitivity to the green modulating input. Figure 12, E and F, shows two second-order kernels generated by the red or green input that gave the first-order kernels shown in Fig. 12C. The two second-order kernels are very similar, having the characteristic signature of second-order kernels from the NA amacrine cells of the catfish (Fig. 9 in Sakai and Naka 1987a). The peaks and valleys of the kernels are elongated along the axis orthogonal to the diagonal. These kernels have no characteristic feature to indicate that their signature can be related to the color of input. The characteristic signatures of these second-order kernels suggest that generation of the kernels can be modeled by a LNL or sandwich cascade where a static nonlinearity LN, is sandwiched between two linear filters, L (Sakai and Naka 1987b; Victor and Shapley 1979). The first L-LN cascade is the Wiener cascade, which allows us to model the four-eye kernel shown in Figs. 3B and 10E. Transformation of a four-eye kernel into the type of kernel shown in Fig. 12, E and F, is illustrated in Fig. 13 in a companion paper by Sakai et al. (1997b). Results shown in Figs. 10 and 12 show that color information is carried mainly by the first-order component, and the second-order kernel identifies the cell's response to a sudden change in the input, regardless of its color. It is expected that a quadratic function such as a second-order kernel does not identify the polarity of an input.

View larger version (157K): [in this window] [in a new window]   FIG. 11. Low-magnification view of tracer-coupled N amacrine cells. *, location of the cell into which Lucifer yellow and neurobiotin were injected. This cell, which was observed in the Lucifer preparation and lost in the neurobiotin preparation, generated the responses shown in Fig. 10. Major axis of these N cells was aligned parallel to the horizontal plane of the fishes' field of vision. Neurobiotin-injected cell was often lost during preparations of neurobiotin samples, but it was seen in Lucifer yellow-stained preparations. Bar, 30 µM.

Interaction between two inputs

In the horizontal cells, presence of another input, steady or modulated, produced same changes in response parameters. It was the mean luminance, but not modulation, that modified the response evoked by the other input. The two modulation responses added linearly to show that there was no dynamic interaction defined by cross-kernel, h_2xu(₁, ₂) in Eq. 4 in Sakai et al. (1997a). In the amacrine cells, modulation responses produced by one color were different depending on whether the other input (color) was steady or modulated. In the cell illustrated in Fig. 12, a modulation of red stimulus, instead of being held at a steady mean, greatly reduced the amplitude of the green first-order kernel. A modulation of one input affected the incremental sensitivity as well as the dynamics of the response evoked by the other input as measured by the amplitude and waveform of the first-order kernel. Therefore there must be changes in response characteristics induced by the modulation of other input. This dynamic interaction is identified partly by cross-kernel h_2xu(₁, ₂) in Eq. 4 in Sakai et al. 1997a.

Most N amacrine cells generated a well-defined cross-kernel. Two typical interaction kernels from two N amacrine cells are shown in Fig. 13. The cell that produced the kernel shown in A produced a red negative first-order (BI) kernel and a green positive triphasic (+TRI) kernel. The cell that produced the kernel shown in Fig. 13B produced a red negative first-order kernel (BI) and a green negative triphasic (-TRI) kernel. Two cross-kernels shown in Fig. 13, A and B, are not symmetric around the diagonal; this is characteristic of cross-kernels. Self-kernels are symmetric around the diagonal. This is because in a self-second-order kernel, two time axes are interchangeable whereas in the cross-kernel, the two time axes are not interchangeable.

In Fig. 13A, the initial valley (- - -) was produced by an interaction of a red (impulse) response with a latency of 30 ms and a green (impulse) response with a latency of 50 ms. This shows that when a red input preceded a green input by 20 ms, the red stimulus depressed the response. Note that the depressed response could not be assigned uniquely either to the red or green input, but the depressed response was due to the interaction between the red and green inputs. Conversely, when a green input preceded a red input by 20 ms, there would be no interaction. The second peak around the diagonal() shows that a red and a green input given almost simultaneously produced a mutual enhancement of the response with a latency of 55 ms. The complex contour of the positive peak shows that the mutual enhancement was a complex phenomenon. In the cross-kernel shown in Fig. 13B, a red stimulus that preceded a green stimulus by 8 ms depressed the response produced 35 ms after a green stimulus. This mutual depression is depicted (- - -). There was an enhancement of response evoked 35 ms after a green flash and 55 ms after a red flash. This mutual enhancement is depicted (). In Fig. 13, C and D, are cross-kernels from a luminosity and chromaticity horizontal cell, respectively. The two kernels do not show any well-defined peak or valley to show that there was no dynamic interaction between the red and green stimuli as we already have noted (Sakai et al. 1997a).

We have found that the interaction component predicted by the interaction kernel could be as large as 15% of the total modulation response in a MSE sense. We do not know if this interaction is a type of color processing or not, but time relationship between the red and green inputs is an important stimulus parameter. Apparently "processing" of color signals in the bichromatic retina of the gourami is a very complex process.

Classification of amacrine cells on the basis of the waveform of the first-order kernel

Information on color is carried by the polarity as well as the waveform of the green first-order kernel (Figs. 10 and 12), whereas the second-order kernels do not appear to carry a color-coded signal. There was no second-order kernel specific to one color. As shown in Figs. 10 and 12, the N cells generated second-order kernels of different signature. However, we do not know whether N cells could be classified into subclasses based on the signature of second-order kernels.

Color- and noncolor-coded responses from N amacrine cells in the gourami retina, therefore, can be classified on the basis of the waveform of the first-order kernels. The waveforms of most first-order kernels can be classified into two basic types: a biphasic type, BI, and a more complex triphasic type, TRI. Each type can be further divided into depolarizing and hyperpolarizing subtypes. Typical examples of these four types of first-order kernel recovered from ganglion cells are shown in Fig. 10 in the accompanying report by Sakai et al. (1997b). The waveform of the red first-order kernel is robust in the sense that the presence or absence of green illumination does not modify the kernel's waveform. Conversely, the green kernel is labile in the sense that its waveform is modified in color-coded cells by the presence of a red input.

Table 1 shows the classification of the waveforms of first-order kernels from 73 N amacrine cells. These kernels were obtained from two-input white-noise experiments in which the resulting individual responses were decomposed into red and green components by cross-correlation. Here we note that all first-order kernels measured in one-input experiments were biphasic, either +BI or BI regardless of the color of the input. Of the 73 cells, 95% generated red kernels with a biphasic waveform, i.e., red kernels were overwhelmingly biphasic, indicating the robust nature of this waveform. Nearly 53% of the green kernels were biphasic and 40% were triphasic. Approximately 26% of the cells examined were noncolor coded, with the remaining 74% being color coded. As we will discuss in our next paper, complex schemes of color coding can be produced by combining simple template waveforms, namely, biphasic and triphasic waveforms, with different polarities. In Table 1, we classified the N amacrine cells into eight classes on the basis of their first-order kernels. If we consider that there are two major types of second-order nonlinearity as well as the cross-term, classification of N cells based on their color-coded response becomes quite complex.

Summary of the results of white-noise analysis of amacrine cells

Table 2 summarizes the results of white-noise analysis of three classes of amacrine cells in the retina of the gourami: C amacrine cells, red-ON (+BI kernel) N amacrine cell, and red-OFF (BI kernel) N amacrine cells. The MSE of the first-order model is indicated by "MSE1", and the MSE of the second-order model is indicated by "MSE2". The latter includes the first-order as well as second-order components. Table 2 shows that the linear component of the C amacrine cell is <10%, and inclusion of the second-order component improves the MSE by 50%. As we will show later, inclusion of higher-order kernels reduces the MSE to <20%. The majority of the cell's response to a modulating input consists of the second-order component. Because the second kernel is a quadratic function, it does not encode the polarity of the input, such as the response to the opponent color or the center-surround response (Sakai and Naka 1992, 1995). The linear component of N cells accounts for ~40% of the modulated response, and there is no statistically significant difference between red-ON and red-OFF amacrine cells (at P = 0.05). Inclusion of the second-order component improves the MSE of the model by 25%, and, again, there is no statistically significant difference between the second-order MSE of red-ON and red-OFF cells (at P = 0.05). As we will show later, inclusion of higher-order components yielded a MSE for N cells of slightly >20%. Table 2 shows that the classification of amacrine cells into C and N cells on the basis of values of MSE is statistically significant.

	DISCUSSION

Abstract Introduction Methods Results Discussion References

"Their (amacrine cells') exact action and its effects on visual phenomena are about the biggest remaining mystery in the physiology of the retina." Walls (1963) wrote this statement >30 years ago, and even now this statement has some validity (Morgan 1992). There have been numerous studies of the morphology, immunochemistry, and flash-evoked responses of amacrine cells, but no clear picture of the basic network function of the cell has emerged. The role of these cells in the formation of the receptive field remains unknown. The lack of knowledge on the cell's function is partly due to the fact that, except for the directionally sensitive amacrine cells, the functional relationship between amacrine and ganglion cells remains unresolved. Moreover, the mode of signal transmission from amacrine cells to ganglion cells remains unknown in most retinae so far studied. The presence of amacrine cells of similar morphology, as well as physiology, in many species indicates that these cells play a key and basic role in signal processing in the retina. In the catfish, three basic functions of amacrine cells have been proposed by Sakai and Naka (1988, 1992). They are: generation of characteristic second-order nonlinearities in C amacrine cells, formation of a concentric field by the linear components in the N amacrine cells, and introduction of faster components in the response in the N cells by means of a fast biphasic (differentiating) linear filter. But these functions are yet to be identified in other retinas.

Flash-evoked response versus the modulation response

As predicated by Walls, amacrine cells have presented vision scientists with a bewildering assortment of morphological features as well as complex flash-evoked responses that have been documented extensively in many past studies (Ammermüler and Kolb 1995; Bloomfield 1992; Chino and Hashimoto 1986; Dacheux and Raviola 1986, 1995; Djamgoz et al. 1989; Freed et al. 1996; Kato et al. 1991; Kolb and Nelson 1996; Peters and Masland 1996; Taylor 1996; Teranishi et al. 1987; Zhou and Fain 1996). The complexity, in addition to the limited range of response amplitudes of flash-evoked responses from amacrine cells, renders analysis of these cells' responses far more difficult than the analysis of the horizontal cell's responses, which are characterized by a large amplitude, a monotonic waveform, and lack of complex transient components. The amplitude of a flash-evoked response has served as a satisfactory measure for characterization of the horizontal cell's response. However, in the amacrine cell, a 1,000-fold change in the magnitude of the stimulus produces less than a fivefold change in the amplitude of the step-evoked response, and the waveform of the response changes dramatically when the magnitude of a pulsatile input is changed (Djamgoz et al. 1990). Responses are classified on the basis of simple static quantities such as sustained and transient or depolarizing and hyperpolarizing, although the waveforms of responses evoked by a pulsatile stimuli given in darkness appear to be quite complex (Ammermüller and Kolb 1995). The dynamic aspects of the amacrine cell's response largely have been ignored although the cell's response to modulation has been shown to be very dynamic. Results of all past studies agree on one point, that the amacrine cell responds to the modulation component of an input. The linear and nonlinear analytic techniques that have proven so valuable in the study of spike discharges from ganglion cells or postganglionic cells (DeAngelis et al. 1995; Reid and Shapley 1992; Schellart and Spekreijse 1972; Victor and Shapley 1980) have not been applied to amacrine cells. Had such analytic techniques been applied in the past, the responses of amacrine cells in other retinae could have been better categorized and quantified on the basis of the dynamics of their modulation responses. There are several putative reasons for the lack of prior interest in the systems approach to the analysis of amacrine cells. First, the waveform of the cell's response evoked by a pulsatile stimulus, in particular that of the sustained cell, is complex, and linear analysis might not be able to identify a significant part of the response. Second, the cell is thought to perform a specialized function such as indicated by the asymmetric receptive field (Naka 1980) or the directional sensitivity (Bloomfield 1992) that cannot be identified by generalized analytic methods such as white-noise analysis. For example, in the turtle retina, amacrine cells were classified into 36 types to demonstrate that the cells might be involved in just as many specialized functions (Ammermüller and Kolb 1995). The functional identification of so many diversified types of cell is clearly beyond our present analytic capacity.

In this study, we showed that a response evoked by a pulsatile stimulus, in particular the response from a N amacrine cell, can be very complex, as already has been well documented by many authors who studied so-called sustained amacrine cells. Responses evoked by a sinusoid or a white-noise input, by contrast, were much simpler in terms of waveform and could be accounted for largely by lower-order kernels. Often, but not always, there was no direct correlation between the waveforms of responses evoked by a pulsatile and a modulation input. A cell's response evoked by a pulsatile input could be a series of depolarizing transients without any sign of a hyperpolarizing component. However, the cell's first-order kernel could be biphasic with an initial hyperpolarizing phase. The first-order component predicts a cell's response with a MSE of nearly 60%. In other words, ~40% of the modulation response is accounted for by the first-order component (Table 2). Therefore, a large hyperpolarizing component must exist in the modulation response. A flash of light in darkness rarely occurs in nature. Animals are exposed most often to modulations of a mean luminance, and the response evoked by such a stimulus is a steady state response, as we would anticipate. In a report by Skottun, de Valois, Grosof, Movshon, Albrecht, and Bonds (1991), the authors wrote " ... the use of relative modulation to classify cells has much to recommend it, and we would commend its use to those who seek a rapid and reliable way to categorize neurons in the striate cortex." There is no reason that this view cannot be applied to retinal amacrine cells, and we have done so in this study.

Tracer coupling of amacrine cells

It has been known for some time that amacrine cells are coupled morphologically as well as functionally. Naka and Christensen (1981) showed that the C amacrine cells in the catfish retina are coupled morphologically through gap junctions and functionally form a space, similar to the S space formed by horizontal cells (Naka and Rushton 1967). Accordingly, there is no (electrical) filtering among C cells, and the spread of current in the space formed by C cells is instantaneous within the temporal resolution of our measurements as it is in the S space (Sakuranaga and Naka 1985). Bidirectional electrical coupling also has been observed between N amacrine cells and between N cells and ganglion cells in the catfish, but such transmission is not instantaneous (Sakai and Naka 1990a). Transmission that is linear is identified by first-order kernels with a measurable but short transport delay or peak response time.

Negishi and Teranishi (1990) injected Lucifer yellow into the interstitial and normally placed amacrine cells in the carp retina and found that several neurons were dye-coupled. The morphology of the amacrine cells reported by Negishi and Teranishi that produced an ON-OFF transient depolarizing response is very similar to that of the N amacrine cells in the gourami, although the gourami's cells had stubbier dendrites. Djamgoz et al. (1989) also reported a class of amacrine cells with similar morphology in the goldfish retina, and a flash stimulus generated a sustained response from these cells. All these amacrine cells had a monolayered dendritic field, which was confined to a narrow stratum in the inner plexiform layer. By injection of biocytin or neurobiotin, Vaney (1991, 1994) showed that a large number of cells of similar type, including amacrine cells, were tracer coupled. Teranishi and Negishi (1994) observed, using neurobiotin, that the majority of amacrine cells that belong to certain similar types were morphologically coupled. Gap junctions also have been observed between amacrine cells in other retinae (Hidaka et al. 1993; Marc et al. 1988). These observations on the tracer coupling of amacrine cells in various types of retina cannot be dismissed simply as artifacts (Vaney 1994); there must be reasons that explain why amacrine cells and, in particular N cells, are extensively tracer-coupled as we have shown in this paper.

C amacrine cells

Since the first description of transient amacrine cells by Kaneko and Hashimoto (1969), transient amacrine cells have been observed in the retinae of most of vertebrate studied to date. For example, transient amacrine cells have been found in the rabbit (Dacheux and Raviola 1995), the goldfish (Djamgoz et al. 1990), the turtle (Ammermüler et al. 1995), and the cat (Freed et al. 1996). All these transient amacrine cells, except in the rabbit (Dacheux and Raviola 1995) and cat (Freed et al. 1995), generated transientON-OFF depolarizing responses to most stimuli and had a bistratified dendritic field. All transient or C amacrine cells have a large receptive field without any specialized spatial structure. Some authors (Djamgoz and Ruddock 1983) have observed that the sustained component in the transient response is color coded, whereas others (Kato et al. 1991) have observed that the transient amacrine cell is not color coded. Although the responses evoked by a red or green stimulus were different in some respects, the responses were all transient depolarization. It appears, then, as if the cell's primary function is to detect changes around a mean luminance regardless of the color of the input. This view is supported by many of the results cited above for this type of cell since its discovery by Kaneko and Hashimoto (1969). Sakai and Naka (1992) reported that both a spot and an annular stimulus produced only a transient depolarization in the C amacrine cells of the catfish. Figure 2A bears a striking resemblance to an earlier figure that was generated by spot or annular flashes and was published by Sakai and Naka in 1992 (Fig. 10 in Sakai and Naka 1992). The earlier data also showed that the second-order kernel generated by an annular input was slightly low-pass, i.e., the second-order kernel generated by the receptive-field center could be modeled by a Wiener cascade, L-N structure, whereas that generated by the surround was modeled by a sandwich cascade, L-NL structure. Similarly, in the gourami C amacrine cells, different cascade structures account for the red and green second-order kernels from C amacrine cells; and a similar observation has been made for kernels from some ganglion cells (Fig. 3 in Sakai et al. 1997b). We do not know whether this difference could represent a means of processing and signaling color.

N amacrine cells

The N amacrine cells in the gourami correspond roughly to the sustained amacrine cells in other retinae (Djamgoz et al. 1990; Kaneko 1970; Murakami and Shimoda 1977). N cells are characterized functionally by the presence of a well-defined first-order component in the responses evoked by a white-noise stimulus. This component accounts for ~40% of the total response in terms of MSE (Table 2). The morphology of the N cell or sustained amacrine cell is characterized by a monolayered dendritic field (Djamgoz et al. 1990; Murkami and Shimoda 1977; Naka et al. 1975). In the gourami, these cells are further defined by extensive tracer-coupling between their stubby dendrites.

N amacrine cells in the gourami differ from those in the catfish in that the cells of the gourami do not generate any DC potential in response to steady illumination, whereas the N cells of the catfish do (Fig. 2 in Sakai and Naka 1992), and no cells produce sustained hyperpolarization during illumination. Judging from the large number of N cells that we have examined, we do not think that this result represents an experimental oversight. Except in a few cases, there was no hyperpolarization after the OFF set of a flash. The records shown in Fig. 8 are an example of one such exceptional case. In ~23% of the N cells studied, the first-order kernel showed an initial hyperpolarization and are classified as BI in Table 1. The +BI and BI first-order kernels are similar to the first-order kernels of the catfish NA (depolarizing) and NB (hyperpolarizing) amacrine cells. The absence of the hyperpolarizing potential in the response to a pulsatile stimulus was due to the fact that such a flash-evoked response was dominated by nonlinear components. In the retina of the gourami, it was not always possible to identify, from flash-evoked responses, whether a N cell was color coded or not. No apparent color-dependent difference was seen when responses were evoked by flashes given in darkness or even in the presence of steady illumination with light of opposing color. Only a modulation response clearly revealed color coding in a cell. In the gourami amacrine cells, only modulation response appears to contain a linear component.

Traditionally, the coding of color information is analyzed on the basis of the hypothesis that one color produces a positive (depolarizing or spike-frequency increasing) response, whereas an opposing color produces a negative (hyperpolarizing or spike-frequency decreasing) response. In the amacrine cells of the gourami, we found that color information was carried by the polarity as well as by the dynamics of the response. The first-order kernels evoked by the red and green stimuli might have had different waveforms to indicate that response dynamics also are related to the color of the input. The complex nature of responses from color-coded amacrine cells is well documented in past studies (Ammermüller and Kolb 1995). Color coding does not necessarily involve a comparison of the polarity of responses, but stimuli of different colors might produce responses with different dynamics. Such is the case for the color-coded responses from gourami ganglion cells (Sakai et al. 1997b). To date, this type of coding of information has not been reported in visual systems. We will discuss, in the following paper (Sakai et al. 1997b), the dynamic interaction between the responses evoked by a simultaneous stimulation by red and green lights.

	ACKNOWLEDGEMENTS

  The authors thank V. Bhanot for editorial assistance.

  This research was supported by National Institutes of Health Grants EY-07738 (K.-I. Naka), EY-08848 (H. M. Sakai), and NS-30772 and National Science Foundation Grant BNS891993. K.-I. Naka thanks Research to Prevent Blindness, New York, NY, for the Jules and Doris Stein professorship and Thudichum Medical Institute, Sakai, Japan, for financial assistance.

	FOOTNOTES

  Address for reprint requests: K.-I. Naka, Dept. of Ophthalmology, New York University Medical Center, 550 First Ave., New York, NY 10016.

  Received 15 April 1997; accepted in final form 15 May 1997.

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