Processing of Color- and Noncolor-Coded Signals in the Gourami Retina. III. Ganglion Cells

Hiroko M. Sakai1, Hildred Machuca1, Michael J. Korenberg3, and Ken-Ichi Naka1, 2

1 Departments of Ophthalmology and 2 Physiology and Neurosciences, New York University Medical Center, New York, New York 10016; and 3 Department of Electrical and Computer Engineering, Queen's University Kingston, Ontario, K7L 3N6 Canada

    ABSTRACT
Abstract
Introduction
Methods
Results
Discussion
References

Sakai, Hiroko M., Hildred Machuca, Michael J. Korenberg, and Ken-Ichi Naka. Processing of color- and noncolor-coded signals in the gourami retina. III. Ganglion cells. J. Neurophysiol. 78: 2034-2047, 1997. The dynamics of intracellular responses from ganglion cells, as well as that of spike discharges, were studied with the stimulus regimens and analytic procedures identical to those used to study the dynamics of the responses from horizontal and amacrine cells (Sakai et al. 1997a,b). The stimuli used were large fields of red and green light given as a pulsatile input or modulation about a mean luminance by a white-noise signal. Spike discharges evoked by a white-noise stimulus were analyzed in exactly the same manner as that used for analysis of analog responses. The canonical nature of kernels allowed us to correlate the first- and second-order components in a spike train with those of the intracellular responses from horizontal, amacrine, and ganglion cells. Both red and green stimuli given alone in darkness produced noncolor-coded responses from all ganglion cells. In the case of some cells, steady red illumination changed the polarity or waveform of the response to green light. Color-coded ganglions responded only to simultaneous color contrast. Nonlinearities recovered from intracellular responses, and spike discharges were similar to those found in responses from amacrine cells and were of two types, one characteristic of the C amacrine cells and the other characteristic of the N amacrine cells. The first-order kernels of most ganglion cells could be divided into two basic types, biphasic and triphasic. The combination of kernels of these two basic types with different polarities can produce a wide range of responses. Addition of two types of second-order nonlinearity could render color coding in this relatively simple retina as an extremely complex process. Color information appeared to be represented by the polarity, as well as the waveform, of the first-order kernel. The response dynamics is a means of transmission of color-coded information. Second-order components carry information about changes around a mean luminance regardless of the color of an input. Some spike discharges produced a well-defined cross-kernel between red and green inputs to show that a particular time sequence of red and green stimuli was detected by the retinal neuron network. The similarity between signatures of second-order kernels for both amacrine and ganglion cells indicates that signals undergo a minimal transformation in the temporal domain when they are transmitted from amacrine to ganglion cells and then transformed into a spike train. Under our experimental conditions, a single spike train carried simultaneously information about red and green inputs, as well as about linear and nonlinear components. In addition, the spike train also carries a cross-talk component. A spike train is a carrier of multiple signals. Conversely, many types of information in a stimulus are independently encoded into a spike train.

    INTRODUCTION
Abstract
Introduction
Methods
Results
Discussion
References

Spike trains from retinal ganglion cells are the end products of signal processing in the retina. Because of their importance, the spectral characteristics of ganglion cells have been studied extensively. Granit (1955) established a paradigm for such studies, and many similar studies have been reported. The organization of a receptive field with respect to the spectral stimulus is also of interest (Daw 1968). Many types of color-coded receptive field have been discovered, such as the double opponent field. The most recent example can be found in the report by Ammermüller, Muller, and Kolb (1995).

In this study, we examined the dynamics of color processing in ganglion cells by using a white-noise method identical to that used in our two previous studies. Intracellular responses and spike discharges from ganglion cells can be identified by a series of kernels, which can be referenced directly to similar kernels from horizontal cells (Sakai et al. 1997a) and amacrine cells (Sakai et al. 1997b). This direct comparison between the slow potential response and spike discharges is possible because of the canonical nature of kernels.

In this study, as in our two previous studies (Sakai et al. 1997a,b), both intracellular and extracellular recorded responses were decomposed into components evoked by red and green stimuli, and each component was decomposed further into linear and nonlinear components. Our extension of white-noise analysis to spike trains, a point process, in contrast to the analog processes as prescribed by Wiener's original theory (Wiener 1958), is based on our heuristic finding that direct, forward cross-correlation between an analog input and a point-process output produces first- and second-order kernels similar to those recovered from an analog process (Sakuranaga et al. 1987). This phenomenon occurs because the process of spike generation is highly nonlinear but approximately static (Korenberg et al. 1989). As in the case of amacrine cells (Sakai et al. 1997b), information about color in ganglion cells is carried mainly by the first-order component and is probably not carried by the second-order component. Stimuli of different colors generate first-order kernels with different waveforms and polarity, whereas the signature of second-order kernels is mostly independent of the input color. Some spike trains produced a well-defined cross-kernel to show that a serial time relationship between red and green inputs is detected. Therefore, response dynamics play a significant role in the processing of color in ganglion cells. Comparison of kernels measured from amacrine and ganglion cells indicates that there is little filtering of signals when signals generated in the amacrine cells are transformed into a spike train. Functional evidence to support this hypothesis has been obtained from studies of the catfish retina (Sakai and Naka 1990).

Our previous studies (Naka and Sakai 1991; Sakai and Naka 1995) and this present series show that a response from neurons in the inner retina contains many components that are combined into a response that includes a spike train. Many types of information in a stimulus are encoded into a single response in cortical neurons, as found by McClurken, Optican, Richmond, and Gawne (1991) and by McClurkin and Optican (1996). Information also can be carried by the time relationships among spikes as indicated by the presence of a well-defined second-order and cross-component in a spike train (Meister et al. 1995).

    METHODS
Abstract
Introduction
Methods
Results
Discussion
References

We used the eye-cup preparation of the kissing gourami, Helostoma rudolfi, for all experiments, and all methods including stimulation and data analysis were identical to those found in the two companion papers (Sakai et al. 1997a,b). In this study, extracellular discharges from ganglion cells were recorded with a tungsten electrode. We used a DAM 50 amplifier (WPI Instruments, Sarasota, FL) as an impedance converter.

Intracellular responses from ganglion cells were analyzed by standard procedures because the spike discharges recorded intracellularly from the ganglion cells of the gourami were usually much smaller in amplitude than the synaptic (analog) potential. Therefore, we did not try to separate the analog and spike components in each ganglion cell's response (cf. Sakuranaga et al. 1987). As in the studies described in the two preceding papers (Sakai et al.1997a,b), we dissected each response into components generated by the red (RF) and green (GF) inputs and then further into linear and second-order components by cross-correlation (Fig. 1A). In the case of extracellular recordings, spike discharges were transformed into unitary pulses of 2 ms in duration, and forward cross-correlation was made with our standard software systems for Wiener analysis, STAR, (Spatio-temporal Analysis Routines) or with the PC-DOS version of the STAR software. In two-input white-noise experiments, as in the analog output experiments, a spike train was dissected into components evoked by the red (RF) and green (GF) inputs (Fig. 1B). Each component was further dissected into the linear and second-order components. Cross-kernels also were measured. The first-order kernels generated by this method are similar to those recovered by the reverse correlation method (de Boer and Kuyper 1968). Both forward and reverse correlation methods avoid the artificial process of assigning spikes to a bin, the method employed in the popular poststimulus time (PST) histogram approach (Gerstein and Kiang 1960).


View larger version (30K):
[in this window]
[in a new window]
 
FIG. 1. Schematic representations of 2-input white-noise experiments with 2 types of output, an analog response and a spike discharge (a point process). Inputs are 2 overlapping large fields of red (RF) and green (GF) lights that covered the entire surface of the retina. Cross-correlation between the 2 inputs and 1 output decomposes the response into the 2 components evoked by the red and green inputs. Same algorithms were used for both the analysis of the analog and spike responses. Self-kernels, the first- and second-order kernels, and cross-kernel were measured from a simple spike train.

Our spike analysis is based on two heuristic findings: white-noise analysis of both synaptic (analog) responses and spike discharges (point-processes) generates similar first- and second-order kernels (Sakuranaga et al. 1987) and the process of spike generation is highly nonlinear but approximately static (Korenberg et al. 1989). In the past, we have used this approach to study the dynamics of receptive-field components (Sakai and Naka 1995) as well as contrast sensitivity (Sakai et al. 1995). As in the two companion papers, the depths of modulation of the red and green inputs were adjusted such that the magnitudes of responses evoked by the two inputs were similar. This procedure was justified because kernels are a measure of sensitivity, adjusted to the power of an input (cf. Eq. 5 in Sakai et al. 1997a), and waveforms of both first- and second-order kernels, including those from a spike train, are identical over a large range of depths of modulation (Sakai et al. 1995). Contrast gain control operates only on a kernel's amplitude (contrast sensitivity) and not on its waveform (dynamics); response dynamics depend only on mean luminance and not on the depth of modulation (cf. Shapley and Victor 1981).

Predictive capacity of kernels

In the case of an analog output, the predictive capacity of kernels can be measured by the mean square error (MSE) of the predicted response in relation to the actual response (see Fig. 10 in Sakai et al. 1997a and Figs. 2 and 5 in Sakai et al. 1997b). This method is not applicable to spike discharges because a spike train is a point process, although exceptions exist where spike discharges were transformed into a PST histogram (Marmarelis and Naka 1973; Pöpel and Eckhorn 1981). Figure 2 shows an attempt to examine the accuracy of the predictions by kernels in the case of a spike train output. Figure 2A is a 9-Hz sinusoidal modulation around a mean; Fig. 2B is the linear prediction, a 9-Hz sinusoid; Fig. 2C is the frequency-doubling second-order prediction; and Fig. 2D is the PST histogram of the spike discharges evoked by the sinusoidal input shown in Fig 2A. The dashed line in Fig. 2D depicts the second-order model, which is the sum of the first-order (Fig. 2B) and second-order (Fig. 2C) predictions. The model was produced by finding the optimal ratio of the first- and second-order components and by establishing an arbitrary threshold to remove the negative part of the prediction. Introduction of an arbitrary threshold can be justified by the fact that the transformation of a slow potential into a spike discharge is a high-order nonlinearity but is approximately static. The fit of the model is reasonably good, although the second-order model fails to mimic the oscillation. Such was also the case for the modeling of an analog response (Fig. 2 in Sakai et al.1997b). Most of the PST (Figs. 6 and 9) histograms that we obtained from spike trains were less complex than that shown in Fig. 2D, suggesting that first- and second-order kernels, with the possible inclusion of higher-order kernels, might describe adequately the dynamics of a spike train. Although the responses evoked by a flash given in darkness are complex, the responses evoked by modulation of a mean luminance tend to be much simpler in terms of waveform as we already discussed (Sakai et al. 1997b).


View larger version (29K):
[in this window]
[in a new window]
 
FIG. 10. First-order kernels obtained from intracellular responses (left) and spike discharges (right). All kernels were generated by a red stimulus in the presence of steady green illumination. Four typical examples from 4 different cells are shown for each type. A1 and B1 are biphasic, +BI, kernels. A2 and B2 are biphasic, -BI, kernels. A3 and B3 are triphasic, +TRI, kernels. A4 and B4 are biphasic, -TRI, kernels. With the exception of the +TRI kernels, kernels obtained from intracellular responses, analog processes, and spike discharges, point processes, are similar. There seems to be no modification of dynamics during the generation of spike discharges.


View larger version (39K):
[in this window]
[in a new window]
 
FIG. 2. Prediction of a response by first- and second-order kernels derived from a spike train. A: input, 9-Hz sinusoids, with a depth of modulation of 36%. B and C: model response to the sinusoid input as indicated by the first- and second-order kernels. D: poststimulus time (PST) histogram(------) and the sum of the 2 model (- - -) responses shown in B and C. Summed model response was fit to the PST histogram by setting an arbitrary threshold. This manipulation is justified by the fact that the higher-order nonlinearity found in the generation of spike discharges is approximately static (Korenberg et al. 1989). The model (- - -) resembles the real response (------) although the model fails to predict the oscillation. D shows that oscillations are synchronized with the input. Calibration bar: 200 spikes/s.


View larger version (27K):
[in this window]
[in a new window]
 
FIG. 5. White-noise experiments performed on the cell the pulsatile-stimulus-evoked responses of which are shown in Fig. 4. A1: 2 red first-order kernels evoked by the red input (- - -) alone and in the presence of steady green illumination (------), respectively. Kernels have an identical waveform and identical amplitude. Red kernel units are 1.3 × 10-7 photons·mm-2·s-1. B1: 2 green kernels evoked by the green input alone and in the presence of steady red illumination, respectively. Red steady illumination reversed the polarity of the green kernel, as in the case of the flash-evoked response shown in Fig. 4B2. Green kernel units are 0.8 × 10-7 mV·photons·mm-2·s-1. A2 and A3: red second-order kernels evoked by the red input alone and in the presence of steady green illumination, respectively. B2 and B3: green second-order kernels evoked by the green input alone and in the presence of steady red illumination, respectively. All second-order kernels share a signature that is characteristic of the NB amacrine cells of the catfish. Green second-order kernel generated in the presence of steady illumination has a longer transport delay of 20 ms.


View larger version (16K):
[in this window]
[in a new window]
 
FIG. 6. PST histograms of spike discharges evoked by red and green pulsatile stimuli. A, 1 and 2: red PST histograms evoked in darkness and in the presence of steady green illumination, respectively. B, 1 and 2: green PST histograms evoked in darkness and in the presence of steady red illumination, respectively. Results in B2 show that the polarity of the green response was reversed in the presence of steady red illumination. Latency of the OFF response in A1 is 40 ms whereas that in A2 is 20 ms as in B1. Latency of the ON response in B2 is 50 ms.


View larger version (18K):
[in this window]
[in a new window]
 
FIG. 9. Spike discharges from 3 color-coded ganglion cells. Responses shown here as PST histograms were generated by a red or green pulsatile stimulus in the presence of steady green or steady red illumination. A, 1 and 2: responses from a red-ON and green-OFF cell. B, 1 and 2: responses from a red-OFF and green-ON cell. C, 1 and 2: responses from a red-OFF and green-ON cell. Oscillatory nature of the response suggests that the green first-order kernel generated by this cell is triphasic, namely, it is a +TRI kernel.

Fast orthogonal search

We have examined the frequency characteristics of first-order kernels by the fast orthogonal search (FOS) method developed by Korenberg (1989). Use of this method has been beneficial because of its robustness to noise contamination and its capability of providing measures of the complexity of kernel waveforms. The method's frequency discrimination is four to five times that derived from the standard discrete Fourier transform. Details of the methodology of applying FOS to study the vertebrate retina can be found elsewhere (Korenberg et al. 1966).

A FOS model of a given time series, e.g., a first-order kernel, is a concise sinusoidal model that consists of the sum of the most significant sine and cosine terms. In the FOS model, the frequencies and coefficients of the sine and cosine terms are estimated by minimizing the MSE between the time series, namely, the first-order kernel, and the model. In this study, we used two measures extracted from first-order kernels: the preferred frequency, namely, the single sinusoidal frequency that provided the best fit, in the least-squares sense, to a kernel, and the number of sinusoids required to reproduce the waveform of a kernel to within an accuracy of 0.2%.

Statistical analysis

Statistical analysis was performed using SigmaStat (Jandel, San Rafael, CA). For comparison of two groups of numbers, the P value was set at 0.05 for variance, normalcy was set at 0.05 and a t-test was made.

    RESULTS
Abstract
Introduction
Methods
Results
Discussion
References

Intracellular recordings

Most ganglion cells were identified from their morphological characteristics, namely, a cell body located in the ganglion cell layer, a large and often round cell body, and slender and tapering principal dendrites. Tracer coupling was far less extensive than in the amacrine cells (Sakai et al. 1997b). Ganglion cells, therefore, can be identified easily from their morphology in both Lucifer yellow- and neurobiotin-stained preparations. In terms of function, the identification of a ganglion cell was less obvious because the spike discharges often had small amplitudes, mostly <5 mV, and the responses of ganglion cells were very similar to those of amacrine cells. The intracellular responses analyzed in this study were all recorded from morphologically identified cells. The responses of all ganglion cells evoked by either a red or green stimulus given in darkness were indistinguishable from one another, as was the case for N amacrine cells (Sakai et al. 1966b). In the presence of steady red illumination, a green stimulus evoked a response from some cells that differed from the response evoked by a green stimulus alone (Figs. 4 and 6). Ganglion cells, therefore, can be classified into two broad classes, color and noncolor coded, generated on the basis of their responses to green stimulus in the presence of a steady red stimulus.


View larger version (24K):
[in this window]
[in a new window]
 
FIG. 4. Responses evoked by pulsatile stimuli from a color-coded ganglion cell. Responses shown in A1 and B1 were evoked by red and green pulsatile stimuli given alone. Responses shown in A2 and B2 were evoked by red and green flashes given in the presence of steady green or red illumination. Presence of steady red illumination converted the response to a green pulsatile stimulus from an OFF to an ON response.

Figure 3 shows an example of a noncolor-coded ganglion cell. The cell produced a transient depolarization in response to any changes (brightening or dimming) produced by red or green stimulation. Although the details of the transient depolarizing responses evoked by a red or a green flash differed (Fig. 3A), the essential features of all responses were similar. The cell did not generate any DC potential during steady illumination. The patterns of responses of this ganglion cell were similar to that of the C amacrine cell shown in Fig. 3 in an accompanying paper by Sakai et al. (1997b). The difference between the amacrine cell and this ganglion cell was that the latter produced clearly defined first-order components. The first-order kernels from this cell, evoked by red and green white-noise stimuli in the presence of steady green or red illumination, are shown in Fig. 3B, in which both kernels are hyperpolarizing. These kernels will be referred to as negative biphasic (-BI) kernels. The flash-evoked responses indicate that this cell can be classified as a transient ON-OFF cell. However, from the waveform of the first-order kernels, this cell can be classified as an OFF cell. Although there is no trace of hyperpolarizing component in the responses evoked by pulsatile stimuli, the modulation responses had a considerable amount of linear component. The red second-order kernel, shown in Fig. 3C1, has a typical four-eye signature, in which the peaks and valleys occupy the four corners of a square, and the contours of both the peaks and valleys are approximately circular. Although the signature of the green second-order kernel, shown in Fig. 3C2, is also four eye, contours of the peaks and valleys are not circular but are elongated along the diagonal. These characteristics suggest, as in the case of the C amacrine cell shown in Fig. 5 of the report by Sakai et al. (1997b), that a low-pass filter transformed the original red four-eye structure into the signature of the green second-order kernel, as illustrated in Fig. 13. The generation of the red kernel shown in Fig. 3C1 can be modeled by a Wiener cascade, L-NL, where L is a dynamic linear filter and NL is a static nonlinearity, whereas the generation of the green kernel shown in Fig. 3C2 can be modeled by a sandwich cascade, L-NL-L (Victor and Shapley 1979a,b). The green kernel has a longer transport delay of 5 ms. The two kernels could be superposed by shifting one kernel along the diagonal by 5 ms. A second-order kernel with a characteristic four-eye signature was generated both by C amacrine cells (Fig. 5 in Sakai et al. 1997b) and by some N amacrine cells (Fig. 10 in Sakai et al. 1997b). As in the case of C amacrine cells, we cannot rule out the possibility that the presence in the green kernel or absence in the red kernel of an extra low-pass filter is related with the processing of color information. C amacrine cells generated only a small linear component, and the first-order kernels were noisy (Fig. 3A in Sakai et al. 1997b), whereas the ganglion cells and N amacrine cells generated well-defined first-order kernels (Figs. 3B and 10, C and D, in Sakai et al. 1997b). In the case of C amacrine cells, the MSE accounted for by the linear model was ~10% (Table 2 in Sakai et al. 1997b) whereas, for the present ganglion cell shown in Fig. 3, the linear component accounted for 45% of the entire modulation response. The presence of a large linear component shows that a steady state modulation response could be very different from a nonsteady state response evoked by a pulsatile stimulus, as we have shown already in a preceding paper (Sakai et al. 1997b). There is no indication of the presence of a large, hyperpolarizing linear component in the transient ON-OFF depolarizing responses evoked by pulsatile stimuli (Fig. 3A).


View larger version (23K):
[in this window]
[in a new window]
 
FIG. 3. Intracellular recording from a noncolor-coded ganglion cell. A: a series of responses evoked by red (bottom) and green (top) inputs. Cell responded with a transient depolarization to any change, regardless of color, of dimming or brightening or of the presence or absence of steady illumination. Depolarizing peaks evoked by red stimuli are larger than those evoked by green stimuli. Presence of steady illumination did not produce any change in membrane potential although the ON and OFF sets of such illumination produced transient depolarization. Spike discharges of smaller amplitude are seen superposed on a large postsynaptic potential, as is characteristic of the intracellular response of ganglion cells of the gourami. In A, red luminance was 1.9 × 1011 photons·mm-2·s-1 and green luminance was 9 × 1011 photons·mm-2·s-1. B: red (------) and green (- - -) first-order kernels. Both kernels are hyperpolarizing, indicating that this cell was an OFF noncolor-coded cell. Mean square error (MSE) of linear components predicted by these kernels was ~40%. Units for the red first-order kernel are 1.3 × 10-7 mV·photons·mm-2·s-1. Green kernel was normalized in respect to the red kernel. C, 1 and 2: red and green second-order kernels. Red kernel has a characteristic "4-eye" signature. This second-order nonlinearity can be modeled by a Wiener cascade in which a linear component is followed by a static nonlinearity that is approximated by a squaring device. Green kernel also has a 4-eye signature, but the peaks and valleys are elongated along the diagonal. Two second-order kernels can be superposed by shifting 1 kernel by 5 ms along the diagonal.


View larger version (36K):
[in this window]
[in a new window]
 
FIG. 13. Transformation of a second-order kernel. A: a second-order kernel with a 4-eye signature. Response that generated this kernel was convoluted by a filter the impulse response of which is shown in D(------). New second-order kernel in B was computed by cross-correlating the original input against the filtered response. Transformed kernel is similar to the second-order kernel shown in Fig. 3C2. Kernel shown in C was generated by convoluting the original response by a filter whose impulse response is shown in D (- - -). New kernel's signature resembles that of the kernels of some N amacrine cells.

 
View this table:
[in this window] [in a new window]
 
TABLE 2. Frequency characteristics of first-order kernels from horizontal, amacrine, and ganglion cells measured by Korenberg's FOS method

Figure 4 shows the responses from a color-coded ganglion cell. Records in Fig. 4, A1 and B1, were evoked, respectively, by a red and a green pulsatile stimulus given alone. Both responses are hyperpolarizing with a transient depolarization at the OFF-set of the flash. Records in Fig. 4, A2 and B2, were evoked, respectively, by a red and a green pulsatile stimulus given in the presence of steady green or steady red illumination. The response to a red pulsatile stimulus was identical whether it was evoked in darkness or in the presence of steady green illumination (Fig. 4A, 1 and 2). However, the latency of OFF transient depolarization differed. The latency was 40 ms when the response was evoked by the red stimulus given alone and was 20 ms when the stimulus was given in the presence of a steady green illumination. This shortening of latency was probably due to the field (light) adaptation induced by the presence of a green steady illumination. The latency of the green OFF transient depolarization was 20 ms. The green pulsatile stimulus given in the presence of steady red illumination produced a response that was very different from the one produced by a green stimulus given alone in darkness (Fig. 4B, 1 and 2). The green response became an ON-depolarizing transient with a prolonged hyperpolarization phase at the OFF-set of the flash (Fig. 4B2). The latency of the ON depolarization was 50 ms. A color-coded response was evoked by a green input in the presence of red illumination, as was the case in N amacrine cells (Sakai et al. 1966b).

The results of white-noise analysis of this cell are shown in Fig. 5. The red first-order kernels (Fig. 5A1), generated by the red input alone or in the presence of steady green illumination, are identical in amplitude and waveform, confirming our observations made on the pulsatile-stimulus-evoked responses (Fig. 4A, 1 and 2). Note that these +BI kernels are similar to those shown in Fig. 3B although the former were from a "transient" cell and the latter were from a "sustained" cell. The green first-order kernel (Fig. 5B1) generated in darkness is initially hyperpolarizing, but its polarity changes in the presence of steady red illumination. The green first-order kernel is now triphasic. This kernel will be referred to as a positive triphasic (+TRI) kernel because of the presence of an initial hyperpolarizing phase, albeit, of small amplitude. The second-order kernels generated by a red input have a similar signature irrespective of whether the kernel is generated by a red stimulus given alone in darkness or in the presence of steady green illumination (Fig. 5A, 2 and 3). The alternating peaks and valleys are elongated orthogonal to the diagonal. The kernel corresponds to kernels that are characteristic of both the NB amacrine cells of the catfish (Sakai and Naka 1987) and of some N amacrine cells in the retina of the gourami (Sakai et al. 1997b). The green second-order kernel generated by the green input alone has a signature similar to that of the red second-order kernel (Fig. 5B2). The green second-order kernel (Fig. 5B3) generated in the presence of steady red illumination also has a similar signature to that of the other kernels, but it has a longer transport delay of ~20 ms. The most dramatic change due to the presence of a steady red illumination is the reversal of the polarity of the first-order kernel evoked by green stimulus. As we have discussed already in the preceding paper (Sakai et al. 1997b), information about color is encoded largely by the linear component, whereas the nature of the second-order nonlinearity appears to remain unchanged under all stimulus conditions. The ganglion cell was detecting color contrast.

Spike discharges

Resembling the intracellular response, spike trains also can be classified into two broad classes, noncolor and color coded. As in the case of intracellular responses, color coding of the green response is revealed only in the presence of steady red illumination. In the absence of such illumination, the patterns of all spike discharges are similar irrespective of whether they are evoked by a red or a green stimulus. An example of a color-coded spike discharge is shown in Fig. 6, in which results are shown as PST histograms. A red pulsatile stimulus inhibits spike discharges, whether it is given alone in darkness (Fig. 6A1) or in the presence of steady green illumination (Fig. 6A2); a conspicuous burst of discharges is seen at the OFF set of the stimulus. Although two OFF discharges looked similar, their latency differed. The latency of OFF discharges evoked by the red stimulus alone was 40 ms, whereas the latency of OFF discharges evoked by the stimulus in the presence of a steady green illumination was 20 ms. A similar observation was made on the intracellular responses shown in Fig. 4. The OFF burst was followed by an inhibitory period of ~90 ms in duration. A green stimulus given alone in darkness generates a histogram very similar to those produced by red stimulus (Fig. 6B1), although the latency of the OFF discharge was 20 ms. The response is transformed into ON discharges with a latency of 50 ms when the same stimulus is given in the presence of a steady red illumination (Fig. 6B2). Discharges seen at the ON set of a green pulsatile stimulus are oscillatory, as seen from the presence of two transient peaks. Green ON responses tend to be more oscillatory (Figs. 8A2 and 9C2) as are the oscillatory OFF discharges in the response to green flashes given alone (Fig. 6B1).


View larger version (23K):
[in this window]
[in a new window]
 
FIG. 8. First-order kernels from spike discharges evoked by a simultaneous stimulation by red (top) and green (bottom) white-noise stimuli. Resulting discharges were decomposed into red and green components through the process of cross-correlation. Discharges were evoked at 4 mean levels of luminance that covered a range of 3 log units. Kernels marked 0 were generated by stimuli without any attenuation. Kernels marked 1-3 were generated by stimuli attenuated by 1-3 log neutral density filters. Although the peak response times of kernels became longer as the mean decreased, the essential features of the waveform remained unchanged. A, 1 and 2: a color-coded cell. In this cell, a red stimulus generated a biphasic kernel with an initial positive peak, a -BI kernel, whereas a green stimulus generated a triphasic kernel the main peaks of which were depolarizing, a +TRI kernel. B, 1 and 2: kernels from a red-OFF and green-ON cell. Over the entire range of mean luminance, the red kernels were biphasic with an initial negative phase, -BI kernels, and the green kernels were also biphasic with an initial positive phase, +BI kernels. C, 1 and 2: kernels from an OFF cell. Kernels evoked by both the red and green inputs were biphasic with an initial negative phase. A positive phase indicates an increase in the frequency of spike firing, and a negative phase indicates a decrease in the frequency of spike firing. Kernels are plotted on a contrast-sensitivity scale.

The results of white-noise analysis of this spike train are shown in Fig. 7. The two first-order kernels, one evoked by red input alone and the other evoked in the presence of steady green illumination, are very similar and of the -BI type (Fig. 7A1). These two kernels, when normalized with respect to amplitude, could be superposed exactly. The waveform of the red kernels shows that this ganglion cell is an OFF cell, confirming the observations made from flash-evoked responses. The presence of steady illumination increased this cell's sensitivity, as indicated by the larger amplitude of the first-order kernel (depicted by a solid line in Fig. 7A1). An increase in sensitivity in the presence of steady illumination of the opposing color was often, but not always, observed. By contrast, the presence of an opposing color modulated by a white-noise signal often decreased the kernel's sensitivity, as seen also in amacrine cells (Fig. 10 in Sakai et al. 1997b). In either case, the response dynamics, as indicated by the kernel waveform, remain unchanged. The green stimulus, given alone in darkness, produced a first-order kernel similar to those produced by red inputs (Fig. 7B1). In the presence of a steady red illumination, the same green stimulus generated a triphasic first-order kernel with a large positive peak, namely, a +TRI type kernel. The presence of a red input caused the cell to become a green-ON cell, as shown by the PST histogram in Fig. 6B2. The transformation of the green response was evident irrespective of whether the red stimulus was applied as steady illumination or white-noise modulated. In the case of a modulated red input, the green kernel may become smaller in amplitude. As shown in Fig. 7, A2-B3, all stimuli produced second-order kernels with a similar signature. The green kernel generated in the presence of red illumination (Fig. 7B3) had a longer transport delay of ~20 ms but had a signature characteristic of those kernels shown in Fig. 7, A2-B2. The results shown in Fig. 7 suggest that the second-order nonlinearity carried by this spike train could have been generated by the N amacrine cells. The first- and second-order kernels shown here are remarkably similar to those obtained from an intracellular response shown in Fig. 5, as are the pulsatile-stimulus-evoked responses shown in Figs. 4 and 6. In both cases, the presence of steady red illumination reversed the polarity of the response or of the green first-order kernels. As indicated by the signature of the second-order kernels, the second-order components were similar irrespective of whether they were evoked by a red or a green input or in the presence or absence of steady illumination. The reversal of the polarity of the response or the kernel also induced a change in the waveform. The first-order kernel in Fig. 7B1 is triphasic (+TRI), whereas all the other kernels are biphasic (-BI). Thus color information is related not only to polarity but also to the dynamics of a response, as we will elaborate on later. The similarity between kernels derived from an intracellular response (Fig. 5), an analog process, and those derived from spike discharges, which are point processes (Fig. 7), support our previous conclusion that the process of spike generation is highly nonlinear but approximately static (Korenberg et al. 1989).


View larger version (31K):
[in this window]
[in a new window]
 
FIG. 7. White-noise experiments performed on the cells for which results are shown in Fig. 6. A1: two first-order kernels generated by red white-noise stimulus in the presence of steady green illumination (------) and in darkness (- - -), respectively. Amplitude of the kernel evoked by a single red input is smaller than that of the kernel evoked by a similar input in the presence of steady green illumination. The waveforms of the 2 kernels are identical. Kernel units are 3.9 × 10-7 spikes·photons·mm-2·s-1. B1: 2 first-order kernels generated by a green white-noise stimulus given in the presence of steady red illumination (------) and in darkness (- - -), respectively. Presence of steady red illumination reversed the polarity of the green kernel. Kernel units were 1.2 × 10-7 spikes·photons·mm-2·s-1. A2 and A3: second-order kernels evoked by a red white-noise stimulus given in darkness and in the presence of steady green illumination, respectively. Two kernels are identical. B2 and B3: second-order kernels generated by a green white-noise stimulus given in darkness and in the presence of steady red illumination, respectively. Steady red illumination lengthened the transport delay of the green kernel by 20 ms but the kernel's principal features remained unchanged.

In both intracellular and spike recordings, latencies of OFF responses evoked by red pulsatile stimulus given alone were ~50 ms, whereas latencies of similar responses evoked in the presence of steady green illumination decreased in the intracellular responses, and spike discharges were 20-30 ms (Figs. 4B1 and 6A2). The waveform of red first-order kernels, on the other hand, was identical whether kernels were generated by red stimulus alone or in the presence of steady green illumination (Figs. 5A1 and 7A1). This is another example of differences between the responses evoked by a pulsatile input given alone and by a modulation of a mean luminance. A response evoked by a modulation of mean luminance is a steady state response. The OFF response evoked by a green stimulus alone had a very short latency of 20 ms and was oscillatory. The latency of the ON responses evoked by green pulsatile stimulus shown in Figs. 4B2 and 6B2 was ~50 ms, reflecting the triphasic nature of the green first-order kernel evoked in the presence of red steady illumination.

Information carried by kernels with different waveforms

Figure 8 shows first-order kernels from three spike trains recorded at four mean luminance levels that extended over a range of 3 log units. Each set of kernels, one for the red and the other for the green input, was computed from a single spike train by cross-correlation and decomposed into red and green components (Fig. 1B). The kernels are all plotted on a contrast-sensitivity scale (Chappell et al. 1985). In spite of the 100-fold difference in mean luminance, the amplitudes of most of kernels do not differ much, with the exception of the amplitudes of the kernels evoked by the dimmest stimuli. This result indicates that the sensitivity of the cells, as determined from the amplitude of the first-order kernel, can be represented by a Weber-Fechner type of relationship; the linear components detect contrast.

The kernels shown in Fig. 8A1, evoked by a red stimulus, are all biphasic with an initial positive peak (+BI) and are spike-frequency increasing, whereas those in Fig. 8A2, evoked by a green stimulus, are all triphasic (+TRI) over a large range of mean luminance. This cell produced an ON discharge in response to a red input, whereas a green input produced a transient and oscillatory ON response. This difference in the dynamics of the responses evoked by red and green stimuli was observed over a large range of mean luminance. Kernels shown in Fig. 8B, 1 and 2, are initially negative (-BI), spike-frequency decreasing, for the red stimulus, and they are positive (+BI), spike-frequency increasing, for a green stimulus. Thus this cell was a red-OFF and green-ON cell. This is an example of classical color-coding described in past literature. The kernels shown in Fig. 8C, 1 and 2, are all initially negative (-BI), spike-frequency decreasing, over a large range of mean luminance. This cell was a noncolor-coded OFF cell.

The results in Fig. 8 show that color signals can be characterized by both the polarity and the dynamics of a response represented by the waveform of a first-order kernel, a conclusion that is valid over a large range of mean luminance. Because both red and green kernels can be computed (decomposed) from a single spike train, a spike train simultaneously carries multiple signals about the colors of inputs. For example, the spike train used to obtain kernels shown in Fig. 8A carries red and green signals with different waveforms or dynamics. The spike train underlying Fig. 8B carries two signals with opposing polarity. Color processing, therefore, cannot be identified by the simplistic notion of an increase (excitation) or decrease (inhibition) of spike discharges. Obviously, this decomposition was possible because we, the experimenters, knew the inputs and because cross-correlation was performed off-line. We do not know how information carried by a spike train is decoded in the actual nervous system (Bialek et al. 1991). Similar differences in the waveform of first-order kernels generated by red and green inputs already have been described for N amacrine cells (Sakai et al. 1997b).

Classification of ganglion cells based on first-order kernels

As expected, we observed many types of color-coded discharge pattern. Spike trains can be classified on the basis of their responses to a pulsatile stimulus or by the waveform (or dynamics) of their first-order kernels. Figure 9 shows PST histograms generated by red or green flashes given in the presence of steady green or red illumination. The cell for which results are shown in Fig. 9A, 1 and 2, was a red-ON and green-OFF cell; for Fig. 9B, 1 and 2, it was a red-OFF and green ON cell; and for Fig. 9C, 1 and 2, it was a red-OFF and green-ON-OFF cell. Some other cells produced more complex responses. In the preceding paper (Sakai et al. 1997b), we discussed two problems associated with the classification of cells on the basis of their responses to pulstile stimuli: the amacrine cells of the gourami do not always produce clearly defined color-coded flash responses and flash-evoked responses are composed of linear and nonlinear components, and the ratio of these components can vary. Linear components can be color coded but nonlinear components probably are not. A pulsatile stimulus given in darkness evokes a nonsteady state response with a large second-order (and high-order) component to give an impression that a cell is not color coded.

We examined a large number (n = 210) of first-order kernels generated from the responses of ganglion cells, and we found that most kernels could be classified as one of two types, namely, biphasic (BI) or triphasic (TRI). Each type could be divided further into depolarizing and hyperpolarizing subtypes. Figure 10 shows four types of first-order kernel. Kernels shown in Fig. 10A were obtained from intracellular analog responses, whereas those shown in Fig. 10B were obtained from spike discharges recorded extracellularly. In all cases, the kernels were obtained in the presence of steady illumination by the opposing color. The kernels shown in Fig. 10, A1 and B1, are positive (depolarizing) biphasic (+BI), and those in Fig. 10, A2 and B2, are negative (hyperpolarizing) biphasic (-BI). The two sets of kernels are mirror images of each other with respect to their waveform. Kernels shown in Fig. 10, A3 and B3, are positive (depolarizing) triphasic (+TRI) since each kernel's main peak is positive, and those shown in Fig. 10, A4 and B4, are negative (hyperpolarizing) triphasic (-TRI). With the exception of the positive triphasic kernels shown in Fig. 10, A3 and B3, the kernels obtained from intracellular responses and spike discharges were similar in their waveform. This result provides further evidence that, as in the catfish retina (Korenberg et al. 1989), the process of spike generation is a high-order nonlinearity that is approximately static. The positive triphasic kernels in Fig. 8A2 were generated by a green input. The combination of the four types of kernel allows many modes of color coding.

Table 1 shows the classification of 88 spike trains that produced either biphasic or triphasic kernels as shown in Fig. 10. Kernels were obtained after simultaneous stimulation by both red light and green light inputs that were modulated by two independent white-noise signals. As in other experiments, the resulting spike discharges were decomposed into red and green components. There are 16 possible combinations, but 9 combinations actually were observed. We noticed that most of the red kernels were biphasic, either positive (83%) or negative (11%), whereas the green kernels were either biphasic (20%) or triphasic (60%) in waveform. Approximately one-half of the cells were red -BI and green +TRI, as shown by examples in Figs. 5, 7, and 8A. These figures correspond to the cell the response of which is shown as PST histograms in Fig. 9C. We do not know why the red inputs generated mostly biphasic kernels, whereas the majority of green kernels were triphasic, i.e., the response evoked by a green stimulus was more oscillatory. The triphasic kernels were clearly faster in their frequency components than the biphasic ones in terms of their frequency components, as shown in Table 2.

 
View this table:
[in this window] [in a new window]
 
TABLE 1. Classification of ganglion (spikes) cells based on the waveform and polarity of first-order kernels

Cross talk between red and green inputs

Figure 11 shows results of an experiment in which spike discharges were generated by two white-noise inputs, red and green. Resulting spike discharges were decomposed into red and green components. Two first-order kernels and two second-order kernels were measured from the red and green components. Two first-order kernels shown in Fig. 11A, one generated by the red (------) and the other by the green(- - -), can be classified as +TRI type because of the large positive peak. There was no marked difference between the two first-order kernels to suggest that linear components were color coded although the green kernel was more oscillatory. Diagonal cuts of two second-order kernels shown in Fig. 11B, one generated by the red input and the other by the green input, had alternating peaks and valleys. These kernels were of a N type, and their signature is similar to those shown in Figs. 5 and 7. Again, there was no marked difference between the two second-order kernels to suggest that second-order components were color coded.


View larger version (21K):
[in this window]
[in a new window]
 
FIG. 11. The first- and second-order and cross-kernels from a spike train. A train of spike discharges was evoked by a simultaneous stimulation by red and green inputs modulated by 2 independent white-noise signals. A: 2 first-order kernels that could be classified as +TRI type. ------, red kernel; - - -, green kernel. Green kernel is more oscillatory. B: diagonal cuts of second-order kernels. Oscillatory peaks and valleys show that kernels were of the N type similar to the kernels shown in Fig. 12, E and F, in Sakai et al. 1997b------, red kernel; - - -, green kernel. C: a cross-kernel. Kernel's signature is similar to the cross-kernels from N amacrine cells shown in Fig. 13 in Sakai et al. 1997b. Kernel is asymmetric around the diagonal. Peaks in slide lines show that a particular time sequence of red and green stimuli produced an enhancement excess of linear summation. A valley(- - -) shows that at a particular time sequence of red and green stimuli inhibited spike discharges in excess of linear summation.

The spike train generated a well-defined cross kernel, which is shown in Fig. 11C. The kernel's signature is composed of two asymmetric elements, one valley and two peaks, one large and one small. The negative valley, spike-frequency decreasing, was produced by an interaction between the red response with a latency of 28 ms and the green response with a latency of 36 ms. When a red input preceded a green input by 8 ms, spike discharges would be inhibited 28 ms later. When a green input preceded a red input by 8 ms, there would be no interaction. The larger positive peak, spike-frequency increasing, was produced by an interaction between the red response with a latency of 55 ms and the green response with a latency of 36 ms. When a green input preceded a red input by 19 ms, spike discharges were enhanced (facilitated) 36 ms later. Another smaller positive peak also shows that there is another mutual enhancement. As in Fig. 13 in Sakai et al. (1997b), this mutual inhibition as well as facilitation could not be contributed to one particular color; the inhibition or facilitation was produced by an interaction of two color (impulse-like) inputs. As a spike train is a point process, it is not possible to estimate the magnitude of contribution by the cross-component but the cross-kernel is the only kernel that showed a clearly defined color-related feature whereas the first- and second-order kernels did not.

The cross kernel shown in Fig. 11C has a signature very similar to that found in the cross-kernel from N amacrine cells (Fig. 13 in Sakai et al. 1997b). A particular temporal sequence of red and green stimuli produced characteristic effects. We do not know whether what we described in Fig. 11 or what we described in Fig. 13 in Sakai et al. 1997b can be referred to as color processing although a particular temporal relationship between red and green inputs was clearly detected. In this paper, this cell was classified as a noncolor-coded cell.

Comparison of the frequency characteristics of first-order kernels

We analyzed the frequency characteristics of the first-order kernels by the FOS method (Korenberg 1989). First-order kernels were obtained after a simultaneous stimulation by both red and green stimuli modulated by two independent white-noise signals. Red and green first-order kernels were recovered from a single response or a single spike train. Table 2 summarizes results from five types of cell, luminosity (n = 115) and chromaticity (n = 45) horizontal cells; C (n = 35), and N (n = 75), amacrine cells; as well as from spike discharges (n = 112). The table shows two parameters, the preferred frequency (R-FREQ or G-FREQ) of the red and green kernels and the number of sinusoids required to model a kernel with a MSE of <0.2% (R-SIN or G-SIN). C amacrine cells had the lowest preferred frequency, ~10 Hz, and N amacrine cells had the highest preferred frequency, 14-17 Hz. For each type of cell, except C amacrine cells, the preferred frequency for the green kernel (G-FREQ) was higher than the similar frequency for the red kernel (R-FREQ). This difference was statistically significant (see METHODS). By contrast, we found no statistically significant difference between the number of sinusoids (R-SIN and G-SIN) required to model the red and green kernels or between the preferred frequencies for the red or green kernels to distinguish luminosity and chromaticity horizontal cells, N amacrine cells, and spike discharges. However, the difference in preferred frequencies between C amacrine cells and other types of cell was statistically significant; the C amacrine cells seemed to have frequency characteristics different from those of horizontal cells, N amacrine cells, and ganglion cells. In the catfish retina, the preferred frequency of C amacrine cells was found to be lower than that of N amacrine cells (Korenberg et al. 1996). In both catfish and gourami, the frequency doubling found in the C amacrine cells does not necessarily produce a faster frequency response. If a measure of the complexity of a response can be approximated by the number of sinusoids needed to model a first-order kernel, the results shown in Table 2 indicate that all cells in the gourami retina produce a response of similar complexity.

Table 2 also shows that the difference in the preferred frequencies of horizontal cells and spike discharges was ~1 Hz, implying that first-order kernels from these two types of cell must be similar in their frequency characteristics. We made simultaneous recordings from a luminosity horizontal cell and a ganglion cell. The former cell produced an analog response and the latter produced a point process. The two first-order kernels shown in Fig. 12A were computed from these two responses. The waveforms of the two kernels were very similar, with almost identical peak-response times, although the spike kernel was slightly more differentiating. Figure 12B shows first-order kernels from a catfish horizontal cell and (intracellular) ganglion cell that were recorded simultaneously. The ganglion-cell response was decomposed into the slow-potential and spike components, and two kernels were computed. In the catfish, kernels from a horizontal and ganglion cell are very different in terms of both the peak-response time and waveform. Kernels from a ganglion cell are differentiating, but the kernel from a horizontal cell is monophasic. In the catfish retina, the preferred frequencies measured by the FOS method increase from 4 Hz in horizontal cells to 13 Hz in ganglion cells (Korenberg et al. 1997). However, in the retina of the gourami, the dynamics of the horizontal cell's response are similar to those of the ganglion cell's response; both cells generated first-order kernels of similar waveform and of similar frequency characteristics as shown in Fig. 12. A progressive increase in the frequency response in the retinal neuron network observed in the catfish is not seen in the retina of the gourami.


View larger version (14K):
[in this window]
[in a new window]
 
FIG. 12. Comparison of first-order kernels from the retinae of the gourami (A) and the catfish (B). Kernels were obtained from luminosity horizontal cells and OFF-ganglion cells. In B there are 2 ganglion-cell kernels. Kernel marked a was obtained from the postsynaptic potential (PSP) whereas the kernel marked p was obtained from a spike train. The PSP and spike discharges were obtained from a single recording and separated into 2 components as described by Sakuranaga et al. 1987. In both gourami and catfish, the response from a horizontal cell and ganglion-cell response were recorded simultaneously. Stimulus was a large field of red light. In the retina of the gourami, the peak-response times, PRT, of the spike kernel was 38 ms, whereas that of the horizontal-cell kernel was 42 ms, the time difference being 4 ms. In the catfish, ganglion-cell kernels had a PRT of 60 ms, and the PST of horizonal-cell kernel was 82 ms. These features indicate that the dynamics of the linear components of the horizontal cell's response and spike discharges in the gourami are similar, whereas the dynamics are different in the catfish retina.

    DISCUSSION
Abstract
Introduction
Methods
Results
Discussion
References

Ganglion cells are the sources of the output from the retinal neuron network. Thus because of their importance, the discharges from optic nerve fibers, the axons of ganglion cells, have been studied extensively, in particular, in relation to color processing in the retina. In most past studies on this subject, responses were evoked by flashes of different colors, and the waveform of resulting responses were examined. The principal measure in such cases is the polarity of the response, such as red-ON and green-OFF (cf. Table 1 in Ammermüler and Kolb 1995). The waveform of a flash-evoked response is complex (cf. Fig. 3 in Vallerga and Djamgoz 1991), and classification of color-coded responses on the basis of a simple measure is problematic. It is expected that color coding is related to the polarity as well as dynamics of the response. There have been many studies in which spike discharges from a ganglion cell were evoked by pulsatile or sinusoidal modulation of a mean luminance. In most of these studies, a train of spike discharges was transformed into an analog form by means of a PST histogram. One such example can be found in the report by Lee, Pokorny, Smith, and Kremers (1994). Although useful information can be obtained by this method, assignment of discharges to an artificial bin is also problematic. The time relationship between two successive discharges is lost.

Schellart and Spekreijse (1972), Victor and Shapley (1979b), and Meister et al. (1995) used a complex input and cross-correlation process to measure the dynamics of a spike train. Their method avoids the assignment of spikes to a bin. Schellart and Spekreijse obtained first-order kernels by the process of reverse correlation invented by de Boer and Kuyper (1968). Schellart and Spekreijse used Fourier transformation to obtain the gain and phase of the linear part of a spike train. Victor and Shapley (1979b) measured the second-order component of spike discharges from cat ganglion cells. Their results showed that the time interval between two spike discharges was an important parameter and that the nonlinearity originated in the layer of amacrine cells. The second-order nonlinearity found by Victor and Shapley could be approximated by a rectifier.

In the present study, as in a previous study of the receptive-field organization of the ganglion cells in the catfish (Sakai and Naka 1995), we used a single sweep of a white-noise stimulus of ~60 s in duration to determine the first- and second-order and cross-kernels from a spike train. In the example shown in Fig. 11, five kernels were extracted from a 60-s data. The formal interpretation of spike kernels, as in the case of the reverse correlation method developed by de Boer and Kuyper (1968), is that the first-order kernel represents the best linear approximation of the optimal waveform of a light stimulus that evokes a spike discharge. This is so because the input is analog in its form whereas the output is a point process. Mathematically, forward and reverse correlations produce identical first-order kernels (Eckhorn et al. 1993; Wang et al. 1996). Our heuristic observation shows that the process of spike generation, although highly nonlinear, is approximately static (Korenberg et al. 1989). If the process of spike generation is approximately static, cross-correlation between a white-noise stimulus, an analog process, and resulting spike discharges identifies the dynamics (as a series of kernels) of the processes that precedes spike generation. Spike trains are equated with slow-potential processes in the retinal neuron network.

Color-coded responses from ganglion cells

As it did in the N amacrine cells, red illumination modified the response produced by a green stimulus. In darkness, both a red and a green stimulus produced similar responses or first-order kernels with similar waveforms. The processing of color information in the gourami retina is detection of simultaneous color contrast; in the absence of red input, the green input does not reveal the possible color-dependent response from both N amacrine and ganglion cells. This mode of color processing has not previously been found in any other retina and might be related to the fact that there are only two classes of cones in the retina, the long- and medium-wavelength-absorbing cones (Kleinschmidt and Harosi 1992). As in N amacrine cells, color processing is related primarily to the polarity, as well as to the waveform, of first-order kernels. First-order kernels can be classified into two basic waveform types, biphasic and triphasic. In many cells, color coding is a transformation of a kernel's waveform from biphasic to triphasic. The combination of four basic waveforms generated by red and green stimuli produces a variety of responses, as shown in Table 1. There are 16 possible combinations, but we have found only 9 combinations. There must be a good reason why some combinations are not found in the gourami retina. This classification scheme is different from the classic scheme, which is based solely on the polarity of a cell's response. Dynamics, including cross talk, are important in the processing of color information, as shown in Figs. 8 and 11.

Responses of ganglion cells and the activity of interneurons

In both the catfish and the gourami, the waveforms of first-order kernels, as well as the signatures of the second-order kernels that we have recovered from ganglion cells, including spike discharges, are very similar to those recovered from amacrine cells. The signatures of the second-order kernels from ganglion cells fall into two broad classes: four- or nine-eye (Fig. 3) and N-type (Figs. 5 and 7) signatures. The studies in catfish have indicated that the four-eye kernel is generated by a process that can be approximated by a cascade of the Wiener type in C amacrine cells. N-type second-order kernels are thought to represent a transformation of a four-eye second-order kernel by a band-pass filter, a process that is likely to occur when the nonlinear component is transmitted from C to N amacrine cells, as presumed in studies of the catfish. The signature of a second-order kernel is very sensitive to filtering, and the fact that the signatures of the second-order kernels from the amacrine (Fig. 3B in Sakai et al. 1997b) and ganglion (Fig. 3C, 1 and 2) cells are similar indicates that there is little filtering during signal processing in the inner retina that leads to the generation of spike discharges. In Fig. 12, we observed that the waveforms of the first-order kernels from horizontal cells and from spike discharges were very similar, and these observations support our hypothesis that there is little filtering or temporal transformation of signals in the inner retina of the gourami.

FOS analysis shows that the preferred frequencies of first-order kernels from horizontal, amacrine, and spike discharges do not differ much. For example, the difference in the preferred frequency of horizontal cell and spike discharges is ~1 Hz. This shows that transmission of signals in the gourami retina must be very fast and, probably, involves a minimum amount of transformation. There is evidence that some of the signal transmission in the inner retina is rapid, as shown by the impulse-like first-order kernels obtained for such transmission (Sakai and Naka 1990; Fig. 10 in Sakai et al. 1997b). An exception to this finding is the C amacrine cell. As in the catfish (Korenberg et al. 1997), C cells seem to have frequency characteristics different from other neurons.

Generation and transformation of second-order kernels

It has been demonstrated heuristically that a C kernel signature can be transformed into an N kernel signature by a filter that is assumed to exist between the two cells (Sakai and Naka 1988); such a filter was recovered by injecting current into a C cell and recording the resulting response from an N cell (Sakai and Naka, unpublished data). Figure 13 shows the results of a similar transformation of a second-order kernel by a linear filter in the gourami. The kernel in Fig. 13A, was recorded from a C amacrine cell of the gourami. The second-order kernel is identical to the kernel from a ganglion cell (Fig. 3C1). Two kernels (Fig. 13, B and C) were generated artificially by convoluting the original response by the two linear filters shown in Fig. 13D. The transformed kernels are similar to some of the second-order kernels shown in this series of papers. For example, the transformed kernel shown in Fig. 13B is similar to the second-order kernel generated by a green stimulus in C amacrine and some ganglion cells (Fig. 5B in Sakai et al. 1997b and Fig. 3C2 in the present report). The kernel in Fig. 13C has characteristics of second-order kernels from some N amacrine cells (Fig. 12, E and F, in Sakai et al. 1997b). In the catfish, all N amacrine cells generated second-order nonlinearities that were characteristic of N cells; no N cell in the catfish retina generated a second-order kernel of the four-eye type shown in Fig. 3C1 in this report, and in Fig. 3B in Sakai et al. 1997b. However, in the retina of the gourami, some N cells generated a second-order kernel of the four- or nine-eye type, suggesting that either the nonlinearity was transmitted from C to N cells without filtering or N cells themselves generated the nonlinearity. The situation becomes more puzzling because the second-order kernels of the nine-eye type (Fig. 10F in Sakai et al. 1997b) do not show any sign of the extra low-pass filter seen in the green second-order kernels of the four-eye type (Fig. 5B in Sakai et al. 1997b and Fig. 3C2). The process of generation of second-order nonlinearity appears to be identical in both the catfish and the gourami, but in the gourami, the process cannot be assigned to a particular type of cell.

Implications

Since the late 1980s, we have been analyzing spike discharges from the retinae of lower vertebrates within the framework of Wiener's theory of nonlinear analysis. Results of these studies, including those of this study have shown consistently that complex signals are carried by a spike train, a fact that escaped detection in many previous studies of spike trains. It is possible to decompose a spike train into different spatial components (Sakai and Naka 1995) or, as we have shown in this report, into different color components. A spike train also can be decomposed into first- and second-order and cross-components. We can refer to this mode of signal transmission by a spike train as a multiplexed process in the sense that several types of information are carried concurrently by a spike train (McClurkin et al. 1991). Conversely, different components in a stimulus are coded independently into a spike train. The results clearly demonstrate that a spike train is not a simple signaling device. A spike train has a time sequence structure that is revealed by the second-order and cross-components, as originally discovered by Victor and Shapley (1979a,b). The relative timing of two spike discharges carries the second-order component, and the existence of clearly defined second-order kernels with signatures similar to those found for the analog process demonstrates that the time relationship of two discharges is an important means for transmission of information. Similarly, the specific time relationship of red and green inputs generates a cross-kernel. Although we did not compute the third-order kernel, it is possible that time relationships among three spike discharges provide a means for carrying a complex signal. A combination of histograms and linear analysis renders the complex problem of spike analysis into a simplistic subject.

In this series of papers, experiments and computations have been made in the context of Wiener's theory, and all our results and conclusions are vested in this methodology. As we have shown in this series of papers, the methodology reveals several new features of color processing in the retinal network hitherto undetected. One such example is the cross-kernel generated by the (second-order) dynamic interaction between the responses evoked by a red and a green stimulus. However, it is hard to believe that our methodology is the optimal method for studies of this subject, and the results that we have described in this series of papers are qualified in that they are mathematically derived but, nevertheless, based on a particular theory (Wiener 1958). Implementation of the theory is also far from exact. Had we used a different methodology, we might have produced an entirely different set of results. As we and some others have discussed, we do not yet know exactly how visual signals are encoded in a spike train and how the information is decoded (Bialek et al. 1991; Naka and Sakai 1991). In a complex multivariate system such as the retina, the results that we obtain reflect what is innate to the system as well as what is inherent to the particular methodology we use. Some of those who have studied central visual pathways already have recognized this difficulty (for review, see DeAngelis et al. 1995; Kaplan 1991).

    ACKNOWLEDGEMENTS

  The authors thank V. Bhanot for editorial assistance.

  This research was supported by grants from the National Institutes of Health, including NS-30772 to K.-I. Naka. 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 1996; accepted in final form 2 June 1997.

    REFERENCES
Abstract
Introduction
Methods
Results
Discussion
References

0022-3077/97 $5.00 Copyright ©1997 The American Physiological Society