Processing of Color- and Noncolor-Coded Signals in the Gourami Retina. I. Horizontal Cells
Hiroko M. Sakai1,
Hildred Machuca1, and
Ken-Ichi Naka1, 2
1 Departments of Ophthalmology and 2 Physiology and Neuroscience, New York University Medical Center, New York, New York 10016
 |
ABSTRACT |
Sakai, Hiroko M., Hildred Machuca, and Ken-Ichi Naka. Processing of color- and noncolor-coded signals in the gourami retina. I. Horizontal cells. J. Neurophysiol. 78: 2002-2017, 1997. There are two types of horizontal cells, the luminosity and the chromaticity cells, in the retina of the kissing gourami, Helostoma rudolfi. Luminosity cells occupy the outermost layer proximal to the receptor terminals, whereas chromaticity cells form a layer proximal to the layer of luminosity cells. Neither type of cell has axons. Responses were evoked by light from red and green light-emitting diodes. The two stimuli were modulated either by a pulsatile or a white-noise signal. The luminosity cell always produced a hyperpolarizing response. The chromaticity cell produced a hyperpolarizing response when stimulated by only one color. However, in the presence of a steady or modulated green input, a red stimulus produced a depolarizing response. Such chromaticity cells were similar to the (spectral) biphasic chromaticity horizontal cells observed in other retinae. The depolarizing phase of the red response was produced by the balance of intensity of the two inputs, red and green. We used white-noise methodology to identify the dynamics of the horizontal cell's modulation response by taking advantage of the fact that a Wiener kernel is a measure of a cell's incremental sensitivity, which includes its response dynamics. Under all conditions, a steady state modulation response by both luminosity and chromaticity cells always was related linearly to the input modulation. The average mean square error (MSE) of the model predicted by the first-order kernel was ~8% for both luminosity (n = 116) and chromaticity (n = 23) cells. In some cases, the MSE was a few percent even when the peak-to-peak response amplitude was nearly 30 mV. The ratio of inputs from red and green cones to both types of horizontal cells was variable; the major input for luminosity cells came from red cones, whereas the major input for chromaticity cells came from green cones. First-order kernels generated by the major input were robust in terms of waveform in the sense that the waveform remained unchanged whether or not there was a steady or modulated illumination by the opposing color. The results reported here do not address the question of the neural circuitry that generates horizontal cell responses, in particular, the depolarizing response. However, whatever that circuitry might be, the high degree of linearity of the modulation response by both types of cell under various stimulus conditions imposes restrictions on the performance of any proposed model as well as on mechanisms that underlie the generation of the horizontal cell response.
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INTRODUCTION |
The processing of signals evoked by stimuli of different spectral composition or color has been analyzed extensively by physiologists who study vision. Color makes a visual scene much more interesting, and it also serves as an important parameter of visual input. Most past analysis of color processing has involved responses evoked by pulsatile stimuli in darkness. Many studies exist on the statics of such a response, with the response amplitude or the increase or decrease in the rate of spike discharges being the principal parameter of interest. Vision normally occurs in the presence of a mean luminance. Therefore, the analysis of the dynamics of color-evoked responses in the presence of a steady or modulated luminance is of obvious importance. In this and two subsequent papers, we describe the dynamics of responses from neurons in the retina that were evoked by two color inputs, red and green, which were modulated either by sinusoidal or white-noise signals. The white-noise-evoked responses were analyzed in the context of Wiener's theory of nonlinear analysis (Wiener 1958
), i.e., each response was decomposed into its linear and nonlinear components by a cross-correlation process (Lee and Schetzen 1965
). We examined how color signals are related to the decomposed components. The response evoked by simultaneous presentation of red and green stimuli, which were modulated by two independent white-noise signals, also was decomposed into its components through the cross-correlation process. Theoretical justification of such multi-input white-noise analysis can be found in the report by Marmarelis and Naka (1974)
.
Few reports have described the analysis of color-coded responses from retinal neurons that are evoked by the random modulation of a mean luminance. Exceptions are early reports by Spekreijse and Norton (1970)
, Schellart and Spekreijse (1972)
, Wheeler and Naka (1977)
, and a recent report by Stone (1994)
. In these studies, a mean luminance was modulated by white-noise signals, and responses were identified by (1st-order) kernels obtained either by reverse or forward first-order correlation (de Boer and Kuyper 1968
; Lee and Schetzen 1965
).
The retina of the kissing gourami was used for the present research because of the relative simplicity of its color processing, which involves detection of simultaneous color contrast. As in our past studies on the catfish retina, our aim was to try to describe holistically the processing of signals in the retinal neuron network on the basis of an established methodology. In this latest series of investigations, we added a new parameter, namely, color.
We found that the modulation responses from horizontal cells always were related linearly to the input modulation. The first-order kernels predicted the modulation response with a reasonable degree of accuracy that was similar to the degree of linearity found for the horizontal cells in other species (Chappell et al. 1985
; Marmarelis and Naka 1973
; Naka et al. 1987
, 1988
; Stone 1994
; Wheeler and Naka 1977
). The presence or absence of different color inputs changed the parameters of the response, but linearity of the modulation response always was maintained. In the two accompanying papers, we will show that processing of signals by neurons in the inner retina involves nonlinearity as well as dynamic interaction between two colors and is much more complex than that in the horizontal cells (Sakai et al. 1997a
,b
).
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METHODS |
Experiments were performed on eye cup preparations of the kissing gourami, Helostoma rudolfi. This fish was chosen after a survey of many preparations, and its retina is characterized by a high proportion of color-coded cells. In addition, the fish features ease of acquisition and maintenance. Kleinschmidt and Harosi (1992)
showed that there were only two classes of cones in the gourami retina, long-wavelength-absorbing cones with
max of 630 ± 5 (SD) nm and medium-wavelength-absorbing cones with
max of 531 ± 5 nm. Kleinschmidt and Harosi did not find short-wavelength-absorbing cones and did not examine the ultraviolet region. Here we use the terms red and green cones or responses even though the terms erthrolabe, red catching, and chlorolabe, green catching, used by Rushton (1972)
might seem more appropriate. The results we describe in this series of papers support the observations of Kleinschmidt and Harosi that the gourami retina is bichromatic under photic conditions. Indeed, in darkness, the gourami fish is inactive and sits still at the bottom of aquarium.
The eye cup preparation was placed in a chamber that was supplied continuously with moist oxygen. Recordings were made intracellularly in the conventional manner. In most experiments, the intracellular electrode was filled with a mixture of Lucifer yellow (L-3510; Sigma, St. Louis, MO) and neurobiotin (Vector Laboratories, Burlingham, CA). We used an S-700A amplifier system with an S7071A input stage (WPI, Sarasota, FL). Data were stored initially on digital audiotape (DAT), with a DAT data recorder (RD-101T; TEAC, Tokyo, Japan), and analyses were made off-line with the STAR software system (Spatio-temporal Analysis Routines), developed by Dr. Masanori Sakuranaga at the National Institute for Basic Biology, Okazaki, Japan. The system ran on a combination of the µVAX 3600 (Digital Equipment Corporation, Maynard, MA) and an array processor, AP-5000 (Floating Point System, Portland, OR). We also used a PC-DOS version of the STAR system and Pentium machines, namely, Dimension P90 and P133C (Dell Computer, Austin, TX). White-noise signals were generated by a burst random noise generator (model 1360; NF Electronic Instruments, Tokyo, Japan), which generated four independent signals. In most experiments, we used a white-noise stimulus the power spectrum of which was nearly flat from close to DC to 60 Hz. The second-order autocorrelogram of the white-noise had no conspicuous peaks, showing that the noise had good first- and second-order characteristics.
Visual stimulation
We used two large overlapping fields of light that covered the entire eye-cup preparation. The fields of light were derived from two light-emitting diodes (LEDs), red and green (H-3000 and HBG-556X; Stanley, Tokyo). The
p of the red LED was 660 nm, and the spectral half-bandwidth was 25 nm (manufacturer's specifications). The
p of the green LED was 550 nm, and the spectral half-bandwidth was 30 nm (manufacturer's specifications). The illuminance of the light stimulus was calibrated with a quantum sensor (model 19C; LI-Cor, Lincoln, NE). Unless otherwise indicated, the mean luminance (quantal flux) was 1.9 × 1011 photons·mm
2·s
1 for the red input and 9 × 1010 photons·mm
2·s
1 for the green input. The strong red stimulus used in the experiment shown in Fig. 8 was brighter by 1 log unit than the value cited above, i.e., a 1-log neutral density filter was removed from the red stimulus channel. In some experiments, a blue LED with
p of 450 nm (model R5P01; Toyoda Gosei, Aichi, Japan) was used to confirm that blue light did not depolarize any horizontal cells.

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| FIG. 8.
Interaction of red and green inputs in a chromaticity cell. A, top 2 traces: timing of red and green stimuli; bottom: response of the chromaticity cell. , green responses in the presence of steady red illumination; and , red responses in the presence of steady green illumination; , red responses without green steady illumination. Magnitudes of the strong and weak red stimuli differed by 1 log unit. Latter stimulus had the standard mean quantal flux (see METHODS). B: one depolarizing kernel and 3 hyperpolarizing kernels were generated under the conditions indicated ( , green white-noise input in the presence of steady red illumination; , strong red white-noise input in the presence of steady green illumination; and , red white-noise input given alone). Depolarizing kernel was generated by a weak red white-noise input (standard mean quantum flux) in the presence of green steady illumination, a condition indicated by in A. Two of the hyperpolarizing kernels have been normalized with respect to their amplitude to match the 3rd hyperpolarizing kernel, which was obtained under the conditions indicated by the filled circles. Absolute amplitudes of the 3 hyperpolarizing kernels differed by 10%. Note that although the waveforms of the responses evoked by pulsatile stimuli were different, 3 hyperpolarizing kernels had identical waveform. Kernel units are 1.8 × 10 7 mV·photons 1·mm 2·s 1 for the hyperpolarizing kernels and 1.2 × 10 7 mV·photons 1·mm 2·s 1 for the depolarizing kernel.
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The signals from LEDs were modulated by pulsatile, sinusoidal, or white-noise signals. In white-noise experiments, three modes of stimulation were used: a red or a green stimulus given alone in darkness (one-input experiments); a red or a green stimulus given in the presence of steady green or red illumination (two-input experiments in which one input was held at a steady luminance); and both red and green stimuli modulated by two independent white-noise signals (two-input experiments in which both inputs were modulated). In the case of two-input white-noise analysis, the depth of modulation of one of two signals was adjusted so that the red and green responses were similar in terms of power. This adjustment was necessary because, if the response evoked by one of the two inputs was much larger than that evoked by the other, estimation of kernels, in particular estimation of second-order kernels, from the smaller response became unreliable (Marmarelis and Naka 1973
). This adjustment in the modulation depth was reasonable because, in lower vertebrate retinae, contrast gain control operates only on the gain of a response and not on its dynamics (Sakai et al. 1995
). Waveforms of first- and second- order-kernels obtained for inputs of various depths of modulation are identical although their amplitudes might differ. The depth of modulation was adjusted by observing the modulation response on the oscilloscope. Such adjustment did not have to be precise and only could be approximate.
In the two-input white-noise experiments in which both inputs were modulated, the response was decomposed into two components, each evoked by a red and green stimulus, by cross-correlation, as shown in Figure 1. In the past, Spekreijse and Norton (1970)
and Schellart and Spekreijse (1972)
used a reverse correlation method (de Boer and Kuyper 1968
) whereas Wheeler and Naka (1977)
and Stone (1994)
used forward correlation (Lee and Schetzen 1965
). However, Kroller (1992)
and Eckhorn, Krause, and Nelson (1993), showed that reverse and forward correlations are mathematically equivalent for the first-order kernels.

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| FIG. 1.
A schematic representation of a 2-input white-noise experiment in which red and green stimuli were presented simultaneously. These 2 stimuli covered the entire surface of the retina. Two independent white-noise signals were modulated by 2 independent Gaussian white-noise signals. Resulting response was decomposed into its components evoked by the red and green stimuli by cross-correlation between the 2 stimuli, marked input, and the 1 response, marked output. Red and green components were decomposed further into their first- and second-order components.
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The methodology we use in the present series of papers is based on the extension of Wiener's (1958) original theory to a multi-input system that was developed by Marmarelis and Naka (1974)
. Consider, for example, a system with two inputs, x(t) and u(t), and a single output, y(t). The stimulus-response function relationship is given by
|
(1)
|
where (h)n is a set of kernels of degree n, and x(t) and u(t) are two independent Gaussian white-noise signals, the red and green stimuli. Terms of different degrees in this series are mutually orthogonal and normalized. The first three terms of this series are given by
|
(2)
|
|
(3)
|
|
(4)
|
where Px is the power density spectrum of the white-noise input x(t) and Pu is that of the other input u(t) (Bendat 1990
). Equation 2 shows the 0th order (DC, direct current) term, Eq. 3 two first-order terms, and Eq. 4 two second-order terms and a cross term. Kernels, h2xx (
1,
2) and h2uu (
1,
2) are symmetric functions of their arguments, i.e., they are symmetric around the diagonal, whereas h2xu(
1,
2) is, in general, an asymmetric function of its arguments. The latter kernel describes the (nonlinear and dynamic) interaction of the two inputs as it affects the output, and it often is referred to as the (second-order) cross kernel; h1x, h2xx, h1w, and h2uu are the self kernels. Self kernels will be described as red or green first- and second-order kernels. Examples of cross kernel will be shown in Fig. 13 in Sakai et al. 1997a
and Fig. 11 in Sakai et al. 1997b
.
These kernels that describe the contribution to the response of each individual input, are given by
|
(5)
|
where E(Z) is the average or expected value of Z over the entire range of data (Bendat 1990
). The 0th-order kernel is the DC component of the response that is evoked by the mean luminance of the white-noise light stimulus. It is equivalent to the mean membrane potential produced by the mean luminance. The first-order model or linear model was obtained by a convolution of the white-noise stimulus with the first-order kernel, and the second-order model was obtained by a twofold convolution of the stimulus with the second-order kernel (Sakuranaga and Naka 1985
).

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| FIG. 11.
Depolarizing (red) and hyperpolarizing (green) kernels from a chromaticity cell. Response evoked by red and green inputs modulated by 2 independent white-noise signals were decomposed into the red and green components. Kernels are plotted on a contrast-sensitivity scale in A1 and B1. These kernels are normalized with respect to their amplitude in A2 and B2. Waveforms of the kernels were almost identical over a 3 log range of mean luminance. Kernels were generated at 4 mean luminance levels. Kernels marked 0 were obtained without any attenuation (standard quantal flux). Kernels marked 1-3 were obtained at mean levels attenuated by 1, 2, and 3 log neutral-density filters. Kernels in A1 and B1 can be converted to the incremental-sensitivity scale by multiplying the ordinate by the attenuation factor. For example, the amplitude of the kernel marked 3 can be multiplied by a factor of 1,000 to convert it into the sensitivity scale. Incremental sensitivity was not exactly Weber-Fechner as seen from the different kernel amplitudes. Kernel units are 2.0 × 10 7 mV·photons 1·mm 2·s 1 for the hyperpolarizing kernels and 1.6 × 10 7 mV·photons 1·mm 2·s 1 for the depolarizing kernel for the kernels marked 0 in A1 and B2.
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Upon examination of Eqs. 2-5, we can see that a kernel is a measure of incremental sensitivity that includes the dynamics and the frequency-dependent characteristics of the cell's response, as shown originally by Naka, Chang, and Yasui (1979) and by Sakuranaga and Ando (1985)
. The incremental sensitivity of retinal neurons is dependent upon the magnitude of the mean luminance, a phenomenon described as field adaptation by Rushton (1965)
. In a constant-gain low-pass system, such as the horizontal cells of the catfish, the amplitude of the kernel is approximated by the local slope of the so-called Michaelis-Menten curve (Naka et al. 1979
). As we will describe below, the gourami horizontal cell is not a constant-gain low-pass system. In this case, the kernel is the local slope of a shifted curve but not of the original Michaelis-Menten curve (Chappell and Naka 1991
). In this paper, a kernel is measured either as contrast or incremental sensitivity. Contrast sensitivity can be converted into incremental sensitivity by simple multiplication of the kernel amplitude by the factor of attenuation of the mean luminance (Chappell et al. 1985
; Sakuranaga and Ando 1985
).
Quantitative measurements
To quantify results, we use mean square errors (MSEs) and peak response times (PRTs). As in the previous papers, the MSE of the first-order model is given by
|
(6)
|
where ymod is the nth-order model of response y, N is the total number of data points, and M is the data points in a kernel. The first M data points y(0), . . ., y(M
1) could not be estimated due to causality. Available data points used for predication of the output were y(M), . . ., y(N
1). The results were normalized and are represented as percentages.
The probability density function, PDF, is given by
|
(7)
|
where N is the total number of data points sampled and Nx is the number of data points falling within the narrow range of x ± d/2, with an interval
x. If a system is linear and the input is Gaussian, the response PDF is also Gaussian. Conversely, the degree of deviation or the skewness of the PDF is an indication of the degree of nonlinearity in the system (Bendat 1990
; McKean 1973
).
In two-input experiments in which two first-order kernels predicted a response to a reasonably degree of accuracy, two MSEs were determined; one was the MSE, denoted as MSE1, of the model predicted by the red kernel alone, and the other was the MSE, denoted as MSE2, of the model predicted by the red and green kernels. The difference between the two sets of MSE represents the contribution, in a MSE sense, of the green or red input to the response. The peak response time, PRT, defines the time to the peak of the first-order kernel. We note here that measurement of the latency of an analogue process, such as the horizontal cell's response or first-order kernel, is arbitrary. For statistical analyses, we used SigmaStat (Jandel Scientific, San Rafael, CA). For comparison of two sets of numbers, normality and equal variance were tested at P = 0.05 before running a t-test.
Morphology:
Lucifer yellow and neurobiotin were used to identify morphologically neurons that were identified functionally. To visualize neurobiotin-injected neurons, we used the procedure described by Vaney (1991)
. Immediately after physiological experiment, eye cups were fixed briefly in 4% paraformaldehyde, 0.1% glutaraldehyde in 0.1 M phosphate buffered saline, PBS, at pH 7.4, and the part of retina that contained injected cells was detached. At this stage, the retina was examined under epi-illumination to register images of cells that had been stained by Lucifer yellow. One example is shown in Fig. 5 in Sakai et al. (1997a)
. The piece of the retina was fixed further overnight at 4°C. After fixation, the tissue was rinsed three times for 5 min each in PBS. The tissue was then incubated in 0.5% Triton X in PBS for 4 h. The tissue was then washed three times for 5 min each with PBS and then incubated with ABC Elite Complex (Vector Laboratories) for 4 h (2 drops of solution A plus 2 drops of solution B in 5 ml of PBS). The tissue then was rinsed three times for 5 min each in PBS. It then was incubated in 0.05% 3,3
-diaminobenzidine (DAB) in PBS and then allowed to react with 0.01% H2O2 in the solution of DAB for 15-20 min. It was rinsed in PBS, dehydrated in an ethanol series, and embedded in flat mount in Epon. Photographic records of neurobiotin-stained cells were obtained immediately after DAB reaction. Some of the preparations were sectioned tangentially for localization of the cell bodies and the level of dendritic arborization. An example is shown in Fig. 1 in Sakai et al. (1997a)
.

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| FIG. 5.
Responses from a luminosity horizontal cell evoked by a series of pulsatile green stimuli over a range of 4 log-units. Pulsatile stimuli were delivered in darkness. All responses are depicted as monotonic hyperpolarization even though the responses evoked by dimmer stimuli were more transient. Two largest responses were obtained with no attenuating filter, i.e., at 0 log. Maximal green luminance at 0 log units, was 9 × 1010 photons·mm 2·s 1.
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Golgi procedure
Fish were dark-adapted for 1 h and then decapitated and their eyes removed. Retinas were isolated from eye cups, fixed in 2% paraformaldehyde, 2.5% glutaraldehyde in 0.05 M phosphate buffer overnight at 4°C, and post-fixed in 2% OsO4 in 0.05 M phosphate buffer. The fixed retinas were immersed in 2.5% K2Cr2O7 and then were transferred to a fresh 0.75% solution of AgNO3 at room temperature in a dark container for 5 days. Retinas finally were transferred to fresh PBS, rinsed, dehydrated and embedded in Epon. Sections were cut tangentially and examined under a conventional-type microscope.
 |
RESULTS |
Types of horizontal cell
The morphology of horizontal cells was studied by the Golgi silver-impregnation method as well as by injection of the marker dyes, Lucifer yellow and neurobiotin. In terms of morphology, we identified two types of cone horizontal cells: H1, luminosity type; and H2, chromaticity type (Stell 1975
; Svaetichin and MacNichol 1958
). Figure 2 shows these two types of horizontal cell, in a flat-mount preparation, stained with neurobiotin. The luminosity cells, marked L, are arranged in a dense array, whereas the chromaticity cells, marked C, are dispersed more widely. This was a consistent finding. The sizes of the two types of cell seen in Lucifer yellow-stained and Golgi silver-impregnated preparations appeared similar, although the dendrites of luminosity cells were stubbier than those of chromaticity cells. In Golgi preparations, the distal processes from the two types of horizontal cells were seen to invaginate receptor terminals. We have not stained or made recordings from rod horizontal cells. The luminosity cells were located just proximal to the layer of receptor terminals, whereas the chromaticity horizontal cells were located between the luminosity cells and the layer of amacrine cells. By contrast to such cells in other teleost retinae, neither type of horizontal cell had any axons (Stell 1975
).

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| FIG. 2.
Neurobiotin-stained horizontal cells in the retina of the gourami. Two injections were made into the luminosity (L) and chromaticity (C) horizontal cells. Former cells form denser clusters than the latter. Luminosity cells are located just proximal to the receptor terminals, and the chromaticity cells usually are located distal to the luminosity cells. Scale bar represents 10 µm.
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Upon stimulation by a red or a green flash in darkness, both the luminosity and the chromaticity cells produced a sustained hyperpolarizing response, giving the impression that there was no color-coded response from the gourami's horizontal cells. Figure 3A shows two responses evoked by red and green pulsatile stimuli from a luminosity cell, and Fig. 3B shows two similar responses from a chromaticity cell. The two sets of responses appear similar, although the transient response seen at the OFF set of the stimulus is more pronounced in the response to the green stimuli. Responses evoked by a pulsatile stimulus given in darkness showed no transient peak at the ON set of the stimulus. Similarly, first-order kernels generated by modulation of a single input were always hyperpolarizing. Figure 7C shows that first-order kernels from a luminosity cell generated by a red or green white-noise stimulus input, given alone, had an identical waveform, and, similarly, Fig. 9B shows that kernels from a chromaticity cell generated by a red or green white-noise stimulus, given alone, had an identical waveform. Responses evoked by a single input, whether it was a pulsatile stimulus or a modulation of a mean luminance, did not show any evidence of color coding.

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| FIG. 3.
Responses of luminosity (A) and chromaticity (B) cells evoked by a pulsatile stimulus given in darkness. When exposed to a pulsatile stimulus in darkness, both luminosity and chromaticity horizontal cells generated similar hyperpolarizing responses. Responses lacked the transients seen at the ON or OFF set of responses obtained in the presence of steady illumination or when the retina was light-adapted.
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| FIG. 7.
Analysis of response from a luminosity cell. A: a series of pulsatile inputs given under 3 conditions: simultaneous stimulation by both red and green pulsatile stimuli in darkness; 2 red pulsatile stimuli given in the presence of steady green illumination; and a green pulsatile stimulus given in the presence of steady red illumination. B: power spectra of the 2 inputs, red and green, marked inputs, which are flat from 1 to 80 Hz. Power spectra of the white-noise-evoked responses are marked red and green. Power spectrum of the green response is more band-pass than that of the red response although both have a peak of similar power at ~30 Hz. In the lower frequency range, the green response has less power (about 10 dB) than the red response. Here results from 2 experiments are combined. In 1, the red input was modulated whereas green input was held at a steady luminance. In the other, the green input was modulated whereas the red input was held at a steady luminance. C: two first-order kernels generated by either a red or a green white-noise input given alone. Kernel amplitudes were normalized to facilitate the comparison of waveforms. Waveforms of these 2 kernels match exactly although their amplitudes differ by 10%. This observation implies that the dynamics of the responses generated by a red or a green input were identical. D: absence of any dynamic interaction between red and green inputs. Two pairs of kernels were evoked by red (R) and green (G) white-noise inputs. In 1 pair ( ), 1 of the 2 inputs was kept unmodulated, and in the other pair (- - -), both red and green inputs were modulated by 2 independent white-noise signals. Kernels generated by green inputs were more band-pass and oscillatory than those generated by red inputs. Kernels were identical irrespective of whether the other input was modulated or was kept at a steady level. Modulation of 1 input did not modify the dynamics of the response evoked by the other input. Kernel units are 1.5 × 10 7 mV·photons 1·mm 2·s 1 for the red kernels and 1.0 × 10 7 mV·photons 1·mm 2·s 1 for the green kernels.
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| FIG. 9.
Interaction between red and green inputs in a chromaticity cell. A: kernels generated by red and green inputs in the presence of another input, which was steady or white-noise-modulated. Red input produced depolarizing kernels, and the green input produced hyperpolarizing kernels. Kernels in  were generated by red or green white-noise input in the presence of a steady green or red illumination with an intensity that corresponded to the mean of white-noise input (1 input). Kernels in - - - were generated by red and green inputs which were modulated by 2 independent white-noise signals (2 inputs). In the 2-input experiment, a single response was decomposed into the red and green components. Two sets of kernels matched exactly. There is no dynamic interaction between the 2 inputs. B: kernels generated by a red or green white-noise input given alone. Hyperpolarizing kernels in both A and B are identical in waveform. In A, units are 0.7 × 10 7 mV·photons 1·mm 2·s 1 for red kernels and 1.0 × 10 7 mV·photons 1·mm 2·s 1 for the green kernels. In B, kernels are normalized with respect to their amplitude to facilitate comparison of waveforms. Two kernels differed in amplitude by <10%. All responses shown here were evoked by the red and green stimuli with the standard mean quantal flux.
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A steady or modulated green input produced a complex red response from chromaticity cells. Figure 4A shows such responses from a chromaticity cell. In Fig. 4A, a red pulsatile stimulus given in the presence of steady green illumination produced a depolarizing response, and a green pulsatile stimulus given in the presence of steady red illumination produced a hyperpolarizing response. During the steady red illumination, the cell depolarized by >5 mV. When the steady illumination was terminated, the membrane became hyperpolarized to the dark level. This observation seems to contradict our previous statement that a red or a green flash given in darkness always hyperpolarized chromaticity cells (Fig. 3B). When the retina was illuminated for more than a few seconds, the cell's membrane potential shifted from the dark level. The polarity of the response recorded at the termination of such illumination depended on the membrane potential during the illumination. In Fig. 4A, the termination of steady red illumination produced a hyperpolarizing response. Note that, during the steady red illumination, the membrane potential was steadily hyperpolarizing. As discussed below, the depolarizing response from a chromaticity horizontal cell was dependent upon the relative intensity of the red and green stimuli, as shown originally by Naka and Rushton (1966)
. Simultaneous stimulation by red and green pulsatile stimuli produced a complex response (last two flash responses in Fig. 4A).

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| FIG. 4.
Responses evoked by pulsatile stimuli from a chromaticity (A) and a luminosity (B) cell. A: in the presence of a steady green input, a red pulsatile stimulus depolarized the chromaticity cell, and the green stimulus, in the presence of a steady red input, produced a hyperpolarizing response. Simultaneous stimulation by both red and green pulsatile stimuli produced a response with a complex waveform. Note that the responses evoked by the last 2 pulsatile stimuli were different in their waveform to show that the state of adaptation was rapidly changing after the termination of steady red illumination. Intensities of the 2 stimuli were adjusted so that the red stimulus produced a large depolarization (see Figure 8). B: both red and green stimuli in any combination produced a hyperpolarizing response from a luminosity cell. Near the end of the 2 experiments, the mean luminance was modulated by white-noise signals. Red luminance was set at 1.9 × 1010 photons·mm 2·s 1. Green luminance was set at 9 × 1010 photons·mm 2·s 1.
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Figure 4B shows the effects of steady illumination on a luminosity cell's responses to a pulsatile input. The presence of steady illumination rendered the responses more transient, as seen from the sharp peaks seen at the ON and OFF sets of the red or green pulsatile stimulus. This result contrasts with the responses shown in Figs. 3 and 5. The ON transient was seen even after the termination of steady illumination, as seen from the sharp ON (hyperpolarizing) peak observed when the responses were evoked in darkness (Fig. 4B, last 2 flash responses). After a few minutes of dark adaptation, the transient disappeared. All the kernels that we describe in this paper were biphasic, showing that the presence of steady illumination, red or green, rendered a response transient. The kernels were measured by a modulation of a mean luminance. The kernels from the horizonal cells of the turtle were similarly biphasic (Chappell et al. 1985
). By contrast, the kernels from catfish horizontal cells were monophasic, showing that the horizontal cell's response was constant-gain low-pass (Fig. 12 in Sakai et al. 1997b
; Sakai and Naka 1988
).

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| FIG. 12.
Mean square errors (MSEs) from luminosity ( ) and chromaticity ( ) horizontal cells. MSEs were obtained from 2-input white-noise experiments in which both red and green inputs were modulated by 2 independent white-noise signals. MSE1 shows the MSE of the first-order model predicted from the red input alone. MSE2 shows the MSE of the first-order model predicted from the sum of the models generated by the red and green kernels. This figure shows, in graphical fashion, that the red cones provided the major input to the luminosity cells whereas the green cones provided the major input to the chromaticity cells. Two clusters, 1 for the luminosity and the other for chromaticity cells are well separated. Same data are shown in Table 1.
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Luminosity horizontal cells
A red or a green pulsatile flash always hyperpolarized the luminosity horizontal cells of the gourami, as has been observed with the luminosity cells in other retinae. The amplitude of the response evoked by a pulsatile stimulus increased monotonically as the magnitude of the input was increased (Fig. 5). Although we have not conducted a detailed study of the relationship between the stimulus and the response, the relationship appears to be of the Michaelis-Menten type (Baylor and Hodgkin 1972). Sharp transients were seen at the ON or OFF sets of responses to a dimmer stimulus. This result contrasts with the responses from luminosity cells in other lower vertebrate retinae, in which a brighter stimulus tended to produce a more transient response (cf. Fig. 4 in Chappell et al. 1985
). This observation might be explained by the fact that the waveform of hyperpolarizing kernels was identical over a large range of mean luminance (Fig. 11). A change in the mean luminance does not modify the dynamics of modulation responses from the gourami horizontal cells. In all other retinae, the dynamics of horizontal-cell responses were dependent upon the mean luminance (Chappell et al. 1985
; Naka et al. 1987
, 1988
).
Resembling those of the luminosity horizontal cells in the lower vertebrate retinae that we have studied to date, the modulation responses were related linearly to the modulation of the input (Chappell et al. 1985
; Naka et al. 1988
). One example is shown in Fig. 6. In this experiment, we used three different measures to evaluate the linearity of the modulation response: comparison of the power spectrum of the actual response with that of the first-order model; prediction of the cell's response to an input of arbitrary waveform by a first-order kernel; and the Gaussian distribution of the PDF of the model predicted by the first-order kernel. Figure 6Ashows the first-order kernel with a rapid and biphasic waveform. The kernel's PRT was 30 ms, and the kernel's entire "epoch" ended within 60 ms. Figure 6B shows the power spectrum of the white-noise input, which is flat from near DC to 60 Hz, together with the power spectra of the actual response and that of the first-order model. Apart from the small deviation seen in the region near DC, these two spectra match exactly, showing that the modulation response was accounted for adequately by the first-order component. Both spectra slightly resembled the band-pass spectra with the
3 dB point around 20 Hz, reflecting the biphasic and rapid waveform of the first-order kernel. Figure 6D shows the PDFs both of the white-noise input with mean luminance of I0 and of the response with a mean hyperpolarizing potential of V0. The brighter the stimulus, the more hyperpolarized the cell's response. In other words, the two PDFs, one for the stimulus and the other for the response, were mirror images of each other. The two measured PDFs were fitted by the (best-fitting) Gaussian function. In Fig. 6D, the four superposed traces are almost indistinguishable from one another. If a system is linear, a Gaussian input elicits a response whose PDF is exactly Gaussian (Bendat 1990
; McKean 1973
), as was true for the modulation response from the luminosity horizontal cell of the gourami and in similar cells in other retinae (see, for example, Fig. 3 in Naka et al. 1987
). In the experiment for which results are shown in Fig. 6C, an arbitrary signal, a sinusoidal sweep, was used as an input to test the predictability of the first-order kernel shown in Fig. 6A. The top trace represents the input and the bottom traces represent the cellular response (
) and the first-order model (- - -). The two traces match very well with only a few, small discrepancies. The first-order kernel even predicts the abrupt transition of the sinusoid from high to low frequencies seen at the beginning of the sinusoid sweep.

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| FIG. 6.
Linearity of the modulation response from a luminosity cell. A red input was modulated by a white-noise signal. A: a first-order kernel with a large hyperpolarizing phase followed by a depolarizing rebound. Kernel settled down to 0 in <100 ms. B: three power spectra, 1 of the input and the other 2 of the actual response and of the first-order model, respectively. Power spectrum of the input white-noise is flat from near DC to 60 Hz. Response power spectrum ( ) is slightly band-pass with a 3 dB point at ~20 Hz. Power spectrum of the first-order model (- - -) is almost identical to that of the response power spectrum with the exception being the frequency range of <1.0 Hz. Cell's modulation response was adequately accounted for by the first-order component. C: response produced by an input of arbitrary waveform, namely, a sinusoidal sweep of the depth of modulation of 62%. Top: input waveform and bottom overlapping traces show the actual response ( ) and the first-order model (- - -). Bottom traces are almost indistinguishable from each other, including the transient seen at the transition from the fastest to the slowest sinusoidal signals. This record shows that the first-order kernel is capable of predicting the cell's response to an input with an arbitrary waveform. Amplitude of the response was 14 mV peak to peak. D: probability density function (PDFs) of the input white-noise and that of the response. Both PDFs are fitted by a best-fitting Gaussian function. Thus the four traces shown here are indistinguishable from one another. These PDFs are displaced in relation to the DC components so that the mean luminance, I0, and resulting mean hyperpolarization, V0, are matched. As expected in a linear system, the PDF of the response is Gaussian. Note that, as the light became brighter, the response became more hyperpolarized. Abscissa represents the probability and has no physical units. Units on the ordinate are photons·cm 2·s 1 for the stimulus PDF and mV for the response PDF. The peak-to-peak amplitude of response was 17 mV. Ordinate was adjusted so that the stimulus and response PDFs were superposed. Voltage scale bar refers to the responses. Kernel unit, 1.0, is 1.5 × 10 7 mV·photons 1·mm 2·s 1.
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The results shown in Fig. 6 demonstrate how the modulation response from luminosity horizontal cells of the gourami could be predicted with a high degree of accuracy by the first-order kernel, even when the amplitude of the modulation response was >15 mV, peak to peak. Sakai et al. (1995)
made a similar observation in their study of contrast sensitivity in the gourami luminosity cell. In their case, the peak-to-peak amplitude of the linear range response was nearly 30 mV. When the mean changed, the response dynamics identified by both the waveform and the amplitude of the kernels changed, but the modulation response remained linearly related to the input modulation. Such piecewise linearization is found in the horizontal cells of the catfish (Marmarelis and Naka 1973
), the turtle (Chappell et al. 1985
), the skate (Naka et al. 1988
), and Xenopus (Stone 1994
).
Interaction of red and green inputs in luminosity cells
The analysis of the response dynamics of a luminosity horizontal cell in the presence of steady illumination is shown in Fig. 7. Both a red and a green pulsatile stimulus given in the presence of steady illumination elicited a hyperpolarizing response with a sharp transient peak at the ON and OFF sets of the stimulus (Fig. 7A). We performed white-noise analysis on this luminosity horizontal cell. The kernels shown in Fig. 7C were generated by either a red or a green white-noise stimulus given alone. These two kernels matched each other exactly with respect to waveform, even though their amplitude differed by 10%. Figure 7D combines the results of two tests: a two-input experiment in which the cell's response was evoked by simultaneous modulation of the red and green inputs by two independent white-noise signals and a two-input test in which the red or green input was modulated by a white-noise signal while the green or red input was kept at a steady level, which corresponded to the mean of the white-noise modulated stimulus. A steady illumination corresponds to an extremely small modulationdepth. The presence of a steady or modulated red input made the amplitude of green kernels smaller and changed the kernels' waveform. Waveforms of the red and green kernels are very different. It was the green kernel that changed its waveform.
Two sets of red and green kernels, shown in Fig. 7D obtained in the presence of a steady or modulated input, match exactly with respect to waveform as well as amplitude, demonstrating that the modulation of one of the two inputs had an effect similar to a steady mean illumination, i.e., there was no dynamic cross-talk between the red and green responses (cf. Marmarelis and Naka 1973
). In each case, the green kernels were more oscillatory than the red kernels. In other words, the hyperpolarizing phase of the green kernels was much smaller than that of the red kernels. Figure 7B shows the power spectra of the red and green inputs, marked inputs, and the power spectra of the red and green responses evoked by a white-noise signal, whereas the other input was kept at a steady level. The red power spectrum is slightly band-pass as seen in Fig. 6B. The green power spectrum clearly shows that the response was band-pass, reflecting the oscillatory as well as the transitory nature of the green response. In the lower-frequency range, the green response had less power (about
10 dB) than the red response, whereas near 20 Hz, both spectra were similar in terms of power. Three pairs of kernels shown in Fig. 7, C and D, predicted the modulation response with MSEs of <10%. Once again, at a steady state, the modulation responses were related linearly to the input modulation. In the luminosity cell, the waveform of the green kernel changed dramatically in the presence of red illumination irrespective of whether the later was held at a steady level or modulated. Such parametric change was produced only by the magnitude and not by the modulation of the mean luminance. The linearity of modulation response was not affected by changes in the response parameters. As we will show below, the red cones provided the major input to the luminosity horizontal cells, and the response evoked by a red stimulus was robust in the sense that the waveform of the red kernels remained unchanged whether or not there was steady green illumination. Indeed, the red kernels shown in Fig. 7, C and D, are identical in terms of waveform. By contrast, the presence of the red input changed the dynamics of the green response, a response evoked by a minor input. This observation suggests that luminosity cells received direct input from red cones whereas the capacity of the green input to generate an hyperpolarizing response was modified easily by the presence of a red input. We note here that the responses evoked by a red pulsatile stimulus was more transient, as well as more oscillatory, than the responses evoked by the green pulsatile stimulus (Fig. 7A). However, the power spectrum, as well as kernels shown in Fig. 7, B and C, showed that the green response was more transient, as well as more oscillatory, than the red response. The results obtained after a pulsatile stimulus and after a white-noise stimulus appear to be contradictory. This contradiction arises because the former stimulus produced a non-steady state response whereas the latter produced a steady state response.
Chromaticity horizontal cells
In chromaticity cells, the depolarizing response was produced by the interplay of red and green inputs (Fig. 8A). A strong green pulsatile stimulus, given in the presence of a steady red input, generated a hyperpolarizing response with transients at the ON and OFF sets of pulsatile inputs. Red pulsatile inputs of different magnitude, given in the presence of a steady green input, produced very different responses. As seen in Fig. 8A, strong red pulsatile inputs produced transient responses (
); weaker red stimuli produced depolarizing responses (
). The weak red stimulus given immediately after the termination of the green steady illumination was associated with a very complex waveform. The amplitude of the response evoked by the second red flash was much larger than that evoked by the first flash, demonstrating that these responses (
) reflected the non-steady state of the processes that generated the horizontal-cell response and that the state of adaptation was changing rapidly after the termination of the steady illumination. Note that during this rapid change in the state of adaptation, the membrane potential remained virtually unchanged.
Figure 8B shows one depolarizing and three hyperpolarizing kernels obtained from the cell the responses of which are shown in Fig. 8A. The depolarizing kernel was obtained when a red stimulus produced the depolarizing response indicated by
in Fig. 8A. The kernel includes a small initial hyperpolarizing phase. There are two possible explanations for this observation: the contribution from green cones was not completely suppressed by the steady green illumination, i.e., the red stimulus excited the green cone; and the initial hyperpolarization originated in the red cones themselves because a strong red stimulus produces a hyperpolarizing response. We do not know which explanation is more plausible. Recordings from red or green cones under a similar stimulus condition will resolve this issue.
Three superposed hyperpolarizing kernels shown in Fig. 8B were obtained under conditions similar to those represented by
and
and
in Fig. 8A. Although the flash-evoked responses were very different in terms of waveform, the waveform of the hyperpolarizing first-order kernels evoked by either the red or green inputs were identical, and these kernels predicted modulation responses with MSEs of <10%. In other words, modulation responses always were related linearly to the input modulation. The hyperpolarizing kernels shown here are biphasic and fast as are the kernels from luminosity cells. The fact that the hyperpolarizing kernels all had the identical waveform suggests that they were generated by identical mechanisms irrespective of whether the response was evoked by a red or a green input. A comparison of pulse-evoked responses and kernels shows clearly that responses evoked by pulsatile inputs were different from those evoked by the modulation of a steady luminance. This difference is due to the fact that a pulsatile stimulus produced sharp transients at the ON and OFF sets of the stimulus whereas such sharp transients were not seen in responses evoked by white-noise stimuli. The absence of transients can be appreciated from the linearity of responses evoked by white noise.
Figure 9 shows six first-order kernels from white-noise experiments performed with a chromaticity cell, as follows: 1) two kernels, depicted in Fig. 9A (- - -), from a two-input experiment in which both red and green stimuli were modulated by two independent white-noise signals, and the resulting response was decomposed into red and green components; 2) two kernels, depicted in Fig. 9A (
), from two-input experiments in which one input was white-noise modulated whereas the other was kept at a steady state that corresponded to the mean of the white-noise stimulus; and 3) two kernels generated by a red or green input given alone, as shown in Fig. 9B. The four hyperpolarizing kernels in Fig. 9, A and B, are identical in terms of waveforms. The presence of green illumination changed the polarity of the red first-order kernels. There was no difference in the waveform of the depolarizing red kernels irrespective of whether the green input was modulated or kept at a steady state; only the mean luminance of the green input produced the changes in the red responses and, hence, the red kernels. This is an example of a parametric change produced by the presence or absence of a mean luminance. Again the response linearity was not affected by a change in response parameter. The observation that the waveform of hyperpolarizing kernels evoked by either a red or green stimulus was almost identical is striking. This result was demonstrated already in Fig. 8 in which the presence of steady red illumination did not affect the dynamics of the hyperpolarizing response in chromaticity cells. We will show later that the green cones provide the major input to the chromaticity cell (Table 1), and the response evoked by green cones is robust as compared with the response evoked by red cones. It is probable that the chromaticity cell receives direct input from a green cone, and the input from a red cone can be modified by the input from a green cone.
Figure 10 shows the linearity of the response from a chromaticity cell. In this figure, results are shown as a time record (left), as well as a PDF (right). The best-fitting Gaussian function is superposed on each response PDF shown in the right column. In this experiment, a response was evoked by simultaneous stimulation by a red stimulus and a green stimulus, each of which was modulated by an independent white-noise signal. Figure 10, A and B, shows the timerecords of the red and green stimuli and their PDFs. Naturally, the PDFs of the two stimuli are Gaussian. The two kernels, one depolarizing and the other hyperpolarizing, both similar to those shown in Fig. 9A, were obtained for the red and green inputs. These two first-order kernels predicted the responses shown in Fig. 10C for the red input and in Fig. 10D for the green input. As we would expect, the two PDFs for the predicted responses are Gaussian. Figure 10E shows the cell's response to simultaneous stimulation by the red and green inputs (
), and the sum of the two predictions, Fig. 10, C and D, by the red and green kernels (- - -). The two traces, the actual response and the predicted response, match each other very well, an indication that the two responses evoked by red and green inputs are summed linearly in the chromaticity cell. This linear summation is maintained even though the peak-to-peak amplitude of the modulation response was nearly 30 mV as shown by the response PDF in Fig. 10E. There was no (dynamic) interaction between the two modulation responses evoked by the red and green inputs that were modulated by white-noise signals. In Fig. 10E, two response PDFs, namely, the PDF of the actual response and the PDF of the predicted response, are superposed, together with their best-fitting Gaussian curves. The four PDFs are indistinguishable, showing that the actual and predicted responses had Gaussian distribution. If a system is linear, the PDF of the response evoked by an input with a Gaussian distribution is also Gaussian (Bendat 1990
; McKean 1973
). This result provides further evidence that, in the chromaticity cell, the large-amplitude response evoked by the red and green inputs was summed linearly in an exact fashion because the MSE of the model response shown in Fig. 10E was 4.2%. From an analysis of step-evoked responses from the chromaticity horizontal cells of the walleye and bowfin, Burkhardt and Hassin (1983)
and Gottesman and Burkhardt (1987)
concluded that the steady state response was linear for responses equal to ~20% of the maximal response and that, in this linear range, a simple linear summation could account for the response evoked by two opponent colors. In white-noise experiments, this linear range was shown to be much larger as we have shown in this study and in the turtle (Wheeler and Naka 1977
) and by Stone (1994)
in the Xenopus horizontal cells.

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| FIG. 10.
Linearity of responses of chromatic horizontal cell generated by red and green stimuli modulated by 2 independent white-noise signals. Time records (left) and PDFs (right) are shown. For each PDF, a best-fitting Gaussian function is also superposed. A and B: red and green inputs that were given simultaneously. Naturally, PDFs of both inputs are Gaussian. C and D: models predicted by the red and green first-order kernels, respectively. Again, the PDFs are Gaussian. E: actual response( ) and the sum of the 2 model responses shown in C and D (- - -).These 2 traces matched well. In the chromaticity cell, the red and green components sum linearly. There are 4 PDFs in E, 2 PDFs for the actual response and the model, and two best-fitting Gaussian functions. The MSE of the model response shown in E was 4.2%, whereas the peak-to-peak response amplitude was as large as 30 mV.
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Figure 11 shows two sets of kernels obtained from a chromaticity cell in two-input white-noise experiments in which both the red and the green inputs were modulated by independent white-noise signals. Experiments were performed at four mean levels that differed by 1 log unit in luminance. Red depolarizing and green hyperpolarizing kernels were measured from a single response. Figure 11, A1 and B1, shows kernels plotted on a contrast-sensitivity scale. Although the amplitude of kernels increased as the mean luminance increased, the amplitude of kernels deviated considerably from the Weber-Fechner relationship (Naka et al. 1979
). If the incremental-sensitivity function represents a Weber-Fechner type of relationship, the contrast sensitivity, as measured by the amplitude of kernels, should be constant over a large range of mean luminance. Such was not the case, however. In Fig. 11, A2 and B2, kernels have been normalized with respect to their amplitude. The two depolarizing kernels for the two lowest mean luminance are not shown because of their noisy waveforms. The four hyperpolarizing kernels generated by the green input are almost identical in waveform, demonstrating that the response dynamics remained constant even though the incremental sensitivity increased 75-fold when the mean was increased by 3 log units. Surprisingly, the response dynamics did not depend on the mean of the white-noise stimulus. With regard to the dynamics of depolarizing kernels generated by the red input, we were unable to draw any definitive conclusion because the kernels were determined at only two mean luminance levels.
Summary of results
Table 1 summarizes the results obtained from gourami horizontal in terms of MSEs. In experiments in which both red and green inputs were modulated simultaneously(GF + RF), the red kernel predicted the response with a MSE (indicated as MSE1) of 19.9% for the luminosity cells and 81.4% for the chromaticity cells. Addition of the green component reduced the MSE (indicated as MSE2) to 7.8% for the luminosity cells and 8.4% for the chromaticity cells. We found no statistically significant difference between the MSEs for the luminosity and chromaticity cells, confirming that the response evoked by simultaneous presentation of red and green inputs can be adequately accounted for by linear components in both cells. As mentioned above (Fig. 10), this degree of linearity could not have been observed unless the two components, one generated by the red and the other by the green input, were summed in a linear fashion. The MSE from two-input experiments provides an approximate measure of the contribution to a response by the red and green cones. In the luminosity cells, the red cones contributed 80% of the input and the green cones contributed 12% (the difference between MSE1 and MSE2). In the chromaticity cells, the red cones contributed 18.6% of the input and the green cones contributed 73% of the input (the difference between MSE1 and MSE2). In the luminosity cells, 7.8% of the response was unaccounted for, and in the chromaticity cells, 8.4% of the response was unaccounted for. Similar degree of residue has been reported in the past studies on luminosity as well as chromaticity cells in the turtle and Xenopus retinae (Chappell et al. 1985
; Stone 1994
; Wheeler and Naka 1977
).
The ratio of red and green inputs to both the luminosity and the chromaticity cells differed considerably from cell to cell, as seen from the large values of standard deviation (Table 2) as well as the scatter of values. This is shown graphically in Fig. 12. The modulation responses from luminosity cells evoked by a red (RF + SG) or a green (GF + SR) input in the presence of a steady green or steady red input also are related linearly to the input modulation, as shown by the MSEs of 8.0 and 8.7%, respectively. There is no statistically significant difference between the two MSEs. We have not yet accumulated sufficient data from chromaticity cells for statistical analysis, but MSEs for single-input experiments were always <10%. Table 1 shows the statistical confirmation of the conclusion drawn in the preceding sections that, under various conditions, the modulation response is related linearly to the input modulation. The values of MSEs shown in this table are similar to those found for horizontal cells in other retinae of lower vertebrates (Chappell et al. 1985
; Naka et al. 1987
, 1988
). In those studies, a response was evoked by a single white-noise input, whereas in this study, some responses were evoked by two white-noise inputs. It is rather surprising that MSEs of modulation responses evoked by a single- and a two-input white-noise experiment were of similar value.
Table 2 shows a summary of the measurements of the PRT of first-order kernels from luminosity (n = 70) and chromaticity (n = 53) cells. For both types of cell, PRTs were measured for the kernels that were generated by simultaneous modulation of red and green inputs. In the luminosity cells, both kernels were hyperpolarized. In the chromaticity cells, red kernels were depolarized and green kernels were hyperpolarized. For both chromaticity and luminosity cells, the PRTs of hyperpolarized kernels were ~40 ms with a small standard deviation, whereas PRTs for depolarized kernels were ~50 ms. The transport delay was ~10 ms longer for the depolarized kernels and standard deviations were larger. There was no statistically significant difference among PRTs for the three hyperpolarizing kernels, whereas there was a statistically significant difference between the PRTs of the hyperpolarizing and depolarizing kernels.
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DISCUSSION |
Analysis
In many past studies of color processing in the retina, responses were evoked by a flash given in darkness. Early examples are provided by the series of studies by Naka and Rushton (1966)
, and more recent examples can be found in reports by Kamermans and his associates (Kamermans and Spekreijse 1995
; Kamermans et al. 1989
, 1991
). In most of these studies, the principal parameter examined was the amplitude of the response, a static measure. In some studies, the waveform of the response evoked by a flash stimulus also was examined. Characteristically, these studies dealt with a non-steady state and emphasized the nonlinear nature of a response because a flash given in darkness is terminated before the response reaches a steady state. The retina is not fully field-adapted to a mean luminance as it is in the natural photic environment. The non-steady state often is suggested by the sharp transient response seen at the ON set of a pulsatile stimulus, which shows that the parameters responsible for the generation of a response are rapidly changing (Figs. 4 and 7A). In spite of these difficulties, this earlier approach has proven quite successful because the response from most horizontal cells is approximately constant-gain low-pass.
Another approach is to evoke a response by modulation of mean luminance, either by a deterministic or a nondeterministic signal. In such cases, the retina is adapted fully to a mean luminance. There are not many studies of retinae that have analyzed processing of color by observing the modulation responses evoked by a random (white-noise) signal, although many such studies have been performed on the postretinal neuron network (e.g., Reid and Shapley 1992
). Spekreijse and Norton (1970)
, Wheeler and Naka (1977)
, and Stone (1994)
evoked responses from horizontal cells by using inputs modulated by a white-noise signal, and they analyzed the resulting responses by cross-correlation. As we will show in the present series of papers (Sakai et al. 1997a
,b
), responses from neurons in the inner retina evoked at a steady state are much simpler in terms of waveform and are easier to analyze.
Detection of color contrast
In all chromaticity cells studied to date, a single light stimulus with a wavelength of
650 nm produced a depolarizing response or a response with a complex waveform (Gottesman and Burkhardt 1987
; Kamermans et al. 1991
; Naka and Rushton 1966
; Stone 1994
; Svaetichin and MacNichol 1985). In the gourami retina, chromaticity cells produced only a hyperpolarizing response when the retina was stimulated with a red pulsatile input (
max = 660 nm). Only in the presence of steady or modulated green illumination did a red input generate a depolarizing response. Such was also the case when the response of a chromaticity cell was evoked by a single input that was modulated by a white-noise signal. The first-order kernel was always hyperpolarizing when it was generated by a red stimulus given alone, as was the case for a green stimulus. Similarly, a color-coded response was not generated by amacrine and ganglion cells when the retina was stimulated by a single input alone (Sakai et al. 1997a
,b
). Only in the presence of steady or modulated green illumination did a red stimulus produce a response from a chromaticity cell that was different from that produced by a red stimulus alone. Thus the chromaticity horizontal cells in the gourami retina detected only simultaneous color contrast.
Luminosity and chromaticity cells
When a response was evoked by simultaneous stimulation by both red and green stimuli, we observed several notable differences between the responses obtained from the two types of horizontal cell. First, the input to the luminosity cell, as defined by the MSE, was derived largely from the red cones, whereas the input to the chromaticity cell was derived largely from the green cones. This result is shown graphically in Fig. 12, in which the data summarized in Table 1 are plotted. The abscissa, marked MSE1, depicts the MSE of the linear component predicted by red kernels alone; the ordinate, marked MSE2, depicts the MSEs of the sum of two linear components predicted by red and green kernels. In this figure, filled circles represent data from luminosity cells and open circles represent the data from chromaticity cells. This figure graphically confirms the conclusion that, in the case of chromaticity cells, the major input comes from green cones, whereas in the case of luminosity cells, the major input comes from red cones. However, there is a considerable degree of scatter in the values of MSEs, showing that the ratio of red and green inputs to the horizontal cells can vary. In both types of cell, the response generated by the dominant input is robust in the sense that the waveforms of kernels obtained under various conditions were almost identical. For example, both the hyperpolarizing kernels of a luminosity cell generated by red cones (Fig. 7) and the hyperpolarizing kernels of a chromaticity cell generated by green cones (Fig. 8) have identical waveforms. In the case of a luminosity cell, kernels generated by a green input in the presence of a red input were labile in terms of waveform, as were kernels generated by red inputs in the chromaticity cell (Fig. 7). The dynamics of the response evoked by the dominant input was invariant of the presence or absence of other input. Similarly, Kamermans and Spekreijse (1995)
concluded that monophasic horizontal cells specifically received major input from the red cones and biphasic horizontal cells specifically received major input from the green cones.
Response dynamics
There are earlier studies that examined the response dynamics of horizontal-cell responses using chromatic stimuli. Spekreijse and Norton (1970)
used linear analysis, namely, the reverse correlation technique originally proposed by de Boer and Kuyper (1968)
, to study the dynamics of goldfish horizontal cells. Their results showed that the transfer characteristics, namely, the gain, were identical for luminosity and chromaticity cells, whereas the latencies, namely, the phase, were different. The other two studies involved standard white-noise analysis of the horizontal cells of the turtle (Wheeler and Naka 1977
) and of Xenopus (Stone 1994
). In these two studies, a response from a chromaticity cell was evoked by the simultaneous presentation of red and green stimuli. The studies of Wheeler and Naka and of Stone showed that the modulation responses were related linearly to the input modulation and that the first-order kernels could predict a cell's response with a MSE of <10%. The results of the present study agree with these two earlier studies in that the modulation response was related linearly to the input modulation in both the luminosity and the chromaticity horizontal cells. These conclusions are, in turn, in agreement with results obtained for the horizontal cells of the catfish (Sakuranaga and Naka 1985
), turtle (Chappell et al. 1985
), and skate (Naka et al. 1988
). In all these horizontal cells, the modulation response could be predicated with a MSE of <10%, in spite of the fact that the peak-to-peak amplitude of the modulation response could be >30 mV. The linear nature of the modulation response probably originates in the receptors (Naka et al. 1987
). The linearity of the modulation response from horizontal cells of the gourami is suggested by four independent observations: MSEs were <10%, under various stimulus conditions, indicating that much of the response could be accounted for by the first-order component (Table 1); the depolarizing and hyperpolarizing components from chromatic cells were summed linearly in the chromaticity cells (Fig. 10); there was no contrast gain control in the horizontal cells (Sakai et al. 1995
); and the PDF of the response evoked by a white-noise input was Gaussian even if the peak response amplitude exceeded 15 mV (Figs. 5 and 10). Resembling the studies of Wheeler and Naka (1977)
and Stone (1994)
, our study showed that there was no appreciable dynamic interaction, as defined by the cross-kernel h2xµ, between the signals generated by the red and green cones (Fig. 7 and 9). This conclusion is derived from two observations: the waveforms of kernels in the two-input experiment were identical irrespective of whether or not the second input was modulated and the cross-kernel showed no apparent peak or valley (Fig. 13 in Sakai et al. 1997a
). Indeed, Fig. 1A in Wheeler and Naka (1977)
and Fig. 6D in Stone (1994)
are strikingly similar to Fig. 9 in this paper. In these three figures, two sets of depolarizing and hyperpolarizing kernels were identical whether they were measured with steady or modulated background illumination. We will show in the companion reports that this is not valid for amacrine and ganglion cells (Sakai et al. 1997a
,b
).
Previous white-noise studies demonstrated that a lower mean luminance induced two parametric changes: higher incremental sensitivity and slower frequency response, which is reflected by the waveform of the kernel (Chappell et al. 1985
; Naka et al. 1987
, 1988
). In the horizontal cells of the gourami, a lower mean luminance induced higher incremental sensitivity but the response dynamics, as defined by the waveform of the kernels, remained unchanged (Fig. 11). Another exception to this general rule is the observation by Mizunami, Tateda, and Naka (1986) that the waveform of first-order kernels from ocellar neurons of the cockroach remained unchanged over a large range of mean luminance. In the ocellus, a modulation response with a peak-to-peak amplitude of >30 mV was related linearly to the input modulation with a MSE of ~10%.
Fast response dynamics are another characteristic of the gourami's horizontal cells. The power spectrum of the response, as well as Fourier transformation of first-order kernels, showed that the cutoff frequency was slightly >20 Hz, whereas in horizontal cells of the catfish and turtle, the cutoff frequency was <10 Hz (Chappell et al. 1985
; Marmarelis and Naka 1973
; Naka et al. 1975, 1987). In the Xenopus luminosity horizontal cells, cutoff frequencies were 12 Hz (Stone 1994
). The cutoff frequency of the model for the carp horizontal cells was <10 Hz (Kamermans et al. 1991
). As we will discuss in a companion paper (Sakai et al. 1997b
), the "preferred" frequency of the kernel obtained from horizontal cells of the gourami by the fast orthogonal search (FOS) method is between 12 and 14 Hz, whereas in the catfish, it is ~4 Hz (Korenberg et al. 1997
). Sakai et al. (1997b)
showed that the waveforms of first-order kernels obtained from horizontal cells and spike trains do not differ much in the retina of the gourami, i.e., there is little difference in their frequency characteristics. In the gourami retina, the frequency response of neurons in the outer retina is as fast as that of neurons in the inner retina.
In her study on Xenopus horizontal cells, Stone (1994)
noted that the peak response time of the first-order kernel from luminosity horizontal cells was always shorter than either the red or blue kernel from chromaticity cells. In the gourami, the PRT of the hyperpolarizing first-order kernels was identical in both luminosity and chromaticity cells (Table 2). FOS analysis also shows that the preferred frequencies of the hyperpolarizing kernels are identical (Sakai et al. 1997b
). In the Xenopus chromaticity cell, a red stimulus given on the dark background produced a depolarizing response as in the other lower vertebrate retinae so far studied. In the Xenopus, the chromaticity cell detected color, whereas in the gourami, the chromaticity cell as well as the amacrine and ganglion cells (Sakai et al. 1997a
,b
), detected color contrast.
Implications
The observation that the modulation response of the horizontal cell was related linearly to the modulation of two inputs, even when the amplitude of the response was large, i.e., a peak-to-peak amplitude of 30 mV, imposes some restrictions on two widely studied issues, namely, the ionic currents that generate the response of the horizontal cell and the neural pathways that generate the horizontal-cell response. Winslow and Knapp (1991)
, noted that many nonlinear currents had been discovered in the isolated horizontal cells (as reviewed by Lasater 1991
), but modulation responses appeared to be linear. Winslow and Knapp attributed this discrepancy to the loss of inputs from cones to the horizontal cells in isolated preparations. However, many other factors might contribute to this discrepancy. For example, the response from horizontal cell axons in the catfish retina is as linear as the response from the soma (Sakai and Naka 1988
). There is no evidence to suggest that the axons received any direct input from receptors. Indeed, the way in which axons received their input remains unknown. Depolarizing and hyperpolarizing components in chromaticity cells are summed linearly, an indication that at least two or more different and nonlinear ionic currents that underlie the generation of these two components do not interact with each other and that the resulting voltages are summed linearly. For example, Yamada, Low, and Djamgoz (1992) have shown that three light-modulated currents contributed to the generation of H1 horizontal cells in the carp retina. Voltages generated by three currents must add or subtract linearly if the modulation response remains linear. Stone, Witkovsky, and Schutte (1987), using Xenopus eyecup preparations, observed that a flash of light generated a spike-like transient from a luminosity horizontal cell in the presence of strontium ions. Nevertheless, the modulation response from the Xenopus horizontal cells was linearly related to the input modulation (Stone 1994
). The pulsatile responses shown in Fig. 7 have a large transient seen at the ON and OFF sets of stimulus. Such fast components are not present in the response evoked by a white-noise stimulus. We cannot predict a horizontal cell's response to a modulating input from that cell's response to a pulsatile stimulus given alone in darkness or vice versa. One reason for this discrepancy is the fact that a pulsatile stimulus contains very high frequency components that constitute the leading edge of the stimulus, whereas a white-noise stimulus, resembling the natural photic environment, has no such components. High frequency components might trigger nonlinear phenomena of the type found in so many studies made on isolated horizontal cells.
We also need to ask whether a feedback mechanism is involved in the generation of the horizontal cell's response. The feedback model was first proposed to account for the generation of concentric receptive field organization (Wu 1991
) as well as for the depolarizing response of chromaticity cells (Stell et al. 1975
). The results of the present study do not directly address the question of the circuitry that generates a chromatic response. This study, like past similar studies, identifies a system, i.e., a system's input-output relationship is defined but not its internal structure. Even so, that relationship imposes some restrictions on the model proposed. If a feedback mechanism is involved as in the so-called Stell model, the transmission in the pathway, cone-luminosity horizontal cell-chromaticity horizontal cell, must be linear over a large modulation amplitude or must involve a mechanism that compensates for the nonlinearity generated at one of the multiple stages of signal transmission. Even with a pulsatile input, Burkhardt and Hassin (1983)
and Gottesman and Burkhardt (1987)
reported that the red and green responses simply summed in the linear response range. Any model that incorporates the idea of lateral feedback has to account for this linear summation of responses evoked by input of different color (cf. Kamermans and Spekreijse 1995
; Kamermans et al. 1989
). There must be a good reason why horizontal cells produce a linear modulation response in all preparations that have been studied to date by the white-noise method, but we do not know what it is. In the following two papers (Sakai et al. 1997a
,b
), we will show that characteristic nonlinearity is generated in the amacrine cells and that such nonlinearity is translated into spike trains.
 |
ACKNOWLEDGEMENTS |
The authors thank V. Bhanot for editing this paper.
This research was supported by National Institutes of Health Grants EY-07738 to K.-I. Naka, EY-08848 to H. M. Sakai, and NS-30772. K.-I. Naka thanks Research to Prevent Blindness, New York, NY, for the Jules and Doris Stein Professorship and Thudichum Medical Institute for financial assistance. The software package, a DOS version, for the Wiener analysis used in this series of papers can be obtained at nominal cost from Thudichum Medical Institute, 1-5-1 Enoki Moto Machi, Sakai, Japan 590.
 |
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 15 May 1997.
 |
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