(Received

(Received
275
J. Phy8iol. (1978), 285, pp. 275-298
With 15 txt -fgure
Prnted in Great Britain
THE EFFECT OF CONTRAST ON THE TRANSFER PROPERTIES
OF CAT RETINAL GANGLION CELLS
BY R. M. SHAPLEY AND J. D. VICTOR
From the The Rockefeller University, New York, New York 10021, U.S.A.
(Received 17 January 1978)
SUMMARY
1. Variation in stimulus contrast produces a marked effect on the dynamics of
the cat retina. This contrast effect was investigated by measurement of the responses of
X and Y ganglion cells. The stimuli were sine gratings or rectangular spots modulated
by a temporal signal which was a sum of sinusoids. Fourier analysis of the neural
response to such a stimulus allowed us to calculate first order and second order
frequency kernels.
2. The first order frequency kernel of both X and Y ganglion cells became more
sharply tuned at higher contrasts. The peak amplitude also shifted to higher temporal
frequency at higher contrasts. Responses to low frequencies of modulation (< 1 Hz)
grew less than proportionally with contrast. However, response amplitudes at higher
modulation frequencies (> 4 Hz) scaled approximately proportionally with contrast.
Also, there was a marked phase advance in these latter components as contrast
increased.
3. The contrast effect was significantly larger for Y cells than for X cells.
4. The first order frequency kernel was measured with single sine waves as well
as with the sum of sinusoids as a modulation signal. The transfer function measured
in this way was much less affected by increases in contrast. This implied that stimulus
energy at one temporal frequency could affect the response amplitude and phase
shift at another temporal frequency.
5. Direct proof was found that modulation at one frequency modifies the response
at other frequencies. This was demonstrated by perturbation experiments in which
the modulation stimulus was the sum of one strong perturbing sinusoid and seven
weak test sinusoids.
6. The shape of the graph of the amplitude of the first order frequency kernel vs.
temporal frequency did not depend on the amplitudes of the first order components,
but rather on local retinal contrast. This was shown in an experiment with a sine
grating placed at different positions in the visual field. The shape of the first order
kernel did not vary with spatial phase, while the magnitudes of the first order responses varied greatly with spatial phase.
7. Models for the contrast gain control mechanism are considered in the Discussion.
276
R. M. SHAPLEY AND J. D. VICTOR
INTRODUCTION
The responses of retinal ganglion cells inform the brain of what the eye has seen.
However, this neural message is not a simple transduction of the optical image.
The image on the retina is transformed by spatial interactions between retinal
interneurones, and this transformation is reflected in the discharge pattern of
ganglion cells. Therefore, to comprehend the purpose and the functional machinery
of the retinal network one needs to understand the activity of ganglion cells.
In our research we have concentrated on the responses of cat retinal ganglion cells
to particular visual stimuli. These stimuli were spatial sine grating patterns which
were amplitude-modulated by a temporal modulation signal which was a sum of
sinusoids. We used sine gratings as spatial stimuli because they allowed us to dissect
apart retinal mechanisms on the basis of spatial resolution (cf. arguments in EnrothCugell & Robson, 1966; Hochstein & Shapley, 1976a). We used a sum of sinusoids
as a temporal modulation signal because it allowed us to tease apart components of
the neural response which are produced by linear transductions from those components
which arise out of non-linear transductions. The linear, or first order, responses
come out at the input frequencies in the sinusoidal sum. The responses of non-linear
elements are present as harmonic frequencies of the input frequencies, or as intermodulation frequencies which are additive combinations of two or more of the input
frequencies (Victor, Shapley & Knight, 1977).
The major question asked in this paper is, how do the first order responses of
retinal ganglion cells depend on contrast? If the retina were basically linear, or if
non-linearities within the retina were connected in a relatively simple, serial manner,
one would expect all the first order responses to be multiplied by the same constant
factor as contrast increased (see Discussion). This is not what is found. Rather, the
temporal transfer functions of retinal pathways are altered by contrast. This effect
of contrast is seen in both X and Y cells of the cat retina, but the effect is larger in
Y cells.
From our experimental observations, we have fashioned a model for the retina
which includes the concept of a contrast gain control. The simplest adequate model
is rather complicated, unfortunately. The mechanism seems to be equivalent to the
shunting of a resistance or speeding up of a rate constant at higher contrast.
It may be thought that the mammalian retina is hopelessly complicated in detail,
because each new series of experiments on the retina seems to unearth yet another
complex non-linear mechanism. However, our work suggests that the situation may
not be so bad, and that the contrast gain control may be directly related to the
previously discovered non-linear subunits of cat Y cells (Hochstein & Shapley, 1976b;
Victor et al. 1977). Our results indicate that the non-linear subunits and the contrast
gain control have similar dependences on temporal frequency, spatial frequency, and
spatial phase. So we have some hope that we can ultimately produce a single explanation for most of the complex, non-linear behaviour of cat retinal ganglion cells.
RETINAL CONTRAST GAIN CONTROL
277
METHODS
Recordings were made from optic tract fibres of anaesthetized (urethane) or decerebrate adult
cats. The cat's e.c.g., e.e.g., blood pressure, core temperature, end-expiratory C02 and optics
were monitored and maintained in the physiological range. Action potentials, recorded extracellularly with tungsten-in-glass microelectrodes, triggered a discriminator circuit which sent
shaped pulses to a PDP 11/20 computer, which recorded their arrival time to within 0-1 msec.
Visual stimulation was accomplished with a cathode ray tube at a distance of 57 cm. The
area of display was 20 cm x 20 cm, which spanned a visual angle of 20° x 200. The mean luminance
of the cathode ray tube was 10-20 cd/M2. Spatial patterns were produced on the cathode ray
tube with a specialized set of circuits (Shapley and Rossetto, 1976) to control the X-, Y-, and
Z-inputs. The spatial patterns used in these experiments were standing sine gratings of arbitrary
spatial phase and spatial frequency (oriented vertically) and rectangular spots of arbitrary
dimensions and positions. The contrast of the pattern was modulated in time by a control
signal from the PDP 11/20 computer. A control voltage of zero produced a uniform display at
the mean luminance; when the control voltage passed through zero, the contrast reversed. The
temporal modulation signal was either a single sinusoid, or a sum of nearly incommensurate
sinusoids. In most of the experiments the signal was made up of eight sinusoids. When a single
sinusoid formed the temporal modulation signal, neural responses were Fourier-analysed at
the modulation frequency. When the sinusoidal-sum signal was used, the neural responses were
Fourier-analysed at each of the input frequencies, as well as each of the second order frequencies
(sums and differences of the input frequencies). The choice of the input frequencies allowed first
and second order frequency kernels to be constructed from the Fourier coefficients (Victor et al.
1977; Victor & Knight, 1978). The input frequency sets used were chosen as described previously
(Victor et al. 1977).
The receptive field of each optic tract fibre was mapped on a tangent screen. The receptive
field centre was positioned in the center of the cathode ray tube display with a mirror, and the
unit was classified as X or Y by a modified 'null test' (Hochstein & Shapley, 1976 a; Victor et al.
1977). Then, the temporal modulation signal was placed under computer control to study
dynamics of the response to many spatial patterns and contrasts. For each spatial pattern,
several contrast levels were presented in interleaved runs. The contrast produced by each
sinusoidal component was typically 0-0125, 0-025, 0-05, and 0-10 in successive runs. (Contrast =
(Imax lmiD)/(Imax+Imin)-) In other experiments, seven of the eight sinusoidal components each
produced one contrast (typically 0.025), and the remaining sinusoid produced a higher contrast
(typically 0-20). In this case, the frequency which was presented at higher contrast varied from
run to run. In all cases, each contrast condition was presented several times, and the Fourier
components from equivalent runs were averaged.
RESULTS
First, we will consider how we measured the first order frequency kernel of retinal
ganglion cells. The spatial pattern used as a visual stimulus was modulated in time
by a sum of sinusoids. The impulse train of the ganglion cell was Fourier-analysed.
The amplitudes and phases of the responses at those temporal frequencies present
in the stimulus make up the first order frequency kernel. Were the retinal transduction from light to nerve impulses linear, the first order frequency kernel would
be the transfer function of that transduction. For a non-linear system, the significance
of the first order frequency kernel is more complex, and the kernel's values may
depend on the input signal used. However, for the particular input signal we used,
the first order frequency kernel represents the transfer function of that linear system
which best approximates the retinal pathway under study, where 'best' means best
by the criterion of least squares. As the number of sine waves in the stimulus modulation signal becomes larger, the first order frequency kernel more and more closely
R. M. SHAPLEY AND J. D. VICTOR
approximates the Fourier transform of the first order Wiener kernel (Victor &
Knight, 1978).
First order kernels: the contrast effect
For a linear system, one would expect that the first order frequency kernel should
grow proportionally with contrast. That is, the response amplitudes should double as
contrast doubles, and the phases of the responses should remain the same. Any
deviation from this behavior implies the presence of third order (or higher odd
order) non-linearities (see Discussion). In fact, almost all optic tract fibres we studied
showed evidence of this kind of non-linearity.
The first order frequency kernel was studied as a function of contrast, with a sine
grating as the spatial stimulus, in thirty-one X cells (twenty-three on-centre, eight
off-centre) and forty-one Y cells (thirty on-centre, eleven off-centre). In each case,
the sinusoidal sum signal was presented at strengths separated by factors of two in
interleaved episodes. The maximum contrast produced by each sinusoid was successively 00125, 0025, 005, and 0.10. The input signal was composed of six or eight
nearly incommensurate sinusoids so the root-mean-squared contrast in successive
episodes was 0-025, 0 05, 0.10, and 0.20 for the eight-sinusoid experiments, and
slightly less for the six-sinusoid experiments.
X cells. Data from a representative X cell are shown in Fig. 1. The unit was an
on-centre X cell stimulated with a 0-2 cycles per degree (c/deg.) grating positioned
to produce a peak first order response. At input temporal frequencies of 2 Hz and
below, the response grew much less than linearly with input contrast. However, at
the higher temporal frequencies of 8 Hz and 15 Hz, the response grew nearly proportionally to input contrast. Over nearly the entire frequency range tested, the
phase shift of the responses advanced by about 0-2 wf radians as constrast increased
over the range 0-0125 up to 0.1 per sinusoid.
To quantify the change in shape of the first order frequency kernel with contrast,
we extracted two parameters from the data. One of these numbers was a ratio: the
amplitude at 15 Hz divided by the amplitude at 0.5 Hz. The growth of this number
as contrast increased quantified the change in the shape of the amplitude curve with
contrast. The second parameter we examined was the phase shift of the response at
8 Hz. This number was a reliable index of the effect of contrast on the speeding-up
of first order responses. Both these parameters are plotted vs. contrast in Fig. 2. Note
that the amplitude ratio is plotted on a logarithmic axis, while the phase is graphed
on a linear axis. This Figure summarizes the data for four X cells. The graph in Fig.
2A summarizes the data presented in Fig. 1. Fig. 2B represents the contrast effect in
an off-centre X cell stimulated with a 0-25 c/deg. grating. Fig. 2C shows the contrast
effect in an on-centre X cell stimulated by a 0 7 c/deg. grating. This is an interesting
example of a large contrast effect in a cell which produced negligible second order
non-linear responses. The graph in Fig. 2D is for an X cell stimulated by a 1 c/deg.
grating. There was no contrast effect in this cell; the first order frequency kernels at
contrasts from 0-0125 up to 041 were parallel. The flat graphs of the amplitude ratio
and phase in Fig. 2D reflect this finding. Such behavior is what one would expect
from a system which is basically linear.
One can see from Fig. 2 that the amplitude ratio of the responses at 15 and 0*5 Hz,
and the phase advance at 8 Hz, are equivalent indices of the effect of contrast on the
278
279
first order frequency kernel. There are theoretical reasons for expecting this equivalence (DeGroot & Mazur, 1969). Later on in this paper we quantify the contrast
effect solely in terms of the phase shift at 8 Hz, for reasons of convenience and
RETINAL CONTRAST GAIN CONTROL
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Fig. 1. First order frequency kernels as a function of stimulus contrast for an on-centre
X cell. The input contrasts were 0-0125 (O), 0-025 ([), 0-05 (A) and 0.10 (I) per
sinusoid. The spatial stimulus was a 0-2 c/deg. grating positioned to elicit a maximal
linear response. In this and all other data illustrated, the mean luminance was 20 cd/
m2. Unit 11/4.
brevity. However, from Fig. 2 (and Fig. 4, below) one many conclude that the phase
shift at 8 Hz is highly correlated with the change in shape of the amplitude curve.
Y cells. Typical Y cells showed a large effect of contrast on the first order kernel.
This implied a greater amount of third order and perhaps higher odd order interactions in Y cells than in X cells. (This finding is not a trivial consequence of frequencydoubling by Y cells, for that is a manifestation of even order nonlinearities only.)
A representative example is illustrated in Fig. 3. The unit was an off-centre Y cell.
The spatial stimulus was a 0-25 c/deg. grating, positioned to produce a peak linear
R. M. SHAPLEY AND J. D. VICTOR
response. At low temporal frequencies the response increased much less than proportionally with contrast. The responses at high temporal frequencies increased
more than proportionally with contrast. As contrast varied over an eightfold range,
the response at 0-5 Hz grew by a factor of about three while the response at 15 Hz
grew by a factor of more than twenty. For input frequencies 1 Hz and higher, the
phases of the responses advanced with increasing contrast. This advance amounted
to 0-35 nf radians at an input frequency of 8 Hz.
280
X cells
Amplitude ratio 8
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Fig. 2. Amplitude ratios and phase shifts of the first order frequency kernel as a function
of stimulus contrast for three on-centre X cells (A, C, D) and one off-centre X cell (B).
The spatial stimuli were sine gratings positioned to elicit a maximal linear response. The
spatial frequencies used were 0-2 c/d (A), 0-25 c/d (B), 0-7 c/d (C) and 1-0 c/deg. (D).
The ratio of the amplitudes of the response at 15 Hz to the response of 0-5 Hz (0), and
the phase shift of the response at 8 Hz (LA), are plotted as functions of the peak contrast
of each sinusoid in the input signal. Units 11/4 (A), 8/4 (B), 18/4 (C) and 20/2 (D).
The amplitude ratio of responses at 15 Hz and 0-5 Hz, and the phase shift at
are plotted for three representative Y cells in Fig. 4. As in Fig. 2, these curves
are summaries of first order frequency kernels obtained at four contrasts from 0-0125
up to 0-1 per sinusoid. Fig. 4A demonstrates the contrast effect for an on-centre Y
cell stimulated with a 0-025 c/deg. grating. Fig. 4B represents the data graphed in
Fig. 3. Fig. 4C summarizes the data from another on-centre Y cell which was
8 Hz,
RETINAL CONTRAST GAIN CONTROL
281
stimulated by a finer pattern, a 1 0 c/deg. grating. Fig. 4C illustrates the point that
a contrast effect was observable in Y cells for any pattern which was effective in
eliciting first order responses. The 1 0 c/deg. grating was near the spatial frequency
resolution limit for this cell, yet at contrasts above 0-025 there was a clear contrast
effect. The curves in Fig. 4 are steeper than those in Fig. 2, and this observation
implies that the contrast effect was stronger in Y cells than in X cells.
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Fig. 3. First order frequency kernels as a function of stimulus contrast for an off-centre
Y cell. The input contrasts were 0-0125 (0), 0O025 (1), 0-05 (A) and 0 10 (-) per
sinusoid. The spatial stimulus was a 0-25 c/deg. sine grating positioned to elicit a
maximal linear response. Unit 12/3.
Several additional observations led us to the conclusion that the contrast effect
stronger in Y cells than in X cells. Besides the larger phase advances at high
temporal frequencies, Y cells often produced more-than-proportional increase of
response with contrast. Also the responses of Y cells to low frequencies of modulation
sometimes even decreased in amplitude as contrast increased. Such very strong
effects of an odd order non-linearity were rarely seen in X cells.
was
282
R. M. SHAPLEY AND J. D. VICTOR
A graphical summary of the magnitude of the contrast effect is given in Fig. 5.
Spatial sine gratings were most often employed as visual patterns in these experiments. Thus, in Fig. 5 the phase advance due to an eightfold increase in contrast of a
spatial sine grating (from a contrast of 0*0125 up to 0.10) is plotted as the ordinate;
the spatial frequency of the grating is the abscissa. These are the pooled data from
the sixty-three retinal ganglion cells tested with eight sinusoids. Units which were
tested with several gratings at different spatial frequencies are represented by several
Y cells
0
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Fig. 4. Amplitude ratios and phase shifts of the first order frequency kernel as a
function of stimulus contrast for two on-centre Y cells (A, C) and one off-centre Y cell
(B). The spatial stimuli were sine gratings positioned to elicit a maximal linear response. The spatial frequencies used were 0-25 c/deg. (A), 0-25 c/deg. (B) and 1-0 c/deg.
(C). The ratio of the amplitudes of the responses at 15 Hz to the responses at 0-5 Hz (0),
and the phase shift of the response at 8 Hz (A), are plotted as functions of the peak
contrast of each sinusoid in the input signal. Units 8/3 (A), 12/3 (B) and 23/1 (C).
points, one for each spatial frequency investigated. It is clear that there is not a strong
dependence of the contrast effect on spatial frequency but rather a gentle decline in
the effect as spatial frequency increases. This decline in the contrast effect may be
in part due to ineffectiveness of the fine gratings, those with spatial frequencies above
1 -0 c/deg., to stimulate any of the retinal pathways strongly. Another fact illustrated
by Fig. 5 is that on and off centre cells are affected similarly by the contrast of the
stimulus.
The use of sine gratings as spatial stimuli was not crucial in our experiments on
the contrast mechanism and its effect on the first order kernel. The same phenomenon
was observed when the spatial stimulus was a spot or a bar (see Fig. 9). However,
the grating stimuli did allow us to compare the spatial characteristics of the contrast
mechanism with the previously studied non-linear excitatory subunits of Y cells
(Hochstein & Shapley, 1976b; Victor et al. 1977). For cells which we stimulated with
gratings over a wide range of spatial frequency, we could compare the strength of
the second order responses with that of the contrast effect, as functions of spatial
frequency. A graph of a representative experiment in a Y cell is displayed in Fig. 6.
The measure of the contrast effect was the phase advance at 8 Hz over the
contrast range from 0-0125 to 0-1. The strength of the second order responses was
calculated by taking the root-mean-square of the second harmonic amplitudes
283
RETINAL CONTRAST GAIN CONTROL
measured at an intermediate contrast of 0-025. Fig. 6 demonstrates that both these
measures have a similar dependence on spatial frequency, with a peak sensitivity
near 0-25 c/deg.
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Fig. 5. Strength of contrast gain control in sixty-three units tested under uniform conditions. The ordinate is a parameter to measure the strength of the contrast effect: the
amount of phase advance of the 8 Hz response over the contrast range 0-0125-0-10 per
sinusoid. The abscissa indicates the spatial frequency of the spatial sine gratings used,
in cycles per degree. Data obtained with diffuse light are plotted at 0-01 c/deg. Filled
symbols indicate X cells; open symbols indicate Y cells. Circles indicate on-centre units;
triangles indicate off-centre units.
It is apparent from Fig. 5 that Y cells tended to show a greater phase advance
than X cells. This is consistent with the fact that the amplitudes of the first order
kernels showed a greater variation with contrast than did the kernels of X cells,
as is evident in the examples of Figs. 2 and 4. A further illustration of the difference
between X and Y cells is given in Fig. 7. This shows some of the data in Fig. 5, namely
the points obtained with either a 0-2 or 0-25 c/deg. grating as a spatial stimulus over
an eightfold range of contrast. A sine grating of 0-25 c/deg. was used as a stimulus
because this spatial frequency is effective in stimulating both first and second order
responses in Y cells. Fig. 7 shows the distribution of units with different degrees of
phase advance. It is apparent that Y cells show a larger contrast effect than X cells
on the average, though there is considerable overlap. The average phase advance for
the nine X cells was 0-14 if radians (a 250). The average phase shift for eighteen
Y cells was 0-28 ff radians (a 50°).
Ohstg<=~ ~ 3-0E
R. M. SHAPLEY AND J. D. VICTOR
284
Responses to single sinusoids compared to responses to suMs of sinusoids
The first order frequency kernels obtained at a series of contrasts were compared
with transfer functions measured with the component sinusoids presented separately.
One would expect these two measurements to be similar if the direct pathway from
photoreceptors to ganglion cells had little odd order non-linearity. Conversely, odd
order non-linearities should result in a dependence of the response at each particular
frequency on the presence or absence of other sinusoidal components in the input
signal.
* Phase shift (8 Hz)
A Second harmonic strength
6-0
0
Cu~~~~~~~~~~~~~~~~~
0
025
075
0-50
Spatial frequency (c/deg)
100
Fig. 6. A comparison of the strengths of the contrast effect (@) and the second order
response (A) in an on-centre Y cell as a function of spatial frequency. The strength of
the contrast effect is measured by the amount of phase advance of the 8 Hz response over
the contrast range 0-0125 per sinusoid to 0-10 per sinusoid. The strength of the second
order response is measured by the root-mean-squared amplitude of the responses at the
second harmonics of the eight input frequencies. Unit 23/1.
In Fig. 8, responses of an on-centre X cell to single sinusoids and to a sum of
sinusoids are compared. The temporal modulation signal was the sum of six sinusoids
of equal amplitude and the following frequencies: 0-641, 1-10, 2-47, 5-37, 12-2,
21-4 Hz. The spatial pattern was a 1-0 c/deg. grating positioned to produce a
maximal first order response. The amplitudes of the first order frequency kernels
measured at different contrast levels (Fig. 8A) are nearly parallel. The phases of the
response advance by at most 0-15 nf radians as contrast increases. Therefore, in this
X cell as in several other X cells, there was not very much effect of contrast on the
first order frequency kernel. The responses elicited by each of the component
sinusoids presented separately are shown in Fig. 8B. In general, the amplitudes and
285
RETINAL CONTRAST CAIN CONTROL
phases of the responses measured in this way are similar to those measured when the
sinusoids, were presented simultaneously.
The situation is different for cells which show -a strong contrast effect. A similar
comparison between the first order kernel (measured with a sum of sinusoids) and
the linear responses to single s~inusoids is presented in Fig. 9. In this case the unit
4
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strength of the contrast effect in X cells and Y cells.
subpopulation of Fig. 5 that were tested with gratings of spatial
frequency 0-2-0-25 c/deg. The parameter of phase advance of the 8 Hz response
(in 7r radians) was used to measure the strength of the contrast gain-control. The mean
phase advance for the nine X cells was 0-14 radians; the mean phase advance for the
radians (means indicated by arrows).
eighteen Y cells was 0-28
Fig.
7.
Histograms
of the
The data consist of the
typical on-centre Y cell. The spatial stimulus was a bar, O-5' wide, that covered
receptive field centre. The temporal modulation consisted of the six-frequency
in Fig. 8A. The frequency kernels indicate the presence of a substantial
used
set
contrast effect. At low temporal frequencies, response barely increased as contrast
rose by a factor of eight. At high temporal frequencies, response increased nearly
was a
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,shifts obtained by analysis of the responses
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The
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the first order frequency
response
single
sinusoids
frequency responses differ in a crucial way from
amplitude functions showed much less of a change in shape with incontrast.
Similarly, the phase advances obtained with single sinusoids were
creasing
smaller than the phase advances obtained with a sum of six sinusoids of equal
These
kernels. The
contrast.
M. SHAPLEY AND J. D. VICTOR
The data of Fig. 9 suggest that the failure of response at some particular frequency
to increase proportionally to contrast is not merely dependent on the strength of the
input sinusoid at that frequency. This effect of contrast is also related to whether or
not other sinusoids are present in the input stimulus. Therefore, the response to
sinusoidal stimulation at a given temporal frequency depends not only on the
strength of the Fourier component of the stimulus at that frequency, but also on
the over-all power in the stimulus.
286
R.
Single sinusoids
Sum of sinusoids
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Fig. 8. A comparison of the first order frequency kernels obtained with a superposition
of six sinusoids (A) and the responses to single sinusoids (B) in an on-centre X cell.
The spatial stimulus was 1-0 c/deg. grating positioned to produce a maximal linear
response. The contrasts used were 0-0125 (0), 0-025 (E]), 0-05 (A) and 0-10 (I) per
sinusoid. Unit 4/2.
The perturbation experiment
The results described above suggest that some function of the over-all power in
the stimulus modifies the linear transfer properties of retinal ganglion cells. This
effect is greatest in Y cells. One would expect that power at different temporal
frequencies should have different degrees of influence on the linear transfer properties.
The temporal frequency dependence of the contrast effect was explored as follows.
A sinusoidal-sum signal was constructed with eight components (0-229, 0-473, 0-961,
RETINAL CONTRAST GAIN CONTROL
287
1.94, 3-89, 7-80, 15-6, 31-2 Hz), but the amplitudes of the sinusoidal components were
not all equal. Seven of the eight sinusoids produced a maximal contrast of 0-025, and
the eighth sinusoid produced a contrast of 0-20. This procedure is illustrated in
Fig. 10. The idea was that the low-contrast sinusoids could serve as probes of the
transfer properties of the ganglion cell in question, by producing small linear responses over a wide frequency range. The eighth sinusoid contained nearly all of the
Single sinusoids
Sum of sinusoids
-)
4,
0
100-0
-
32-0
-
10-0
-
A
B
C
D
-T
._
E0E
3-2 1*0 -
0
c
0
L-
-
-0-5
-1-0
C0
CA
-1-5
-2-0
l.
I
0-32
I
I
1
3-2
II I
I
32
I I I
I
0-32
1
Temporal frequency (Hz)
10
3-2
10
32
Fig. 9. A comparison of the first order frequency kernels obtained with a superposition
of six sinusoids (A) and the responses to single sinusoids (B) in an on-centre Y cell.
The spatial stimulus was a 0-5 deg bar positioned to produced a maximal linear response.
The contrasts used were 0-0125 (0), 0-025 (l), 0-05 (A) and 0-10 (0) per sinusoid.
Unit 5/5.
in the input signal. Its presence perturbed the responses at the other fundamental frequencies. The frequency of the high-contrast sinusoid was varied from
episode to episode, so that the effect of power at a wide range of temporal frequencies
could be observed. The perturbation of the linear responses to the low-contrast
sinusoids was assayed by observing changes in phase shifts.
Results from two such experiments on Y cells are shown in Fig. 11. The unit of
Fig. I I A was on-centre; the unit of Fig. I I B was off-centre. In each case, the spatial
stimulus was a 0-12 c/deg. grating. In the left side of each panel, we have plotted the
power
R. M. SHAPLEY AND J. D. VICTOR
288
phase shifts obtained in a perturbation experiment. The abscissa indicates the
frequency of the perturbing sinusoid presented at a contrast of 0-20. The remaining
seven asay sinusoids each produced a maximal contrast of 0-025. The ordinate
measures the phase shift of the response at a given assay frequency. This phase shift is
measured relative to the phase of the response obtained when all eight sinusoids were
presented with a contrast of 0-025 per sinusoid. Three temporal frequencies (3-9 Hz,
A
B
V'
VvMXWW\WVVWVwVWW
Fig. 10. The composition of sum-of-sinusoids signals for the perturbation experiment.
The individual components are shown above the dashed line; their sum, which constitutes the input signal, is shown below the dashed line. The initial 4 sec of the 65 sec
stimulus are illustrated. In A, the sinusoidal component whose frequency is near 1 Hz
has an amplitude eight times that of the other seven components. In B, the sinusoidal
component whose frequency is near 8 Hz has an amplitude eight times that of the other
seven components.
7-8 Hz, and 15-6 Hz) were used as assay frequencies; the responses at these frequencies
showed the largest shifts with contrast. Each curve contains only seven data points,
because a frequency could be used as an assay frequency only when it was not the
perturbing frequency. The right half of each panel shows the relative phase shifts
obtained when all sinusoids were presented at equal strength. The abscissa is the
contrast per sinusoid; the ordinate is the phase shift relative to the phase measured
when all the sinusoids had an equal contrast of 0-025 per sinusoid.
It is apparent that the first order responses of both units showed a significant
phase advance with contrast. The assay frequency at which the phase advance was
maximal was 7-8 Hz for the unit in Fig. IIA, and 15-6 Hz for the unit in Fig. lIB.
From graphs like those shown in Fig. 11, we determined which temporal frequencies
were most effective in producing phase advances. There were the temporal frequencies
in the range 4-15 Hz, the same temporal frequencies that were most influenced by
contrast.
In Fig. 11 B, the curves of phase advance as a function of perturbing frequency
have roughly the same shape, independent of the temporal frequency used to assay
the phase shift. In this regard, the data of Fig. 11 A are somewhat different. The
apparent effectiveness of various input frequencies in producing phase shifts
RETINAL CONTRAST GAIN CONTROL
289
depends slightly on the assay frequency. The implications of this phenomenon for
modelling the mechanism of the parametric dependence on contrast will be discussed
below.
0*4 0-3
0-2
-
0-1
-
c0
._
t,
03
01
0
0-10
1
3-2
10
0-32
Pertubing temporal frequency (Hz)
32
0-10
0025
Contrast
Fig. 11. Perturbation experiments in two Y cells. The first order frequency kernel was
measured with a signal composed of seven sinusoids producing a contrast of 0-025 each,
and one sinusoid producing a contrast of 0-20. In the left panels are shown the phase
shifts at several assay frequencies (3-9 Hz (@), 7-8 Hz (U), and 15-6 Hz (A)) as a
function of the perturbing frequency. In the right panels, this comparison was made for
input signals consisting of equal-strength sinusoids, producing contrasts of 0-025, 0-05,
and 0410 per sinusoid. In all cases, the spatial stimulus was a 0-12 c/deg. grating positioned to produce a peak linear response. Units 7/7 (A) and 7/9 (B).
Second order kernels and the perturbation experiment
The results of the perturbation experiments indicate the dynamic characteristics
of the contrast mechanism. We suspected that there was a relation between the
non-linear subunits, which generate the second order responses of Y cells, and the
contrast mechanism. Therefore, we compared the temporal frequency dependence of
the contrast effect with that of the second order frequency kernels (Victor et at. 1977).
IO
PHY
285
R. M. SHAPLEY AND J. D. VICTOR
This was done for the Y cells of Fig. 11. Contour maps of the amplitudes of the
second order kernels are shown in Fig. 12A, B.
290
The conventions for the display of the second order frequency kernel as a contour map are as
follows: The co-ordinates in the plane range independently over the frequencies in the input
stimulus. The height of the surface at a point at (F1, P.) indicates the amplitude of the response
at the frequency F1 + F2. This is the amplitude of the second order frequency kernel, IK2(F1, FA) I .
Similarly, the height of the surface at a point (- F1, F.) indicates the amplitude of the response
at F. -F1, which is IK2(- F1, F,) 1. For each pair of temporal frequencies f1 and ft in the input
signal, these values were determined at points ( ±fj, ft) by Fourier analysis of the impulse train.
For combinatorial reasons, the Fourier component at 2fi was doubled to obtain K2(f1, fi). Also,
the values K,( -fjf,), which correspond to an output frequency of zero, are not defined. These
values, along with the values IK,( ± F1, F) for frequencies F1 and/or F, not in the stimulus were
interpolated by a standard two-dimensional cubic spline. The resulting surface was plotted as
a contour map, with a vertical scale in which one contour line indicates one spike per second.
The tickmarks point downhill. The identity K,(F1, F2) = K2(F2, F1) results in a line of mirror
symmetry running on a 450 angle through the sum frequency region (the upper half of the map).
This is the line F1 = F,, the line of second harmonics. Similarly, the relationship K2(- F,, F) =
K2(F,, F1) creates a line of mirror symmetry running at a 450 angle through the difference
frequency region (the lower half of the map). This line, F. = - F1, is the line of zero output
frequency. It is perpendicular to the first symmetry line, the line of second harmonics.
The amplitudes of the second order kernels for these Y cells are typical in having
a peak at intermediate input frequencies (4-8 Hz) and a steep roll-off at low and
high input frequencies. The best frequencies for producing second order responses
are also those frequencies which produce most contrast effect, as measured by the
phase advances in Fig. 11. This is illustrated for the second harmonic frequencies
from the second order frequency kernels in Fig. 12. The graphs of the second harmonic
amplitudes v8. input frequency are located above the appropriate contour map.
Parametric dependence on contrast: independence of spatial phase
It is important to know whether the shape of the first order frequency kernel
depends on retinal contrast or rather on the size ofthe first order responses themselves.
We could control independently retinal contrast and size of response by variation
of the spatial phase of the grating used as a visual stimulus. By re-positioning a
grating of a given contrast at several spatial phases, we varied first order responses
without changing retinal contrast. If the shape of the first order frequency kernel
(aside from absolute magnitude) depended on the spatial phase, we could conclude
that the size of the responses themselves, rather than contrast alone, is the cause of
this change of shape. This was not the case (as shown below), so we concluded that
response size per se is irrelevant to the contrast effect. Alternatively, we could vary
retinal contrast but maintain an approximately constant size of response, by comparing the frequency kernel of a low contrast grating at a peak spatial phase with
that of a high contrast grating near the spatial phase for a null response. This is
another test of whether response size rather than retinal contrast determines the
shape of the frequency kernels, for under that hypothesis two such kernels should be
similar in shape. In fact, these frequency kernels were different in shape. Thus we
concluded that it is retinal contrast which alters the shape of the first order frequency
kernels.
Results from two such experiments are shown in Fig. 13. The data of Fig. 13 were
291
RETINAL CONTRAST GAIN CONTROL
obtained from an on-centre X cell by varying the spatial phase of a 0-1 c/deg.
grating. The size of the response to the grating presented with a temporal
modulation of 0-10 per sinusoid was reduced by a factor of approximately ten by
moving the grating from a peak position to a spatial phase near the null position. But
z
0
10 -
10
0
V)
._
CD
cA
0
E
5-
5-
'D
-c
C.
E0U
0
-oC
0-
C,)
0I
I
I
I
I
I
31
2-7
9-1
023 0-78
Input temporal frequency (Hz)
F2 (Hz)
31
9-1
2-7
0-78
0-23
1
1
I
I
I
I
I
I
2-7
31
0-23
Input temporal frequency (Hz)
F2 (Hz)
31
2-7
0-23
l
31
9-1
2-7
'C
0-78-
0-23-
0-23-
0-78-
931
Fig. 12. Second order frequency kernels and slices along the second harmonic diagonal
of the two Y cells in Fig. 11. The frequency kernels were obtained with a temporal
stimulus consisting of eight sinusoids, each with a contrast of 0-025, and a spatial
grating of frequency 0-12 c/deg. positioned to produce a maximal linear response.
(This configuration was the reference condition for the perturbation experiments.)
IO-2
292
R. M. SHAPLEY AND J. D. VICTOR
despite the change in the absolute magnitude of the response, the shape of the first
order frequency kernel was essentially unaltered. The comparison of the high contrast grating near its null with a low contrast grating (0-0125 contrast) at its peak
position is also instructive. The responses to these two stimuli were roughly equal on
the average. Nevertheless, there is a striking difference between the shapes of the
two frequency response curves. Previously we have used the phase shift at 8 Hz as
an assay of the contrast effect. In this experiment too this measurement is instructive.
The phase shifts for the two responses to the grating at 0410 contrast were -0-27 if
radians (peak) and -035 if (near null). The phase shift for the low contrast grating
was 0-53 7T.
A
0 Low contrast, peak
A High contrast, peak
A High contrast, near null
3200
-~10-0
.:32
a,
=1-0
E
0-32
0-32
1-0
3-2
10-0 32-0
0-32 1-0
Temporal frequency (Hz)
3-2
1-0
32-0
Fig. 13. A comparison of the effects of changing the contrast and of changing the spatial
phase of a sine grating on the first order frequency kernel. For the on-centre X cell of
A, data were obtained with a 0- 10 c/deg. grating positioned to produce a maximal
linear response with contrasts of 0-0125 (0) and 0-10 (A) per sinusoid. When the
grating was positioned close to the null position, a contrast of 0-10 per sinusoid (A)
was used. For the on-centre Y cell of B, the spatial stimulus was a 0-25 c/deg. grating.
In a position of peak linear response, contrasts of 0-0125 (0) and 0-05 (A) per sinusoid
were used. Near the null position, the temporal signal produced a contrast of 0-05 per
sinusoid (A). Units 24/2 (A) and 8/6 (B).
Essentially the same behaviour is shown by the data obtained from an on-centre
Y cell and presented graphically in Fig. 13B. Here, the spatial phase of a 0-25 c/deg.
grating at a contrast of 0-05 was varied to attenuate the first order response by
a factor of four. Only the magnitude of the first order frequency kernel, not its shape,
varied with spatial phase. However, attenuation of the contrast of the grating by
a factor of four, to 0-0125, had a profound effect on the shape of the first order
frequency kernel. The temporal frequency at which the first order response was
maximal shifted from 8 Hz down to approximately 2 Hz. In this unit again, phase
shift at 8 Hz was a reliable assay of the contrast effect. The phase shifts for the high
contrast gratings were - 0-59 7i (peak) and - 0-60 if (near null). For the low contrast
grating the phase shift was - 0-91 IT.
RETINAL CONTRAST CAIN CONTROL
293
DISCUSSION
The results reported here lead to the hypothesis of a distinct non-linear mechanism
in the cat retina. This mechanism adjusts the sensitivity and dynamic characteristics
of the retina contingent on the average contrast of visual stimuli presented to the
retina. This mechanism affects the first order responses of both X and Y cells, though
it has a stronger effect on Y cells. We will refer to this non-linear mechanism as the
contrast gain control or the contrast mechanism. Crucial features of the contrast
gain control are as follows: (1) it affects phase shifts at high temporal frequencies as
well as amplitudes at low temporal frequencies, (2) it allows energy at one temporal
frequency to affect amplitude and phase shift at other frequencies, (3) it is relatively
insensitive to slow modulation frequencies and the mean light level and (4) it is
independent of spatial phase and not greatly dependent on the spatial frequency of
the visual pattern.
The contrast effect is not trivial
First we show that the contrast effect must reflect internal properties of the retina.
What must be excluded is the hypothesis that the change in shape of the first order
frequency kernels is the consequence of a static saturation. This hypothesis is
excluded because: (1) as contrast increases, the responses which were already large
get even larger, (2) a major effect of contrast is on phase shift of the first order
responses and (3) retinal contrast, rather than response size, controls the shape of
the first order responses. The last fact also excludes the possibility that a peculiarity
of the spike-generating mechanism (or indeed any other transduction after final
spatial pooling) is responsible for the effects we have reported.
We can also exclude light or dark adaptation as an explanation of the effects of
contrast. Fast temporal frequencies (4-15 Hz) were most effective in exerting an
influence on the transfer characteristics (see Fig. 11). Thus any mechanism which is
primarily sensitive to mean level, such as the gain control of light adaptation (EnrothCugell & Shapley, 1973), is ruled out.
Models for the effect of contrast on the first order frequency kernel
On general grounds, a change in shape of the first order frequency kernel with
contrast requires the existence of third order or higher odd order interactions.
One can calculate directly the frequency kernels for a system whose non-linearities are of
finite order. This class of systems does not include systems that contain sharp non-linearities.
Nevertheless, the calculation is useful because it demonstrates the minimal formal requirements
for a contrast effect on the first-order frequency kernel. Suppose for example that the nonlinearities in a system are of order no higher than three. In this instance, the first order frequency
kernel has the form
Q
Y akg3(ffk, -fk) + 3a,3g3(fj,,f,
KI(f1) alg1(fj) + 3aJ k=1
=
fj) (1)
k~j
In this equation, aj and fj are the amplitude and frequency of the jth sinusoidal component in
the input signal. The functions g,, depend only on the system under study, and are Fourier
transforms of the Volterra kernels. In particular, the function g1 is the small signal transfer
function.
R. M. SHAPLEY AND J. D. VICTOR
294
The first order frequency kernel (eqn. (1)) depends not only on g1, but also on g3. (In fact, all
higher order odd order interactions g3, g9, 97... would influence the first order frequency kernel,
were they present in the system.) Since the coefficients of g3 are cubic in the input amplitude, the
contributions of these terms will not scale linearly with input amplitude. The result is that the
first order frequency kernel K1 may change shape as input amplitude increases, for it is the
sum of components that scale as different powers (first and third powers) of the input amplitude.
Yet there are many non-linear systems which contain high odd order non-linear
interactions and which nevertheless do not show such a contrast effect. These nonlinear systems are those that consist of an arbitrary linear filter, L1 followed by
a static non-linearity N, followed by a second linear filter, L2 (Fig. 14A). The first
order frequency kernel for such a system has the approximate form
K1(f1) = c1L1(f1)L2(f1)
(2)
where Li and t2 are the transfer functions of the two linear filters. This formula
follows from the close relationship (Victor & Knight, 1978) of the frequency kernels
and the Fourier transform of the Wiener kernels (Wiener, 1958). In eqn. (2), cl is a
real number that depends on the input signal power and on the characteristics of
the non-linear element N. Eqn. (2) fails to explain the qualitative features of our
ganglion cell data. This is because changing cl can only change the over-all size
rather than the shape of the frequency kernel.
A
-+
L,
N
B
Fig. 14. Simple model non-linear systems rejected as candidates to explain the contrast
gain-control. In A, the input signal is transformed in sequence by a linear filter, L1, a
static nonlinearity, N, and a second linear filter, L.. The model of B is a parallel
combination of two 'sandwiches,' but with different linear and non-linear components.
We are therefore forced to consider non-linear systems more general than a linear/
non-linear/linear sandwich, for example a network that consists of a parallel combination of such sandwiches. A hypothetical system consisting of two linear/nonlinear/linear sandwiches in parallel combination (Fig. 14B) can produce a contrast
effect in some ways similar to what we have observed, provided that the prefilters
(L1, L") and the static non-linearities (N,N') have different characteristics.
RETINAL CONTRAST GAIN CONTROL
295
A particularly attractive 'multiple sandwich' hypothesis is that one path corresponds to the classical 'centre' mechanism and the other corresponds to the classical
'surround'. The predictions of this model are at variance with major qualitative
features of our data: (1) the dependence of the shape of the first order frequency
kernel on input contrast persists for spatial sine gratings of high spatial frequency,
which do not stimulate the classical surround substantially (Figs. 2C, 4C, and 5)
and (2) since the contrast effect is independent of spatial phase (Fig. 13), it is therefore
independent of the degree of net stimulation of either the center or the surround of
the unit in question.
Ic
A
/D
Fig. 15. A two-input non-linear system contemplated as a model for the contrast gaincontrol. The filter L transforms its direct input, ID linearly, provided that the contrast
input, Ic is fixed. I, is extracted from the input signal by the nonlinear network, C,
whose output contains only even order components. The signal Ic alters the characteristics of L in a dynamic fashion.
Two-input models. The spatial phase invariance of the shape of the first order
frequency kernel is a highly constraining fact. Therefore we developed a model that
contains this feature in its initial formulation. This model is shown in Fig. 15.
We consider the classical centre/surround mechanisms of a ganglion cell's receptive
field to constitute the approximately linear filter, L, and its direct input, ID. This
direct pathway is approximately linear in space as well as time, so its response to
inputs along this pathway varies sinusoidally with the spatial phase of the stimulus.
We postulate that its deviations from linearity are gentle, inessential ones that
can be ignored in the stimulus range used in these studies. However, the linear
element receives another input, IC. The signal IC is produced by the contrast gain
control C. We hypothesize that C measures the contrast of the stimulus at many
separated points in the visual field over a region at least as large as the conventional
centre and surround. In this way, the signal Ic can be independent of the spatial
phase of a grating stimulus. (The spatial phase independence would not apply to
spatial gratings so low in spatial frequency that they are equivalent to diffuse light.)
Since contrast, rather than intensity, is measured by IC, the network C which produces
Ic must contain an even order non-linearity. We propose that, given a fixed contrast
signal IC, the filter in the direct pathway transforms its direct input, InD in a linear
R. M. SHAPLEY AND J. D. VICTOR
296
manner. This formalizes the concept that L is a basically linear filter, but that the
filter characteristics are parameteric in local retinal contrast.
The interaction of IC and ID. The contrast signal Ic may be thought of as primarily
a steady level which may have a small modulated component. If the contrast gain
control signal Ic had a large modulation, the phase shift curves in Fig. 11 would
depend strongly on the assay frequency used, and they do not.
The effect of contrast on both amplitude and phase rules out hypotheses that the
contrast signal Ic affects only the gain or only the phase shift of L. We need to
hypothesize a mode of action of Ic on L that alters both amplitude and phase of the
first order frequency kernel. As contrast increases, the responses at the high frequencies are enhanced relative to the responses at low frequencies. This suggests that
the effect of contrast may be to decrease the number of effective low pass stages in
the linear filter of the direct pathway, L. This would produce a phase advance at
frequencies above the corner frequency of the low pass filters involved. In addition,
elevated contrast levels signalled by IC might act to shorten time constants in the
direct pathway. This would produce a phase advance over those frequencies between
the corner frequency of the high frequency roll-off at low contrast and the corner
frequency at high contrast.
However, these mechanisms do not explain why the amplitudes of the response at
low temporal frequencies (2 Hz or below) grow much less than proportionally with
contrast. An increase in the effective number of high pass stages in the direct pathway filter, L, might explain this behavior. Furthermore, such a parametric dependence on the contrast signal, Ic, will also cause a phase change at low temporal
frequencies, in agreement with the data. Another possible model that could create
the necessary high and low frequency changes with a single mechanism is one in
which the contrast signal, IC increases the amount of feedback in a 'self inhibiting'
loop within the filter L.
Characteristics of the contrast network
The fact that the contrast gain control, C, measures contrast, rather than
illumination, implies that its response must be even order in light intensity.
A contrast-resversed pattern has to produce in C the same response as the original
pattern. Thus, C must produce only even order non-linear responses. But the fact that
relatively fine gratings are adequate stimuli for this network implies that the spatial
pooling which occurs before the even order non-linearity must be limited in extent.
In addition, the fact that the output of this network is insensitive to spatial phase
implies that its response must contain contributions from many spatial pools. (This is
precisely the argument used to deduce the existence of subunits in the receptive
field of Y cells from the existence of a spatial phase-invariant frequency-doubled
response (Hochstein & Shapley, 1976b; Victor et al. 1977).
It is likely that the non-linear subunits involved in generation of the contrast
signal are the same subunits that lead to the characteristic frequency-doubled
responses of Y cells (Hochstein & Shapley, 1976b; Victor et al. 1977). The perturbation experiments show that the temporal properties of the input to the contrast
mechanism are similar to the temporal properties of the second order frequency
kernels of Y cells. Also, the spatial characteristics of patterns which are effective
RETINAL CONTRAST GAIN CONTROL
297
stimuli for the contrast mechanism and the Y cell non-linear pathway are similar,
as was shown directly in Fig. 6. We cannot exclude now the possibility that the
subunits involved in C are distinct from those involved in generating the non-linear
excitatory response of Y cells. However, it must be true that these two non-linear
mechanisms have similar spatial and temporal characteristics.
Therefore, a plausible though speculative hypothesis is that there is one major
essential non-linearity in the retina. It drives the Y cells directly and excites them.
By another pathway, it suppresses the responses of all ganglion cells to slow changes
but speeds up and perhaps boosts the responses to high temporal frequencies of
modulation.
Relation to previous work
The contrast mechanism required by our findings can be invoked to provide an
explanation for many other seemingly diverse results. For example, the responses
of cat ganglion cells to square wave illumination of an ascending series of intensities
become more transient and have a reduced latency (Cleland & Enroth-Cugell, 1970).
These effects could be accounted for by the automatic gain control responsible for
light adaptation (Cleland & Enroth-Cugell, 1970; Enroth-Cugell & Shapley, 1973).
However, the latency changes and changes in dynamics suggest that the contrast
mechanism may be even more important in the production of these effects. In comparable experiments performed in our laboratory, we have observed a similar
phenomenon in the responses of X and Y cells to square-wave contrast reversal of
sine gratings. As contrast was increased, the square-wave responses became more
transient and the latency decreased (Hochstein, S., Kaplan, E., Shapley, R. M. and
Victor, J. D., unpublished results). The latency decreased about twice as much for
Y cells as for X cells. The magnitude and characteristics of this effect suggest that
the contrast mechanism is probably involved. The fact that the contrast gain control
affects Y cells more than X cells may explain why the square-wave responses of
Y cells tend to be more transient than those of X cells (Cleland, Dubin & Levick,
1971) when high contrast stimuli are used. The square wave responses of X and Y
cells can be quite similar at lower contrast (Hochstein & Shapley, 1976a).
The idea of two gain controls originated with Werblin's work on adaptation in
the mudpuppy retina (Werblin, 1972; Werblin & Copenhagen, 1974). The flux gain
control affected bipolar cells and therefore every other element in the retina proximal
to the bipolars. The gain control for change, what we refer to here as the contrast
gain control, was born in the inner plexiform layer and affected amacrine and ganglion cell responses. The mudpuppy experiments were done with a spinning windmill
pattern. This windmill was the spatio-temporal visual stimulus UWed to excite the
contrast gain control. Other workers have used similar stimuli on cat ganglion cells.
Using a spinning windmill or a rotating radial grating, they have found evidence
for a 'suppressive surround' inX, Y, andW ganglion cells (Jakiela, 1978, and personal
communication; Cleland & Levick, 1974). This 'suppressive surround' is, we believe,
another name for the contrast gain control. In another paper it will be shown that
the characteristics of the 'suppressive surround' are the same as those of the
contrast mechanism (Shapley, R. M. and Victor, J. D., in preparation).
298
R. M. SHAPLEY AND J. D. VICTOR
We thank F. Ratliff for his advice and encouragement. This work was supported by grants
from the U.S. National Eye Institute nos. EY 188, EY 1428 and EY 1472. One of us (R.M.S.)
was supported by a Career Development Award from the National Eye Institute. Also, we thank
Dr William Scott of Hoffmann-LaRoche for his gift of diallyl-bis-nortoxiferine used in the
experiments.
REFERENCES
CLELAND, B. G., DUBIN, M. W. & LEvIcE, W. R. (1971). Sustained and transient neurones in
the cat's retina and lateral geniculate nucleus. J. Phy8iol. 217, 473-496.
CLELaNim, B. G. & ENROTE-CUGELL, C. (1970). Quantitative aspects of gain and latency in the
cat retina. J. Physiol. 206, 73-91.
CLELAND, B. G. & LEVIOK, W. R. (1974). Brisk and sluggish concentrically organized ganglion
cells in the cat's retina. J. Physiol. 240, 421-456.
DE GROOT, S. R. & MIAZUR, P. (1969). Non-equilibrium Thernodynamic, pp. 143-150. Amsterdam: North-Holland Publishing Co.
ENROTE-CUGELL, C. & ROBSON, J. G. (1966). The contrast sensitivity of retinal ganglion cells of
the cat. J. Physiol. 187, 517-552.
ENROTE-CUGELL, C. & SHArPLEY, R. M. (1973). Adaptation and dynamics of cat retinal ganglion
cells. J. Physiol. 233, 271-309.
HocusTriN, S. & SE.ArLEY, R. M. (1976a). Quantitative analysis of retinal ganglion cell classifications. J. Phy8iol. 262, 237-264.
Hocns~rw, S. & SIArLEy, R. M. (1976b). Linear and nonlinear spatial subunits in Y cat retinal
ganglion cells. J. Phvyeiol. 262, 265-284.
JAIE A, H. G. (1978). The Effect of Retinal Image Motion on the Responsiveness of Retinal
Ganglion Cells in the Cat. Ph.D. dissertation, North-Western University, Evanston, Illinois,
U.S.A.
SHAErEY, R. M. & RossETro, M. (1976). An electronic visual stimulator. Behav. Res. Meth. &
Instrum. 8, 15-20.
VICTOR, J. D. & K.NIGHT, B. W. (1978). Nonlinear analysis with an arbitrary stimulus ensemble.
Quart. apple. Math., (In the Press.)
VICTOR, J. D., SEAPLEY, R. M. & K.NIGHT, B. W. (1977). Nonlinear analysis of cat retinal ganglion cells in the frequency domain. Proc. natn. Acad. Sci. U.S.A. 74, 3068-3072.
WERBLIN, F. S. (1972). Lateral interactions at the inner plexiform layer of the retina: antagonist response to change. Science, N.Y. 175, 1008-1009.
WRRBLN F. S. & COPENHAGEN D. R. (1979). Control of retinal sensitivity. III. Lateral interactions at the inner plexiform layer. J. gen. Physiol 63, 88-110.
WImNER, N. (1958). Nonlinear Problems in Random Theory. New York: The Technology Press
of M.I.T. and Wiley.
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