Functional Circuitry of the Retinal Ganglion Cell’s Nonlinear Receptive Field

Functional Circuitry of the Retinal Ganglion Cell’s Nonlinear Receptive Field
The Journal of Neuroscience, November 15, 1999, 19(22):9756–9767
Functional Circuitry of the Retinal Ganglion Cell’s Nonlinear
Receptive Field
Jonathan B. Demb, Loren Haarsma, Michael A. Freed, and Peter Sterling
Department of Neuroscience, University of Pennsylvania School of Medicine, Philadelphia, Pennsylvania 19104-6058
A retinal ganglion cell commonly expresses two spatially overlapping receptive field mechanisms. One is the familiar “center/
surround,” which sums excitation and inhibition across a region
somewhat broader than the ganglion cell’s dendritic field. This
mechanism responds to a drifting grating by modulating firing
at the drift frequency (linear response). Less familiar is the
“nonlinear” mechanism, which sums the rectified output of
many small subunits that extend for millimeters beyond the
dendritic field. This mechanism responds to a contrastreversing grating by modulating firing at twice the reversal
frequency (nonlinear response). We investigated this nonlinear
mechanism by presenting visual stimuli to the intact guinea pig
retina in vitro while recording intracellularly from large brisk and
sluggish ganglion cells. A contrast-reversing grating modulated
the membrane potential (in addition to the firing rate) at twice
the reversal frequency. This response was initially hyperpolarizing for some cells (either ON or OFF center) and initially
depolarizing for others. Experiments in which responses to bars
were summed in-phase or out-of-phase suggested that the
single class of bipolar cells (either ON or OFF) that drives the
center/surround response also drives the nonlinear response.
Consistent with this, nonlinear responses persisted in OFF
ganglion cells when ON bipolar cell responses were blocked by
L-AP-4. Nonlinear responses evoked from millimeters beyond
the ganglion cell were eliminated by tetrodotoxin. Thus, to relay
the response from distant regions of the receptive field requires
a spiking interneuron. Nonlinear responses from different regions of the receptive field added linearly.
Key words: in vitro retina; guinea pig; nonlinear subunit; shift
effect; spiking amacrine cell; bipolar cell; tetrodotoxin; L-AP-4
A retinal ganglion cell encodes information from at least two
computational mechanisms. One is familiar, the “linear” receptive field, which computes local temporal contrast by combining
excitatory and inhibitory signals over both a narrow region (the
“center”) and a wider region (the antagonistic “surround”) (Barlow, 1953; Kuffler, 1953; Rodieck, 1965; Enroth-Cugell and Pinto,
1970). The other mechanism is less familiar, the “nonlinear”
receptive field, which computes global changes in contrast magnitude by summing signals from independent regions (“subunits”)
(Enroth-Cugell and Robson, 1966; Hochstein and Shapley, 1976;
Victor and Shapley, 1979a; Cox and Rowe, 1996). The subunit,
described in detail for the cat’s Y (a) cell, is considered nonlinear
because it increases activity to a contrast increment more than it
decreases activity to a contrast decrement (or vice versa); in other
words, the subunit rectifies its input signal (Hochstein and Shapley, 1976; Victor, 1988). The subunit covers a region narrower
than the ganglion cell’s dendritic field, but the mosaic of subunits
is much broader, extending for millimeters beyond the dendritic
field. When the visual scene contains mostly high spatial frequencies, the nonlinear receptive field can dominate the ganglion cell’s
output to the brain (Enroth-Cugell and Robson, 1966; Hochstein
and Shapley, 1976; Derrington et al., 1979; Victor and Shapley,
1979a).
Although the circuit for the center/surround receptive field is
fairly well understood, the circuit for the nonlinear receptive field
remains to be elucidated (Wässle and Boycott, 1991; Sterling,
1998). One would like to know: how does the subunit rectify; how
does its signal travel millimeters across the retina; and how do
signals from multiple subunits combine at the ganglion cell? To
answer these questions, we recorded intracellularly from ganglion
cells in the intact guinea pig retina in vitro. There, we could apply
antagonists to transmitter receptors and ion channels to manipulate specific aspects of the circuit.
Received June 14, 1999; revised Aug. 18, 1999; accepted Sept. 7, 1999.
This work was supported by National Institutes of Health, National Eye Institute
Grants F32-EY06850 (J.B.D.), T32-EY07131 (L.H.), EY11138 (M.A.F.), and
EY00828 (P.S.).
We thank Robert Smith and Yen-Hong Kao for technical advice, Madeleine
Johnson for technical assistance, and Sharron Fina for help in preparing this
manuscript.
Drs. Demb and Haarsma contributed equally to this work.
Correspondence should be addressed to Dr. Jonathan B. Demb, Department of
Neuroscience, University of Pennsylvania School of Medicine, 123 Anatomy/Chemistry Building, Philadelphia, PA 19104-6058. E-mail: [email protected]
upenn.edu.
Copyright © 1999 Society for Neuroscience 0270-6474/99/199756-12$05.00/0
MATERIALS AND METHODS
In vitro retina. Our experiments employed a superf used, flattened preparation of the intact mammalian retina (Jensen, 1991; Dacey and Lee,
1994). A guinea pig (350 –700 gm) was anesthetized with ketamine –
xylazine and overdosed with pentobarbital. Both eyes were enucleated in
room light and placed in oxygenated (95%–5% carboxy mixture) Ames
medium (Sigma, St. L ouis, MO) with sodium bicarbonate (1.9 gm / l) and
glucose (0.8 gm / l). Each eye was hemisected, and the anterior half
(cornea, lens, and vitreous) was gently peeled away from the posterior
eyecup. The retina, with pigment epithelium, choroid, and sclera still
attached, was flattened by cutting five to six radial slits and applied scleral
side down to filter paper. The retina was placed in a chamber on the stage
of an upright microscope and superf used (2–3 ml /min) with oxygenated
Ames medium at 34°C. Drugs dissolved in superf usate were kept in
reservoirs connected by valves to the chamber. Agents used were tetrodotoxin (TTX) (Sigma) and L-2-amino-4-phosphonobutyric acid (LAP-4) (Research Biochemicals, Natick, M A). Glass electrodes (tip resistance of 150 – 400 M[SCAP]V) were filled with 1% pyranine (Molecular
Probes, Eugene, OR) to visualize the pipette tip and 2% Neurobiotin
(Vector Laboratories, Burlingame, CA) in 1 M KC l buffered with 0.1 M
Tris, pH 7.4. In some experiments, lidocaine N-ethyl bromide (QX-314)
(Research Biochemicals) was added to the pipette solution.
Intracellular recording. To visualize ganglion cells, 5–10 drops of acri-
Demb et al. • Circuitry of Nonlinear Receptive Field
J. Neurosci., November 15, 1999, 19(22):9756–9767 9757
Figure 1. Ganglion cells were studied in the visual streak. A, Schematic of flattened retina showing visual streak (shaded reg ion), location of recorded
cells (open circles), and location of cell in B ( filled circles). B, ON center ganglion cell (arrow marks axon). C, As a sine wave grating drifts over a ganglion
cell, each bright phase evokes depolarization and spiking. To measure the response in the membrane potential, spikes were removed by linear
interpolation (see Materials and Methods), and 20 consecutive cycles were averaged. In the following figures, unless noted otherwise, gratings are
sinusoidal, 100% contrast, and presented at 2 Hz; central gratings are 0.5 mm OD; peripheral gratings are 2.5 mm inner diameter (I D). Coarse gratings
(low spatial frequency) are 1.1 cycles/mm; fine gratings (high spatial frequency) are 4.3 cycles/mm. The gray dashed line indicates the average resting
potential measured immediately before and 1 sec after the stimulus was presented.
dine orange (0.001%; Molecular Probes) were added to the superf usate.
Dye accumulated in ganglion cell somas and fluoresced to near-UV light
(400 – 440 nm) from a 50 W mercury arc lamp transmitted through the
microscope’s 403 objective. Large somas (15–25 mm in diameter) in the
visual streak were selected for intracellular recording. The membrane
potential was amplified (NeuroData IR-283; NeuroData Instruments
Corp., Delaware Water Gap, PA), continuously sampled at 2 kHz, and
stored on computer (AxoScope software; Axon Instruments, Foster C ity,
CA). Following recording, Neurobiotin was injected (10.5 nA with 50%
duty cycle, 3–10 min).
The retina was fixed in 4% paraformaldehyde in 0.1 M phosphate
buffer (PB), pH 7.4, for 45– 60 min at room temperature and then stored
in PB overnight at 4°C. To visualize the filled cells, the retina was
isolated and reacted for streptavidin-C Y3 at room temperature: 1 hr in
6% normal goat serum (NGS), 1% Triton X-100 (TX), and 0.5% DMSO
in 0.05 M Tris-buffered saline (TBS); 2 hr in 0.2% streptavidin-C Y3, 3%
NGS, 1% TX, and 0.5% DMSO in 0.05 M TBS; and rinsed for 30 min in
0.05 M TBS. The retina was mounted in Vectashield, and cells were
visualized with fluorescence microscopy.
Stimuli. C ells were classified as ON or OFF center using spots and
annuli, and then the nonlinear receptive field was probed using gratings.
Sine wave or square wave gratings of various spatial frequencies drifted
or contrast-reversed at 2 Hz. Stimuli were defined in terms of Michelson
contrast: (Imax 2 Imin)/(Imax 1 Imin), where Imax and Imin are the peak and
trough intensities. Thus, the mean intensity stayed constant over time,
and stimulus intensity varied around the mean with a maximum possible
contrast of 100%. We programmed the stimuli in Matlab (MathWorks,
Natick, M A), using extensions provided by the high-level Psychophysics
Toolbox (Brainard, 1997) and the low-level Video Toolbox (Pelli, 1997).
The stimulus was displayed on a 1-inch-diameter computer monitor
with green (P43) phosphor (L ucivid MR1–103; MicroBrightField,
Colchester, V T), projected through the top port of the microscope and
focused onto the retina with a 2.53 objective. The mean intensity of the
stimulus was 28 nW/mm 2 at 545 nm light. Given the peak sensitivity of M
cones, which predominate in the guinea pig visual streak (530 nm)
(Jacobs and Deegan, 1994; Rohlich et al., 1994), this translates to ;10 6
isomerizations per cone per second. The monitor resolution was 640 3
480 pixels with 60 Hz vertical refresh; stimuli were confined to a square
region of 430 pixels on a side (3.7 mm on the retina). The relationship
between voltage and monitor intensity was linearized in the software
with a lookup table.
We measured the optical line spread at the plane of the retina. A bright
edge was stepped across a 200-mm-diameter aperture mounted on a
radiometer (IL1400A; International Light Inc., Newburyport, M A). The
measured relative intensity at each position was fit by the expected
relative intensity convolved with a gaussian with SD of 19 mm (f ull width
at half height of 40 mm).
Data anal ysis. Data were analyzed with programs written in Matlab.
Spikes were detected off-line by analyzing the first derivative of the
membrane potential response and finding points above a threshold.
Poststimulus time histograms were accumulated across 20 stimulus cycles
(bin width of 16.7 msec). To analyze changes in the membrane potential,
spikes were removed by linear interpolation of the voltage trace from 5
msec before each spike to 8 –13 msec after each spike. This did not affect
the subsequent Fourier analysis at the low stimulus temporal frequency.
The average membrane potential was analyzed across 20 stimulus cycles
(Fig. 1C). To quantif y the signal, we measured amplitude at the stimulus
frequency, Fourier F1 component (2 Hz), and twice the stimulus frequency, Fourier F2 component (4 Hz).
RESULTS
Fifty ganglion cells were studied, mostly in the visual streak (Fig.
1 A). Somas were 15–25 mm in diameter with monostratified
dendritic fields spanning 350 –700 mm; the tracer-filled axons
could be followed toward the optic disk (Fig. 1 B). Most cells were
OFF center (n 5 42), depolarizing when a small spot dimmed
over the dendritic field. The population included both “brisk”
cells whose depolarizations peaked in 50 –150 msec, and “sluggish” cells whose depolarizations peaked in 200 –250 msec (Cleland and Levick, 1974). All cells exhibited nonlinear responses to
contrast-reversing gratings (i.e., a dominant F2 response component), and so none were homologous to linear X cells in cat
retina. Because drug effects were similar in brisk and sluggish
cells, the results have been combined in the population analyses.
9758 J. Neurosci., November 15, 1999, 19(22):9756–9767
Demb et al. • Circuitry of Nonlinear Receptive Field
A cell was considered healthy as long as the membrane potential (Em) was more negative than 245 mV and stable. The average
resting potential was 254 6 8 mV (mean 6 SD), and it often held
steady for 0.5– 4 hr. Nearly half of the cells lasted for .1 hr.
Resting spike rates averaged 12 6 11 spikes/sec. The most stable
recordings gave slightly higher spontaneous rates (15 6 7 spikes/
sec; n 5 11) and maximal evoked responses of 119 6 48 spikes/
sec. The guinea pig ganglion cells in our experiments fired spontaneously at the same rate as cat Y cells and gave evoked
responses of similar magnitude (Troy and Robson, 1992). This
seemed remarkable given that the cat recordings were made
extracellularly in the intact animal; whereas the present cells were
penetrated by a sharp electrode in a flattened retina bathed in
artificial medium.
Linear and nonlinear responses are represented in the
membrane potential
Our first finding was that guinea pig retina contains ganglion cells
that express both linear and nonlinear responses (Figs. 2–5). The
linear response was evoked by a drifting grating, which strongly
modulated the membrane potential at the drift rate, producing a
large amplitude at the stimulus frequency (Fourier F1 component) (Figs. 1C, 2). The nonlinear response was evoked by a
contrast-reversing grating, which strongly modulated the membrane potential at twice the reversal rate, producing a large
amplitude at twice the stimulus frequency (Fourier F2 component) (Fig. 2). This distinction between the linear and nonlinear
responses has been thoroughly described for Y cells and nonlinear W cells in cat (Hochstein and Shapley, 1976; Troy et al., 1989,
1995; Rowe and Cox, 1993) and for “Y-like” cells in monkey
(Kaplan and Shapley, 1982).
The specific properties of the F1 and F2 response components
observed in the spike train were clearly evident in the membrane
potential. Thus, the F1 component was sensitive to the spatial
position of a contrast-reversing grating and was absent at certain
positions (“null phases”); whereas the F2 component was similar
at all grating positions (Fig. 3) (Hochstein and Shapley, 1976). We
measured the ratio of the average F2 component to the maximal
F1 component in response to a contrast-reversing grating of high
spatial frequency at several grating positions (n 5 12, 2 ON, 10
OFF). Across cells, the F2/ F1 component ratio was similar for the
membrane potential response (ratio, 2.0 6 1.0) and the spike
response (ratio, 2.2 6 1.4). This ratio is similar to that reported
for Y cells and Y-like cells (Enroth-Cugell and Robson, 1966;
Hochstein and Shapley, 1976; Kaplan and Shapley, 1982).
The membrane potential’s F1 response component was maximal to a coarse contrast-reversing grating (bar width approximately equal to dendritic field width); whereas the F2 response
component was maximal to a fine contrast-reversing grating (approximately one-twentieth of the dendritic field width) (Figs. 3, 4)
(Hochstein and Shapley, 1976). The membrane potential also
displayed the expected relative F1 and F2 response components to
both central and peripheral contrast-reversing gratings. Thus, the
F1 component was maximal to a central, coarse stimulus; whereas
the F2 component was maximal to a fine stimulus in both center
and periphery (Fig. 5) (Derrington et al., 1979). Because all key
features of the F1 and F2 response components are represented in
the membrane potential, we could measure them when the ganglion cell spikes were blocked.
Figure 2. Frequency-doubled, nonlinear response emerges when a fine
grating reverses contrast. Lef t column, OFF center cell depolarizes to the
dark phase of a coarse grating drifted over its receptive field and hyperpolarizes to the bright phase. The response to drifting gratings includes a
large Fourier component at the drift frequency (F1 component). Combining gratings drifting leftward and rightward forms a stationary grating
that reverses contrast (sine wave reversal). This contrast-reversing grating
evokes an “observed” response (thin line), ; 10 mV peak-to-peak, nearly
as large as the “predicted” response, corresponding to the summed
responses to the two drifting gratings (DL 1 DR ; thick line). The difference is mostly caused by a small F2 response component that emerges to
the contrast-reversing grating, calculable by Fourier analysis, but not
obvious in the trace. Bar graph shows a good match between the predicted
and observed F1 component and a slightly higher than predicted F2
component in response to a coarse, contrast-reversing grating. Right
column, Fine drifting grating evokes a small response at the drift frequency. A contrast-reversing grating evokes a large response at twice the
rate of contrast reversal (a large F2 component, arrows). The observed
response is quite different from the predicted response. Bar graph shows
that the observed F2 component in the response to a fine, contrastreversing grating was significantly greater than predicted (*p , 0.05; t 5
2.84; one-tailed t test; df 5 4). The average F2 component in the response
to a fine, contrast-reversing grating was just under half the amplitude of
the average F1 component in the response to a coarse, contrast-reversing
grating.
Nonlinear response to a peripheral grating can be
initially depolarizing or hyperpolarizing
The nonlinear response measured in the spike train to a peripheral contrast-reversing grating was generally considered an excitatory response, i.e., firing above the background rate (Kruger
and Fischer, 1973; Derrington et al., 1979) (but see Fischer et al.,
1975; Watanabe and Tasaki, 1980). However, the responses measured in the membrane potential demonstrated two distinct patterns. As expected, some cells (14 of 41) initially depolarized
50 –100 msec after each contrast reversal of a peripheral grating,
and this increased spiking above the mean level (Fig. 6, left
columns). However, most cells (27 of 41) initially hyperpolarized
Demb et al. • Circuitry of Nonlinear Receptive Field
J. Neurosci., November 15, 1999, 19(22):9756–9767 9759
Figure 4. Linear and nonlinear responses are tuned reciprocally over a
wide range of spatial frequencies. A, OFF center cell response to the
coarse, contrast-reversing gratings had a large F1 component and small F2
component; response to fine gratings had a small F1 component and a
large F2 component. B, Plot of F1 and F2 response components for cell in
A. C, Same plot for the average response of five cells (error bars indicate
SEM). Horizontal lines mark average noise levels for F1 component (thin)
and F2 component (thick) measured in a baseline condition (0% contrast)
at the same mean luminance.
with a sharp transient 50 –100 msec after each contrast reversal
that suppressed spiking. This was followed by depolarization that
drove spiking above the mean rate (Fig. 6, right columns). This
grouping, based on positive or negative changes following contrast reversal, necessarily divides the cells into two groups, but
this separation may be meaningful because L-AP-4 affected the
two cell groups differently (see below).
The two patterns of response to a peripheral contrast-reversing
grating did not correspond to whether the ganglion cell was ON
versus OFF center. For example, an OFF cell could display either
one of the two response patterns (Fig. 6, top row). However, there
was some relationship between the response to a peripheral
grating and the time course of the center response. Thus, most
OFF cells with an initially depolarizing response were sluggish
(7of 9), whereas, most OFF cells with an initially hyperpolarizing
response were brisk (14 of 20).
The nonlinear response measured to a central contrastreversing grating [500 mm outer diameter (OD)] was typically
4
Figure 3. Nonlinear response is independent of grating position. Lef t
column, Coarse grating reversed contrast and was presented at six positions, offset successively by 30° (grating cycle is 360°). ON center cell’s F1
response component was maximal at first and last positions (arrows). F2
response component was approximately equal at all positions but most
apparent in middle traces where F1 component is small. T hick line shows
for each trace the sine waves (summed after subtracting the mean)
corresponding to the F1 and F2 components. Graph shows F1 and F2
component amplitudes as a f unction of grating position [each trace above
contributes two points at the recorded position (e.g., 21°) and by reanalyzing after shifting by one half-cycle (e.g., 201°)]. F1 component reaches
a maximum amplitude of 2 mV (or 15 spikes) and modulates with spatial
position, whereas F2 component is ;0.5 mV (or 6 spikes) amplitude and
invariant with spatial position. Fitted f unctions are a negative cosine (F1
component) and a line (F2 component). Right column, To a fine grating,
F2 response component was stronger than F1 component at all spatial
positions. A similar result was observed in 11 additional cells (1 ON, 10
OFF; see Results).
9760 J. Neurosci., November 15, 1999, 19(22):9756–9767
Figure 5. Nonlinear response evoked by a peripheral, contrast-reversing
grating far beyond the ganglion cell’s dendritic field has lower amplitude but the same spatial tuning as nonlinear response evoked by a
central grating. Central grating was 2.3 mm OD; peripheral grating was
presented as an annulus with 2.5 mm I D. Other conventions are the same
as Figure 4C.
biphasic. The response could be initially hyperpolarizing then
depolarizing, or vice versa, and its waveform varied markedly
across cells. A qualitative grouping suggested four to five types of
waveform (n 5 15), but a detailed classification remains to be
done. For the current study, however, the drug effects on the
nonlinear response to a central grating were similar across cells,
and so they have been combined in the population analyses.
Evidence that a single class of cone bipolar cell can
generate the nonlinear response
The ganglion cells studied here are monostratified, branching in
either the inner or outer strata of the inner plexiform layer. Thus,
each receives synapses from a single class of cone bipolar cell
(ON or OFF), which can generate the ganglion cell’s classical
center/surround response (Wässle and Boycott, 1991; Sterling,
1998). A center spot (bright for ON ganglion cells, dim for OFF
ganglion cells) would increase the bipolar cell’s glutamate release,
whereas an annulus (bright for ON ganglion cells, dim for OFF
ganglion cells) would decrease the bipolar cell’s glutamate release. A monostratified amacrine cell’s contribution to the surround response would also be driven by the same class of bipolar
cell. Physiological evidence for this model comes from measurements of ganglion cell center/surround responses while blocking
ON bipolar responses with L-AP-4 (Shiells et al., 1981; Slaughter
and Miller, 1981). Both the center response to a spot and the
surround response to an annulus were blocked by L-AP-4 in ON
ganglion cells but not in OFF ganglion cells (Schiller, 1982;
Knapp and Mistler, 1983; Bolz et al., 1984).
Might the ganglion cell’s nonlinear response also arise from a
single class of bipolar cell (ON or OFF)? To investigate this, we
presented two sets of bars that reversed contrast over time (i.e.,
black 4 3 white). Each set of bars occupied half the area of the
Demb et al. • Circuitry of Nonlinear Receptive Field
receptive field center, and they were spatially complementary.
Combined in-phase, they created a spot and combined out-ofphase, they created a contrast-reversing grating (Fig. 7A). The
responses to the two sets of bars when summed in-phase matched
the shape of the response to a spot and nearly matched the
amplitude. Presumably, the match arises because both a spot and
the complementary sets of bars excite the same OFF bipolar cells.
The responses to the two sets of bars when summed out-of-phase
matched the shape of the response to a contrast-reversing grating
and most of the amplitude. In short, over the dendritic field, both
the center response to the spot and the nonlinear response to the
contrast-reversing grating could be predicted simply by summing
the responses elicited by the same sets of bars.
We performed a similar experiment in the periphery. Two
complementary sets of contrast-reversing bars were presented
that combined in-phase to create an annulus and combined outof-phase to create a peripheral contrast-reversing grating (Fig.
7B). The responses to the two sets of bars when summed in-phase
matched the shape of the response to an annulus. Presumably, the
match arises because both an annulus and the complementary
sets of bars inhibit the same OFF bipolar cells. The responses to
the two sets of bars when summed out-of-phase matched the
shape of the response to a peripheral contrast-reversing grating.
In short, beyond the dendritic field, both the surround response to
the annulus and the nonlinear response to the contrast-reversing
grating could be predicted simply by summing the responses
elicited by the same sets of bars.
This result, that the summation of bar responses could predict
both center/surround responses to a spot/annulus and nonlinear
responses to a grating in both center and periphery held for all
cells studied (seven OFF, one ON), including both sluggish and
brisk (Fig. 7). That the same component responses, added inphase or out-of-phase, could predict both center/surround and
nonlinear responses, suggested that the input driving the two
mechanisms is the same. Because the center/surround is driven by
a single class of bipolar cell (ON or OFF), it follows that the
nonlinear mechanism is driven by the same single class of bipolar
cell.
L-AP-4 does not reduce the nonlinear response in OFF
ganglion cells
If the nonlinear response in an OFF center ganglion cell were
driven solely by OFF bipolar cells, the response should be undiminished when ON bipolar cell light responses are blocked by
L-AP-4 (Shiells et al., 1981; Slaughter and Miller, 1981; Nawy and
Jahr, 1990). To test this, we applied L-AP-4 (10 mM, n 5 2; 40 mM,
n 5 12). An ON ganglion cell’s light responses were blocked in 20
sec, indicating full block of ON cone bipolar cells (Fig. 8 A). In
OFF ganglion cells, the resting potential was unchanged (initial,
251 6 9mV; L-AP-4, 250 6 11 mV; n 5 14), but to a central
contrast-reversing grating, the average F2 response component
increased by fourfold (4.2 6 2.9) (Fig. 8). When the drug was
washed out, the F2 response component declined to 2.1 6 1.1
times the initial level (Fig. 8 B). To a peripheral contrast-reversing
grating, the average F2 response component in cells with an
initially hyperpolarizing response increased in the presence of
L-AP-4 by fourfold at the three highest contrasts (4.3 6 3.1 times
initial) (Fig. 9). To the same stimulus, the average F2 response
component in cells with initially depolarizing responses decreased ;25% in the presence of L-AP-4 at the three highest
contrasts (0.75 6 0.76 times wash) (Fig. 9), but responses were
significantly lower only at 12.5 and 25% contrast (t 5 2.47 and
Demb et al. • Circuitry of Nonlinear Receptive Field
J. Neurosci., November 15, 1999, 19(22):9756–9767 9761
2.51; both p , 0.05; one-tailed t test; df 5 4). In these cells, the F2
component in the response to a central grating was not affected by
L-AP-4.
On the whole, the nonlinear response in OFF ganglion cells is
not blocked by L-AR-4’s blocking of ON bipolar cells. For most
cells and in most conditions, the nonlinear response is enhanced,
possibly because of a general reduction of inhibition attributable
to L-AP-4 effects on type III metabotropic glutamate receptors
(mGluR) that distribute widely on amacrine processes (Hartveit
et al., 1995; Koulen et al., 1996). This agreement between the bar
summation experiment and the L-AP-4 effects suggests that nonlinear responses arise from a single class of bipolar cell.
In those cells with an initially depolarizing response to a
peripheral contrast-reversing grating, L-AP-4 significantly reduced responses at low contrast. This might suggest that ON
bipolar cells contribute to these responses at low contrast. However, it seems more plausible that this effect could also arise from
the effect of L-AP-4 on amacrine cell type III mGluRs. In Figure
7, both cells displayed a depolarizing response to a peripheral
grating, which could be predicted in the bar summation experiment. Therefore, it seems most likely that, even in these cells, the
nonlinear response to a peripheral grating is driven by the same
single class of bipolar cells that drives the center/surround.
Nonlinear response to a peripheral grating requires
action potentials
Figure 6. Initial response to a peripheral, contrast-reversing grating can
be either depolarizing or hyperpolarizing. Lef t column, C ertain cells,
both OFF center (top) and ON center (middle), respond to each square
wave reversal (arrows) of a peripheral grating with a transient depolarization and a burst of spikes above the mean rate (horizontal line). Mean
response (dark trace) 6 SD ( gray reg ions) for two ON and 12 OFF cells
is shown (bottom). Right column, Other ganglion cells, both OFF (top) and
ON (middle), responded to each square wave reversal (arrows) with a
transient hyperpolarization and a pause in spiking followed by a burst in
spiking above the mean rate. The initially hyperpolarizing response had a
shorter latency and faster rise. Mean 6 SD response for five ON and 22
OFF cells is shown (bottom).
The nonlinear response to a peripheral, contrast-reversing grating is relayed to a ganglion cell over more than a millimeter. To
test whether action potentials are required, we evoked this nonlinear response while applying TTX (100 nM). Approximately 20
sec after TTX reached the retina, spiking ceased in the ganglion
cell. Although the resting potential changed only slightly (initial,
257 6 9mV; TTX, 260 6 8mV; n 5 15), the F2 response
component was abolished. This was true both in cells with initially hyperpolarizing and initially depolarizing responses (Fig.
10). In the presence of TTX, F2 response components at the three
highest contrasts decreased to 0.28 6 0.49 times the initial level
and were indistinguishable from noise (0% contrast response)
(Fig. 10). After ;5 min of wash, spiking returned, and both the
resting potential (257 6 12 mV; n 5 13) and the response to the
peripheral grating returned to initial levels. After TTX washed
out, F2 response components at the three highest contrasts returned to 1.4 6 1.1 times the initial level and were clearly above
the noise (Fig. 10).
We considered whether TTX abolished the response to a
peripheral grating by blocking spikes in the recorded ganglion cell
or spikes in retinal interneurons. To test this, we included lidocaine N-ethyl bromide (QX-314; 25–50 mM) in the electrode to
block spikes from inside the recorded ganglion cell. The response
to a peripheral grating persisted but was then abolished by TTX
(Fig. 10 B). Thus, lateral relay of the nonlinear response from the
periphery requires action potentials in retinal interneurons.
TTX did not abolish but rather increased the response to a
central contrast-reversing grating (n 5 2) (Fig. 11 A). Because
TTX abolished the response to a peripheral grating and enhanced the response to a central grating by an equal amount, the
response to simultaneous stimulation by a full-field grating was
primarily unaffected (Fig. 11 B). The F2 response component
increased to 1.4 6 1.4 times the initial level in the presence of
TTX and remained at 1.6 6 1.5 times the initial level during the
wash. The F1 response component to these stimuli was small
Demb et al. • Circuitry of Nonlinear Receptive Field
9762 J. Neurosci., November 15, 1999, 19(22):9756–9767
because the grating was fine, but it did also increase to 1.3 6 1.2
times the initial level in the presence of TTX and remained at
1.4 6 1.2 times the initial level during the wash (n 5 9).
Nonlinear response sums linearly at the ganglion cell
The F2 response component to a contrast-reversing grating in the
receptive field center was much stronger than the F2 response
component to the same grating in the periphery (Fig. 12 A).
However, the response to a full-field grating was less than the sum
of the response amplitudes to the gratings presented in concentric
rings (Fig. 12 A). This was because the responses were slightly
out-of-phase. When responses were summed (taking into account
phase, as well as amplitude), the result equaled the response to a
full-field grating. This result, shown for a particular cell in Figure
12 B, was true for most cells and can be seen in the average
response of the population (Fig. 12C). Thus, spatial summation of
the ganglion cell’s nonlinear responses is linear.
DISCUSSION
We can now address the questions raised in the introductory
remarks concerning the ganglion cell’s nonlinear receptive field:
how the subunit rectifies, how its signal travels millimeters across
the retina, and how signals from multiple subunits combine at the
ganglion cell.
Model for the nonlinear circuit
Figure 13 suggests a working model for the nonlinear receptive
field. When a grating reverses contrast, cones under a dimming
bar depolarize, and cones under a brightening bar hyperpolarize.
Consequently, an OFF bipolar cell under the dimming bar releases more transmitter, and an OFF bipolar cell under the
brightening bar releases less transmitter. A wide-field amacrine
cell costratifying with the OFF bipolar synaptic terminals is
depolarized by the first bipolar cell but not equivalently hyperpolarized by the second bipolar cell. This nonlinearity is assumed
to arise at the bipolar–amacrine synapse (see below). The nonlinearity is then transmitted via the spiking amacrine cell to the
ganglion cell and/or its presynaptic bipolar cell. The spiking
amacrine cell probably releases GABA (Vaney, 1990) and would
4
Figure 7. C enter/surround and nonlinear responses arise from the same
bipolar pathway. A1, The bars, presented over half of the receptive field
center, reversed from black to white repeatedly, while the rest of the field
remained gray. OFF ganglion cells depolarize at dark onset. This represents half of the classical center response. A2, Same bars over the complementary regions of the center also evoke half of the center response.
A3, Both sets of bars (A1 1 A2) when combined form a dark spot over the
entire receptive field center. OFF cells strongly depolarize at dark onset
(thin trace). This represents the entire center response. This response
closely matches the summed responses to the bar stimuli (thick trace). The
match is worse for the brisk cell, probably because of a summation
property of the cell, such as a saturating nonlinearity, that limited the
amplitude of the measured response. A4, When A2 bars are phase-shifted
in time by 180° (i.e., they start off bright instead of dark) and added to the
A1 bars, they form a contrast-reversing grating. OFF cells depolarize (thin
traces) at each contrast reversal (arrows mark square wave reversal).
When the A2 response is phase-shifted in time by 180° and added to the
A1 response, the sum (thick traces) closely matches the frequency-doubled
response to the contrast-reversing grating. The center response to the spot
is driven by a single class of cone bipolar cells (OFF bipolar cells, see
Results). Because the same component responses to the bars predicted
both the center response to the spot and the nonlinear response to the
contrast-reversing grating, they are probably both driven by the same
single class of bipolar cells (OFF bipolars). B1–B4, Same design as for A,
but stimuli were restricted to the far periphery. Responses to stimuli B1
and B2 predicted the responses to stimuli B3 and B4.
Demb et al. • Circuitry of Nonlinear Receptive Field
J. Neurosci., November 15, 1999, 19(22):9756–9767 9763
Figure 8. Nonlinear response in OFF ganglion cells to a central grating
depends only on OFF bipolar pathway. A, Nonlinear response of an OFF
ganglion cell to a central, contrast-reversing grating remained and was
enhanced when ON bipolar cell light responses were blocked with 40 mM
L-AP-4 (arrows mark square wave contrast reversal). Nonlinear response
of an ON ganglion cell was abolished. B, On average, 10 – 40 mM L-AP-4
enhanced the F2 response component in OFF ganglion cells. Error bars
indicate SEM; dashed lines indicate F2 component noise level recorded in
a baseline condition at the same mean luminance (0% contrast).
thus initially hyperpolarize the ganglion cell at each contrast
reversal. A similar mechanism could explain the initially depolarizing response to a peripheral grating if a local, inhibitory amacrine synapse were interposed between the spiking amacrine cell
and the ganglion cell. The model would work equally well for ON
ganglion cells driven by ON bipolar and amacrine cells.
This model implies that the fine subunits comprising the nonlinear receptive field correspond to the bipolar cell receptive field
(Victor and Shapley, 1979b). The subunits resolve a grating at
least 10-fold finer than the ganglion cell dendritic field (Figs. 4, 5).
Each subunit would be ;50 mm in diameter, approximately the
size of a bipolar cell receptive field center (Nelson and Kolb,
1983; Cohen and Sterling, 1992; Sterling, 1998). Also, the subunit’s extent, like that of the bipolar cell center, is approximately
constant with eccentricity (Figs. 4, 5) (Derrington et al., 1979).
Finally, the same bipolar cell that drives the nonlinear subunit
apparently also drives the classical center/surround. This is supported by Figure 7, which shows that the same component responses can predict both center/surround and nonlinear receptive
field responses.
The subunit’s underlying nonlinearity might well arise at the
synaptic output of a specific category of cone bipolar cell (Figs. 8,
9). An OFF bipolar cell of this category would strongly increase
its transmitter release to light offset (sluggishly or briskly) and
weakly decrease transmitter release to light onset. This asymmetry is equivalent to “half-wave rectification.” When a ganglion cell
sums two such responses out-of-phase, it gives a characteristic
frequency-doubled response (Fig. 7). The cat b1 bipolar cell,
presynaptic to the Y cell, provides an example of this behavior. Its
release rate is low during steady light (;1 vesicle per synapse/
sec), so light onset can evoke a large increment in transmitter
release, but because of the low sustained rate, light offset cannot
cause a comparable decrement (Freed, 1993; M. Freed, unpublished observations). Alternatively, the proposed mechanism of
half-wave rectification via low basal release could apply to elements downstream from the bipolar cell.
Signals from the periphery of the nonlinear receptive field
Figure 9. Nonlinear response in OFF ganglion cells to a peripheral
grating depends only on OFF bipolar pathway. A, In response to a
peripheral, contrast-reversing grating (50% contrast), a cell’s initially
hyperpolarizing response increased with L-AP-4 (arrows mark square
wave reversal). Line graph shows that, on average (6SEM), the F2
response component in OFF cells with an initially hyperpolarizing response increased with L-AP-4, whereas the F1 component was unaffected.
(Wash response recorded in 4 of 5 cells.) B, In response to a peripheral,
contrast-reversing grating (50% contrast), a cell’s initially depolarizing
response was abolished by L-AP-4 but returned during the wash. On
average, the F2 response component in OFF cells with an initially depolarizing response decreased with L-AP-4, especially at low contrasts,
suggesting possible effects on group III mGluRs on amacrine cells (see
Results), whereas the F1 response components were unaffected. (Initial
response recorded in 3 of 5 cells.) Wash recordings were taken 6 6 2 min
after L-AP-4 was removed from the bath.
9764 J. Neurosci., November 15, 1999, 19(22):9756–9767
Demb et al. • Circuitry of Nonlinear Receptive Field
Figure 10. Nonlinear response to a peripheral grating is eliminated by tetrodotoxin. A, In response to a peripheral, contrast-reversing grating, both a
cell with an initially hyperpolarizing response and a cell with an initially depolarizing response had their responses abolished by 100 nM TTX (arrows
mark square wave reversal). B, In response to a peripheral, contrast-reversing grating, both the strongest F2 components to a fine grating (High SF ) and
more modest responses to a coarse grating (Low SF ) were abolished by TTX. When QX-314 was included in the pipette to block ganglion cell
voltage-dependent sodium currents from the inside, the F2 response components remained but were subsequently abolished by TTX. F1 response
components to the coarse grating increased and remained high during the TTX washout. Wash recordings were taken 15 6 7 min after TTX was removed
from the bath.
almost certainly reach the ganglion cell via a spiking interneuron.
These signals travel at ;0.34 m /sec, consistent with a spiking
mechanism (Fischer et al., 1975; Derrington et al., 1979). Furthermore, the nonlinear response to a peripheral grating was
abolished by tetrodotoxin (Fig. 10). These signals could be transmitted by an amacrine cell with multiple axons that extend for
millimeters across the retina (Vaney et al., 1988; Dacey, 1989;
Famiglietti, 1992a-c; Bloomfield, 1996; Freed et al., 1996; Stafford
and Dacey, 1997). The guinea pig retina contains such amacrine
cells with axons that extend up to 3 mm (Kao et al., 1999).
It is notable that the nonlinear receptive field, which extends
for millimeters, is summed linearly at the ganglion cell (Fig. 12).
This linear summation was not tested previously over such a wide
region, but it is consistent with the original model of the nonlinear subunits (Hochstein and Shapley, 1976; Victor and Shapley,
1979b). It implies that the subunits operate independently and
therefore may not interact synaptically.
Does the nonlinear receptive field extend beyond the
classical surround?
In cat Y cells, the nonlinear receptive field was initially described
as extending beyond the classical surround (Fischer et al., 1975;
Derrington et al., 1979). However, it now appears that the surround extends f urther than previously thought, ;2 mm retinal
distance from the receptive field center (Troy et al., 1993). Thus,
in the cat Y cell, the nonlinear receptive field, and the classical
surround are primarily coextensive. In the present experiment,
the nonlinear receptive field in brisk and sluggish guinea pig
Figure 11. Nonlinear response to a central grating is not eliminated by
tetrodotoxin. A, In response to a central, contrast-reversing grating, an
OFF cell’s nonlinear response not only survived 100 nM TTX, it actually
grew larger during the application and washout. The response to a
peripheral contrast-reversing grating was completely abolished by TTX
but recovered promptly during washout. B, In response to a full-field
contrast-reversing grating, the average F2 component was unaffected by
TTX, presumably because, as the response to peripheral stimulation was
attenuated, the response to central stimulation was enhanced.
Demb et al. • Circuitry of Nonlinear Receptive Field
Figure 12. Nonlinear response sums linearly at the ganglion cell. A, Fine
grating reversed contrast in regions a–d, or at all locations ( f ull field). On
average, the F2 response component (mean 6 SEM) was strongest for a
but always remained well above the noise (horizontal line). F1 response
component was strongest for a and then fell toward the noise. B, Responses in an OFF cell to gratings at each location were summed to
predict the response to a f ull-field grating. The close correspondence
between the two traces demonstrates that the nonlinear response sums
linearly across the receptive field. C, Across all cells (1 ON, 16 OFF),
average responses to gratings at each location were summed to predict the
average response to a full-field grating. The close correspondence between the traces demonstrates that, on average, the nonlinear response
sums linearly across the receptive field.
ganglion cells was also coextensive with the classical surround
(Fig. 7B).
Most ganglion cell types express a nonlinear
receptive field
The nonlinear receptive field seems to be expressed by most
ganglion cell types in all mammalian species. In guinea pig, all
cells we have studied so far (;7 wide-field types) express a
nonlinear receptive field (Sterling et al., 1999). In cat retina, Y
and W cells express a nonlinear receptive field (Hochstein and
Shapley, 1976; Troy et al., 1989; Rowe and Cox, 1993; Pu et al.,
1994; Troy et al., 1995), and even X cells, generally considered to
be linear, express nonlinear responses from the periphery (Barlow et al., 1977; Hamasaki and Maguire, 1985). Furthermore,
nonlinear receptive fields are expressed by ganglion cell types in
rabbit (C aldwell and Daw, 1978; Watanabe and Tasaki, 1980),
mouse (Stone and Pinto, 1993), and monkey (Kruger et al., 1975;
Kaplan and Shapley, 1982). In monkey retina, there may be
certain cell types that are completely linear and do not, under any
condition, express a nonlinear receptive field (Kaplan and Shap-
J. Neurosci., November 15, 1999, 19(22):9756–9767 9765
Figure 13. C ircuit diagram to explain the origin of the initially hyperpolarizing response to a peripheral, contrast-reversing grating. When a
grating reverses contrast in the periphery, it evokes asynchronous responses in adjacent cones and thus in their postsynaptic OFF bipolar cells.
The latter release transmitter asynchronously onto an OFF wide-field
spiking amacrine cell. Assuming that the nonlinearity arises at the bipolar– amacrine synapse (see Discussion), it is then transmitted via the
spiking amacrine cell to the ganglion cell and /or its presynaptic bipolar
cell. The spiking amacrine cell releases an inhibitory transmitter, such as
GABA, and hyperpolarizes the ganglion cell at each contrast reversal,
creating the characteristic nonlinear response.
ley, 1982; Benardete et al., 1992). However, at least one class of
neurons in the magnocellular layer of the lateral geniculate nucleus has a local nonlinear receptive field (Kaplan and Shapley,
1982; Benardete et al., 1992), and a larger percentage may show
a peripheral nonlinear receptive field (Kruger, 1977).
Function of the nonlinear receptive field for vision
Although nonlinear responses were observed long ago, they were
described as mere “effects” (the “McIlwain,” “periphery,” or
“shift” effect), and only later were these related to the Y cell
nonlinear subunit (McIlwain, 1964, 1966; Fischer et al., 1975;
Derrington et al., 1979). Yet we are impressed that these responses are not oddities but reflect powerful circuits for computing contrast magnitude over a wide region. The ganglion cell
might use this information to tune its linear receptive field. For
example, when the nonlinear receptive field is stimulated continuously with a fine, drifting grating, the gain of the linear center is
sharply reduced (Werblin, 1972; Caldwell and Daw, 1978;
Enroth-Cugell and Jakiela, 1980). Alternatively, when the peripheral nonlinear receptive field is stimulated, the linear center of
certain cells may be enhanced (McIlwain, 1964). This gain control might serve psychophysical “masking” whereby the ability to
detect a small spot is modulated by surrounding stimuli (Derrington, 1984; He and Loop, 1990; Fuhr and Kuyk, 1998). However, the nonlinear receptive field may have other functions. For
example, the nonlinear receptive field is still expressed by geniculate neurons, so it must be relayed to cortex where it might carry
a message complementary to that of the linear receptive field (So
and Shapley, 1979; cf. Spitzer and Hochstein, 1987).
It is a matter of great current interest that a nonlinear mech-
9766 J. Neurosci., November 15, 1999, 19(22):9756–9767
anism in the cortex computes “second order” contrast boundaries.
In a scene where average luminance stays constant over space,
object boundaries are determined by changes in local contrast on
a fine scale. Such contrast boundaries are invisible to a linear
mechanism that computes only “first order” luminance boundaries on a coarse scale (Mareschal and Baker, 1998, 1999). Shown
psychophysically, this nonlinear mechanism was composed of fine
subunits and insensitive to orientation (McGraw et al., 1999).
Most studies have assumed a cortical mechanism. However, the
ganglion cell nonlinear receptive field might also contribute to
this visual computation.
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