Functional circuitry of the retinal ganglion cell's nonlinear receptive field

Abstract

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 contrast-reversing 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.

Fig. 1.

Ganglion cells were studied in the visual streak.A, Schematic of flattened retina showing visual streak (shaded region), 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 (ID). 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.

Fig. 2.

Frequency-doubled, nonlinear response emerges when a fine grating reverses contrast. Left 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 (D_L + D_R;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, contrast-reversing grating was significantly greater than predicted (*p < 0.05; t = 2.84; one-tailed t test; df = 4). The average F₂ component in the response to a fine, contrast-reversing grating was just under half the amplitude of the average F₁component in the response to a coarse, contrast-reversing grating.

Fig. 3.

Nonlinear response is independent of grating position. Left 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. Thick line shows for each trace the sine waves (summed after subtracting the mean) corresponding to the F₁ and F₂components. Graph shows F₁ and F₂ component amplitudes as a function 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 F₂component is ∼0.5 mV (or 6 spikes) amplitude and invariant with spatial position. Fitted functions 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).

Fig. 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 F₂component (thick) measured in a baseline condition (0% contrast) at the same mean luminance.

Fig. 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 ID. Other conventions are the same as Figure4C.

Fig. 6.

Initial response to a peripheral, contrast-reversing grating can be either depolarizing or hyperpolarizing. Left column, Certain 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) ± SD (gray regions) 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 ± SD response for five ON and 22 OFF cells is shown (bottom).

Fig. 7.

Center/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 + 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, WhenA₂ bars are phase-shifted in time by 180° (i.e., they start off bright instead of dark) and added to theA₁ bars, they form a contrast-reversing grating. OFF cells depolarize (thin traces) at each contrast reversal (arrows mark square wave reversal). When theA₂ 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 andB₂ predicted the responses to stimuliB₃ andB₄.

Fig. 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 μml-AP-4 (arrows mark square wave contrast reversal). Nonlinear response of an ON ganglion cell was abolished.B, On average, 10–40 μml-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).

Fig. 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 (±SEM), 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 withl-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 ± 2 min after l-AP-4 was removed from the bath.

Fig. 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. F₁response components to the coarse grating increased and remained high during the TTX washout. Wash recordings were taken 15 ± 7 min after TTX was removed from the bath.

Fig. 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 F₂component was unaffected by TTX, presumably because, as the response to peripheral stimulation was attenuated, the response to central stimulation was enhanced.

Fig. 12.

Nonlinear response sums linearly at the ganglion cell. A, Fine grating reversed contrast in regionsa–d, or at all locations (full field). On average, the F₂ response component (mean ± SEM) was strongest for a but always remained well above the noise (horizontal line). F₁ response component was strongest for aand then fell toward the noise. B, Responses in an OFF cell to gratings at each location were summed to predict the response to a full-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.

Fig. 13.

Circuit 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.