Spatial segregation of adaptation and predictive sensitization in retinal ganglion cells

Abstract

Sensory systems change their sensitivity based upon recent stimuli to adjust their response range to the range of inputs, and to predict future sensory input. Here we report the presence of retinal ganglion cells that have antagonistic plasticity, showing central adaptation and peripheral sensitization. Ganglion cell responses were captured by a spatiotemporal model with independently adapting excitatory and inhibitory subunits, and sensitization requires GABAergic inhibition. Using a simple theory of signal detection we show that the sensitizing surround conforms to an optimal inference model that continually updates the prior signal probability. This indicates that small receptive field regions have dual functionality—to adapt to the local range of signals, but sensitize based upon the probability of the presence of that signal. Within this framework, we show that sensitization predicts the location of a nearby object, revealing prediction as a new functional role for adapting inhibition in the nervous system.

INTRODUCTION

Visual scenes are correlated in space and time due to the properties of environmental conditions, objects, eye movements, and self motion (Field, 1987; Frazor and Geisler, 2006). Because of this statistical regularity, it has long been thought that the visual system might improve its efficiency and performance by adjusting its response properties to the recent history of visual input (Barlow et al., 1957; Blakemore and Campbell, 1969; Laughlin, 1981).

In early sensory systems, studies of how stimulus statistics influence the neural code have focused mainly on adaptation. Given the recent stimulus distribution, response properties change over multiple time scales to encode more information and remove predictable parts of the stimulus (Fairhall et al., 2001; Hosoya et al., 2005; Ozuysal and Baccus, 2012; Wark et al., 2009). Underlying studies of adaptation is the idea that early sensory systems should maximize information transmission for processing in the higher brain (Atick, 1992; van Hateren, 1997).

Studies in the higher brain and behavior often have a different perspective: the goal is to generate a behavior given a stimulus (Kording and Wolpert, 2006; Schwartz et al., 2007; Yuille and Kersten, 2006). Accordingly, such studies have revealed that choosing the appropriate action benefits from predicting future stimuli by performing an ongoing inference based on the prior probability of sensory input.

Recent results indicate that many ganglion cells encode specific features with a sharp threshold, implying that these ganglion cells make a decision as to the presence of a feature (Olveczky et al., 2003; Zhang et al., 2012). If so, one might expect that retinal plasticity also take advantage of the principles of signal detection and optimal inference. At the photoreceptor to bipolar synapse, even though at the dimmest light level the synapse threshold is close to the optimal level for signal detection, it does not appear that any adjustment occurs due to the prior signal probability (Field and Rieke, 2002). This problem, however, has not been explored in ganglion cells. Given the complex circuitry of the inner retina and the different types of ganglion cell plasticity (Hosoya et al., 2005; Kastner and Baccus, 2011; Olveczky et al., 2007), we examined this plasticity in the context of both adaptation and signal detection.

Here we systematically mapped the spatial arrangement of plasticity in retinal ganglion cells, finding that many ganglion cells adapted to a localized stimulus, but sensitized in the surrounding region. A computational model composed of independently adapting excitatory subunits, producing localized adaptation, and larger adapting inhibitory subunits, producing sensitization, captured the spatiotemporal properties of this plasticity.

Using knowledge of the detailed computation, we then combined theories of signal detection and optimal inference to account for several properties of sensitization. This analysis indicated that sensitization creates a regional prediction of future input based upon prior information of local signal correlations in space and time. We then test this theory in a more natural context by showing that object motion sensitive ganglion cells use sensitization to predict the location of a camouflaged object.

Finally, we show that sensitization requires GABAergic inhibition, and that different levels of inhibition can account for differences in sensitization between ganglion cell types. Together these results show how two functional roles of plasticity are combined in a single cell—to adapt to the range of signals, and predict when those signals are more likely to occur. Furthermore, these results establish a functional role for adapting inhibition in predicting the likelihood of future sensory input based upon the recent stimulus history.

RESULTS

We measured the spatiotemporal region whose statistics control the sensitivity of a cell—the adaptive field. Previous measurements of spatial properties of the adaptive field focused primarily on fast adaptation—changes in sensitivity occurring within the integration time of a cell. These fast, suppressive, effects in the retina and lateral geniculate nucleus extend beyond the receptive field center (Bonin et al., 2005; Olveczky et al., 2003; Solomon et al., 2002; Victor and Shapley, 1979; Werblin, 1972). Much less effort has been devoted to measurements of the adaptive field as to changes in sensitivity lasting longer than the cell’s integration time. Recent results have shown that delayed changes in sensitivity in salamander, mouse, and rabbit retinas have two opposing signs, adaptation and sensitization (Kastner and Baccus, 2011). Although it is known that small regions of the ganglion cell receptive field adapt somewhat independently (Brown and Masland, 2001), spatial properties of sensitization have not been measured.

To measure prolonged changes in sensitivity at different spatial locations, we presented a low contrast flickering checkerboard. Every 20 s, one region of space changed to high contrast for 4 s (Figure 1A,B). The high contrast stimulus was presented at different locations, allowing for the creation of a spatial map of slow changes in sensitivity. We compared the firing rate during two time intervals after the high contrast spot disappeared: L_early, 0.5 to 3 s after the transition to all low contrast, and L_late, 13.5 to 16 s after the transition to all low contrast, a time that approximated the steady state.

Figure 1. Three different adaptive fields in the retina.

(A) A single frame of the stimulus when a high contrast square was presented. (B) Temporal sequence of the binary stimulus in the different regions. High contrast was 100% Michelson contrast in a single region, indicated by the black box in (A). Low contrast was 5%. (C) Response of an On (left), fast Off adapting (middle), and fast Off sensitizing cell (right). PSTHs are shown with the high contrast region (square) located at two positions relative to the receptive field center (circle), and show the average response for > 60 stimulus sequences. Data binned at 0.5 s. Colored responses indicate when all regions were low contrast. Black indicates the time of the local high contrast. (D) Adaptive indices for all cells. The color of each point in the polar plot indicates the cell’s adaptive index when the adapting square was at that location. The origin indicates the cell’s receptive field center. Data comes from 9 On, 21 sensitizing, and 74 adapting Off cells. For sensitizing cells, adaptive fields are shown during L_early (top), and during L_{0 – 0.5}, 0 – 0.5 s after high contrast (bottom) (E) Average adaptive index for each cell type as a function of distance from the cell’s center. Results were averaged across angles in (D), and colors correspond to (C). Solid black lines are single or difference of Gaussian fits to the data with a standard deviation of 0.41 mm for sensitizing cells, 0.30 mm (larger) and 0.11 mm (smaller) for adapting Off cells, and 0.32 mm for On cells.

Center-surround adaptive fields

Fast Off adapting and sensitizing cells are two defined cell types that each form an independent mosaic in the salamander retina (Kastner and Baccus, 2011). In response to a spatially global transition between high and low temporal contrasts, adapting cells decrease their sensitivity following a high contrast stimulus, whereas sensitizing cells increase their sensitivity.

Fast Off cells that adapted to a global contrast change also adapted when the high contrast spot was directly over their receptive field center. However, when the high contrast spot neighbored their receptive field center they sensitized, increasing their response during L_early relative to L_late (Figure 1C,D). Thus, the adaptive field of this type of cell exhibited spatial antagonism, showing central adaptation but peripheral sensitization.

Sensitizing cells also had a spatially varied response to a local high contrast spot. These cells sensitized both in their central and surround region (Figure 1C,D). However, upon examination of the firing rate at an earlier time, from 0 – 0.5 s after the transition from high contrast (L_{0 – 0.5}), sensitizing cells also adapted in their center (Figure 1D). Thus both cell types had an adapting center and sensitizing surround, although with apparently different dynamics to their adaptation (Figure 1C,D). In comparison, all On cells had a spatially monophasic adaptive field, adapting both in the central and surround regions.

To determine whether local changes in visual sensitivity accompanied the changes in firing rate, we computed the sensitivity at each spatial location during L_early and L_late (see experimental procedures). In all cell types, a prolonged adaptive change in sensitivity, as measured using a spatiotemporal linear-nonlinear (LN) model, underlay the changes in activity (Figure S1). Therefore, three different populations of cells—fast Off adapting, fast Off sensitizing and On cells—had distinct spatiotemporal plasticity, with Off cells exhibiting center-surround adaptive fields.

A model unifies the three adaptive fields

To gain insight into both the computation performed by the adaptive field and its potential mechanisms, we modeled the center-surround adaptive field by extending a previous model that produced sensitization (Kastner and Baccus, 2011). In this model, adapting excitation and inhibition combine, such that a high contrast stimulus causes inhibitory transmission to adapt, thus reducing inhibition and generating a residual sensitization after the high contrast ceases.

To extend the previous model we added adapting spatial subunits for both excitatory and inhibitory pathways (Figure 2A). Excitatory subunits, representing bipolar cells, had receptive fields smaller than that of the ganglion cell, and inhibitory subunits were three times larger than excitatory subunits (Figure 2A). This size ratio was taken from a difference of Gaussians fit to the center-surround adaptive field (Figure 1E), otherwise, the parameters of the model were taken from previous uniform-field experiments with fast Off sensitizing cells (Kastner and Baccus, 2011). In the model, each excitatory subunit received spatially weighted input from adapting inhibitory subunits. The ganglion cell then received spatially weighted input from the adapting excitatory subunits (Figure 2B).

Figure 2. Amount of adapting inhibition can determine the type of adaptive field.

(A) Subunits in a model of a ganglion cell with a center-surround adaptive field (see Supplemental Experimental Procedures). Colored bars show different locations used for high contrast. Line thickness indicates the weight of each subunit onto the ganglion cell. (B) Both inhibitory and excitatory subunits are composed of spatiotemporal receptive fields, nonlinearities, and adaptive blocks (arrow in circle). Inhibition from inhibitory to excitatory subunits had a spatial weighting (w_I) equal to the spatial overlap between each excitatory and inhibitory subunit. The excitatory population was likewise spatially weighted (w_E) and then passed through a threshold to yield the model output. The average responses for two excitatory subunits are shown in response to a spot centered over the ganglion cell receptive field (colored bar in (A) matching the low contrast response). Markers in the top right corner of the two subunit responses correspond to their weighting w_E in the model output and their spatial location in (A). (C) Top, output of the model for three different locations of high contrast corresponding to the colored bars in (A) that match the low contrast responses. Bottom, example data PSTHs from fast Off adapting cells. (D) Adaptive indices from models with different maximal inhibitory weighting (w_max) (see Supplemental Experimental Procedures). The adaptive index is plotted for when the high contrast spot was located directly above or just neighboring the ganglion cell receptive field. Line colors correspond to the bars in (A). Green and purple icons represent the type of adaptive fields measured during L_early that correspond to that range of w_max.

Using a stimulus similar to that shown in Figure 1, the model produces an output that either adapts or sensitizes depending upon the location of the high contrast (Figure 2C), consistent with the responses of cells with center-surround adaptive fields. Thus, a different spatial scale of adapting excitation and inhibition yields a center-surround adaptive field. Because the three types of adaptive field had distinct properties, one might expect that different circuitry would be required to generate the different adaptive fields. However, we reproduced all three adaptive fields by simply changing the strength of the inhibitory weighting onto the excitatory subunits (Figure 2D). The adaptive fields of sensitizing cells resulted from the strongest adapting inhibition, center-surround adaptive fields resulted from intermediate inhibition, and an exclusively adapting monophasic adaptive field resulted from the weakest inhibition. Thus, all three adaptive fields, as well as intermediate examples not encountered experimentally, could arise solely by changing the strength of inhibition.

The adaptive field (AF) model predicts several distinct features of the data. Sensitizing cells produce less sensitization when they were directly centered under a high contrast spot than when the spot was slightly offset from the receptive field center (Figure 1E, S1A,B, and 2D). The model also predicts that when the high contrast region was further from the receptive field center, the cell had a larger steady state response at low contrast than high, but an elevated response at the transition to both low and high contrast (Figure 2C). This occurs because in the periphery of the receptive field center inhibition exceeds excitation by virtue of the greater spatial spread of inhibition (Figure 2A). However, a delay in inhibitory transmission causes excitation to be transiently greater than inhibition at the onset of high contrast. Thus, a model with independently adapting excitation and inhibition predicts multiple distinct spatiotemporal properties of the adaptive field.

Subcellular sensitizing and adapting subunits

The AF model contains subunits with independent plasticity, with the final response exhibiting the summed adaptive behavior of each subunit. Because these subunits are smaller than the receptive field center, the model predicts that individual regions of the response of the cell may sensitize, even when the overall firing rate adapts (Figure 2B,C). We tested whether the AF model, fit to a coarser spatial stimulus (Figure 1), would predict changes in sensitivity at a high spatial resolution within a single cell without refitting the model. We stimulated the retina with a low contrast white noise stimulus composed of concentric flickering annuli centered on a single ganglion cell (Figure 3A,B). In the central 200 μm, every 20 s, the stimulus was a uniform circle that flickered with high contrast for 4 s. The diameter of the high contrast spot was smaller than the receptive field center of a cell.

Figure 3. Changes in sensitivity within the receptive field center.

(A) A single stimulus frame used to map sensitivity changes at high resolution, composed of concentric annuli with radii increasing by 50 μm that were modulated independently with 5 % contrast. In the central 200 μm, the stimulus alternated between 16 s of the 5 % low contrast stimulus, and 4 s of a uniform circle that flickered with a 100% Michelson contrast. (B) Normalized spatial sensitivity of an adapting Off cell during L_late, computed as the rms value of the spatiotemporal receptive field at each distance. Because annuli had a different area, unlike a checkerboard stimulus, the sensitivity at each distance was normalized by the annulus area. The vertical dotted line shows the point of zero crossing, defining the receptive field center. (C) Average normalized difference in spatial sensitivity between L_early and L_late for adapting Off cells (left) (n = 7) and the model from Figure 2 (right). The solid vertical line shows the extent of the central circle that experienced high contrast. The dotted vertical line indicates the average boundary of the receptive field center.

We measured subcellular changes in sensitivity following high contrast during L_early and L_late using a spatiotemporal LN model, similar to Figure S1A, except that each spatial region represented an annulus (Figure 3C). Cells with a center-surround adaptive field showed local adaptation and peripheral sensitization even within the receptive field center, just as predicted by the AF model. Thus, even though the AF model was fit using different experimental data (full field and checkerboard changes in contrast), the model predicted subcellular adaptation and sensitization using concentric annuli. Previously, it was shown that adaptation occurs at a subcellular scale (Brown and Masland, 2001). The present result shows that interneurons contribute spatially localized plasticity both for adaptation and sensitization.

Adaptation and sensitization in a rapidly changing environment

Under natural viewing conditions, rapid changes in contrast occur due to frequent eye movements (Frazor and Geisler, 2006). We therefore tested whether the model fit to the localized step change in contrast (Figure 1A,B) predicted the response when all regions were activated together by a uniform field stimulus whose contrast changed with a broad temporal bandwidth. We presented a uniform field Gaussian stimulus where the temporal contrast changed randomly every 0.5 s (Figure 4A). We then computed a temporal filter representing the average effect of a brief increase in contrast by correlating the spiking response with the random sequence of contrast (Figure 4B). This temporal filter represented the temporal adaptive field, which is the spatial average of the spatiotemporal adaptive field. This computation measures the average contribution of both increases and decreases in contrast, analogous to how the linear receptive field averages both increases and decreases in intensity. These functions had a large peak in the first time bin, from 0 – 0.5 s, because higher contrast invariably produces a higher firing rate. To examine the temporal adaptive field, we focused on the temporal filter outside of the first 0.5 s, representing how the recent history of contrast outside the cell’s integration time influenced the firing rate.

Figure 4. Temporal adaptive fields during rapidly changing contrast.

(A) A Gaussian white noise stimulus with a contrast that changed randomly every 0.5 s drawn from a uniform distribution between 0 and 35 % contrast. (B) Example temporal adaptive fields, calculated as the spike triggered average of the contrast. (C) Average temporal adaptive fields for ganglion cells (left), and the output of the AF model from Figure 2 (right). In the data figure, the width of the lines indicates the s.e.m. The abscissa begins at 0.5 s to highlight slower changes due to changing contrast. All filters are normalized in amplitude to have the same rms value.

The three cell types had distinct temporal adaptive fields (Figure 4B,C). On cells had a slow negative monophasic filter, indicating that a brief increase in contrast decreased activity between 0.5 – 3 s. Sensitizing cells had a biphasic filter, such that elevations of contrast initially decreased activity, but only for a duration of up to 1 s. With a delay of ~1 s, contrast, on average, increased activity, consistent with previous results showing that the onset of sensitization occurs with a time constant of 0.55 s (Kastner and Baccus, 2011). The effect then decayed after ~3 s.

Adapting Off cells had a temporal adaptive field that was negative and monophasic, but with a more rapid decay than that of On cells (Figure 4C). Just as with the spatial adaptive field, where adapting Off cells showed a mixture of adaptation and sensitization, the temporal adaptive field of adapting Off cells was a mixture of the time courses of the two extremes. Although sensitization did not completely cancel adaptation, adaptation was reduced at later times.

We then evaluated whether the AF model could reproduce the different temporal adaptive fields using the same stimulus that rapidly changed in contrast (Figure 4A). For each of the three cell types, we used a model with a different strength of adapting inhibition, but with otherwise identical spatial parameters fit using only the spatial map of the adaptive field (Figure 1). We found that a different weighting of adapting inhibition in the model reproduced the different behaviors of the three cell types, indicating that the same circuitry that underlies the spatial adaptive field can sufficiently account for the temporal adaptive field. In addition, the time course of adaptation of adapting Off cells, which lies in between that of On cells and sensitizing Off cells, can be explained by an intermediate level of adapting inhibition.

Although the full spatio-temporal model (Figure 2) produces more complex behavior, such as asymmetric responses at increases and decreases in contrast, the combined effects of the subunits in the spatiotemporal model predict the response to rapidly varying contrast. The interplay between local and global contrast changes has recently been explored during steady state adaptation (Garvert and Gollisch, 2013). For the dynamic changes studied here, because the model with independent subunits fit to local adaptation predicts the sum total adaptation for spatially global stimuli, we conclude qualitatively that excitatory and inhibitory subunits within the adaptive field adapt independently.

Feature detection in Fast Off cells

Having characterized the combined spatiotemporal computation of adaptation and sensitization, we considered the functional relevance of sensitization within the adaptive field. Many sensory neurons encode specific visual features using a high and sharp threshold, signaling when the stimulus matches that feature (Ringach and Malone, 2007). In the retina, for example, object motion sensitive (OMS) (Olveczky et al., 2003) and W3 cells (Zhang et al., 2012) selectively report the presence of differential motion.

We assessed how one aspect of feature selectivity related to sensitization by measuring both differential motion sensitivity and sensitization in the same cells. We found that fast Off adapting cells were OMS cells, whereas fast Off sensitizing cells were not (Figure 5 and S2). Although they receive different levels of peripheral inhibition, the two cell types fire synchronously in response to a stimulus with no spatial structure, and thus respond to the same local stimulus features (Kastner and Baccus, 2011). Consistent with a role as a feature detector, Off cells had a more strongly rectified nonlinearity than On cells using a previously described index of rectification. This index measures the logarithm of the ratio of the maximum slope of the nonlinearity to the slope at zero input (Chichilnisky and Kalmar, 2002). Off cells had an index of 2.2 ± 0.1 (n = 80), whereas On cells had an index of 1.3 ± 0.2 (n = 9), meaning that relative to the slope at an input of zero (the average input), Off cells increased their slope ~8 times more than On cells.

Figure 5. Distinct cell types for object motion sensitivity and global sensitization.

(A) Schematic diagram of the stimulus to test for object motion sensitivity. A central object region was shifted either together with the background (global motion), or at a different time (differential motion). (B) Histogram of the response ratio between global and differential motion for adapting (n = 59) and sensitizing (n = 16) fast Off cells.

Encoding a signal in a noisy environment

To better understand the function of sensitization, we formalized the apparent role of fast Off cells as feature detectors using a simple model of optimal signal detection that changes with stimulus history. In a signal detection problem the position of the optimal threshold depends upon the distributions of signal and noise, as has been examined at the photoreceptor to bipolar cell synapse (Field and Rieke, 2002). Although the threshold at the photoreceptor to bipolar cell synapse does not appear to change according to the prior probability of photons, we considered that changes in the response function of ganglion cells reflects the changing likelihood of a signal.

By recording intracellularly from Off bipolar cells in response to a repeated Gaussian 5 % contrast stimulus, we found that the noise was 0.44 ± 0.12 (n = 5, mean ± s.d.) times the standard deviation of the recorded membrane potential fluctuations (Figure 6A and S3A). Thus, for weak, low contrast, signals the probability distribution of an input, v, given the presence of a signal, p(v|s), greatly overlaps with the probability distribution of that same input in the presence of only noise, p(v|η). This overlap creates a benefit from a careful threshold placement to discriminate between the two conditions. Although both positive and negative signals are distinguishable from noise, we focused on positive signal deviations because many ganglion cells have monotonic response curves.

Figure 6. Sensitization reflects an increased prior expectation of a signal.

(A) Conditional probability of an input, v, given either signal, s, (5 % contrast) or noise, η (0 % contrast). Thick line p(v|s) is the distribution of measured voltages from an Off bipolar cell responding to 5 % contrast. Thick line p(v|η) is the estimated noise measured from repeated presentations of the same stimulus. Thin lines are Gaussian fits to the data. (B) Schematic diagram of a recursive model whereby a one-dimensional spatiotemporal input, v_x,t, illustrated as a bright stimulus at one point in space, x, is combined with a prior stimulus probability, p(s_x,t), to yield a posterior, p(s_x,t|v_x,t). The colored curves indicate p(s_x,t|v_x,t) as a function of v_x,t given different values of p(s_x,t). The posterior p(s_x,t|v_x,t) is then smoothed by a spatial filter, h(k), to yield a new prior p(s_x,t+1). The integral of h(k) was 0.96, reflecting the fact that signals may disappear due to saccadic eye movements. To convert the posterior probability to a firing rate p(s_x,t|v_x,t) is passed through a rectifying function, N_p(p(s|v)), which was normalized by the average ganglion cell firing rate. (C) Top, posterior probability p(s_x,t|v_x,t) at each point in space and time in the inference model in (B), in response to a stimulus that changed between 5 % contrast and a 35 % contrast bar applied at the region and time interval indicated by the thick black lines. Bottom, average time course of p(s_x,t|v_x,t) at the spatial location indicated by the arrow. The average is taken over 1000 trials of different intensity sequences but the same change in contrast. (D) Top, average posterior, 〈p(s|v)〉, of the model in the center of the object during L_early and L_late. Bottom, firing rate nonlinearities for a ganglion cells compared with the model firing rate output during L_early and L_late. (E) Comparison of slope (top) and midpoint (bottom) of sigmoid fits to data and model nonlinearities during L_early and L_late. The abscissa is in units of s.d. at 5 % contrast. Also compared are the change in nonlinearity slope and midpoint between L_early and L_late(Δ) for the data and model. The dotted line is the identity.

The probability that a particular voltage arises from the signal distribution depends upon the prior probability, p(s), of a signal. Thus, when p(s) increases, the optimal threshold decreases (Field and Rieke, 2002). What then would lead to an increase in the prior signal probability? For the visual system, an important source of prior information comes from the strong spatial and temporal correlations present in natural visual stimuli (Geisler and Perry, 2009). Objects do not suddenly disappear, therefore once detected they are highly likely to be present nearby in space. We incorporated this natural visual prior into a spatiotemporal version of an optimal inference model (Figure 6B), similar to that used previously (DeWeese and Zador, 1998; Wark et al., 2009). The model has two steps. First, at each point in time and space, a new measurement of intensity, v_x,t, combines with the prior probability of a signal, p(s_x,t), at that location to yield a new posterior estimate of signal probability, p(s|v_x,t) (see experimental procedures). Second, at each point in time, the prior, p(s_x,t+1), is updated from the posterior at the previous point in time, p(s|v_x,t), smoothed by a Gaussian function, h(x) (see experimental procedures), representing the diffusion of an object or edge due to the random walk movement of fixational drift eye movements. The integral of h(x) was less than 1, reflecting the occasional possibility of saccadic eye movements that redirect gaze to a different image location.

When presented with a brief strong stimulus—35% contrast—on a background of weak input—5% contrast—this optimal model maintained a spatiotemporal bias, predicting an increased probability that a signal was present outside of the spatial range of the object, even after the object was no longer detectable (Figure 6C). This optimal behavior was qualitatively similar to the sensitizing field we observed in Off cells (Figure 1).

We compared how the changes in the response function during sensitization corresponded to the changes expected from this framework of ideal signal detection. The effect of a changing prior value, p(s), on the posterior probability, p(s|v), depends upon the shapes of p(v|s) and p(v|η). For the case where p(v|s) and p(v|η) are both Gaussian with a different width, when p(s) decreases the slope decreases, the threshold decreases and the baseline increases, reflecting the increased bias towards the presence of the signal (Figure 6B).

After a transition to low contrast, sensitization, by definition, consists of a decrease in threshold (Kastner and Baccus, 2011). By intracellularly recording from sensitizing ganglion cells we found that an increased baseline of the nonlinearity accompanied the decreased threshold during L_early (Figure S3B). This depolarization was 35 ± 18 % of the membrane potential standard deviation during L_late (n = 3). Finally, even though sensitization decreases the threshold during L_early, it also decreased the slope in the spiking nonlinearity, as measured from extracellular recordings (Figure S3C). This indicates that sensitization differs from changes in sensitivity due to adaptation, where the slope increases when the threshold decreases (Baccus and Meister, 2002). The decrease in slope occurs because of the bias conferred by an increased p(s). When a signal is more likely, a greater influence on p(s|v) comes from the prior, p(s), and a smaller influence comes from the new input, v. In the extreme, when p(s) = 1, the posterior will always be 1, and the cell always fires, regardless of the input, v. This reduced dependence on the current input is consistent with a decrease in mutual information between stimulus and response during the higher firing rate of L_early reported previously for sensitizing cells (Kastner and Baccus, 2011).

During L_early, sensitization displays all three properties expected from an ideal model of signal detection: decreased threshold, increased baseline, and decreased slope. Thus, changes in the response curve during sensitization parallel an ideal model of signal detection when the probability of the signal increases.

We then quantitatively compared the output of the optimal model to the change in firing rate seen in the nonlinearities from L_early and L_late. Low values of input should yield near zero firing rate in ganglion cells, owing to the apparent pressure to convey information about the stimulus using few spikes (Pitkow and Meister, 2012). To convert the prior probability, p(s|v), to a firing rate, we used a nonlinearity, N_p(p(s|v)) (Figure 6B), optimized to map p(s|v) to the firing rate averaged over all cells during both L_early and L_late conditions, i.e. only a single function was used for all cells and all conditions. This function had a sharp threshold corresponding to approximately a p(s|v) of ~0.5. Thus, a comparison of ganglion cell firing with the optimal signal detection model allowed us to interpret that the cell fired when it was more likely than not that a signal was present. We then examined how closely the model matched the nonlinearity during L_early. Although the optimal signal detection model was not optimized to account for any difference between L_early and L_late, it predicted the magnitude of the change in both midpoint and slope of the nonlinearity between L_early and L_late (Figure 6D,E).

In the signal detection model, the time course that the signal probability increased was faster than when it decayed, differing by a factor of 3 (Figure 6C). This temporal asymmetry reflects that it is easier to detect an increase in contrast than a decrease in contrast because an increase in contrast quickly brings extreme intensity values inconsistent with the previous low contrast (DeWeese and Zador, 1998). This asymmetry corresponded to our measurements, as sensitization decayed with a tau 4.4 times longer than sensitization developed—2.4 s versus 0.55 s (Kastner and Baccus, 2011). Therefore, both qualitatively and quantitatively, sensitization within the adaptive field conforms to an optimal model of signal detection in the presence of background noise.

Sensitization maintains the location of an object

We thus propose that the sensitizing field provides a bias for the detection of a signal based upon the prior probability of that signal, conditioned on the stimulus history. We tested this idea in a more natural context relating to the motion of objects, which represents an important source of visual signals. In a natural environment, objects do not suddenly disappear, therefore once detected they are highly likely to remain nearby in space. We thus presented a stimulus where changes in spatiotemporal contrast were generated by changes in object velocity against background motion arising from fixational drift eye movements. We chose the spatial texture of the object and background to be identical, and thus the object was camouflaged and could only be detected by its motion. When the object moved, it stimulated the retina with both differential motion and an increase in spatio-temporal contrast; however, once the object ceased its differential motion relative to the background, it became indistinguishable from the background, and thus any information about its location could only arise as a prediction based upon prior measurements.

The background stimulus consisted of vertical lines, with intensities drawn randomly from a Gaussian distribution, that jittered in one dimension to mimic fixational drift eye movements (Olveczky et al., 2003) (Figure 7A). Every 8 s, three neighboring bars, representing an object, moved together for 250 ms at a speed of 1.1 mm/s (for a total distance of 275 μm). This prolonged period was used only to provide a steady baseline for the measurement, as experiments changing contrast every 0.5 s (Figure 4) show that sensitization occurs even in a rapidly changing environment. Thus the object part of the stimulus changed its spatio-temporal contrast by virtue of its changing motion—fast motion represented high contrast, and background motion represented low contrast.

Figure 7. Sensitization predicts future object location.

(A) Camouflaged stimulus (top), shown in space (vertical axis) and time (horizontal axis), was composed of 50 μm bars, of 15 % contrast. The dashed vertical line indicates the time the object stopped moving relative to the background. Average firing rate response of sensitizing cells (n = 7, bottom), normalized for each cell by the average steady state response for that cell during jittering background motion, 5 – 8 s after the object stopped moving. (B) Average normalized response for On (left) (n = 5), adapting Off (OMS cells, middle) (n = 39) and sensitizing cells (right) (n = 7), where each cell experienced > 1000 stimulus trials. Firing rate in (A) and (B) is shown as a function of distance from the center of the object’s trajectory during the time interval ‘Early’ in (A), 0.5 – 1.25 s after the object stopped moving relative to the background. Error was s.e.m. and was computed across the number of trials contributing to each spatial bin.

We measured the responses of the different populations of ganglion cells to the camouflaged object at many different retinal locations. We computed the average firing rate of each population as a function of the distance between the cell and the center of the object’s trajectory. As expected, when the object moved, cells responded strongly in the location of the moving object (Figure 7A).

After the object stopped its differential motion, disappearing into the background, On cells decreased their activity within 0.5 mm of the object, consistent with their monophasic adaptive fields (Figure 7B). Sensitizing cells, however, showed persistent elevated activity in the location where the object recently moved (Figure 7A,B). This activity was significantly (p < 0.002) above the steady state response for 2.8 s after the object stopped its motion relative to the background. We compared the duration of this elevated activity to the duration of the immediate response, defined as the time that cells under the moving object fell below the baseline firing rate, reflecting the end of the linear filter and the onset of brief local adaptation. Sensitizing cells showed elevated activity for 21 times longer than their immediate response to the fast motion, which was 133 ms. Thus, sensitizing cells functionally stored the location of the previously moving object with locally increased activity.

Adapting Off cells had diminished activity in the immediate location where the object stopped, indicated by a distance of zero in Figure 7. However, adjacent to the location of the moving object these cells increased their activity (Figure 7B). Like sensitizing cells, this increased activity remained significantly (p < 0.005) above the steady state response for 2.8 s after the object stopped moving, 12 times longer than their immediate response to the fast motion, which was 233 ms. When one considers the total magnitude of the peripheral increase in activity from sensitization, as measured by the area under the curve (Figure 7B), this was at least as large as (1.1 times) the central decrease in activity caused by adaptation. These results were consistent with the center-surround organization of their adaptive fields (Figure 1D,E). Therefore, following the motion of a camouflaged object, adapting Off cells stored and transmitted a prediction of the location of the boundaries of the object after its motion ceased.

Inhibition is necessary for sensitization and the establishment of the adaptive field

Guided by the AF model (Figure 2), we tested whether inhibitory neurotransmission was necessary for sensitization. We measured the responses of sensitizing cells to a uniform-field stimulus that changed in contrast during the application of 100 μM picrotoxin, which blocks ionotropic GABAergic receptors. Picrotoxin abolished the ability of these cells to respond during L_early (Figure 8A), and turned the sensitizing response into an adapting response (Figure 8B). The change of plasticity was specific to picrotoxin because sensitization persisted in the presence of strychnine, a glycinergic antagonist, and APB, which blocks the On pathway (Figure S4). Thus, GABAergic transmission underlies sensitization, enabling sensitizing ganglion cells to respond quickly after a contrast decrement.

Figure 8. Sensitization requires GABAergic transmission.

(A) Top, the stimulus changed back and forth for 80 trials between a global high contrast (35 %) for 4 s and a global low contrast (3 %) for 16 s. Middle, example average responses for sensitizing cells during the 30 min prior to drug addition (left), and from 30 min to 1h after drug addition (right), for a cell in 100 μM picrotoxin. Bottom, same for a different sensitizing cell in 200 μM bicuculline methiodide. (B) Average adaptive indices for sensitizing cells in (top) picrotoxin (n = 4) or (bottom) bicuculline (n = 5). Error bars are obscured by the data. (C) The response of a cell with a center-surround adaptive field to the stimulus from Figure 1A,B before and during the addition of 75 μM picrotoxin. High contrast stimulus was positioned in the sensitizing region of the cell. (D) Average adaptive indices as a function of distance for fast Off adapting cells (top) (n = 68) and sensitizing cells (bottom) in control solution and 75 μM (n = 12, closed circles) or 200 μM (n = 6, open circles) picrotoxin. Responses are shown before drug (colored circles) and after drug (black circles). Error bars are s.e.m.

In the AF model, inhibition combines with the excitatory pathway prior to its threshold (Figure 2B). This is necessitated because inhibition delivered after the threshold would produce a vertical shift during sensitization instead of a horizontal shift (Kastner and Baccus, 2011). Such connectivity is most consistent with amacrine cells inhibiting bipolar cell terminals. Salamander bipolar cell terminals express GABA_C receptors that can be blocked by Picrotoxin, but not by Bicuculline, which blocks GABA_A receptors found on amacrine and ganglion cells (Lukasiewicz et al., 1994). Therefore our model predicts that sensitization should persist in the presence of Bicuculline, which was indeed the case (Figure 8A,B).

Previous studies have shown that intracellular recordings of bipolar cells can reveal effects of inhibition at their synaptic terminals, in particular those bipolar cells that are likely to convey input to OMS cells (Olveczky et al., 2007). Interpreting the excitatory subunits of the AF model to be bipolar cells, the model predicts that during L_early bipolar cell terminals receive less steady inhibition than during L_late. As previously reported (Baccus and Meister, 2002; Rieke, 2001) we found that some bipolar cells had a hyperpolarized membrane potential during L_early compared to L_late. However, we also found bipolar cells with a depolarized membrane potential during L_early compared to L_late (Figure 9A,B). The existence of such bipolar cells has also recently been reported in zebrafish (Nikolaev et al., 2013).

Figure 9. Depolarization of bipolar cells during sensitization.

(A) Top, stimulus consisting of biphasic flashes that changed from high (100 %, black) to low (7 %, blue) contrast. The low contrast stimulus was composed of 9 randomly interleaved intensity flashes. Inset shows transition from high to low contrast, colors indicate different flash amplitudes. Each flash amplitude was repeated a total of 3 times at each time point. Bottom, average response of a bipolar cell. (B) Change in membrane potential between L_early (0.8 – 3.2 s after high contrast) and L_late (12 – 16 s after high contrast) at each flash amplitude averaged over bipolar cells that showed an afterdepolarization (n = 4 cells) or afterhyperpolarization (n = 3 cells) following high contrast. (C) Average response of a ganglion cell simultaneously recorded with the bipolar cell from (A) to a low contrast flash while a +500 pA or −500 pA pulse was injected into the bipolar cell. (D) Changes in the firing rate of all simultaneously recorded adapting Off (n = 4) and sensitizing (n = 6) ganglion cells within 0.2 mm of bipolar cells that showed an afterdepolarization.

Although the existence of bipolar cells that depolarize during L_early is consistent with the AF model, these bipolar cells must connect to fast Off adapting and sensitizing cells. Therefore, while recording intracellularly from the bipolar cells that showed an afterdepolarization we simultaneously recorded extracellularly from ganglion cells (Asari and Meister, 2012). Injecting depolarizing and hyperpolarizing current into these bipolar cells changed the response of all neighboring fast Off ganglion cells (Figure 9C,D). Current injected into bipolar cells changed the ganglion cells’ response from 7.4 ± 1.5 Hz upon depolarization of the bipolar cell to 4.3 ± 1.3 Hz upon hyperpolarization of the bipolar cell (p < 0.0003), indicating that these bipolar cells reside within the fast Off ganglion cell circuitry.

The AF model predicts that different strength of inhibition generates the different adaptive fields (Figure 2D). We therefore tested whether a lower concentration of picrotoxin would transform a center surround adaptive field into a monophasic adapting adaptive field, and transform the sensitizing adaptive field into a center-surround adaptive field. For cells with a center-surround adaptive field, 75 μM picrotoxin caused the surround of a cell to change from sensitizing to adapting (Figure 8C,D). Thus, GABAergic transmission was also necessary for sensitization in fast Off adapting cells. In addition, when the high contrast region was close to the receptive field center of the cell, at an average distance of 100 μm, inhibition acted to oppose adaptation. The magnitude of the adaptive index increased in the absence of inhibition (−0.47 ± 0.05 control, −0.59 ± 0.06 picrotoxin, p < 0.0125).

We then examined the effect of 75 μM picrotoxin on sensitizing cells. We found that cells located closer to the high contrast region changed from sensitizing to adapting, whereas those further away from the high contrast region still sensitized, but to a lesser degree (Figure 8D). Sensitization was completely abolished at all distances by 200 μM picrotoxin (Figure 8D). Thus, a partial block of GABAergic transmission transformed the sensitizing adaptive field into a center-surround adaptive field (Figure 8D). This confirms that a combination of excitation and inhibition constructs the adaptive field. As predicted by the AF model (Figure 2D), reductions in the strength of one broad class of inhibition changed the adaptive field from sensitizing to center-surround and then to adapting.

One potential concern with experiments using picrotoxin is that an increased firing rate might cause increased adaptation to mask intact sensitization. In picrotoxin, the high contrast response increased by 38 ± 18 %, and the steady state low contrast response increased by 123 ± 14 %. However, an increased firing rate can also occur with stronger stimuli in control solution. Therefore we compared the response of individual sensitizing cells (n = 8) in two different contrast transitions (35 – 5 % vs. 100 – 7 %) (Figure S4C). Sensitizing cells increased their high contrast response by 61 ± 17 % in 100 % contrast compared to 35 % contrast. They also increased their steady state low contrast response by 153 ± 51 % in 7 % contrast compared to 5 % contrast. Even with a firing rate higher than in picrotoxin, sensitizing cells continued to sensitize under the higher contrast condition, as the adaptive index was 0.36 ± 0.06 for 35 to 5 % contrast, and 0.21 ± 0.01 for 100 to 7 % contrast (Figure S4C).

DISCUSSION

Here we have studied multiple aspects of how adaptation and sensitization combine in single ganglion cells. As to the general phenomenon, fast Off ganglion cells have center-surround adaptive fields, showing central adaptation but peripheral sensitization (Figure 1). Furthermore, spatial antagonism of plasticity occurs at a subcellular scale (Figure 3) and sensitization occurs in a rapidly changing contrast environment (Figure 4). As to the computation, a model with independently adapting excitatory and inhibitory subunits explains spatiotemporal plasticity within the adaptive field (Figure 2 – 4). The model further shows that varying inhibitory strength can generate the different adaptive fields. As to the underlying mechanisms, a membrane potential depolarization underlay sensitization of the firing rate (Figure S3B). Sensitization also requires GABAergic inhibition, but not transmission through GABA_A receptors (Figure 8). Certain bipolar cells depolarize following high contrast, and connect to ganglion cells that show sensitization (Figure 9). Furthermore, partial blockade of GABAergic transmission supports the idea that different levels of inhibition produce different types of adaptive field. As to the functional relevance of sensitization, OMS cells have a center-surround adaptive field and act as feature detectors (Figure 5). Fast Off sensitizing cells, although not OMS cells, have a similarly sharp threshold and respond to the same local features as fast Off adapting cells (Kastner and Baccus, 2011). Finally, as to a theoretical understanding of these results, the sensitizing effect on nonlinearities is consistent with a simple model showing that inhibition acts as a bias in the detection of an effective stimulus (Figure 6). Furthermore, the spatiotemporal sensitizing field conforms to a recursive inference model that updates the prior probability of a signal, predicting a sensitizing surround larger than the immediate response. Testing this idea with a stimulus representing a camouflaged object, we showed that sensitization enables the prediction of a future object position (Figure 7).

Adaptive and receptive fields

Even though the classical receptive field (Barlow, 1953; Kuffler, 1953) incompletely describes the response of a cell, part of its usefulness comes from the fact that, to some extent, different spatial regions provide independent contributions to the response of the cell. Similarly, our measurements of the adaptive field indicate that excitatory and inhibitory subunits contribute independently towards adaptation and sensitization. Toward that end, we confirmed that the adaptive field could be used to explain and interpret responses to different (global stimuli) and more ecological stimuli (moving objects). We thus expect that the basic model of the adaptive field should prove useful for other visual stimuli. Recently it was shown that at the level of the ganglion cell membrane potential all adaptive properties for a uniform stimulus with changing contrast could be explained by a model of synaptic adaptation (Ozuysal and Baccus, 2012). If local sites of adaptation contribute independently, this implies that spatiotemporal plasticity may be explained substantially by knowledge of the local adaptive properties of synapses and of anatomical circuitry.

A functional role for adapting inhibition

A strong parallel exists between the role of inhibition in the receptive field, and the role of adapting inhibition in the adaptive field. Just as the receptive field surround relies on inhibition with a wider spatial extent than excitation (Thoreson and Mangel, 2012), our AF model (Figure 2) and pharmacological experiments (Figure 8) indicate that different levels of adapting inhibition produce the various spatial adaptive fields. Although adaptation in inhibitory amacrine cells was known to exist (Baccus and Meister, 2002), it lacked any apparent role in the plasticity of ganglion cells (Beaudoin et al., 2007; Brown and Masland, 2001; Manookin and Demb, 2006; Rieke, 2001). Our results and model show that by opposing excitatory adaptation and producing sensitization, inhibitory synaptic transmission plays a critical role in retinal plasticity.

However, the classical linear surround and sensitization likely arise from different sources of inhibition. Fast Off adapting cells have a stronger inhibitory surround than sensitizing cells (Kastner and Baccus, 2011), yet sensitizing cells appear to have stronger input from adapting inhibition (Figure 8). Accordingly, we found a minimal correlation between the strength of the linear surround and the adaptive index within adapting Off (r² = 0.051) and sensitizing (r² = 0.009) cells.

At a faster timescale, amacrine transmission can produce local inhibition and peripheral increases in sensitivity in a manner analogous to the slower effects observed here (de Vries et al., 2011). Additionally, inhibitory transmission is necessary for fast spatially localized gain control (Bölinger and Gollisch, 2012).

Different levels of sensitization in different cell types

Three different cell types showed different levels of sensitization, with On cells showing no sensitization, and OMS cells showing intermediate sensitization. Because On cells have a shallower response curve than Off cells (Chichilnisky and Kalmar, 2002; Zaghloul et al., 2003), On cells act less as a feature detector, and therefore may benefit less from sensitization. As to OMS cells, because they receive information from the wider surround, indicating whether a differential motion signal is present, they may rely less on prior information in the form of sensitization.

Updating the prior probability of a stimulus

Models that use ongoing inference to adjust the prior probability are consistent with behavior (Kording and Wolpert, 2006; Schwartz et al., 2007), but a similar question has not been explored in early sensory systems. Furthermore, previous theoretical work has suggested that an optimal model that updated its prior probability is inconsistent with observed physiological data precisely because such a model would not predict adaptation (‘repulsion’ of a tuning curve), but an opposite effect (‘attraction’) (Stocker and Simoncelli, 2006). In fact, in the primate LGN and primary visual cortex, stimulus-specific enhancement of sensitivity from peripheral stimuli has been explained by a model containing adaptation of an inhibitory surround pathway analogous to what we have proposed (Camp et al., 2009; Wissig and Kohn, 2012). As to whether this behavior might be consistent with updating of a prior stimulus probability, it has been noted that during low contrast or noisy stimuli, prior information would become particularly important, but these conditions have not been thoroughly explored (Schwartz et al., 2007)—most likely because conditions of strong stimuli are often more amenable to experimentation. In fact, we observed sensitization under conditions of weak stimuli, when prior information from nearby or previous strong stimuli is most critical in detecting signals in a noisy environment.

Integrating information at the bipolar cell synaptic terminal

Several lines of evidence suggest that sensitization first arises in the bipolar cell presynaptic terminal, although a definitive confirmation must come from more mechanistic future experiments. Sensitization produces a horizontal shift on the ganglion cell nonlinearity (Kastner and Baccus, 2011). For such a shift to occur a steady change in inhibition must be delivered prior to a strong threshold, as occurs at the bipolar cell terminal (Heidelberger and Matthews, 1992). Furthermore, although GABAergic transmission is required for sensitization (Figure 8), transmission through GABA_A receptors is not. Thus, GABAergic transmission directly onto ganglion cells is not required for sensitization (Figure 8), indicating a requirement for transmission through GABA_C receptors on bipolar cell terminals. Finally, recordings from a subset of bipolar cells show a depolarization after high contrast. These bipolar cells connect to fast Off cells (Figure 9). Consistent with this proposal, a recent study shows that an increased transmission from bipolar cells in zebrafish requires GABAergic transmission, and depression of amacrine transmission to bipolar cell terminals may underlie sensitization in ganglion cells (Nikolaev et al., 2013).

The depolarization observed in bipolar cells could underlie the shift in threshold, and potentially the decrease in slope seen during sensitization. Inactivation of voltage dependent ion channels or synaptic depression at the bipolar cell terminal could potentially decrease the slope of the nonlinearity when the bipolar cell is depolarized, although future studies must be performed to identify the biophysical mechanisms underlying the observed changes in sensitivity. Studies of GABAergic receptors on bipolar cell terminals indicate that transmission through GABA_C receptors does indeed undergo depression, with a recovery time constants of seconds, somewhat longer than the time course of recovery of depression of excitatory transmission at the terminal (Li et al., 2007; Sagdullaev et al., 2011).

The threshold at the bipolar cell terminal plays a key role in establishing certain ganglion cells as feature detectors. Taking the functional point of view that the steady level of inhibition relates to the prior probability of a signal (Figure 6), then the bipolar cell terminal adapts to the range of local signals, and steady presynaptic inhibitory input provides information about how likely those signals are to occur.

One may wonder why the retina, as opposed to the higher brain, computes the bias underlying sensitization. The sharp threshold of ganglion cells acting as feature detectors again provides the answer. If a signal fails to cross this threshold, it cannot be detected at a higher level independent of any future computation. Consistent with this idea, previous results indicate that sensitization preserves signals that would otherwise be lost in cells with less sensitization (Kastner and Baccus, 2011). Thus, for the brain to take the greatest advantage of prior knowledge about simple spatiotemporal correlations, the sensitizing signal must be delivered prior to this threshold.

The retinal neural code and the statistics of objects

The detection, classification, and representation of objects is a difficult task that occurs throughout the visual hierarchy (Logothetis and Sheinberg, 1996). The retina takes advantage of the distinct statistics of objects to encode an object’s location and trajectory. For example, the trajectory of an object necessarily differs from background motion due to eye movements, a property used by OMS cells to detect the presence of objects (Olveczky et al., 2003). Objects often move smoothly, a property the retina uses to anticipate the location of a moving object (Berry et al., 1999). Additionally, an object’s identity remains constant, a property underlying the cognitive representation of object permanence (Bower, 1967). Thus object constancy provides the basis for an inference about the source of a visual stimulus.

However, objects present the retina with signals of vastly differing strengths depending upon motion, ambient lighting, or context. With respect to the problem of maintaining a continuous representation of an object, a camouflaged object presents a particularly difficult stimulus. Motion reveals the object, causing it to pop out from its surroundings, a property that may arise due to OMS cells (Olveczky et al., 2003). Yet, once the object stops, it nearly disappears into its surroundings. In this case, the visual system must rely upon prior information to represent the object, as occurs higher in the brain (Graziano et al., 1997). Due to object constancy, sensitization preserves an object’s location across changes in object motion, thus contributing to the stable representation of objects. Because a saccade will change an object’s retinal location, it is expected that this preservation of object location will function within a saccadic fixation.

Although a number of sophisticated computations have been described in the retina, these are typically studied in isolation (Gollisch and Meister, 2010; Schwartz and Rieke, 2011). Here we have shown that several computations—adaptation, sensitization and object motion sensitivity—combine to enable a prolonged representation of an object in the retina. The basic principles of adaptation and prediction are common to all sensory regions of the brain. Similar synaptic mechanisms can accomplish adaptation both in the retina and in the cortex (Chance et al., 2002; Jarsky et al., 2011; Ozuysal and Baccus, 2012). Given the simple underlying mechanism of adaptation of inhibitory transmission that we propose to generate predictive sensitization, one might expect that similar processes underlie prediction elsewhere in the nervous system.

EXPERIMENTAL PROCEDURES

Electrophysiology

Retinal ganglion cells of larval tiger salamanders were recorded using an array of 60 electrodes (Multichannel Systems) as described (Kastner and Baccus, 2011). A video monitor projected stimuli at 30 Hz. The video monitor was calibrated using a photodiode to ensure the linearity of the display. Stimuli had a constant mean intensity of 10 mW/m². Contrast was defined as the standard deviation divided by the mean of the intensity values, unless otherwise noted.

Simultaneous intracellular and multielectrode recordings were performed as described (Manu and Baccus, 2011). Sensitizing ganglion cells were identified by their level in the retina, spiking response and sensitizing behavior. Off bipolar cells were identified by their flash response, receptive field size, and level in the retina.

Receptive fields and sensitivity

To measure sensitivity in different spatial regions of the receptive field, a spatiotemporal linear-nonlinear (LN) model was computed by the standard method of reverse correlation (Hosoya et al., 2005), described further in Supplemental Experimental Procedures.

Adaptive field model

The AF model (Figure 2) was a spatiotemporal version of a previous model that produced sensitization to a spatially uniform stimulus (Kastner and Baccus, 2011), and is described further in Supplemental Experimental Procedures.

Temporal adaptive field

To measure the temporal adaptive field we presented a stimulus whose contrast was drawn randomly from a uniform distribution of 0 – 35% contrast every 0.5 s. The intensities presented for each contrast were randomly drawn from a Gaussian distribution defined by the contrast of that time point. Since the intensities were randomly drawn, as the input for the filter we computed the contrast from the mean, M, and standard deviation, W, of the sequence of intensities that were presented, which were 0 – 66%. The contrast, σ, was σ = W/M.

Signal detection model

The probability, p(v|s), of an input, v, given a signal, s, was taken from a Gaussian fit from the distribution of bipolar cell membrane potentials at 5 % contrast. The probability of an input, v, given that no signal was present, p(v|η), was estimated as a Gaussian distribution from repeated presentation of the same 5 % contrast stimuli. For the model, the average ratio of the s.d. of a Gaussian fit to p(v|η) and p(v|s) was the only parameter taken from the data. For the recursive spatiotemporal inference model at each time point the posterior probability, p(s_x,t|v_x,t) was computed from Bayes’ rule as

$$p\left(s_{x,t}\mid v_{x,t}\right)=\frac{p\left(v_{x,t}\mid s_{x,t}\right)p\left(s_{x,t}\right)}{p\left(v_{x,t}\mid s_{x,t}\right)p\left(s_{x,t}\right)+p\left(v_{x,t}\mid \eta \right)\left(1-p\left(s_{x,t}\right)\right)}.$$ (1)

The denominator, p(v), reflected the fact that p(s) + p(η) = 1 (either a signal is present or it is not). The prior probability, p(s_x,t), was updated from the previous posterior probability at each time point by convolving a Gaussian smoothing filter, h(k), with p(s_x−k,t−1|v_x−k,t−1) according to

$$p\left(s_{x,t}\right)=\int h(k)p\left(s_{x-k,t-1}\mid v_{x-k,t-1}\right)dk.$$ (2)

The average posterior, 〈 p(s|v)〉, during L_early and L_late was computed. Further details are given in Supplemental Experimental Procedures.

Highlights.

• Many retinal ganglion cells show central adaptation and peripheral sensitization

• Different levels of GABAergic inhibition create different levels of sensitization

• Sensitization conforms to an inference model, updating the prior signal probability

• Sensitization acts to predict the future location of an object