Transformation of stimulus correlations by the retina

Abstract

Redundancies and correlations in the responses of sensory neurons may seem to waste neural resources, but they can also carry cues about structured stimuli and may help the brain to correct for response errors. To investigate the effect of stimulus structure on redundancy in retina, we measured simultaneous responses from populations of retinal ganglion cells presented with natural and artificial stimuli that varied greatly in correlation structure; these stimuli and recordings are publicly available online. Responding to spatio-temporally structured stimuli such as natural movies, pairs of ganglion cells were modestly more correlated than in response to white noise checkerboards, but they were much less correlated than predicted by a non-adapting functional model of retinal response. Meanwhile, responding to stimuli with purely spatial correlations, pairs of ganglion cells showed increased correlations consistent with a static, non-adapting receptive field and nonlinearity. We found that in response to spatio-temporally correlated stimuli, ganglion cells had faster temporal kernels and tended to have stronger surrounds. These properties of individual cells, along with gain changes that opposed changes in effective contrast at the ganglion cell input, largely explained the pattern of pairwise correlations across stimuli where receptive field measurements were possible.

Figure 1. Natural and artificial stimuli vary in correlation structure.

(A) Spatial correlation functions from four natural images (at higher resolution than the stimuli used in our experiments), in gray. Black line shows average correlation function over a large database of natural images. Although all images' correlation functions have the same general shape, there are clear differences between images. (B) Examples of the stimuli used in this work. Traces above frames show the spatial correlation function of each stimulus; traces below frames show the temporal correlation function. Stimuli were displayed at 30 Hz in alternating 10-minute blocks. Spatial scale bar (below white noise frame) for stimulus frames and spatial correlation functions is 400 µm; temporal scale bar for temporal correlation functions is .

Figure 2. Retinal ganglion cell receptive fields measured using a multi-electrode array.

(A) Receptive field locations of 31 cells recorded simultaneously from guinea pig retina. Each curve shows the 70% contour line of one receptive field. Scale bar is 200 µm. (B) Best-fitting temporal kernels for 75 cells, clustered into four classes. Classes were obtained by manually clustering temporal filters on the basis of the projection onto their first three principal components. (C) Maximum likelihood estimates of spatio-temporal receptive fields (STRFs) for an example cell. STRFs were computed separately using responses to white noise (left) or exponential spatio-temporally correlated stimuli (right). Scale bar is 200 µm.

Figure 3. Retinal output correlations are largely constant between stimulus conditions.

(A) Instantaneous spike train correlation coefficients between pairs of ganglion cells, comparing responses to natural movies and to white noise. Dashed black line is the diagonal. Cell pairs of the same class are indicated by colors in the legend. Different- class pairs are separated into ON-OFF (gray) and ON-ON or OFF-OFF pairs (black). The excess correlation, , is the deviation of the slope of the best fit line (gray) from the diagonal. (B) Same as (A) but for spatio-temporal exponentially correlated stimulus. (C) Excess correlation measured from ganglion cells responding to the indicated stimulus, compared to white noise. Numbers below bars indicate the number of cell pairs in each condition; all recorded cells are included. Error bars are 95% bootstrap confidence intervals computed over 50,000 random samples with replacement from the set of cell pairs. (D) Comparison of measured excess correlation (white) to non-adapting model predictions (gray) for the indicated stimuli. Model values were derived from LN neurons with parameters fit to white noise data. Only cells whose receptive fields met a quality threshold are used here, in contrast to (C).

Figure 4. Analysis of pairwise correlations.

(A) Excess correlations for natural stimuli. Left and middle bars show excess correlation when scrambled natural movies and intact natural movies, respectively, are compared to white noise in the data and in a population of non-adapting model neurons. Right bars show excess correlation when responses to natural movies are compared to scrambled natural movies directly. A non-adapting model predicts larger output correlations in response to the correlated natural input than seen in the data. (B) Output correlations under the spatio-temporal exponential stimulus compared with white noise as predicted by LN models with parameters fit to the data. The two leftmost bars (“data” and “WN model (no adaptation)”) reproduce the spatio-temporal “data” and “model” bars in Fig. 3D. (Note the difference in scale.) For the other bars, we simulated a population of neurons using linear filters measured from each stimulus but gains measured only from white noise (“filter adaptation model”) or using experimentally derived estimates of both linear filters and gains for each stimulus (“filter+gain adaptation model”). In the fully adapted model, excess correlations are consistent with the data. (C) Pairwise output correlation as a function of the distance between receptive field centers. Top row: Output correlations for white noise checkerboard (left) and natural movies (middle) and the difference in correlation between these conditions (right) for experiments where natural movies were presented. Bottom row: Output correlations for white noise checkerboard (left) and spatio-temporal exponential noise (middle) and the difference in correlation between these conditions (right) for experiments where spatio-temporal exponential noise was presented. Each point corresponds to one simultaneously recorded cell pair; within a row, the same pairs are represented in all three panels. Blue lines are the median correlation within bins chosen to contain 30 cell pairs each. Solid lines are median correlations for same-polarity cell pairs; dashed lines are for opposite-polarity pairs.

Figure 5. Adaptation of the linear temporal filter.

(A) Temporal filters are faster under spatio-temporal exponentially correlated noise (C) than white noise (W). (B) Power spectrum of correlated noise input (C, black dashed line) has more low frequency power than white noise (W, gray dashed line). The power spectrum of the temporal filter for correlated noise (C, black solid line) has more high frequency power. (C) Power spectra of filter outputs: White-noise filter acting on white stimulus (solid gray); White-noise filter acting on correlated stimulus (dashed); Adapting correlated-noise filter acting on correlated stimulus (solid black). In adapted cases, output power spectra are similar between stimuli – i.e., temporal kernels compensate to maintain invariant output autocorrelation. (D) The difference in normalized filter power spectra between the correlated and white stimuli, for spatio-temporal (top) and spatial (bottom) exponential experiments. The power spectra of all filters in each stimulus were normalized by removing the DC component and dividing by the sum of squared amplitudes. The population change in temporal filters shows a consistent increase in high-frequency power relative to low-frequency power for the spatio-temporal, but not the spatial, stimulus. (E) Total power above 5 Hz divided by total power below 5 Hz for filters computed in response to correlated vs. white noise stimuli shows a shift towards high-pass signaling across the population. Arrow and gray circle indicate the pair shown in A–C. (F) Same analysis as in (E) applied to the filter output in (C). Points near the diagonal indicate near-complete compensation for stimulus changes; points below the diagonal indicate incomplete compensation.

Figure 6. Adaptation of the spatio-temporal receptive field and gain.

(A) Center latency (time to peak of the temporal kernel) is shorter for spatio-temporal exponentially correlated noise. Histogram shows adaptation indices (corr−white)/(corr+white) for center latency (). (B,C) Changes in center latency (corr−white) for spatio-temporally correlated (B) and temporally correlated (C) stimuli, in milliseconds. Almost all cells have a decreased time to peak when responding to a correlated stimulus. (D) Adaptation indices, computed as in (A), for relative surround strength (surround/center ratio) show a slight skew toward a stronger surround for spatio-temporally correlated noise (). (E, F) Difference in surround strength for the spatio-temporal (E) and spatial (F) exponential stimuli. (G) Gain adaptation. Gains were defined as the slope of the LN model nonlinearity, and obtained separately for the response to white noise and to the spatio-temporally correlated exponential stimulus. Effective contrast, the standard deviation of the linear filter output, was similarly measured in both stimuli. The difference in gain, correlated value minus white noise value, is plotted against the difference in effective contrast. Increases in effective contrast tend to invoke compensating decreases in gain ().