Retinal ganglion cells act largely as independent encoders

Correlated ®ring among neurons is widespread in the visual system. Neighbouring neurons, in areas from retina to cortex, tend to ®re together more often than would be expected by chance. The importance of this correlated ®ring for encoding visual information is unclear and controversial. Here we examine its importance in the retina. We present the retina with natural stimuli and record the responses of its output cells, the ganglion cells. We then use information theoretic techniques to measure the amount of information about the stimuli that can be obtained from the cells under two conditions: when their correlated ®ring is taken into account, and when their correlated ®ring is ignored. We ®nd that more than 90% of the information about the stimuli can be obtained from the cells when their correlated ®ring is ignored. This indicates that ganglion cells act largely independently to encode information, which greatly simpli®es the problem of decoding their activity. A principal goal in vision research is to understand how visual stimuli are encoded in the activity of the ganglion cells, as these cells provide all the information about the visual world that the brain receives. Several studies have proposed that visual stimuli are encoded in a complex way that depends on correlated activity. Such activity has been described in many species, including several mammals (cat, rabbit and monkey). The proposal is that this activity carries information about visual stimuli that is not present in non-correlated activity. If correlated ®ring carries information, then strategies for understanding how ganglion cells encode visual stimuli must take the correlations into account. This means that the activity of a single ganglion cell cannot be evaluated by itself, but rather must be decoded in the context of the ®ring patterns of other ganglion cells. If, on the other hand, correlated ®ring does not carry visual information, then the ®ring of a ganglion cell can be evaluated independently of other cells. It has been reported that correlated activity can carry information, but the methods used in these reports were indirect. Here we addressed the problem directly using an information theoretic approach. We compared the amount of information that could be obtained from pairs of ganglion pairs when their correlations were taken into account with the amount of information that could be obtained from the pairs when their correlations were ignored. The extent to which information is lost when correlations are ignored is the extent to which correlations are important for encoding information. We used the isolated mouse retina. The stimuli were natural movies, each 7 s long and repeated 300 times, and the ganglion cell responses were recorded using a multielectrode array. We used an array with closely spaced electrodes (25±100 mm apart) to ensure that we recorded from many pairs of neighbouring ganglion cells, which tend to have overlapping receptive ®elds and show correlated activity. The data were screened for pairs of responses that passed two criteria. First, both responses had to be clean of contaminating spikes from other cells. This was tested by computing the autocorrelation function for each response, which gives the ®ring rate as a function of time relative to each spike. As neurons have a refractory period of approximately 1 ms, the autocorrelation function for a single cell should contain a central peak ̄anked on either side by zero ®ring rate for 1 ms. Non-zero ®ring rates in this 1-ms window re ̄ect contamination from electronic noise or spikes from other cells. Only responses showing less than 2% contamination were used. Second, both responses had to have average ®ring rates above 0.5 Hz. Typical responses are shown in Fig. 1. The dataset contained 76 cells, with 5±20 cells per retina (six retinas). This gave a total of 498 cell pairs, with 10±190 pairs per retina. We ®rst determined the degree of correlated activity for each pair (Fig. 2a±c). This was measured as the fraction of correlated spikes produced by the pair above chance, taking into account correlations induced by the stimulus. We called this the excess correlated fraction (ECF; see Methods). The ECFs ranged from ±1% to +34% (Fig. 2b), in close agreement with similar measurements reported for other mammalian species (the highest excess fraction is 27% in cat and 28% in rabbit). It is also similar to that found for pairs of cells in cat lateral geniculate nucleus (LGN), in which the highest fraction of correlated spikes is, on average, 28% (ref. 13). We then determined the timescale over which the correlations occurred (Fig. 2c). The range was from , 1 ms to 11 ms. This is similar to that observed in cat and rabbit, although it extends to slightly shorter values. Similar short timescales (, 1 ms) are found in cat LGN. To measure the amount of information the pairs of ganglion cells carried about the stimuli when their correlations were taken into account, we used standard information theoretic techniques. We treated the movie as a series of segments of ®xed temporal length, with each segment regarded as a separate stimulus. We presented the movie several hundred times to generate a large set of responses (spike trains) to each segment. This allowed us to estimate the probability of getting a particular pair of responses given a particular movie segmentÐthat is, to estimate P r1; r2js, where r1 was the response of cell 1, r2 was the response of cell 2 and s was the movie segment. Given these conditional probabilities, we then calculated the amount of information, I, between the responses and the stimulus segments, using the standard expression