Over the brief time intervals available for processing retinal output, roughly 50 to 300 msec, the number of extra spikes generated by individual ganglion cells can be quite variable. Here, computer-generated spike trains were used to investigate how signal/noise might be improved by utilizing spatiotemporal correlations among retinal neurons responding to large, contiguous stimuli. Realistic correlations were produced by modulating the instantaneous firing probabilities of all stimulated neurons by a common oscillatory input whose amplitude and temporal structure were consistent with experimentally measured field potentials and correlograms. Whereas previous studies have typically measured synergy between pairs of ganglion cells examined one at a time, or alternatively have employed optimized linear filters to decode activity across larger populations, the present study investigated a distributed, non-linear encoding strategy by using Principal Components Analysis (PCA) to reconstruct simple visual stimuli from up to one million oscillatory pairwise correlations extracted on single trials from massively-parallel spike trains as short as 25 msec in duration. By integrating signals across retinal neighborhoods commensurate in size to classical antagonistic surrounds, the first principal component of the pairwise correlation matrix yielded dramatic improvements in signal/noise without sacrificing fine spatial detail. These results demonstrate how local intensity information can distributed across hundreds of neurons linked by a common, stimulus-dependent oscillatory modulation, a strategy that might have evolved to minimize the number of spikes required to support rapid image reconstruction.
The conditions under which retinal ganglion cells transmit visual signals synergistically remains a topic of considerable debate (Latham & Nirenberg, 2005;Schneidman, Bialek, & Berry, 2003;Schnitzer & Meister, 2003). Measurements of synergy between small groups of neurons have found evidence for everything from redundancy (Gawne & Richmond, 1993;Puchalla, Schneidman, Harris, & Berry, 2005;Warland, Reinagel, & Meister, 1997) to statistical independence (Nirenberg, Carcieri, Jacobs, & Latham, 2001;Panzeri, Schultz, Treves, & Rolls, 1999;Reich, Mechler, & Victor, 2001; E. T. Rolls, Franco, Aggelopoulos, & Reece, 2003) to both modest (Dan, Alonso, Usrey, & Reid, 1998) as well as more substantial levels of synergy (deCharms & Merzenich, 1996;Gat & Tishby, 1999 ;Hirabayashi & Miyashita, 2005;Riehle, Grun, Diesmann, & Aertsen, 1997;Samonds, Allison, Brown, & Bonds, 2004;Singer, 1999;Vaadia et al., 1995). Several studies have looked specifically for synergy among larger ensembles (Bezzi, Diamond, & Treves, 2002;Frechette et al., 2005;Narayanan, Kimchi, & Laubach, 2005;Stanley, Li, & Dan, 1999), yet it remains an open question as to how a non-linear code based on spatiotemporal correlations between hundreds of ganglion cells, corresponding to hundreds-of-thousands of coactive neuron pairs, might convey local pixel-by-pixel intensity information that could not be obtained by analyzing the same spike trains individually, especially over the short time scales-approximately 50 to 300 msec-available for interpreting retinal signals (Bacon-Mace, Mace, Fabre-Thorpe, & Thorpe, 2005;Kirchner & Thorpe, 2006;Edmund T. Rolls, Tovee, & Panzeri, 1999;Thorpe, Fize, & Marlot, 1996).
Here, Principal Components Analysis (PCA) was used to explore how local pixel intensities could be encoded in a non-linear manner by exploiting oscillatory spatiotemporal correlations among co-activated ganglion cell pairs. Coherent oscillations in response to diffuse stimuli have been reported in many species, including frog (Ishikane, Gangi, Honda, & Tachibana, 2005;Ishikane, Kawana, & Tachibana, 1999), mudpuppy (Wachtmeister & Dowling, 1978), rabbit (Ariel, Daw, & Rader, 1983;Yokoyama, Kaneko, & Nakai, 1964), cat (Doty & Kimura, 1963;Laufer & Verzeano, 1967;Neuenschwander, Castelo-Branco, & Singer, 1999;Neuenschwander & Singer, 1996;Steinberg, 1966), monkey (Frishman et al., 2000;Laufer & Verzeano, 1967) and humans (De Carli et al., 2001;Wachtmeister, 1998). Short segments of computer-generated spike train data, from 25 to 400 msec in duration, were used to simulate a retinal patch containing up to one thousand output neurons, represented by a single ganglion cell type whose receptive field centers precisely tiled a square rectilinear grid. Both background and stimulated firing rates were chosen so as to encompass much of the measured dynamic range of cat retinal ganglion cells in response to diffuse, sinusoidally varying stimuli (Troy & Enroth-Cugell, 1993). Realistic spatiotemporal correlations were generated by simultaneously modulating the instantaneous firing probabilities of all stimulated cells using a common, oscillatory waveform whose amplitude and temporal structure was consistent with both optic tract recordings (Doty & Kimura, 1963;Laufer & Verzeano, 1967;Steinberg, 1966) and with single and multi-unit correlation functions (Ishikane et al., 1999;Neuenschwander & Singer, 1996). Over a nearly 16fold range of stimulated firing rates, the present results show that without sacrificing fine spatial detail, oscillatory pairwise correlations can support rapid pixel-by-pixel reconstructions of large, contiguous visual stimuli that are far superior to analogous reconstructions based on Poissondistributed event trains that contained the same average number of spikes at each stimulus intensity,.
The present findings imply that oscillatory correlations consistent with those reported between retinal ganglion cells in several species can substantially augment the stimulus information conveyed by a simple rate-code, the latter being defined by a code in which local pixel intensity is conveyed entirely by the number of spikes produced by the corresponding ganglion cell. Neither purely spatial correlations in the number of spikes, nor purely temporal correlations within the individual spikes trains, could by themselves account for the superior quality of the image reconstructions obtained here by fully exploiting both spatial and temporal correlations simultaneously. Spatiotemporal correlations mediated performance levels on an ON/OFF pixel discrimination task that, if instead mediated by an independent rate-code, would have required approximately four times as many spikes to achieve similar accuracy. By distributing local intensity information across an extended neighborhood of contiguously activated cells, the present findings indicate that rapid image reconstructions can be accomplished using far fewer impulses than would otherwise be required.
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