The neural code of the retina.

Finally, the analysis of retinal processing will benefit greatly from the fruitful application of information theory. It has long been recognized that the essential substance transmitted by neurons is not electric charge or neurochemicals, but information (MacKay and McCulloch 1952xThe limiting information capacity of a neuronal link. MacKay, D.M. and McCulloch, W.S. Bull. Math. Biophys. 1952; 14: 127–135Crossref | Scopus (162)See all ReferencesMacKay and McCulloch 1952). In analyzing a neural system, it is essential to measure and track the flow of this substance, just as in studies of the vascular system one might want to measure blood flow. Fortunately, there exists a well established formalism by which to measure information and analyze its processing (102xShannon, C.E. and Weaver, W. See all References, 87xRieke, F., Warland, D., de Ruyter van Steveninck, R.R., and Bialek, W. See all References). A recent study implemented a specific model of retinal coding to attempt a reconstruction of the visual stimulus directly from the spike trains of salamander ganglion cells (Warland et al. 1997xDecoding visual information from a population of retinal ganglion cells. Warland, D.K., Reinagel, P., and Meister, M. J. Neurophysiol. 1997; 78: 2336–2350PubMedSee all ReferencesWarland et al. 1997). A local group of four cells from different functional types was found to transmit information about the visual stimulus at approximately 8 bits/s. This can be interpreted as resolving 28 = 256 different visual features every second and, thus, provides at least one answer to the question posed at the outset of this review. It is also possible to measure the information content of spike trains in a model-independent fashion, which requires no knowledge or assumptions about the stimulus–response relationship (Strong et al. 1998xEntropy and information in neural spike trains. Strong, S.P., Koberle, R., de Ruyter van Steveninck, R.R., and Bialek, W. Phys. Rev. Lett. 1998; 80: 197–200CrossrefSee all ReferencesStrong et al. 1998). Remarkably, this latter method yields information rates about three times higher (M. J. B. and M. M., unpublished data), suggesting that the current model captures only about one third of what the ganglion cells really communicate. Such an objective measure is essential in assessing how close we come to understanding what the neural code is.Information theory also offers an understanding of why the neural code is the way it is. At a simple level, one may regard the retina as a device that attempts to compress the visual scenes provided by the natural world so they can be transmitted through a small number of fibers of limited dynamic range. To this end, it would be important to avoid redundancy, namely a situation where several optic nerve fibers are reliably communicating the same signal. Natural images contain a great deal of redundancy, for example, because nearby points of the same object tend to have the same intensity. It could be beneficial to process the image with a simple spatial filter before encoding it (12xSome informational aspects of visual perception. Attneave, F. Psychol. Rev. 1954; 61: 183–193Crossref | PubMed | Scopus (1255)See all References, 14xPossible principles underlying the transformation of sensory messages. Barlow, H.B. See all References). Given the actual image statistics of the natural world, one can formalize this problem and calculate the spatial filter that would optimally reduce the redundancy between different points in the image; by similar arguments, one can propose filters that reduce redundancy in the time domain and in the spectral domain. Remarkably, this optimal solution correctly predicts the dominant features of retinal ganglion cell receptive fields: lateral inhibition in space, band-pass filtering in time, and even the observed spectral sensitivity curves (110xPredictive coding (a fresh view of inhibition in the retina) . Srinivasan, M.V., Laughlin, S.B., and Dubs, A. Proc. R. Soc. Lond. B Biol. Sci. 1982; 216: 427–459Crossref | PubMedSee all References, 31xTrichromacy, opponent colours coding and optimum colour information transmission in the retina. Buchsbaum, G. and Gottschalk, A. Proc. R. Soc. Lond. B Biol. Sci. 1983; 220: 89–113Crossref | PubMedSee all References, 9xCould information theory provide an ecological theory of sensory processing?. Atick, J.J. Network. 1992; 3: 213–251Crossref | Scopus (360)See all References, 11xUnderstanding retinal color coding from first principles. Atick, J.J., Li, Z., and Redlich, A.N. Neural Comput. 1992; 4: 559–572CrossrefSee all References, 35xEfficient coding of natural scenes in the lateral geniculate nucleus (experimental test of a computational theory) . Dan, Y., Atick, J.J., and Reid, R.C. J. Neurosci. 1996; 16: 3351–3362PubMedSee all References). At low light levels, when visual processing is seriously affected by noise, a certain degree of redundancy is beneficial to safeguard reliable transmission. Again, one can compute how the optimal spatial filter should change depending on the signal-to-noise ratio, and the result predicts correctly the measured profiles of ganglion cell receptive fields at different light levels (10xWhat does the retina know about natural scenes?. Atick, J.J. and Redlich, A.N. Neural Comput. 1992; 4: 196–210CrossrefSee all References, 119xA theory of maximizing sensory information. van Hateren, J.H. Biol. Cybern. 1992; 68: 23–29Crossref | PubMed | Scopus (121)See all References). Given the simplicity of the assumptions, it is surprising how well this interpretation works. In fact, this is currently the only framework that predicts the functional properties of retinal ganglion cells from a simple underlying principle. It seems compelling to conclude that data compression is truly an important purpose of retinal circuitry and that evolution has adapted its strategies to the visual ensemble provided by the environment. One hopes that as we elaborate other aspects of retinal coding, they will find a similarly satisfying interpretation.*To whom correspondence should be addressed (e-mail: meister@biosun.harvard.edu).