Statistical dependencies in the responses of sensory neurons govern both the amount of stimulus information conveyed and the means by which downstream neurons can extract it. Although a variety of measurements indicate the existence of such dependencies 1-3 , their origin and importance for neural coding are poorly understood. Here we analyse the functional significance of correlated firing in a complete population of macaque parasol retinal ganglion cells using a model of multi-neuron spike responses 4,5 . The model, with parameters fit directly to physiological data, simultaneously captures both the stimulus dependence and detailed spatio-temporal correlations in population responses, and provides two insights into the structure of the neural code. First, neural encoding at the population level is less noisy than one would expect from the variability of individual neurons: spike times are more precise, and can be predicted more accurately when the spiking of neighbouring neurons is taken into account. Second, correlations provide additional sensory information: optimal, model-based decoding that exploits the response correlation structure extracts 20% more information about the visual scene than decoding under the assumption of independence, and preserves 40% more visual information than optimal linear decoding 6 . This model-based approach reveals the role of correlated activity in the retinal coding of visual stimuli, and provides a general framework for understanding the importance of correlated activity in populations of neurons.How does the spiking activity of a neural population represent the sensory environment? The answer depends critically on the structure of neuronal correlations, or the tendency of groups of neurons to fire temporally coordinated spike patterns. The statistics of such patterns have been studied in a variety of brain areas, and their significance in the processing and representation of sensory information has been debated extensively 2,3,7-13 .Author Information Reprints and permissions information is available at www.nature.com/reprints. Correspondence and requests for materials should be addressed to J.W.P. (E-mail: pillow@gatsby.ucl.ac.uk). Full Methods and any associated references are available in the online version of the paper at www.nature.com/nature.Supplementary Information is linked to the online version of the paper at www.nature.com/nature. Previous studies have examined visual coding by pairs of neurons 11 and the statistics of simultaneous firing patterns in larger neural populations 14,15 . However, no previous approach has addressed how correlated spiking activity in complete neural populations depends on the pattern of visual stimulation, or has answered the question of how such dependencies affect the encoding of visual stimuli. NIH Public AccessHere we introduce a model-based methodology for studying this problem. We describe the encoding of stimuli in the spike trains of a neural population with a generalized linear model (Fig. 1a), a generalization of th...

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Current understanding of many neural circuits is limited by our ability to explore the vast number of potential interactions between different cells. We present a new approach that dramatically reduces the complexity of this problem. Large-scale multi-electrode recordings were used to measure electrical activity in nearly complete, regularly spaced mosaics of several hundred ON and OFF parasol retinal ganglion cells in macaque monkey retina. Parasol cells exhibited substantial pairwise correlations, as has been observed in other species, indicating functional connectivity. However, pairwise measurements alone are insufficient to determine the prevalence of multi-neuron firing patterns, which would be predicted from widely diverging common inputs and have been hypothesized to convey distinct visual messages to the brain. The number of possible multi-neuron firing patterns is far too large to study exhaustively, but this problem may be circumvented if two simple rules of connectivity can be established: (1) multi-cell firing patterns arise from multiple pairwise interactions, and (2) interactions are limited to adjacent cells in the mosaic. Using maximum entropy methods from statistical mechanics, we show that pairwise and adjacent interactions accurately accounted for the structure and prevalence of multi-neuron firing patterns, explaining ϳ98% of the departures from statistical independence in parasol cells and ϳ99% of the departures that were reproducible in repeated measurements. This approach provides a way to define limits on the complexity of network interactions and thus may be relevant for probing the function of many neural circuits.

Functional asymmetries in the ON and OFF pathways of the primate visual system were examined using simultaneous multi-electrode recordings from dozens of retinal ganglion cells (RGCs) in vitro. Light responses of RGCs were characterized using white noise stimulation. Two distinct functional types of cells frequently encountered, one ON and one OFF, had non-opponent spectral sensitivity, relatively high response gain, transient light responses, and large receptive fields (RFs) that tiled the region of retina recorded, suggesting that they belonged to the same morphological cell class, most likely parasol. Three principal functional asymmetries were observed. (1) Receptive fields of ON cells were 20% larger in diameter than those of OFF cells, resulting in higher full-field sensitivity. (2) ON cells had faster response kinetics than OFF cells, with a 10-20% shorter time to peak, trough and zero crossing in the biphasic temporal impulse response. (3) ON cells had more nearly linear light responses and were capable of signaling decrements, whereas OFF cells had more strongly rectifying responses that provided little information about increments. These findings suggest specific mechanistic asymmetries in retinal ON and OFF circuits and differences in visual performance on the basis of the activity of ON and OFF parasol cells.

A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.

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Existing epiretinal implants for the blind are designed to electrically stimulate large groups of surviving retinal neurons using a small number of electrodes with diameters of several hundred micrometers. To increase the spatial resolution of artificial sight, electrodes much smaller than those currently in use are desirable. In this study, we stimulated and recorded ganglion cells in isolated pieces of rat, guinea pig, and monkey retina. We used microfabricated hexagonal arrays of 61 platinum disk electrodes with diameters between 6 and 25 microm, spaced 60 microm apart. Charge-balanced current pulses evoked one or two spikes at latencies as short as 0.2 ms, and typically only one or a few recorded ganglion cells were stimulated. Application of several synaptic blockers did not abolish the evoked responses, implying direct activation of ganglion cells. Threshold charge densities were typically <0.1 mC/cm2 for a pulse duration of 100 micros, corresponding to charge thresholds of <100 pC. Stimulation remained effective after several hours and at high frequencies. To show that closely spaced electrodes can elicit independent ganglion cell responses, we used the multielectrode array to stimulate several nearby ganglion cells simultaneously. From these data, we conclude that electrical stimulation of mammalian retina with small-diameter electrode arrays is achievable and can provide high temporal and spatial precision at low charge densities. We review previous epiretinal stimulation studies and discuss our results in the context of 32 other publications, comparing threshold parameters and safety limits.

A white noise technique is presented for estimating the response properties of spiking visual system neurons. The technique is simple, robust, efficient and well suited to simultaneous recordings from multiple neurons. It provides a complete and easily interpretable model of light responses even for neurons that display a common form of response nonlinearity that precludes classical linear systems analysis. A theoretical justification of the technique is presented that relies only on elementary linear algebra and statistics. Implementation is described with examples. The technique and the underlying model of neural responses are validated using recordings from retinal ganglion cells, and in principle are applicable to other neurons. Advantages and disadvantages of the technique relative to classical approaches are discussed.