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.

Multineuron firing patterns are often observed, yet are predicted to be rare by models that assume independent firing. To explain these correlated network states, two groups recently applied a second-order maximum entropy model that used only observed firing rates and pairwise interactions as parameters (Schneidman et al., 2006; Shlens et al., 2006). Interestingly, with these minimal assumptions they predicted 90 -99% of network correlations. If generally applicable, this approach could vastly simplify analyses of complex networks. However, this initial work was done largely on retinal tissue, and its applicability to cortical circuits is mostly unknown. This work also did not address the temporal evolution of correlated states. To investigate these issues, we applied the model to multielectrode data containing spontaneous spikes or local field potentials from cortical slices and cultures. The model worked slightly less well in cortex than in retina, accounting for 88 Ϯ 7% (mean Ϯ SD) of network correlations. In addition, in 8 of 13 preparations, the observed sequences of correlated states were significantly longer than predicted by concatenating states from the model. This suggested that temporal dependencies are a common feature of cortical network activity, and should be considered in future models. We found a significant relationship between strong pairwise temporal correlations and observed sequence length, suggesting that pairwise temporal correlations may allow the model to be extended into the temporal domain. We conclude that although a second-order maximum entropy model successfully predicts correlated states in cortical networks, it should be extended to account for temporal correlations observed between states.

The primate retina communicates visual information to the brain via a set of parallel pathways that originate from at least 22 anatomically distinct types of retinal ganglion cells. Knowledge of the physiological properties of these ganglion cell types is of critical importance for understanding the functioning of the primate visual system. Nonetheless, the physiological properties of only a handful of retinal ganglion cell types have been studied in detail. Here we show, using a newly developed multielectrode array system for the large-scale recording of neural activity, the existence of a physiologically distinct population of ganglion cells in the primate retina with distinctive visual response properties. These cells, which we will refer to as upsilon cells, are characterized by large receptive fields, rapid and transient responses to light, and significant nonlinearities in their spatial summation. Based on the measured properties of these cells, we speculate that they correspond to the smooth/large radiate cells recently identified morphologically in the primate retina and may therefore provide visual input to both the lateral geniculate nucleus and the superior colliculus. We further speculate that the upsilon cells may be the primate retina's counterparts of the Y-cells observed in the cat and other mammalian species.

Sensory experience typically depends on the ensemble activity of hundreds or thousands of neurons, but little is known about how populations of neurons faithfully encode behaviorally important sensory information. We examined how precisely speed of movement is encoded in the population activity of magnocellular-projecting parasol retinal ganglion cells (RGCs) in macaque monkey retina. Multi-electrode recordings were used to measure the activity of approximately 100 parasol RGCs simultaneously in isolated retinas stimulated with moving bars. To examine how faithfully the retina signals motion, stimulus speed was estimated directly from recorded RGC responses using an optimized algorithm that resembles models of motion sensing in the brain. RGC population activity encoded speed with a precision of approximately 1%. The elementary motion signal was conveyed in approximately 10 ms, comparable to the interspike interval. Temporal structure in spike trains provided more precise speed estimates than time-varying firing rates. Correlated activity between RGCs had little effect on speed estimates. The spatial dispersion of RGC receptive fields along the axis of motion influenced speed estimates more strongly than along the orthogonal direction, as predicted by a simple model based on RGC response time variability and optimal pooling. on and off cells encoded speed with similar and statistically independent variability. Simulation of downstream speed estimation using populations of speed-tuned units showed that peak (winner take all) readout provided more precise speed estimates than centroid (vector average) readout. These findings reveal how faithfully the retinal population code conveys information about stimulus speed and the consequences for motion sensing in the brain.

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