The analysis of stimulus/response patterns using information theoretic approaches requires the full probability distribution of stimuli and response. Recent progress in using information-based tools to understand circuit function has advanced understanding of neural coding at the single cell and population level. In advances over traditional reverse correlation approaches, the determination of receptive fields using information as a metric has allowed novel insights into stimulus representation and transformation. The application of maximum entropy methods to population codes has opened a rich exploration of the internal structure of these codes, revealing stimulus-driven functional connectivity. We speculate about the prospects and limitations of information as a general tool for dissecting neural circuits and relating their structure and function.

We examine the effect of the phase-resetting curve on the transfer of correlated input signals into correlated output spikes in a class of neural models receiving noisy superthreshold stimulation. We use linear-response theory to approximate the spike correlation coefficient in terms of moments of the associated exit time problem and contrast the results for type I vs type II models and across the different time scales over which spike correlations can be assessed. We find that, on long time scales, type I oscillators transfer correlations much more efficiently than type II oscillators. On short time scales this trend reverses, with the relative efficiency switching at a time scale that depends on the mean and standard deviation of input currents. This switch occurs over time scales that could be exploited by downstream circuits.

Describing the collective activity of neural populations is a daunting task. Recent empirical studies in retina, however, suggest a vast simplification in how multi-neuron spiking occurs: the activity patterns of retinal ganglion cell (RGC) populations under some conditions are nearly completely captured by pairwise interactions among neurons. In other circumstances, higher-order statistics are required and appear to be shaped by input statistics and intrinsic circuit mechanisms. Here, we study the emergence of higher-order interactions in a model of the RGC circuit in which correlations are generated by common input. We quantify the impact of higher-order interactions by comparing the responses of mechanistic circuit models vs. “null” descriptions in which all higher-than-pairwise correlations have been accounted for by lower order statistics; these are known as pairwise maximum entropy (PME) models. We find that over a broad range of stimuli, output spiking patterns are surprisingly well captured by the pairwise model. To understand this finding, we study an analytically tractable simplification of the RGC model. We find that in the simplified model, bimodal input signals produce larger deviations from pairwise predictions than unimodal inputs. The characteristic light filtering properties of the upstream RGC circuitry suppress bimodality in light stimuli, thus removing a powerful source of higher-order interactions. This provides a novel explanation for the surprising empirical success of pairwise models.

The mechanisms and impact of correlated, or synchronous, firing among pairs and groups of neurons are under intense investigation throughout the nervous system. A ubiquitous circuit feature that can give rise to such correlations consists of overlapping, or common, inputs to pairs and populations of cells, leading to common spike train responses. Here, we use computational tools to study how the transfer of common input currents into common spike outputs is modulated by the physiology of the recipient cells. We focus on a key conductance, g(A), for the A-type potassium current, which drives neurons between "type II" excitability (low g(A)), and "type I" excitability (high g(A)). Regardless of g(A), cells transform common input fluctuations into a tendency to spike nearly simultaneously. However, this process is more pronounced at low g(A) values. Thus, for a given level of common input, type II neurons produce spikes that are relatively more correlated over short time scales. Over long time scales, the trend reverses, with type II neurons producing relatively less correlated spike trains. This is because these cells' increased tendency for simultaneous spiking is balanced by an anticorrelation of spikes at larger time lags. These findings extend and interpret prior findings for phase oscillators to conductance-based neuron models that cover both oscillatory (superthreshold) and subthreshold firing regimes. We demonstrate a novel implication for neural signal processing: downstream cells with long time constants are selectively driven by type I cell populations upstream and those with short time constants by type II cell populations. Our results are established via high-throughput numerical simulations and explained via the cells' filtering properties and nonlinear dynamics.