Stochastic Neural Oscillators

We seek to understand collective neural phenomena such as synchronization, correlation transfer and information propagation in the presence of additive broadband noise. Our findings contribute to a growing scientific literature that has shown that uncoupled type II neural oscillators synchronize more readily under the influence of noisy input currents than do type I oscillators. We use stochastic phase reduction and regular perturbations to show that the type II phase response curve (PRC) minimizes the Lyapunov exponent. We also derived expressions for the correlation between output spike trains using the steady state probability distribution of the phase difference between oscillators. Over short time scales we find that, for a given level of input correlation, spike trains from type II membranes show greater output correlation than from type I. However, we find the reverse is true for oscillators observed over long time scales, in agreement with recent results. Previous investigations of specific ion channels have generated insights into mechanisms by which neuromodulators can switch the bifurcation structure of an oscillator. In a similar vein, we undertake an exploratory and qualitative study of the influence of the A-type potassium current on spike train synchrony, correlation transfer and information content in a reduced 3-dimensional neuron model that exhibits both type I and type II oscillations, as well as a bifurcation to bursting dynamics. Using the local Lyapunov exponent in place of the PRC as a measure of sensitivity to perturbation, we find that the region of bursting dynamics shows prolonged elevated sensitivity during the inter-burst interval. In the oscillatory regime, a similar phenomenon occurs near the bifurcation to bursting, and we see that the magnitude of the PRC grows markedly as this border is approached. Furthermore, we find that the highly sensitive dynamics result in a combination of spike time reliability and increased ISI variability that produces greater mutual information between a spike train and a broadband input signal. These findings suggest that there may be an optimal balance of dynamical sensitivity and stability that maximizes the computationally relevant statistical dependence between input signals and output spike trains

The type II phase resetting curve is optimal for stochastic synchrony

The phase-resetting curve (PRC) describes the response of a neural oscillator to small perturbations in membrane potential. Its usefulness for predicting the dynamics of weakly coupled deterministic networks has been well characterized. However, the inputs to real neurons may often be more accurately described as barrages of synaptic noise. Effective connectivity between cells may thus arise in the form of correlations between the noisy input streams. We use constrained optimization and perturbation methods to prove that PRC shape determines susceptibility to synchrony among otherwise uncoupled noise-driven neural oscillators. PRCs can be placed into two general categories: Type I PRCs are non-negative while Type II PRCs have a large negative region. Here we show that oscillators with Type II PRCs receiving common noisy input sychronize more readily than those with Type I PRCs.Comment: 10 pages, 4 figures, submitted to Physical Review

Correlation transfer in stochastically driven oscillators over long and short time scales

In the absence of synaptic coupling, two or more neural oscillators may become synchronized by virtue of the statistical correlations in their noisy input streams. Recent work has shown that the degree of correlation transfer from input currents to output spikes depends not only on intrinsic oscillator dynamics, but also depends on the length of the observation window over which the correlation is calculated. In this paper we use stochastic phase reduction and regular perturbations to derive the correlation of the total phase elapsed over long time scales, a quantity which provides a convenient proxy for the spike count correlation. Over short time scales, we derive the spike count correlation directly using straightforward probabilistic reasoning applied to the density of the phase difference. Our approximations show that output correlation scales with the autocorrelation of the phase resetting curve over long time scales. We also find a concise expression for the influence of the shape of the phase resetting curve on the initial slope of the output correlation over short time scales. These analytic results together with numerical simulations provide new intuitions for the recent counterintuitive finding that type I oscillators transfer correlations more faithfully than do type II over long time scales, while the reverse holds true for the better understood case of short time scales.Comment: 9 pages, 7 figures, submitted to Physical Review