To understand the interspike interval (ISI) variability displayed by visual cortical neurons (Softky and Koch, 1993), it is critical to examine the dynamics of their neuronal integration as well as the variability in their synaptic input current. Most previous models have focused on the latter factor. We match a simple integrate-and-fire model to the experimentally measured integrative properties of cortical regular spiking cells (McCormick et al., 1985). After setting RC parameters, the post-spike voltage reset is set to match experimental measurements of neuronal gain (obtained from in vitro plots of firing frequency vs. injected current). Examination of the resulting model leads to an intuitive picture of neuronal integration that unifies the seemingly contradictory "1= p N " and "random walk" pictures that have previously been proposed. When ISI's are dominated by post-spike recovery, 1= p N arguments hold and spiking is regular; after the "memory" of the last spike becomes ne...

We propose a biophysical mechanism for the high interspike interval variability observed in cortical spike trains. The key lies in the nonlinear dynamics of cortical spike generation, which are consistent with type I membranes where saddle-node dynamics underlie excitability (Rinzel & Ermentrout, 1989). We present a canonical model for type I membranes, the θ-neuron. The θ-neuron is a phase model whose dynamics reflect salient features of type I membranes. This model generates spike trains with coefficient of variation (CV) above 0.6 when brought to firing by noisy inputs. This happens because the timing of spikes for a type I excitable cell is exquisitely sensitive to the amplitude of the suprathreshold stimulus pulses. A noisy input current, giving random amplitude “kicks” to the cell, evokes highly irregular firing across a wide range of firing rates; an intrinsically oscillating cell gives regular spike trains. We corroborate the results with simulations of the Morris-Lecar (M-L) neural model with random synaptic inputs: type I M-L yields high CVs. When this model is modified to have type II dynamics (periodicity arises via a Hopf bifurcation), however, it gives regular spike trains (CV below 0.3). Our results suggest that the high CV values such as those observed in cortical spike trains are an intrinsic characteristic of type I membranes driven to firing by “random” inputs. In contrast, neural oscillators or neurons exhibiting type II excitability should produce regular spike trains.

Neurons are sensitive to correlations among synaptic inputs. However, analytical models that explicitly include correlations are hard to solve analytically, so their influence on a neuron’s response has been difficult to ascertain. To gain some intuition on this problem, we studied the firing times of two simple integrate-and-fire model neurons driven by a correlated binary variable that represents the total input current. Analytic expressions were obtained for the average firing rate and coefficient of variation (a measure of spike-train variability) as functions of the mean, variance, and correlation time of the stochastic input. The results of computer simulations were in excellent agreement with these expressions. In these models, an increase in correlation time in general produces an increase in both the average firing rate and the variability of the output spike trains. However, the magnitude of the changes depends differentially on the relative values of the input mean and variance: the increase in firing rate is higher when the variance is large relative to the mean, whereas the increase in variability is higher when the variance is relatively small. In addition, the firing rate always tends to a finite limit value as the correlation time increases toward infinity, whereas the coefficient of variation typically diverges. These results suggest that temporal correlations may play a major role in determining the variability as well as the intensity of neuronal spike trains.

Neurons communicate with each other via sequences of action potentials. The purpose of this study is to approximate the interval between action potentials which is also called the First Passage Time (FPT), the first time the membrane voltage passes a threshold. The subthreshold depolarization of a neuron receiving a multitude of random synaptic inputs has often been modelled as the Ornstein–Uhlenbeck (OU) process. This model provides an analytically tractable formalism of neuronal membrane voltage mean and variance in terms of a neuron’s membrane time constant and the mean of input voltage. Some authors obtained an approximate mean and variance of the FPT for Stein’s model with a constant threshold for firing by using Stein’s method. They approximated the mean and variance of FPT by using the first term of the Taylor’s series expansion. We expect this procedure works for the OU process, a diffusion process. This study finds that Stein’s method works well for the OU process with the small Wiener process parameter. After adding a few other terms of the Taylor’s series, the parameter range in which

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