Analysis of a stochastic neuronal model with excitatory inputs and state-dependent effects (original) (raw)
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The European Physical Journal Special Topics, 2021
Neurons in the nervous system are submitted to distinct sources of noise, such as ionic-channel and synaptic noise, which introduces variability in their responses to repeated presentations of identical stimuli. This motivates the use of stochastic models to describe neuronal behavior. In this work, we characterize an intrinsically stochastic neuron model based on a voltage-dependent spike probability function. We determine the effect of the intrinsic noise in single neurons by measuring the spike time reliability and study the stochastic resonance phenomenon. The model was able to show increased reliability for non-zero intrinsic noise values, according to what is known from the literature, and the addition of intrinsic stochasticity in it enhanced the region in which stochastic-resonance is present. We proceeded to the study at the network level where we investigated the behavior of a random network composed of stochastic neurons. In this case, the addition of an extra dimension, represented by the intrinsic noise, revealed dynamic states of the system that could not be found otherwise. Finally, we propose a method to estimate the spike probability curve from in vitro electrophysiological data.
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We present for the rst time an analytical approach for determining the time of ring of multicomponent nonlinear stochastic neuronal models. We apply the theory of rst exit times for Markov processes to the Fitzhugh-Nagumo system with a constant mean gaussian white noise input, representing stochastic excitation and inhibition. Partial differential equations are obtained for the moments of the time to rst spike. The observation that the recovery variable barely changes in the prespike trajectory leads to an accurate one-dimensional approximation. For the moments of the time to reach threshold, this leads to ordinary differential equations that may be easily solved. Several analytical approaches are explored that involve perturbation expansions for large and small values of the noise parameter. For ranges of the parameters appropriate for these asymptotic methods, the perturbation solutions are used to establish the validity of the one-dimensional approximation for both small and large values of the noise parameter. Additional veri cation is obtained with the excellent agreement between the mean and variance of the ring time found by numerical solution of the differential equations for the one-dimensional approximation and those obtained by simulation of the solutions of the model stochastic differential equations. Such agreement extends to intermediate values of the noise parameter. For the mean time to threshold, we nd maxima at small noise values that constitute a form of stochastic resonance. We also investigate the dependence of the mean ring time on the initial values of the voltage and recovery variables when the input current has zero mean.