Simulation of noise in neurons and neuronal circuits

Stochastic behavior of ion channels, neurotransmitter release mechanisms and synaptic connections in neurons emerge as a source of variability and noise in neuronal circuits, causing uncertainty in the computations performed by the brain. One can gain insight into this important aspect of brain mechanism via computational modeling. Stochastic behavior in neurons is usually modeled with fine-grained, discrete-state, continuous-time Markov Chains (MCs). Although these models are considered as the golden standard, they become computationally prohibitive in analyzing multi-neuron circuits. Thus, several approximate models, where the random behavior is captured by coarse-grained, continuous-state, continuous-time Stochastic Differential Equations (SDEs), were proposed. In this paper, we first present a general, fine-grained modeling framework based on MC models of ion channels and synaptic processes. We then develop a formalism for automatically generating the corresponding SDE models, based on representing generic/abstract MCs as a set of chemical reactions and by utilizing techniques from stochastic chemical kinetics. With this formalism, we can exploit the sparsity and special structure in the MC models and arrive at compact SDE models. We present results obtained by our neuronal circuit simulator based on the proposed methodology in analyzing stochasticity in neurons and neuronal circuits. We employ numerical simulation techniques that were previously developed for noise in electronic circuits. We point to the use of non Monte Carlo noise analysis techniques for large-scale analysis of noise in the nervous system.