Abstract
The simulation of ion-channel noise has an important role in computational neuroscience. In recent years several approximate methods of carrying out this simulation have been published, based on stochastic differential equations, and all giving slightly different results. The obvious, and essential, question is: which method is the most accurate and which is most computationally efficient? Here we make a contribution to the answer. We compare interspike interval histograms from simulated data using four different approximate stochastic differential equation (SDE) models of the stochastic Hodgkin-Huxley neuron, as well as the exact Markov chain model simulated by the Gillespie algorithm. One of the recent SDE models is the same as the Kurtz approximation first published in 1978. All the models considered give similar ISI histograms over a wide range of deterministic and stochastic input. Three features of these histograms are an initial peak, followed by one or more bumps, and then an exponential tail. We explore how these features depend on deterministic input and on level of channel noise, and explain the results using the stochastic dynamics of the model. We conclude with a rough ranking of the four SDE models with respect to the similarity of their ISI histograms to the histogram of the exact Markov chain model.
Highlights
Channel noise is important because it contributes to spike-time variability (Sigworth, 1980; White et al, 2000) and has been shown to be essential for subthreshold oscillations in stellate cells (White et al, 1998; Dorval and White, 2005), and for response variability in sensory cells (Fisch et al, 2012)
The inter-spike intervals (ISIs) distribution is quite similar for all these models over a large range of deterministic inputs, I, and over a large range of channel numbers, which are proportional to A, the membrane area used
In addition we explore how each of the features of the ISI distribution depends on I, the input to the model neuron, and on the number of channels in play, which is functionally related to the standard deviation of the noise in the system
Summary
Channel noise is important because it contributes to spike-time variability (Sigworth, 1980; White et al, 2000) and has been shown to be essential for subthreshold oscillations in stellate cells (White et al, 1998; Dorval and White, 2005), and for response variability in sensory cells (Fisch et al, 2012). In addition it contributes importantly to intrinsic irregular firing in cortical interneurons (Englitz et al, 2008; Stiefel et al, 2013), while in certain small neurons a single channel opening can initiate a spike (Lynch and Barry, 1989). In this paper we compare published SDE approximation methods that simulate the stochastic Hodgkin-Huxley (HH) neuron model, by comparing the inter-spike-interval (ISI) distributions produced when driven by a constant DC current I. In all cases the deterministic model used as a basis for the various stochastic schemes is the classical model of Hodgkin and Huxley (1952). This model was introduced to describe action potentials in the squid giant axon, and remains a foundation of modern neuroscience.
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