Abstract

To study the effects of stochastic ion channel fluctuations on neural dynamics, several numerical implementation methods have been proposed. Gillespie's method for Markov Chains (MC) simulation is highly accurate, yet it becomes computationally intensive in the regime of a high number of channels. Many recent works aim to speed simulation time using the Langevin-based Diffusion Approximation (DA). Under this common theoretical approach, each implementation differs in how it handles various numerical difficulties such as bounding of state variables to [0,1]. Here we review and test a set of the most recently published DA implementations (Goldvvyn et al., 2011; Linaro et al., 2011; Dangerfield et al., 2012; Ode and Soudry, 2012; Schmandt and Galan, 2012; Guler, 2013; Huang et al., 2013a), comparing all of them in a set of numerical simulations that assess numerical accuracy and computational efficiency on three different models: (1) the original Hodgkin and Huxley model, (2) a model with faster sodium channels, and (3) a multi-compartmental model inspired in granular cells. We conclude that for a low number of channels (usually below 1000 per simulated compartment) one should use MC which is the fastest and most accurate method. For a high number of channels, we recommend using the method by Ono and Seudry (2012), possibly combined with the method by Schmandt and Galen (2012) for increased speed and slightly reduced accuracy. Consequently, MC modeling may be the best method for detailed multicompartment neuron models in which a model neuron with many thousands of channels is segmented into many compartments with a few hundred channels.