Ian C Bruce (2007)
Implementation issues in approximate methods for stochastic Hodgkin-Huxley models
Annals of Biomedical Engineering, 35(2):315-318.
The article by Mino et al.compares four different algorithms for implementing Hodgkin–Huxley models with stochastic sodium channels: Strassberg and DeFelice(1993), Rubinstein (1995), Chow & White (1996), and Fox (1997). The first three algorithms utilize exact methods for describing channel kinetics with finite-state Markov process models. In contrast, the algorithm of Fox uses stochastic differential equations (SDEs) to approximate the Markov process models. In addition to being simpler, the approximate method of Fox is around 7 times faster than the Chow & White algorithm, the fastest of the exact methods. However, for simulations of a patch of membrane with 1,000 sodium channels, Mino et al. reported that the approximate method of Fox produced quite different action potential (AP) statistics than the other methods. They consequently argued that, in spite of its computational advantage, the Fox algorithm may be too inaccurate in some circumstances to use reliably as an approximation to the exact methods. In repeating the simulations of Mino et al., I have found that some (but not all) of the inaccuracies that they reported were due to aspects of their implementation of the Fox algorithm, and that these inaccuracies become practically insignificant with an alternative implementation of the algorithm.