Evaluation of Approximate Stochastic Hodgkin-Huxley Models

Fox and colleagues [1], [2] derived an algorithm based on stochastic differential equations for approximating the kinetics of ion channel gating that is substantially simpler and faster than “exact” algorithms for simulating Markov process models of channel gating. However, Mino and colleagues [3] argued that the approximation may not be sufficiently accurate in describing the statistics of action potential generation. Bruce [4] subsequently showed that some of the inaccuracies described in [3] were due to implementation choices, but several important inaccuracies remained. The objective of this study was to develop a framework for analyzing the remaining inaccuracies and determining their origin. Simulations of a patch of membrane with voltage-gated sodium and potassium channels were performed using an exact algorithm for the kinetics of channel gating and the approximate algorithm of Fox. The Fox algorithm assumes that channel gating particle dynamics have a stochastic term that is uncorrelated, zero-mean Gaussian noise, whereas the simulation results of this study demonstrate that in many cases the stochastic term in the Fox algorithm should be correlated and non-Gaussian noise with a non-zero mean. The results indicate that the source of these differences in noise statistics is that the Fox algorithm does not adequately describe the combined behavior of the multiple activation particles in each sodium and potassium channel (three and four, respectively).