title: Evaluation of stochastic differential equation approximation of ion channel gating models.
abstract: Fox and Lu derived an algorithm based on stochastic differential equations for approximating the kinetics of ion channel gating that is simpler and faster than "exact" algorithms for simulating Markov process models of channel gating. However, the approximation may not be sufficiently accurate to predict statistics of action potential generation in some cases. The objective of this study was to develop a framework for analyzing the 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 & Lu. The Fox & Lu algorithm assumes that channel gating particle dynamics have a stochastic term that is uncorrelated, zero-mean Gaussian noise, whereas the results of this study demonstrate that in many cases the stochastic term in the Fox & Lu algorithm should be correlated and non-Gaussian noise with a non-zero mean. The results indicate that: (i) the source of the inaccuracy is that the Fox & Lu algorithm does not adequately describe the combined behavior of the multiple activation particles in each sodium and potassium channel, and (ii) the accuracy does not improve with increasing numbers of channels.
authors.affiliation: Department of Electrical and Computer Engineering, Room ITB-A213, McMaster University, 1280 Main Street West, Hamilton, ON L8S 4K1, Canada. ibruce@ieee.org
authors.forename: Ian C
authors.initials: IC
authors.lastname: Bruce
mesh_terms: D000200:Action Potentials / Q000502:physiology; D000465:Algorithms; D003198:Computer Simulation; D015640:Ion Channel Gating / Q000502:physiology*; D007473:Ion Channels / Q000502:physiology*; D007700:Kinetics; D008390:Markov Chains; D008564:Membrane Potentials / Q000502:physiology; D008954:Models, Biological; D015221:Potassium Channels / Q000502:physiology; D015222:Sodium Channels / Q000502:physiology; D013269:Stochastic Processes
chemical_list: D007473:Ion Channels; D015221:Potassium Channels; D015222:Sodium Channels