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Journal article
Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics
Neural computation, Vol.32(10), pp.1775-1835
10/01/2020
PMID: 32795235
Web of Science ID: WOS:000565731400001
Abstract
Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the HodgkinHuxley (HH) system. They derived a Fokker-Planck equation with state-dependent diffusion tensor D and suggested a Langevin formulation with noise coefficient matrix S such that SS inverted perpendicular = D. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this article, we present a natural 14-dimensional dynamics for the HH system in which each directed edge in the ion channel state transition graph acts as an independent noise source, leading to a 14 x 28 noise coefficient matrix S. We show that (1) the corresponding 14D system of ordinary differential equations is consistent with the classical 4D representation of the HH system; (2) the 14D representation leads to a noise coefficient matrix S that can be obtained cheaply on each time step, without requiring a matrix decomposition; (3) sample trajectories of the 14D representation are pathwise equivalent to trajectories of Fox and Lu's system, aswell as trajectories of several existing Langevin models; (4) our 14D representation (and those equivalent to it) gives the most accurate interspike interval distribution, not only with respect to moments but under both the L-1 and L-infinity metric-space norms; and (5) the 14D representation gives an approximation to exactMarkov chain simulations that are as fast and as efficient as all equivalent models. Our approach goes beyond existing models, in that it supports a stochastic shielding decomposition that dramatically simplifies S with minimal loss of accuracy under both voltage- and current-clamp conditions.
Details
- Title
- Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics
- Publication Details
- Neural computation, Vol.32(10), pp.1775-1835
- Resource Type
- Journal article
- Publisher
- MIT Press
- Format
- link
- Grant note
- Simons Foundation Oberlin College Department of Mathematics Mathematical Biosciences Institute DMS-1440386; DMS-1413770; DEB-1654989 / National Science Foundation; National Science Foundation (NSF)
- Identifiers
- WOS:000565731400001; 99380498997106600
- Academic Unit
- Hal Marcus College of Science and Engineering ; Mathematics and Statistics
- Language
- English