title: Accurate Langevin approaches to simulate Markovian channel dynamics.
abstract: The stochasticity of ion-channels dynamic is significant for physiological processes on neuronal cell membranes. Microscopic simulations of the ion-channel gating with Markov chains can be considered to be an accurate standard. However, such Markovian simulations are computationally demanding for membrane areas of physiologically relevant sizes, which makes the noise-approximating or Langevin equation methods advantageous in many cases. In this review, we discuss the Langevin-like approaches, including the channel-based and simplified subunit-based stochastic differential equations proposed by Fox and Lu, and the effective Langevin approaches in which colored noise is added to deterministic differential equations. In the framework of Fox and Lu's classical models, several variants of numerical algorithms, which have been recently developed to improve accuracy as well as efficiency, are also discussed. Through the comparison of different simulation algorithms of ion-channel noise with the standard Markovian simulation, we aim to reveal the extent to which the existing Langevin-like methods approximate results using Markovian methods. Open questions for future studies are also discussed.
authors.affiliation: Department of Physics, Xiamen University, Xiamen 361005, People's Republic of China.
authors.forename: Yandong
authors.initials: Y
authors.lastname: Huang
authors.forename: Sten
authors.initials: S
authors.lastname: Rüdiger
authors.forename: Jianwei
authors.initials: J
authors.lastname: Shuai
mesh_terms: D000465:Algorithms; D002462:Cell Membrane / Q000502:physiology; D003198:Computer Simulation; D015640:Ion Channel Gating; D008390:Markov Chains; D008564:Membrane Potentials / Q000502:physiology*; D008959:Models, Neurological; D015233:Models, Statistical; D009474:Neurons / Q000502:physiology*