论文标题
随机Hodgkin-Huxley动力学的快速准确的Langevin模拟
Fast and Accurate Langevin Simulations of Stochastic Hodgkin-Huxley Dynamics
论文作者
论文摘要
Fox和Lu引入了一个兰格文框架，用于随机门控离子通道的离散时间随机模型，例如Hodgkin-Huxley（HH）系统。他们得出了一个带有状态扩散张量$ d $的fokker-planck方程，并建议使用噪声系数矩阵$ s $ s $ s $ ss^\ intercal = d $。随后，几位作者为HH系统介绍了各种Langevin方程。在本文中，我们为HH系统提供了自然的14维动力学，其中每个\ emph {定向}边缘在离子通道状态过渡图中充当一个独立的噪声源，从而导致$ 14 \ times 28 $噪声系数矩阵$ s $ s $。我们表明（i）普通微分\ rev {equation}的相应14D系统与HH系统的经典4D表示一致； （ii）14D表示会导致噪声系数矩阵$ s $，在每个时间段上可以便宜地获得，而无需矩阵分解； （iii）14D表示的样品轨迹路径等效于Fox和Lu系统的轨迹，以及几种现有的Langevin模型的轨迹； （iv）我们的14D表示（以及相当于它的表示）给出了最准确的尖峰间隔分布，不仅在时刻方面，而且在$ l_1 $和$ l_ \ infty $ metric $ metric-space norms下都提供了； （v）14D表示与精确的Markov链模拟的近似值与所有等效模型一样快，有效。我们的方法超出了现有模型，因为它支持了随机屏蔽分解，该分解极大地简化了$ s $，在电压和电流钳条件下的准确性损失最小。
Fox and Lu introduced a Langevin framework for discrete-time stochastic models of randomly gated ion channels such as the Hodgkin-Huxley (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 $SS^\intercal=D$. Subsequently, several authors introduced a variety of Langevin equations for the HH system. In this paper, we present a natural 14-dimensional dynamics for the HH system in which each \emph{directed} edge in the ion channel state transition graph acts as an independent noise source, leading to a $14\times 28$ noise coefficient matrix $S$. We show that (i) the corresponding 14D system of ordinary differential \rev{equations} is consistent with the classical 4D representation of the HH system; (ii) the 14D representation leads to a noise coefficient matrix $S$ that can be obtained cheaply on each timestep, without requiring a matrix decomposition; (iii) sample trajectories of the 14D representation are pathwise equivalent to trajectories of Fox and Lu's system, as well as trajectories of several existing Langevin models; (iv) our 14D representation (and those equivalent to it) give the most accurate interspike-interval distribution, not only with respect to moments but under both the $L_1$ and $L_\infty$ metric-space norms; and (v) the 14D representation gives an approximation to exact Markov 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.
