Fraser James A, Huang Christopher L-H
Physiological Laboratory, Department of Physiology, Development and Neuroscience, University of Cambridge, Downing Street, Cambridge, UK.
Prog Biophys Mol Biol. 2007 Jul;94(3):336-72. doi: 10.1016/j.pbiomolbio.2006.10.001. Epub 2006 Nov 2.
The membrane potential (E(m)) is a fundamental cellular parameter that is primarily determined by the transmembrane permeabilities and concentration gradients of various ions. However, ion gradients are themselves profoundly influenced by E(m) due to its influence upon transmembrane ion fluxes and cell volume (V(c)). These interrelationships between E(m), V(c) and intracellular ion concentrations make computational modelling useful or necessary in order to guide experimentation and to achieve an integrated understanding of experimental data, particularly in complex, dynamic, multi-compartment systems such as skeletal and cardiac myocytes. A variety of quantitative techniques exist that may assist such understanding, from classical approaches such as the Goldman-Hodgkin-Katz equation and the Gibbs-Donnan equilibrium, to more recent "current-summing" models as exemplified by cardiac myocyte models including those of DiFrancesco & Noble, Luo & Rudy and Puglisi & Bers, or the "charge-difference" modelling technique of Fraser & Huang so far applied to skeletal muscle. In general, the classical approaches provide useful and important insights into the relationships between E(m), V(c) and intracellular ion concentrations at steady state, providing their core assumptions are fully understood, while the more recent techniques permit the modelling of changing values of E(m), V(c) and intracellular ion concentrations. The present work therefore reviews the various approaches that may be used to calculate E(m), V(c) and intracellular ion concentrations with the aim of establishing the requirements for an integrated model that can both simulate dynamic systems and recapitulate the key findings of classical techniques regarding the cellular steady state. At a time when the number of cellular models is increasing at an unprecedented rate, it is hoped that this article will provide a useful and critical analysis of the mathematical techniques fundamental to each of them.
膜电位（E(m)）是一个基本的细胞参数，主要由各种离子的跨膜通透性和浓度梯度决定。然而，由于E(m)对跨膜离子通量和细胞体积（V(c)）的影响，离子梯度本身也受到E(m)的深刻影响。E(m)、V(c)与细胞内离子浓度之间的这些相互关系使得计算建模对于指导实验以及实现对实验数据的综合理解变得有用或必要，特别是在诸如骨骼肌和心肌细胞等复杂、动态、多隔室系统中。存在多种定量技术可辅助这种理解，从经典方法如戈德曼 - 霍奇金 - 卡茨方程和吉布斯 - 唐南平衡，到最近的“电流求和”模型，如心肌细胞模型所示范的，包括迪弗朗西斯科和诺布尔、罗和鲁迪以及普格利西和贝斯的模型，或者弗雷泽和黄应用于骨骼肌的“电荷差”建模技术。一般来说，经典方法在稳态下为E(m)、V(c)与细胞内离子浓度之间的关系提供了有用且重要的见解，前提是其核心假设被充分理解，而最新技术允许对E(m)、V(c)和细胞内离子浓度的变化值进行建模。因此，本工作回顾了可用于计算E(m)、V(c)和细胞内离子浓度的各种方法，目的是确定一个既能模拟动态系统又能概括经典技术关于细胞稳态的关键发现的综合模型的要求。在细胞模型数量以前所未有的速度增加的时代，希望本文能对它们各自所基于的数学技术进行有用且批判性的分析。
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