A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials.
A multiscale approach to modelling electrochemical processes occurring across the cell membrane with application to transmission of action potentials.
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一种多尺度方法，用于模拟跨细胞膜发生的电化学过程，并应用于动作电位的传输。
DOI：
10.1093/imammb/dqn027
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发表时间：
2009
期刊：
影响因子：
--
通讯作者：
Giles Richardson
中科院分区：
文献类型：
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作者：
Giles Richardson
通过应用匹配渐近展开式，从泊松-能-普朗克电化学方程正式导出了离子选择性渗透膜附近动态电化学过程的简化偏微分方程（PDE）模型。结果表明，在细长轴突的限制下，该简化模型将自身简化为霍奇金和赫胥黎用来描述无髓鞘鱿鱼巨轴突中动作电位传播的电缆方程。从简化的PDE模型到电缆方程的渐近化简导致了其他不明显的见解；其中包括对乌贼巨大轴突直径达到1毫米的原因的解释。简化后的PDE模型比霍奇金-赫胥黎缆索方程具有更广泛的应用，例如可以用来描述动作电位在有髓鞘轴突和神经元细胞体中的传播。
By application of matched asymptotic expansions, a simplified partial differential equation (PDE) model for the dynamic electrochemical processes occurring in the vicinity of a membrane, as ions selectively permeate across it, is formally derived from the Poisson-Nernst-Planck equations of electrochemistry. It is demonstrated that this simplified model reduces itself, in the limit of a long thin axon, to the cable equation used by Hodgkin and Huxley to describe the propagation of action potentials in the unmyelinated squid giant axon. The asymptotic reduction from the simplified PDE model to the cable equation leads to insights that are not otherwise apparent; these include an explanation of why the squid giant axon attains a diameter in the region of 1 mm. The simplified PDE model has more general application than the Hodgkin-Huxley cable equation and can, e.g. be used to describe action potential propagation in myelinated axons and neuronal cell bodies.