能斯特方程
物理
奇异摄动
泊松方程
离子
摄动(天文学)
稳态(化学)
分段
数学分析
经典力学
数学
量子力学
化学
电极
物理化学
作者
Amit Singer,Dirk Gillespie,John W. Norbury,Robert S. Eisenberg
出处
期刊:European Journal of Applied Mathematics
[Cambridge University Press]
日期:2008-10-01
卷期号:19 (5): 541-560
被引量:97
标识
DOI:10.1017/s0956792508007596
摘要
Ion channels are proteins with a narrow hole down their middle that control a wide range of biological function by controlling the flow of spherical ions from one macroscopic region to another. Ion channels do not change their conformation on the biological time scale once they are open, so they can be described by a combination of Poisson and drift-diffusion (Nernst-Planck) equations called PNP in biophysics. We use singular perturbation techniques to analyse the steady-state PNP system for a channel with a general geometry and a piecewise constant permanent charge profile. We construct an outer solution for the case of a constant permanent charge density in three dimensions that is also a valid solution of the one-dimensional system. The asymptotical current-voltage (I-V ) characteristic curve of the device (obtained by the singular perturbation analysis) is shown to be a very good approximation of the numerical I-V curve (obtained by solving the system numerically). The physical constraint of non-negative concentrations implies a unique solution, i.e., for each given applied potential there corresponds a unique electric current (relaxing this constraint yields non-physical multiple solutions for sufficiently large voltages).
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