A Study of Poisson-Nernst-Planck Equations for Ion Channels
Date Issued
2010
Date
2010
Author(s)
Chen, Jyun-Yang
Abstract
In this paper, we use the perturbation methods and numerical simulations to observe the behavior of the solution of Poisson-Nernst-Planck equations. First, we do the low-concentration limit case to derive the Goldman-Hodgkin-Katz formula which can be used to explain the occurrence of the nerve impulse. In addition, we obtain a sufficient condition such that current and voltage hold a linear relationship. And for the channel with different wall shapes, we find the numerical solutions. Furthermore, by the energetic variational approach, we derive the modifier Nernst-Planck equation corresponding different geometries of channel. By the modifier equation, we find an approximate solution when the wall shape function of ion channel is an exponential function.
Subjects
Poisson-Nernst-Planck equations
ion channe
perturbation method
numerical simulation
energetic variational approach
Type
thesis
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