Analytical and Numerical Studies of One-Dimensional Poisson-Nernst-Planck Models for Ion Channels
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Issue Date
2008-08-01Author
He, Feng
Publisher
University of Kansas
Format
52 pages
Type
Thesis
Degree Level
M.A.
Discipline
Mathematics
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This item is protected by copyright and unless otherwise specified the copyright of this thesis/dissertation is held by the author.
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Show full item recordAbstract
We study the event of ion flow through ion channel proteins modeled with a one-dimensional Poisson-Nernst-Planck system in presence of two or three types of ions with permanently charges located inside the channel. A singular parameter ε, related to the Debye length, is presented in the PNP system. In the case of two ions, the boundary conditions for the charged region can be specifically solved by solving a scaled algebraic equation. These conditions are then used to solve the PNP system numerically. Multiple solutions emerge from the computation and are probably indicative of more complex functions of ion channels. The system can be solved using numerical approaches and examples of these results are presented in this paper. The PNP system contains information of the current-voltage (I-V) relations of ion channels when reaching steady-state. Analysis of the I-V property is shown and some representative results discussed.
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