@Article{CiCP-23-1549,
author = {Jie Ding, Hui Sun, Zhongming Wang and Shenggao Zhou},
title = {Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations},
journal = {Communications in Computational Physics},
year = {2018},
volume = {23},
number = {5},
pages = {1549--1572},
abstract = {<p style="text-align: justify;">The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective
model for the description of ionic transport in ion channels. It is observed that an ion
channel exhibits voltage-dependent switching between open and closed states. Different
conductance states of a channel imply that the ssPNP equations probably have
multiple solutions with different level of currents. We propose numerical approaches
to study multiple solutions to the ssPNP equations with multiple ionic species. To find
complete current-voltage (I-V) and current-concentration (I-C) curves, we reformulate
the ssPNP equations into four different boundary value problems (BVPs). Numerical
continuation approaches are developed to provide good initial guesses for iteratively
solving algebraic equations resulting from discretization. Numerical continuations on
V, I, and boundary concentrations result in S-shaped and double S-shaped (I-V and
I-C) curves for the ssPNP equations with multiple species of ions. There are five solutions
to the ssPNP equations with five ionic species, when an applied voltage is given
in certain intervals. Remarkably, the current through ion channels responds hysteretically
to varying applied voltages and boundary concentrations, showing a memory effect.
In addition, we propose a useful computational approach to locate turning points
of an I-V curve. With obtained locations, we are able to determine critical threshold
values for hysteresis to occur and the interval for V in which the ssPNP equations have
multiple solutions. Our numerical results indicate that the developed numerical approaches
have a promising potential in studying hysteretic conductance states of ion
channels.</p>},
issn = {1991-7120},
doi = {https://doi.org/10.4208/cicp.OA-2017-0134},
url = {http://global-sci.org/intro/article_detail/cicp/11226.html}
}