Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson-Nernst-Planck Equations
Year: 2018
Communications in Computational Physics, Vol. 23 (2018), Iss. 5 : pp. 1549–1572
Abstract
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.
You do not have full access to this article.
Already a Subscriber? Sign in as an individual or via your institution
Journal Article Details
Publisher Name: Global Science Press
Language: English
DOI: https://doi.org/10.4208/cicp.OA-2017-0134
Communications in Computational Physics, Vol. 23 (2018), Iss. 5 : pp. 1549–1572
Published online: 2018-01
AMS Subject Headings: Global Science Press
Copyright: COPYRIGHT: © Global Science Press
Pages: 24
Keywords: Poisson-Nernst-Planck equations multiple solutions I-V curve turning point continuation hysteresis memory effect.
-
Hysteresis and linear stability analysis on multiple steady-state solutions to the Poisson-Nernst-Planck equations with steric interactions
Ding, Jie | Sun, Hui | Zhou, ShenggaoPhysical Review E, Vol. 102 (2020), Iss. 5
https://doi.org/10.1103/PhysRevE.102.053301 [Citations: 1] -
A positive and energy stable numerical scheme for the Poisson–Nernst–Planck–Cahn–Hilliard equations with steric interactions
Qian, Yiran | Wang, Cheng | Zhou, ShenggaoJournal of Computational Physics, Vol. 426 (2021), Iss. P.109908
https://doi.org/10.1016/j.jcp.2020.109908 [Citations: 25] -
Do Bistable Steric Poisson–Nernst–Planck Models Describe Single-Channel Gating?
Gavish, Nir | Liu, Chun | Eisenberg, BobThe Journal of Physical Chemistry B, Vol. 122 (2018), Iss. 20 P.5183
https://doi.org/10.1021/acs.jpcb.8b00854 [Citations: 8] -
Positivity preserving finite difference methods for Poisson–Nernst–Planck equations with steric interactions: Application to slit-shaped nanopore conductance
Ding, Jie | Wang, Zhongming | Zhou, ShenggaoJournal of Computational Physics, Vol. 397 (2019), Iss. P.108864
https://doi.org/10.1016/j.jcp.2019.108864 [Citations: 24] -
Structure-preserving and efficient numerical methods for ion transport
Ding, Jie | Wang, Zhongming | Zhou, ShenggaoJournal of Computational Physics, Vol. 418 (2020), Iss. P.109597
https://doi.org/10.1016/j.jcp.2020.109597 [Citations: 16]