Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation

Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation

Year:    2021

Author:    Weizhang Huang, Weishi Liu, Yufei Yu

Communications in Computational Physics, Vol. 30 (2021), Iss. 2 : pp. 486–514

Abstract

Ionic flow carries electrical signals for cells to communicate with each other. The permanent charge of an ion channel is a crucial protein structure for flow properties while boundary conditions play a role of the driving force. Their effects on flow properties have been analyzed via a quasi-one-dimensional Poisson-Nernst-Planck model for small and relatively large permanent charges. The analytical studies have led to the introduction of flux ratios that reflect permanent charge effects and have a universal property. The studies also show that the flux ratios have different behaviors for small and large permanent charges. However, the existing analytical techniques can reveal neither behaviors of flux ratios nor transitions between small and large permanent charges. In this work we present a numerical investigation on flux ratios to bridge between small and large permanent charges. Numerical results verify the analytical predictions for the two extremal regions. More significantly, emergence of non-trivial behaviors is detected as the permanent charge varies from small to large. In particular, saddle-node bifurcations of flux ratios are revealed, showing rich phenomena of permanent charge effects by the power of combining analytical and numerical techniques. An adaptive moving mesh finite element method is used in the numerical studies.

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Journal Article Details

Publisher Name:    Global Science Press

Language:    English

DOI:    https://doi.org/10.4208/cicp.OA-2020-0057

Communications in Computational Physics, Vol. 30 (2021), Iss. 2 : pp. 486–514

Published online:    2021-01

AMS Subject Headings:    Global Science Press

Copyright:    COPYRIGHT: © Global Science Press

Pages:    29

Keywords:    Ion channel permanent charge flux ratio bifurcation finite element method.

Author Details

Weizhang Huang

Weishi Liu

Yufei Yu

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