arrow
Volume 30, Issue 2
Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation

Weizhang Huang, Weishi Liu & Yufei Yu

Commun. Comput. Phys., 30 (2021), pp. 486-514.

Published online: 2021-05

Export citation
  • 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.

  • AMS Subject Headings

65L10, 65L50, 92C35

  • Copyright

COPYRIGHT: © Global Science Press

  • Email address
  • BibTex
  • RIS
  • TXT
@Article{CiCP-30-486, author = {Huang , WeizhangLiu , Weishi and Yu , Yufei}, title = {Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation}, journal = {Communications in Computational Physics}, year = {2021}, volume = {30}, number = {2}, pages = {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.

}, issn = {1991-7120}, doi = {https://doi.org/10.4208/cicp.OA-2020-0057}, url = {http://global-sci.org/intro/article_detail/cicp/19122.html} }
TY - JOUR T1 - Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation AU - Huang , Weizhang AU - Liu , Weishi AU - Yu , Yufei JO - Communications in Computational Physics VL - 2 SP - 486 EP - 514 PY - 2021 DA - 2021/05 SN - 30 DO - http://doi.org/10.4208/cicp.OA-2020-0057 UR - https://global-sci.org/intro/article_detail/cicp/19122.html KW - Ion channel, permanent charge, flux ratio, bifurcation, finite element method. AB -

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.

Weizhang Huang, Weishi Liu & Yufei Yu. (2021). Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation. Communications in Computational Physics. 30 (2). 486-514. doi:10.4208/cicp.OA-2020-0057
Copy to clipboard
The citation has been copied to your clipboard