Permanent Charge Effects on Ionic Flow: A Numerical Study of Flux Ratios and Their Bifurcation (Communications in Computational Physics, 2021)
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 flowproperties have been analyzed via a quasi-one-dimensional Poisson-Nernst-Planckmodel for small and relatively large permanent charges. The analytical studies haveled to the introduction of flux ratios that reflect permanent charge effects and have auniversal property. The studies also show that the flux ratios have different behaviorsfor small and large permanent charges. However, the existing analytical techniquescan 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 tobridge 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. Inparticular, saddle-node bifurcations of flux ratios are revealed, showing rich phenomena of permanent charge effects by the power of combining analytical and numericaltechniques. An adaptive moving mesh finite element method is used in the numericalstudies.