Axioms, Vol. 13, Pages 790: Cubic-Like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions

Axioms, Vol. 13, Pages 790: Cubic-Like Features of I–V Relations via Classical Poisson–Nernst–Planck Systems Under Relaxed Electroneutrality Boundary Conditions

Axioms doi: 10.3390/axioms13110790

Authors: Hong Li Zhantao Li Chaohong Pan Jie Song Mingji Zhang

We focus on higher-order matched asymptotic expansions of a one-dimensional classical Poisson–Nernst–Planck system for ionic flow through membrane channels with two oppositely charged ion species under relaxed electroneutrality boundary conditions. Of particular interest are the current–voltage (I–V) relations, which are used to characterize the two most relevant biological properties of ion channels—permeation and selectivity—experimentally. Our result shows that, up to the second order in ε=λ/r, where λ is the Debye length and r is the characteristic radius of the channel, the cubic I–V relation has either three distinct real roots or a unique real root with a multiplicity of three, which sensitively depends on the boundary layers because of the relaxation of the electroneutrality boundary conditions. This indicates more rich dynamics of ionic flows under our more realistic setups and provides a better understanding of the mechanism of ionic flows through membrane channels.