Effects on zero current ionic flow and reversal potential from two piecewise permanent charges in opposite signs

Jianing Chen; Yao Qi; Jianing Chen; Yao Qi

doi:10.3934/math.2026734

AIMS Mathematics

2026, Volume 11, Issue 6: 18026-18056. doi: 10.3934/math.2026734

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Research article

Effects on zero current ionic flow and reversal potential from two piecewise permanent charges in opposite signs

Jianing Chen ^{1
,},
Yao Qi ^{2
,
,}

1.
School of Mathematical Sciences, Zhejiang Normal University, Jinhua 321004, China; jianingchen@zjnu.edu.cn
2.
School of Mathematical Sciences, Beijing University of Posts and Telecommunications, Beijing 100876, China

Received: 22 April 2026 Revised: 01 June 2026 Accepted: 12 June 2026 Published: 18 June 2026
MSC : 34A26, 34B16, 34D15, 37D10, 92C35

Through this work, we investigated a quasi-one-dimensional Poisson-Nernst-Planck (PNP) system containing two segments of permanent charges with opposite signs. Under a zero current condition, the internal dynamics of ionic flows inside of an open ion channel including two types of ion species, one cation and one anion, were the main focus of this work. The existence and local uniqueness solution was proved along the framework of geometric singular perturbation theory, combining with the concrete structure of this model. Furthermore, we obtained three governing equations during the construction of a connecting orbit, which played a fundamental role in subsequent investigations for the impact of permanent charges on zero current ionic flow and reversal potential. In particular, richer dynamical behaviors were demonstrated under the set-up of a multiple nonzero permanent charge distribution, which is also more realistic to the practical problem.
- PNP,
- ion channel,
- permanent charges,
- zero current ionic flow,
- reversal potential
Citation: Jianing Chen, Yao Qi. Effects on zero current ionic flow and reversal potential from two piecewise permanent charges in opposite signs[J]. AIMS Mathematics, 2026, 11(6): 18026-18056. doi: 10.3934/math.2026734

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Abstract

Through this work, we investigated a quasi-one-dimensional Poisson-Nernst-Planck (PNP) system containing two segments of permanent charges with opposite signs. Under a zero current condition, the internal dynamics of ionic flows inside of an open ion channel including two types of ion species, one cation and one anion, were the main focus of this work. The existence and local uniqueness solution was proved along the framework of geometric singular perturbation theory, combining with the concrete structure of this model. Furthermore, we obtained three governing equations during the construction of a connecting orbit, which played a fundamental role in subsequent investigations for the impact of permanent charges on zero current ionic flow and reversal potential. In particular, richer dynamical behaviors were demonstrated under the set-up of a multiple nonzero permanent charge distribution, which is also more realistic to the practical problem.

References

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