In this paper, we study effects of permanent charges on ion flows through membrane channels via a quasi-one-dimensional classical Poisson-Nernst-Planck sys- tem. This system includes three ion species, two cations with different valences and one anion, and permanent charges with a simple structure, zeros at the two end re- gions and a constant over the middle region. For small permanent charges, our main goal is to analyze the effects of permanent charges on ionic flows, interacting with the boundary conditions and channel structure. Continuing from a previous work, we investigate the problem for a new case toward a more comprehensive understanding about effects of permanent charges on ionic fluxes.
Acknowledgements
The authors thank the reviewers for their comments and suggestions that improve the manuscript. Ning Sun was partially supported by the Joint Ph.D. Training Program sponsored by the China Scholarship Council, a Graduate Innovation Fund of Jilin University and National Natural Science Foundation of China (No. 12301220). Weishi Liu was partially supported by Simons Foundation Mathematics and Physical Sciences-Collaboration Grants for Mathematicians 581822.
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