{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2025,12,18]],"date-time":"2025-12-18T14:27:43Z","timestamp":1766068063374,"version":"build-2065373602"},"reference-count":69,"publisher":"MDPI AG","issue":"11","license":[{"start":{"date-parts":[[2024,11,15]],"date-time":"2024-11-15T00:00:00Z","timestamp":1731628800000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"Simons Foundation USA","award":["628308","Z6124034"],"award-info":[{"award-number":["628308","Z6124034"]}]},{"name":"Linyi University","award":["628308","Z6124034"],"award-info":[{"award-number":["628308","Z6124034"]}]}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Axioms"],"abstract":"<jats:p>We focus on higher-order matched asymptotic expansions of a one-dimensional classical Poisson\u2013Nernst\u2013Planck system for ionic flow through membrane channels with two oppositely charged ion species under relaxed electroneutrality boundary conditions. Of particular interest are the current\u2013voltage (I\u2013V) relations, which are used to characterize the two most relevant biological properties of ion channels\u2014permeation and selectivity\u2014experimentally. Our result shows that, up to the second order in \u03b5=\u03bb\/r, where \u03bb is the Debye length and r is the characteristic radius of the channel, the cubic I\u2013V 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.<\/jats:p>","DOI":"10.3390\/axioms13110790","type":"journal-article","created":{"date-parts":[[2024,11,19]],"date-time":"2024-11-19T11:58:07Z","timestamp":1732017487000},"page":"790","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":5,"title":["Cubic-like Features of I\u2013V Relations via Classical Poisson\u2013Nernst\u2013Planck Systems Under Relaxed Electroneutrality Boundary Conditions"],"prefix":"10.3390","volume":"13","author":[{"given":"Hong","family":"Li","sequence":"first","affiliation":[{"name":"Department of Mathematics, Jiujiang University, Jiujiang 332005, China"}]},{"given":"Zhantao","family":"Li","sequence":"additional","affiliation":[{"name":"Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA"}]},{"ORCID":"https:\/\/orcid.org\/0000-0003-2964-7249","authenticated-orcid":false,"given":"Chaohong","family":"Pan","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Hunan First Normal University, Changsha 410205, China"}]},{"given":"Jie","family":"Song","sequence":"additional","affiliation":[{"name":"School of Mathematics and Statistics, Linyi University, Linyi 276000, China"}]},{"ORCID":"https:\/\/orcid.org\/0000-0002-8249-4758","authenticated-orcid":false,"given":"Mingji","family":"Zhang","sequence":"additional","affiliation":[{"name":"Department of Mathematics, New Mexico Institute of Mining and Technology, Socorro, NM 87801, USA"}]}],"member":"1968","published-online":{"date-parts":[[2024,11,15]]},"reference":[{"key":"ref_1","doi-asserted-by":"crossref","first-page":"1960","DOI":"10.1529\/biophysj.107.105478","article-title":"Steric selectivity in Na channels arising from protein polarization and mobile side chains","volume":"93","author":"Boda","year":"2007","journal-title":"Biophys. 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