{"paper":{"title":"Computational Study on Hysteresis of Ion Channels: Multiple Solutions to Steady-State Poisson--Nernst--Planck Equations","license":"http://arxiv.org/licenses/nonexclusive-distrib/1.0/","headline":"","cross_cats":[],"primary_cat":"math.NA","authors_text":"Hui Sun, Jie Ding, Shenggao Zhou, Zhongming Wang","submitted_at":"2017-11-16T11:35:56Z","abstract_excerpt":"The steady-state Poisson-Nernst-Planck (ssPNP) equations are an effective model for the description of ionic transport in ion channels. It is observed that an ion channel exhibits voltage-dependent switching between open and closed states. Different conductance states of a channel imply that the ssPNP equations probably have multiple solutions with different level of currents. We propose numerical approaches to study multiple solutions to the ssPNP equations with multiple ionic species. To find complete current-voltage (I-V ) and current-concentration (I-C) curves, we reformulate the ssPNP equ"},"claims":{"count":0,"items":[],"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"source":{"id":"1711.06038","kind":"arxiv","version":1},"verdict":{"id":null,"model_set":{},"created_at":null,"strongest_claim":"","one_line_summary":"","pipeline_version":null,"weakest_assumption":"","pith_extraction_headline":""},"references":{"count":0,"sample":[],"resolved_work":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57","internal_anchors":0},"formal_canon":{"evidence_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"author_claims":{"count":0,"strong_count":0,"snapshot_sha256":"258153158e38e3291e3d48162225fcdb2d5a3ed65a07baac614ab91432fd4f57"},"builder_version":"pith-number-builder-2026-05-17-v1"}