Existence of Approximate Solutions for Modified Poisson Nernst-Planck Describing Ion Flow in Cell Membranes

• 作者: Abidha Monica Gwecho Onyango Thomas Mboya Shu Wang
• 来源期刊: 美国计算数学期刊(英文)
• 学科: 数学
• 关键词: Lennard Jonnes Potential Finite Size Effects Ion Channel Modified PNP
• 年，卷（期）: 2020,（3）
• 页码范围: 473-484
• 页数: 12页
• 分类号: O17

摘要

Dynamics of ions in biological ion channels has been classically analyzed using several types of Poisson-Nernst Planck (PNP) equations. However, due to complex interaction between individual ions and ions with the channel walls, minimal incorporation of these interaction factors in the models to describe the flow phenomena accurately has been done. In this paper, we aim at formulating a modified PNP equation which constitutes finite size effects to capture ions interactions in the channel using Lennard Jonnes (LJ) potential theory. Particularly, the study examines existence and uniqueness of the approximate analytical solutions of the mPNP equations, First, by obtaining the priori energy estimate and providing solution bounds, and finally constructing the approximate solutions and establishing its convergence in a finite dimensional subspace in <em>L</em>², the approximate solution of the linearized mPNP equations was found to converge to the analytical solution, hence proof of existence.