Mathematical modeling of membrane transporters and ion channels helps researchers obtain a thorough understanding of the complex regulation process between membrane transporters, estimate the changes and uncertainties of their mechanisms, and study how disorders in these procedures may cause disease. A unified mathematical framework that includes most available models for ion channels and transporters can help scientists choose the appropriate model more conveniently. In this regard, this work presents a comprehensive, up-to-date set of currently available mathematical equations for modeling ion channel and membrane transporter mechanisms. This paper aims to provide a mathematical framework for modeling molecule transport, such as nutrients, inorganic ions, drugs, and toxins, across the cell through membrane transporters and ion channels. Our purpose is to substantially save the time and resources needed to find the mathematical models available for different classes of membrane transporters and improve communication between scientists with different backgrounds interested in this field.

膜转运蛋白和离子通道的数学建模有助于研究人员全面了解膜转运蛋白之间复杂的调控过程，估计其机制的变化和不确定性，并研究这些过程中的障碍如何导致疾病。一个统一的数学框架，包括大多数可用的离子通道和转运模型，可以帮助科学家更方便地选择合适的模型。在这方面，这项工作提出了一套全面、最新的当前可用数学方程，用于模拟离子通道和膜转运机制。本文旨在提供一个数学框架，用于模拟通过膜转运蛋白和离子通道穿过细胞的分子转运，例如营养物质、无机离子、药物和毒素。