槽容控制和电解质平衡的泵漏模型的数学性质
Mathematical Properties of Pump-Leak Models of Cell Volume Control and Electrolyte Balance
摘要：
细胞体积和细胞内电解质含量的稳态控制是生理学中的基本问题，并且是上皮系统功能的中心。这些生理过程使用泵泄漏模型来建模，泵泄漏模型是描述离子和水流过细胞膜的平衡的微分代数方程系统。尽管它们被广泛使用，但人们对其数学性质知之甚少。在这里，我们建立了分析结果的存在性和稳定性的一般类泵泄漏模型的稳定状态。我们治疗两个病例。当离子通道电流具有线性的电流-电压关系时，我们证明了至多存在一个稳态，并且该稳态是全局渐近稳定的。如果没有稳定状态，则单元体积随时间趋于无穷大。当最小的假设放在离子通道电流的属性，我们表明，有一个渐近稳定的稳态，只要泵电流不是太大。关键的分析工具是一个自由能关系满足一般类的泵泄漏模型，它可以被用来作为一个李雅普诺夫函数来研究稳定性。
英文摘要：
Homeostatic control of cell volume and intracellular electrolyte content is a fundamental problem in physiology and is central to the functioning of epithelial systems. These physiological processes are modeled using pump-leak models, a system of differential algebraic equations that describes the balance of ions and water flowing across the cell membrane. Despite their widespread use, very little is known about their mathematical properties. Here, we establish analytical results on the existence and stability of steady states for a general class of pump-leak models. We treat two cases. When the ion channel currents have a linear current-voltage relationship, we show that there is at most one steady state, and that the steady state is globally asymptotically stable. If there are no steady states, the cell volume tends to infinity with time. When minimal assumptions are placed on the properties of ion channel currents, we show that there is an asymptotically stable steady state so long as the pump current is not too large. The key analytical tool is a free energy relation satisfied by a general class of pump-leak models, which can be used as a Lyapunov function to study stability.
机构、总结、中文摘要均由AI分析而来，可能存在错误，请以论文正文为准。
