Movileanu L, Flonta M L, Mihailescu D, Frangopol P T
Division of Cell Biology and Biophysics, University of Missouri-Kansas City, School of Biological Sciences 64110-2499, USA.
Biosystems. 1998 Feb;45(2):123-40. doi: 10.1016/s0303-2647(97)00071-3.
A general mathematical version of the cell model of a leaky epithelium for the NaCl absorption is presented, analysed and integrated numerically. The model consists in the adequate differential equations that describe the rate of change of the intracellular ion concentrations and are expressed in strict accordance with the law of mass conservation. The model includes many state variables representing ion concentrations, the cell volume, and membrane potentials. Ion movements are described by the Michaelis-Menten kinetics or by the constant field flux equation (Goldman-Hodgkin-Katz). In this paper, we model the intracellular ion concentrations, change in the cell volume, the transmembrane flux and membrane potentials of intestinal epithelium of both fresh water and sea water fish, and generate several simulations (in both the steady state and the transient state analysis) that appear to accord with prior experimental data in this area. For the ion movements of the sea water fish intestine, there were included a Na+/K+ pump, a K(+)-Cl- symport system, the K+ and Cl- channels in the basolateral membrane, whereas a Na(+)-K(+)-2Cl- cotransporter for NaCl absorption and K+ channels are located in the apical membrane. In the fresh water fish intestinal cells, the NaCl absorption is performed by two coupled antiporters Na+/H+ and Cl-/HCO3- presumably responsible for the intracellular pH regulation. In this type of cells, Na+ and K+ channels are located within the apical membrane, whereas Cl- channels are located within the basolateral membrane. The osmotically induced water transport across the apical and basolateral membranes has been taken into account as well. The simulations plot the steady state values for membrane potential difference, short-circuit current and intracellular ionic concentrations using the magnitude of the transmembrane flux through the Na+/K+ pump and Na(+)-K(+)-2Cl- cotransporter, or the basolateral Cl- permeability as dependent variables. The model behaves appropriately with regard to several experimental studies regarding the hyperpolarization (sea water fish intestine) and depolarization (fresh water fish intestine) of the apical membrane potential and inhibition of the short-circuit flux with reduced NaCl absorption. The model is also used to make several analytical predictions regarding the response of the membrane potential and ionic concentrations to variations in the basolateral Cl- flux. Furthermore, maintaining conservation of both mass and electroneutrality and taking into account the osmolar forces is an important advantage, because it allows a rigorous analysis of the relationship between membrane potential difference, volume and flux. The model can be used in the analysis and planning of the experiments and is capable of predicting the instantaneous values of ionic fluxes and intracellular concentrations and of cell volume.
本文提出了一种用于NaCl吸收的渗漏上皮细胞模型的通用数学版本,并进行了数值分析与整合。该模型由适当的微分方程组成,这些方程描述了细胞内离子浓度的变化率,并严格按照质量守恒定律来表示。该模型包含许多表示离子浓度、细胞体积和膜电位的状态变量。离子运动通过米氏动力学或恒定场通量方程(戈德曼-霍奇金- Katz方程)来描述。在本文中,我们对淡水鱼和海水鱼肠道上皮细胞的细胞内离子浓度、细胞体积变化、跨膜通量和膜电位进行了建模,并生成了几个模拟结果(包括稳态和瞬态分析),这些结果似乎与该领域先前的实验数据相符。对于海水鱼肠道的离子运动,模型中包括一个Na+/K+泵、一个K(+)-Cl-协同转运系统、基底外侧膜中的K+和Cl-通道,而用于NaCl吸收的Na(+)-K(+)-2Cl-协同转运体和K+通道位于顶端膜中。在淡水鱼肠道细胞中,NaCl的吸收由两个耦合的反向转运体Na+/H+和Cl-/HCO3-完成,它们可能负责细胞内pH的调节。在这类细胞中,Na+和K+通道位于顶端膜内,而Cl-通道位于基底外侧膜内。还考虑了渗透诱导的水通过顶端膜和基底外侧膜的运输。模拟使用通过Na+/K+泵和Na(+)-K(+)-2Cl-协同转运体的跨膜通量大小,或基底外侧Cl-通透性作为因变量,绘制了膜电位差、短路电流和细胞内离子浓度的稳态值。该模型在关于顶端膜电位超极化(海水鱼肠道)和去极化(淡水鱼肠道)以及NaCl吸收减少时短路通量抑制的几项实验研究中表现得当。该模型还用于对膜电位和离子浓度对基底外侧Cl-通量变化的响应进行一些分析预测。此外,保持质量和电中性守恒并考虑渗透压是一个重要优点,因为它允许对膜电位差、体积和通量之间的关系进行严格分析。该模型可用于实验的分析和规划,并且能够预测离子通量、细胞内浓度和细胞体积的瞬时值。