Weinstein A M, Stephenson J L
Biophys J. 1979 Aug;27(2):165-86. doi: 10.1016/S0006-3495(79)85209-1.
A simple transporting epithelium is represented as a cellular compartment, compliant in all dimensions, and a paracellular channel, of arbitrary shape, between well-stirred mucosal ans serosal baths. The equations for mass balance, Poiseuille flow, and the Nernst-Planck equation are used to describe the continuous behavior of the system along cell and channel, whereas passive transport across membranes is given by the relations of Kedem and Katchalsky. Time-dependent terms are retained to permit study of transient phenomena. Boundary conditions at the baths demand only mass conservation and specify no a priori estimates of the system variables. A numerical model containing Na+,K+,Cl-, and impermeant cellular anions is formulated with membrane parameters taken from the literature on Necturus gallbladder. The differential equations are represented as a finite difference scheme and solved using Newton's method. It appears that apical cellular NaCl cotransport is necessary to obtain a reasonable cell chloride concentration. Investigation of the osmolality of the transepithelial flow shows that at steady state a leaky epithelium cannot separate baths of substantially different tonicity, although this does not guarantee isotonic transport between equiosmolar media. Changes in bath pressure, application of transepithelial electrical potential, and simulation of ion-substitution experiments are performed to understand the role of membrane permeabilities in determining the dynamic behavior of the epithelium.
一个简单的转运上皮被表示为一个在所有维度上都具有顺应性的细胞隔室，以及一个形状任意的细胞旁通道，该通道位于充分搅拌的黏膜浴和浆膜浴之间。质量平衡方程、泊肃叶流方程和能斯特 - 普朗克方程用于描述系统沿细胞和通道的连续行为，而跨膜的被动转运则由凯德姆和卡察尔斯基的关系式给出。保留与时间相关的项以允许研究瞬态现象。浴槽处的边界条件仅要求质量守恒，并且未指定系统变量的先验估计值。构建了一个包含Na⁺、K⁺、Cl⁻和非渗透性细胞阴离子的数值模型，其膜参数取自关于美洲蟾螈胆囊的文献。微分方程被表示为有限差分格式，并使用牛顿法求解。结果表明，顶端细胞NaCl共转运对于获得合理的细胞氯化物浓度是必要的。对跨上皮流渗透压的研究表明，在稳态下，一个渗漏的上皮不能分隔张力显著不同的浴槽，尽管这并不能保证等渗介质之间的等渗转运。进行浴槽压力变化、施加跨上皮电势以及模拟离子替代实验，以了解膜通透性在确定上皮动态行为中的作用。
