Steady-state voltages, ion fluxes, and volume regulation in syncytial tissues

Equations are developed that describe the steady-state relationships among ion fluxes, solute fluxes, water flow, voltage, concentration of solute, and hydrostatic pressure in a spherically symmetrical syncytial tissue. Each cell of the syncytium is assumed to have membrane channels for Na, K, and Cl, a membrane pump for Na/K, and some concentration of intracellular protein of net negative charge. However, the surface cells and inner cells of the tissue are assumed to have different distributions of membrane transport properties, hence there is a radial circulation of fluxes and a radial distribution of forces. Some reasonable approximations are made that allow analytic solutions of the nonlinear differential equations. These solutions are used to analyze data from the frog lens and are shown to account for the known steady-state properties of this tissue. Moreover, these solutions are used to make predictions on other steady-state properties, which have not been directly measured, and graphical results on the circulation of water, ions and solute through the frog lens are presented.