Steady states and the effects of ouabain in the Necturus gallbladder epithelium: a model analysis

A simple numerical model for the Necturus gallbladder epithelium is presented. K+, Na+ and Cl- cross the mucosal and serosal membranes as well as the junctions by means of electrodiffusion; furthermore the mucosal membrane contains a neutral entry mechanism for NaCl and the serosal membrane contains an active pump for K+ and Na+. The values which have been used for the model are taken from the literature. The model can only attain steady states if the resistance of the serosal membrane is lower than 1000 omega cm2. Values reported in the literature for the resistance of this membrane vary from about 3000 to about 100 omega cm2. We shall argue, however, that the higher estimates are in error because they are derived from a model of the tissue in which each membrane and the junction are modeled by a resistor; this procedure is invalid because the resistance of the lateral intercellular space relative to the resistance of the tight junctions is neglected and consequently the resistance of the serosal membrane is overestimated by a factor of about four. Apart from predicting a realistic steady state at normal external concentrations the model can predict quantitatively several experimental results obtained from the living epithelium. We have focused on the experiments which test the permeabilities of the serosal membrane and the properties of the pump: i) Replacement of serosal Cl- by an impermeant ion. ii) Replacement of serosal K+ by Na+. iii) Inhibiting the (Na+, K+)-pump. The best correspondence between model and experiments is obtained when the pump is assumed to be electrogenic (or rheogenic) with a ratio of coupling between Na+ and K+ of 3:2. In this case both model and direct experiments (also presented in this paper) show an initial abrupt depolarization of 6 to 7 mV. The model also shows that it cannot be concluded from i and ii that the Cl- permeability of the serosal membrane is low. The model explains, even with high passive Cl- permeabilities, why the intracellular Cl- concentration is relatively unaffected by paracellular currents, a fact which in other epithelia has been taken as an implication of a low Cl- permeability of the serosal membranes.