Cell volume regulation during anisotonic challenge is investigated in a mathematical model of a tight epithelium. The epithelium is represented as compliant cellular and paracellular compartments bounded by mucosal and serosal bathing media. Model variables include the concentrations of Na, K, and Cl, hydrostatic pressure, and electrical potential, and the mass conservation equations have been formulated for both steady-state and time-dependent problems. Ionic conductance is represented by the Goldman constant field equation (Civan, M.M., and R.J. Bookman. 1982. Journal of Membrane Biology. 65:63-80). A basolateral cotransporter of Na, K, and Cl with 1:1:2 stoichiometry (Geck, P., and E. Heinz. 1980. Annals of the New York Academy of Sciences. 341:57-62.) and volume-activated basolateral ion permeabilities are incorporated in the model. MacRobbie and Ussing (1961. Acta Physiologica Scandinavica. 53:348-365.) reported that the cells of frog skin exhibit osmotic swelling followed by a volume regulatory decrease (VRD) when the serosal bath is diluted to half the initial osmolality. Similar regulation is achieved in the model epithelium when both a basolateral cotransporter and a volume-activated Cl permeation path are included. The observed transepithelial potential changes could only be simulated by allowing volume activation of the basolateral K permeation path. The fractional VRD, or shrinkage as percent of initial swelling, is examined as a function of the hypotonic challenge. The fractional VRD increases with increasing osmotic challenge, but eventually declines under the most severe circumstances. This analysis demonstrates that the VRD response depends on the presence of adequate intracellular chloride stores and the volume sensitivity of the chloride channel.

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