Models of coupled salt and water transport across leaky epithelia

A general formulation is presented for the verification of isotonic transport and for the assignment of a degree of osmotic coupling in any epithelial model. In particular, it is shown that the concentration of the transported fluid in the presence of exactly equal bathing media is, in general, not a sufficient calculation by which to decide the issue of isotonicity of transport. Within this framework, two epithelial models are considered: (1) A nonelectrolyte compartment model of the lateral intercellular space is presented along with its linearization about the condition of zero flux. This latter approximate model is shown to be useful in the estimation of deviation from isotonicity, intraepithelial solute polarization effects, and the capacity to transport water against a gradient. In the case of uphill water transport, some limitations of a model of fixed geometry are indicated and the advantage of modeling a compliant interspace is suggested. (2) A comprehensive model of cell and channel is described which includes the major electrolytes and the possible presence of intraepithelial gradients. The general approach to verification of isotonicity is illustrated for this numerical model. In addition, the insights about parameter dependence gained from the linear compartment model are shown to be applicable to understanding this large simulation.