A mathematical model of solute coupled water transport in toad intestine incorporating recirculation of the actively transported solute

A mathematical model of an absorbing leaky epithelium is developed for anal ysis of solute coupled water transport. The non-charged driving solute diff uses into cells and is pumped from cells into the lateral inter-cellular sp ace (lis). All membranes contain water channels with the solute passing tho se of tight junction and interspace basement membrane by convection-diffusi on. With solute permeability of paracellular pathway large relative to para cellular water flow, the paracellular flux ratio of the solute (influx/outf lux) is small (2-4) in agreement with experiments. The virtual solute conce ntration of fluid emerging from lis is then significantly larger than the c oncentration in lis. Thus, in absence of external driving forces the model generates isotonic transport provided a component of the solute flux emergi ng downstream lis is taken up by cells through the serosal membrane and pum ped back into lis, i.e., the solute would have to be recirculated. With inp ut variables from toad intestine (Nedergaard, S., E.H. Larsen, and H.H. Uss ing, J. Membr: Biol. 168:241-251), computations predict that 60-80% of the pumped flux sterns from serosal bath in agreement with the experimental est imate of the recirculation flux. Robust solutions are obtained with realist ic concentrations and pressures of lis, and with the following features. Ra te of fluid absorption is governed by die solute permeability of mucosal me mbrane. Maximum fluid flow is governed by density of pumps on lis-membranes . Energetic efficiency increases with hydraulic conductance of the pathway carrying water from mucosal solution into lis. Uphill water transport is ac complished, but with high hydraulic conductance of cell membranes strength of transport is obscured by water flow through cells. Anomalous solvent dra g occurs when back flux of water through cells exceeds inward water flux be tween cells. Molecules moving along the paracellular pathway are driven by a translateral flow of water; i.e., the model generates pseudo-solvent drag . The associated flux-ratio equation is derived.