A pump-leak model of epithelia reveals the roles of paracellular pathways in water transport & the importance of boundary conditions

We develop a pump-leak model of epithelial transport, where the flux of water through the epithelium is modeled as a compartment, or sink, whose volume grows linearly with time. A method is described for calculating the voltage in the sink compartment, as well as analytical solutions to the system of equations. We show how growing boundary conditions can be used to model a scenario where water and ion fluxes are possible in the steady state. It is possible to drive a continuous flux of water through an epithelium that is powered by the Na+ pump establishing small osmotic gradients between compartments. We show that paracellular pathways play a crucial role in the operation of epithelial transport by ensuring that the flux through the epithelium is electroneutral. For the Na+ pump situated on the basolateral membrane, water fluxes can be directed in the same direction as the Na+ ion by having a high Na+ conductance on the apical membrane and high K+ conductance on the basolateral membrane. Flipping these conductances changes the direction of water fluxes. We introduce a graphic formalism that makes clear the precise mechanism of water transfer, showing the osmotic and electrical constraints. We demonstrate that it is possible when the extracellular osmolarity is low (~10mOsm) for the intracellular osmolarity to exceed that of the former considerably and produce a hyperosmolar solution.