Mathematical model of cooperative work of ion pump, symport and antiport in epithelial cells

Transcellular transport in epithelial cells plays an important role in providing such physiological functions as excretion of cytotoxic substances or reabsorption of metabolites useful for the body life activity. These functions have been shown to be performed by the mechanisms - symport, antiport, ion pumps, and channels - that often function cooperatively. Kinetic models of the substrate transport with the aid of the above mechanisms are widely described in the literature. Much less attention is paid to modeling of cooperative activity of transporters that have different transport mechanisms. In this work we propose a mathematical model for flux coupling of three transporters - the ion pump, symporter, and antiporter as well as of two substrates, one of which (A) can be transported simultaneously by the symport and antiport mechanisms, while the other (B) - only by the latter mechanisms. Analysis of the model has shown that for the pair of substrates (A and B) the flux coupling becomes possible if the following conditions are met: (1) the substrate A flux into the internal cell volume using the symport mechanism is to exceed its antiporter-realized flux in the opposite direction; (2) probability of reorientation from one side of membrane to the other side for the antiporter loaded with the substrate is to be essentially higher than that for empty transporter. The proposed model can be used for comparing efficiency both of excretion and of reabsorption of cell metabolites in representatives of different taxa.