A Mathematical Model of the Proton Balance in the Outer Mantle Epithelium of Anodonta cygnea L.

Abstract

In the freshwater mollusc Anodonta cygnea and other unionids, the mantle plays an important role in the regulation of the movements of ions between the shell and the extrapaleal fluid. In this report, a mathematical model that attempts to describe the cell metabolic mechanisms underlying the operation of the outer mantle epithelium as a source of protons is presented. We encoded the information gathered by studying the epithelium in vitro, which includes the electrophysiology of the preparation, measurements of basic rates of transport of protons and base, the effect of metabolic and transport inhibitors on its electrical behavior and the dynamic measurements of pHi. The model was conceived so that the short-circuit current (Isc) and fluxes of Na+, K+ and Cl(-); intracellular volume; electrical potential; and ionic concentrations can be computed as a function of time. Furthermore, the analytical descriptions of all ionic fluxes involved are such that the effect of transport inhibitors can be simulated. In all the simulations performed, it was possible to reproduce the experimental results obtained with specific inhibitors of transport systems on the Isc and on pHi. In some cases, it was necessary to make alterations to one or more parameters of the reference condition. For each simulation carried out, the analysis of the results was consistent. The model is an analytical tool that can be used to show the internal coherence of the qualitative model previously proposed and to plan further experiments.