Non linear modeling of the carrier mediated transport across the biological membrane

A mathematical method was introduced to analyze the optimally controlled carrier mediated material transport across the biological membrane. The rate constants were set as functions of concentrations of the species. Thus, the transfer rates of ligands changed as the transport state proceeded. The optimal control that minimized the deviations from the target concentrations of the species produced characteristic pattern of temporal changes in the concentrations of the species. The present method will be useful for evaluating the biological and artificial membrane functions