Theoretical model for the optimal control mechanism of cellular membrane transport with active transport as control variable

Abstract

AbstractAn optimal control model is proposed to study active transport across biological membranes. the membrane is assumed to be three layers thick. Our concept is based on the teleological creation and the need of biological systems to prefer homeostasis. the active transport was set as an optimal control input for import and export across a membrane separating the cell from the outer world. Temporal changes in particle concentrations throughout the layer are expressed by linear simultaneous differential equations. the minimized performance differential equations. the minimized performance function involves the rates of the time‐dependent change in concentrations of particles static deviations from the target concentrations of particles in all membrane layers. These concentrations are considered simultaneously with the consumption of energy necessary for active transport. the present optimization problem is to form the boundary values problem; the system equations were solved by a multiple shooting method. the optimized temporal changes of the concentrations in layer 1 (the outermost layer) and layer 3 (the innermost layer) are rapid while those of the concentration in the middle layer are gradual. the concentrations in layer 1 and layer 3 are influenced significantly by changes in the transport rate within the membrane and the weighting coefficients that describe the relative magnitude of the minimization of the quantities involved in the performance function. the concentration in the middle layer is not influenced by these changes. the characteristic temporal behaviors of the concentrations in these layers are produced by the optimal control input so as to compensate the disturbed states of the membrane transport and to improve stability.This theoretical investigation is available to produce artificial tissue membranes and evaluate the transport function of these membranes.