Optimal control of active transport across a biological membrane

Abstract

We propose an optimal control principle for active transport across a biological membrane. The modeling of the membrane is based on Hill and Kedem's thermodynamic model. The performance function used to evaluate the optimality of the transport involved the rate of time-dependent changes in the concentration of particles in all the membrane layers as the state variables, and the number of receptor sites on the membrane as the control input. We decided that the optimal transport state is achieved when this cost function has been minimized under the constraints of the system equations characterizing the membrane modeling. The changes in the number of particles in the membrane layer evoked by changes in the kinetic parameters can be explained by the compensatory action of the optimal control strategy in order to prevent excessive decrease or increase of the molecular particles in all the membrane layers. The changes in the number of receptors in the paths of some physiological states can be explained by the optimal control modeling of the membrane transport. This model will be made available to create and evaluate an artificial membrane.