Optimization criteria of the mechanism governing the stability of the membrane potential.

Abstract

For small changes in ion concentration within the physiological range the membrane potential transients can be explained in terms of two linear models both for passive and active transport. Using frog sartorius muscle as a suitable model system the ion pump is considered to work within the steepest range of the flux-concentration characteristic. Further for the small perturbations the equations describing passive ion transport can be safely linearized. The conclusion appears inescapable that for the muscle membrane the intracellular ion concentration adjusts itself in some optimal manner to the level of the extracellular ions. The active ion transport represents a control parameter for the membrane potential. The model structure corresponds to a dynamic system, the control processes of which are optimized with respect to a quadratic integral-criterion function. Here, both the performance index of the control sequence in the membrane processes and the energy consumed by the ion fluxes have been considered for small perturbations of Na+, K+, and Cl− in the neighbourhood of the physiological working point. As it is, the control system governing the active and passive ion transport processes is essentially optimized with respect to a minimal energy usage. The amount of energy consumed during the transients predicted by the model has been calculated.