Kinetic model of the effects of electrogenic enzymes on the membrane potential

Electrogenic enzymes contribute to the electrical field existing across biological membranes by using a source of free energy to generate an ionic current. The model introduced here permits one to evaluate this contribution. Since the model incorporates the electrogenic enzyme in the form of a sequential kinetic diagram, it permits one to study the kinetic effects of the concentration of the enzyme, the substrates and the different ligands on the membrane potential. Ionic electrodiffusion is expressed in terms of a chemical reaction; ionic permeabilities are thus treated as voltage-dependent rate constants. We use the condition of global electroneutrality to obtain an expression for the electrical potential difference across the membrane; such expression constitutes an extension of the Goldman-Hodgkin-Katz equation. The enzyme-related terms appear in the equation as functions of the rate constants and the diverse concentrations. The model is used to analyze the case of a cell membrane traversed by Na+ and K+ by simple diffusion, and by electrogenic transport mediated by a Na+-K+ ATPase. The enzyme reaction is represented by the six-step scheme proposed by Chapman et al. (1983, J. membr. Biol. 74, 139-153). The main results of the numerical calculations are that, within a certain interval, the membrane potential difference depends linearly on the enzyme density and hyperbolically on the ATP concentration. A similar behavior has been experimentally observed for the electrogenic proton pump of Neurospora crassa. Thus, the model here can be useful in the explanation and prediction of effects of electrogenic enzymes on the membrane potential.