A theory for the membrane potential of living cells

We give an explicit formula for the membrane potential of cells in terms of the intracellular and extracellular ionic concentrations, and derive equat ions for the ionic currents that flow through channels, exchangers and elec trogenic pumps. We demonstrate that the work done by the pumps equals the c hange in potential energy of the cell, plus the energy lost in downhill ion ic fluxes through the channels and exchangers. The theory is illustrated in a simple model of spontaneously active cells in the cardiac pacemaker. The model predicts the experimentally observed intracellular ionic concentrati on of potassium, calcium and sodium. Likewise, the shapes of the simulated action potential and five membrane currents are in good agreement with expe riment. We do not see any drift in the values of the concentrations in a lo ng time simulation, and we obtain the same asymptotic values when starting from the full equilibrium situation with equal intracellular and extracellu lar ionic concentrations.