The Resting Potential Equations Incorporating Ionic Pumps and Osmotic Concentration

A mathematical model based on the Hodgkin-Horowicz model (J. Physiol. 1959, 148, 127-160) for the resting potential (RP) that incorporates ionic pumps, cell volume, and intracellular osmotic concentration is presented. Analysis of the model results in three main conclusions: (i) dependence of the RP on the Na+-K+ pump current has a U-shaped distribution; (ii) membrane depolarization is accompanied by an increase in intracellular osmotic pressure or/and cell volume; (iii) activation of the Na+-K+ pump increases the hyperpolarizing effect rather than the depolarizing effect of a neurotransmitter which opens channels with mixed Na+ and K+ conductance. ctivity of the Na+-K+ pump is sufficiently high and ion conductivities are constant, then activation of the pump can result in depolarization. In this case the depolarizing effect of the potassium active influx prevails over the hyperpolarizing effect of the sodium active efflux because of influence of the fluxes on the ion concentrations in condition of intracellular bulk electroneutrality. If [Na+]e > [K+]e , the indication for the depolarizing state of the pump are described by the inequality RP > (EK[K+]i + ENa [Na+]i)/([K]i + [Na]i), where EK and ENa are Nernst equilibrium potentials for K+ and Na+ ions, [K+]i and [Na+]i are their intracellular concentrations. ture of the U-shaped dependence of the RP on the Na+-K+ pump activity, and a diastolic pacemaker depolarization of vertebrate myocardial cells are discussed.