The resting membrane potential of cells are measures of electrical work, not of ionic currents

Abstract

Living cells create electric potential force,E, between their various phases by at least three distinct mechanisms. Charge separation,

$$F = \frac{{Q_1 Q_2 }}{{4\Pi \varepsilon _O \varepsilon _r r^2 }}\left( {Eqn{\text{ }}1} \right)$$

(1)

creates the potential,$F = \frac{Q}{{4\Pi \varepsilon _O \varepsilon _r r^2 }}$} of -120 to -145 mV between cytoplasmic and mitochondrial phases by unbalanced proton expulsion powered by the redox energy of the respiratory chain. Electrically unbalanced flow of Na⁺ through voltage gated Na⁺ channels raises the potential of nerve from -85 to +30 mV. The so-called resting potential of cells, which varies from-85 mV in heart to -4.5 mV in red cell, does not appear to result from the unbalanced flow of ions between phases, but rather to be a measure of the work required to move ions between phases. Movement of an ion between phases entails three types of energy. Concentration work is that required to move an ion between phases containing different concentrations of ions:

$$\Delta G_{Concentration{\text{ }}Energy} = RT\ln \frac{{\left[ {ion^Z } \right]out}}{{\left[ {ion^Z } \right]in}}\left( {Eqn{\text{ }}2} \right)$$

(2)

Electrical work is that work required to move an ion from phases with differing electric potentials:

$$\Delta G_{Electrical{\text{ }}Energy} = zFE\left[ {ion^2 } \right]_{out/in} \left( {Eqn{\text{ }}3} \right)$$

(3)

The Nernst potential of an ion existing at different concentrations in two phases is:

$$E_{out/in} = \frac{{RT\ln \left[ {Permeant{\text{ }}ion^z } \right]_{out/in} }}{{zF}},\left( {Eqn{\text{ 5}}} \right)$$

(5)

required to transport the most permeant ions in a Gibbs-Donnan near-equilibrium system, either K⁺ or Cl⁻ or both, between the phases of an aqueous system during the flow of current required to measure potentials with intracellular KCl electrodes or during ion movements brought about during normal cellular activity.

The resting electrical potential results from the existence of a mono-ionic Gibbs-Donnan near-equilibrium system between the extra- and intracellular phases of cell wherein the activity of free H₂O within all phases of the system is equal and the energy of the gradients of the nine major inorganic ions, ΔG[ion^z]_out/in, are in near-equilibrium with one another, with the potential between the phases,E _N, and with the energy of ATP hydrolysis. ΔG _{ATP Hydrolysis}. ranges from a low of -55 to slightly over -60 kJ/mole in all cell types. While the classic inanimate Gibbs-Donnan system has only one ratio of ion concentrations between phases,r, cellular Gibbs-Donnan systems have three differentr’s representing three different equal energy ion groups or quanta, ΔG[ion^z] _out/in . In heart, the quanta of ΔG [Na⁺] _out/in , [Mg²⁺] _out/in and [H₂PO ⁻₄ ] _out/in was 1/3 of ΔG _{ATP Hydrolysis}; the quanta of ΔG [H⁺] _out/in , [HCO ⁻₃ ] _out/in and [Cl⁻] _out/in quanta was 1/3 of ΔG[Na⁺] _out/in . The ΔG [K⁺] _out/in in heart or ΔG[Cl⁻] _out/in in liver is 0 and represents the resting potential.

In all cell types, a drop in the ΔG _{ATP Hydrolysis}. resulting from anoxic or most other forms of injury decreases the extent of the Na⁺ gradients between extra- and intracellular phases. This leads to a steoreotypic response characterized by gain of intracellular Na⁺, loss of intracellular K⁺, decrease in resting potential and gain in intracellular H₂O. A better understanding of the nature of the electrical potential between the extra- and intracellular phases of cells gives new insights into the relationship of fluid and ion changes that occur in cellular injury and apoptosis, the nature and treatment of cardiac arrhythmias and refractory seizures, as well as states of altered gene expression, such as malignant transformation and common diseases of ion transport.