On the concept of resting potential--pumping ratio of the Na⁺/K⁺ pump and concentration ratios of potassium ions outside and inside the cell to sodium ions inside and outside the cell.

In animal cells, the resting potential is established by the concentration gradients of sodium and potassium ions and the different permeabilities of the cell membrane to them. The large concentration gradients of sodium and potassium ions are maintained by the Na⁺/K⁺ pump. Under physiological conditions, the pump transports three sodium ions out of and two potassium ions into the cell per ATP hydrolyzed. However, unlike other primary or secondary active transporters, the Na⁺/K⁺ pump does not work at the equilibrium state, so the pumping ratio is not a thermodynamic property of the pump. In this article, I propose a dipole-charging model of the Na⁺/K⁺ pump to prove that the three Na⁺ to two K⁺ pumping ratio of the Na⁺/K⁺ pump is determined by the ratio of the ionic mobilities of potassium to sodium ions, which is to ensure the time constant τ and the τ-dependent processes, such as the normal working state of the Na⁺/K⁺ pump and the propagation of an action potential. Further, the concentration ratios of potassium ions outside and inside the cell to sodium ions inside and outside the cell are 0.3027 and 0.9788, respectively, and the sum of the potassium and sodium equilibrium potentials is -30.3 mV. A comparative study on these constants is made for some marine, freshwater and terrestrial animals. These findings suggest that the pumping ratio of the Na⁺/K⁺ pump and the ion concentration ratios play a role in the evolution of animal cells.