A quantitative analysis of cell volume and resting potential determination and regulation in excitable cells

This paper quantifies recent experimental results through a general physical description of the mechanisms that might control two fundamental cellular parameters, resting potential (Em) and cell volume (Vc), thereby clarifying the complex relationships between them. Em was determined directly from a charge difference (CD) equation involving total intracellular ionic charge and membrane capacitance (Cm). This avoided the equilibrium condition dEm/dt = 0 required in determinations of Em by previous work based on the Goldman-Hodgkin-Katz equation and its derivatives and thus permitted precise calculation of Em even under non-equilibrium conditions. It could accurately model the influence upon Em of changes in Cm or Vc and of membrane transport processes such as the Na+-K+-ATPase and ion cotransport. Given a stable and adequate membrane Na+-K+-ATPase density (N), Vc and Em both converged to unique steady-state values even from sharply divergent initial intracellular ionic concentrations. For any constant set of transmembrane ion permeabilities, this set point of Vc was then determined by the intracellular membrane-impermeant solute content (X-i) and its mean charge valency (zX), while in contrast, the set point of Em was determined solely by zX. Independent changes in membrane Na+ (PNa) or K+ permeabilities (PK) or activation of cation-chloride cotransporters could perturb Vc and Em but subsequent reversal of such changes permitted full recovery of both Vc and Em to the original set points. Proportionate changes in PNa, PK and N, or changes in Cl- permeability (PCl) instead conserved steady-state Vc and Em but altered their rates of relaxation following any discrete perturbation. PCl additionally determined the relative effect of cotransporter activity on Vc and Em, in agreement with recent experimental results. In contrast, changes in Xi- produced by introduction of a finite permeability term to X- (PX) that did not alter zX caused sustained changes in Vc that were independent of Em and that persisted when PX returned to zero. Where such fluxes also altered the effective zX they additionally altered the steady state Em. This offers a basis for the suggested roles of amino acid fluxes in long-term volume regulatory processes in a variety of excitable tissues.