How to formulate membrane potential in a spatially homogeneous myocyte model?

Abstract

Membrane potential in a mathematical model of a cardiac myocyte can be formulated in different ways. Assuming a spatially homogeneous myocyte that is strictly charge-conservative and electroneutral as a whole, two methods will be compared: (1) the differential formulation dV/dt=-I/C_m of membrane potential used traditionally; and (2) the capacitor formulation, where membrane potential is defined algebraically by the capacitor equation V=Q/C_m. We examine the relationship between the formulations, assumptions under which each formulation is consistent, and show that the capacitor formulation provides a transparent, physically realistic formulation of membrane potential, whereas use of the differential formulation may introduce unintended and undesirable behavior, such as monotonic drift of concentrations. We prove that the drift of concentrations in the differential formulation arises as a compensation for failure to assign all currents in concentrations. As an example of these considerations, we present an electroneutral, explicitly charge-conservative formulation of Winslow et al. model (1999), and extend it to describe membrane potentials between intracellular compartments.