Membrane Potential - Physical Basis - Equivalent Circuit

Equivalent Circuit

Electrophysiologists model the effects of ionic concentration differences, ion channels, and membrane capacitance in terms of an equivalent circuit, which is intended to represent the electrical properties of a small patch of membrane. The equivalent circuit consists of a capacitor in parallel with four pathways each consisting of a battery in series with a variable conductance. The capacitance is determined by the properties of the lipid bilayer, and is taken to be fixed. Each of the four parallel pathways comes from one of the principal ions, sodium, potassium, chloride, and calcium. The voltage of each ionic pathway is determined by the concentrations of the ion on each side of the membrane; see the Reversal potential section above. The conductance of each ionic pathway at any point in time is determined by the states of all the ion channels that are potentially permeable to that ion, including leakage channels, ligand-gated channels, and voltage-gated ion channels.

For fixed ion concentrations and fixed values of ion channel conductance, the equivalent circuit can be further reduced, using the Goldman equation as described below, to a circuit containing a capacitance in parallel with a battery and conductance. Electrically this is a type of RC circuit (resistance-capacitance circuit), and its electrical properties are very simple. Starting from any initial state, the current flowing across either the conductance or capacitance decays with an exponential time course, with a time constant of τ = RC, where C is the capacitance of the membrane patch, and R = 1/g_net is the net resistance. For realistic situations the time constant usually lies in the 1—100 millisecond range. In most cases changes in the conductance of ion channels occur on a faster time scale, so an RC circuit is not a good approximation; however the differential equation used to model a membrane patch is commonly a modified version of the RC circuit equation.