## Electrical Circuit Model of the Cell Membrane

Since the cell membrane separates charge, it can be viewed as a capacitor. The capacitance of any insulator is defined as the ratio of the charge across the capacitor to the voltage potential necessary to hold that charge, and is denoted by

From standard electrostatics (Coulomb's law), one can derive the fact that for two parallel conducting plates separated by an insulator of thickness d, the capacitance is ke0

where k is the dielectric constant for the insulator and e0 is the permittivity of free space. The capacitance of cell membrane is typically found to be 1.0 ^F/cm2. Using that e0 = (10—9/(36n))F/m, we calculate that the dielectric constant for cell membrane is about 8.5, compared to k = 3 for oil.

A simple electrical circuit model of the cell membrane is shown in Fig. 2.11. It is assumed that the membrane acts like a capacitor in parallel with a resistor (although not necessarily ohmic). Since the current is defined by dQ/dt, it follows from (2.73) that the capacitive current is CmdV/dt, provided that Cm is constant. Since there can be no net buildup of charge on either side of the membrane, the sum of the ionic and capacitive currents must be zero, and so dV

Outside o