## The Cell Membrane as an Electrical Capacitor

An electrical capacitor is a charge-storing device, which consists of two conducting plates separated by an insulating barrier. Because the lipid bilayer of the plasma membrane forms an insulating barrier separating the electrically conductive salt solutions of the ICF and ECF, the plasma membrane behaves as a capacitor. When a capacitor is hooked up to a battery as shown in Figure C-1, the voltage of the battery causes electrons to leave one conducting plate and to accumulate on the other plate. This charge separation continues until the resulting voltage gradient across the capacitor equals the voltage of the battery. The amount of charge, q, stored on the capacitor at that time will be given by q = CV, where V is the voltage across the capacitor and C is the capacitance

Figure C-1 When a battery is connected to a capacitor, charge accumulates on the capacitor until the voltage across the capacitor equals the voltage of the battery.

Battery of voltage = V

Voltmeter

of the capacitor. Capacitance is directly proportional to the area of the plates (bigger plates can store more charge) and inversely proportional to the distance separating the two plates. Capacitance also depends on the characteristics of the insulating material between the plates, which is the lipid of the plasma membrane in cells.

The unit of capacitance is the farad (F): a 1 F capacitor can store 1 coulomb of charge when hooked up to a 1V battery. Biological membranes have a capacitance of approximately10-6 F (that is, 1 microfarad, or ^F) per cm2 of membrane area. From this value of membrane capacitance, the thickness of the insulating lipid portion of the membrane can be estimated using the following relation:

In this equation, x is the distance between the conducting plates (that is, the ICF and the ECF), C is the capacitance of the plasma membrane (1 ^.F/cm2), £0 is the permittivity constant (8.85 x 10-8 ^F/cm), and K is the dielectric constant of the insulating material separating the two conducting plates (k = 5 for membrane lipid). The calculated membrane thickness is approximately 4.5 nm, which is similar to the membrane thickness of approximately 7.5 nm estimated with electron microscopy. The thickness estimated from capacitance is less because it is determined by the insulating portion of the membrane, whereas the total membrane thickness, including associated proteins, is observed through the electron microscope.

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