Summary of elementary circuit theory

Cell membranes are modeled with electrical circuits

The plasma membrane can be modeled as an electrical circuit. Fig. AppD.1 A is a schematic view of the structure of a biological membrane with a single open K ⁺ –selective ion channel. This physical entity is electrically equivalent to the circuit shown in Fig. AppD.1 B. The circuit consists of a resistor in series with a battery, and this combination is in parallel with a capacitor. In Fig. AppD.1 , we follow the convention that the positive pole of a battery is represented by a longer bar. The electrical behavior of most resting biological membranes is, in fact, indistinguishable from a circuit similar to that shown in Fig. AppD.1 B. Therefore we can use such equivalent circuits to obtain quantitative descriptors of membrane electrical behavior, such as the length constant and the membrane time constant ( Chapter 6 ). The equivalent circuit is also used to describe current flow across membranes and the effect of current flow on membrane potential ( V _m ), such as how the action potential is generated and propagated along an elongated structure such as an axon or a skeletal muscle cell ( Chapter 7 ).

Definitions of electrical parameters