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 ).

Fig. AppD.1, (A) Schematic drawing of a lipid bilayer membrane containing a single open K + channel. A K + concentration gradient exists across the membrane. (B) The electrical equivalent of the membrane shown in (A). The open K + channel is modeled as a conductor (or equivalently, a resistor) with a conductance, γ K , equal to that of the open channel. The resistor is in series with a battery that represents the K + concentration gradient, and it has a voltage equal to E K . The capacitor, with capacitance C m , represents the ability of the lipid bilayer to separate charge and is parallel to the channel.

Definitions of electrical parameters

Electrical potential and potential difference

The potential difference between two points is the amount of work done per unit charge to move charge from one point to the other. The unit of measure of potential difference is the volt. Potential difference (often called voltage ) reflects the electrostatic force exerted on a charge. We use the symbol E to represent theoretical potentials, such as the equilibrium potential of an ion ( Chapter 4 ), and the symbol V for actual voltages, such as V m .

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