Generation and Conduction of Action Potentials

Observations on Membrane Potentials

When a sharp microelectrode (tip diameter, <0.5 µm) is inserted through the plasma membrane of a neuron, a difference in potential is observed between the tip of the microelectrode inside the cell and an electrode placed outside the cell. The internal electrode is approximately 70 mV negative with regard to the external electrode, and this difference is referred to as the resting membrane potential or, simply, the resting potential (see Chapter 1 for details on the basis of the resting potential). (By convention, membrane potentials are expressed as the intracellular potential minus the extracellular potential.) Neurons have a resting potential that typically is around −70 mV.

One of the signature features of neurons is their ability to change their membrane potential rapidly from rest in response to an appropriate stimulus. Two such classes of responses are action potentials and synaptic potentials, which are described in this chapter and the next, respectively. Current knowledge about the ionic mechanisms of action potentials comes from experiments with many species. One of the most studied is the squid because the large diameter (up to 0.5 mm) of the squid giant axon makes it an excellent model for electrophysiological research with intracellular electrodes.

The Passive Response

To understand how an action potential is generated and why it is needed, it is necessary to understand the passive electrical properties of the nerve cell membrane. The term passive properties refers to the fact that components of the cell membrane behave very similarly to some of the passive elements of electric circuits, including batteries, resistors, and capacitors. This is very useful because the properties of these elements are well understood. In particular, a piece of membrane containing ion channels responds to changes in voltage across it much as a circuit containing a resistor and capacitor in parallel (parallel RC circuit) would: The ion channels correspond to the resistor, and the lipid bilayer acts as a capacitor. When a battery is first connected across the two terminals of a parallel RC circuit, all of the current flows through the branch of the circuit with the capacitor, causing the voltage across it to begin changing (recall that for a capacitor, I $\tilde{\alpha }$ dV/dt). Over time, however, the current flow through the capacitor decreases, whereas that through the resistor increases. As this happens, the rate of voltage change across the capacitor (and resistor) slows, and the voltage approaches a steady-state value. This change in voltage has an exponential time course whose specific characteristics depend on the resistance (R) and capacitance (C) of the resistor and capacitor. Moreover, a time constant, τ, for this circuit can be defined by the equation τ = R × C, and it equals the time it takes for the voltage to rise (or fall) exponentially by approximately 63% of the difference between its initial and final values.

With regard to how an axon actually responds to electrical stimulation, Fig. 5.1 illustrates the results of an experiment in which the membrane potential of an axon is altered by passing rectangular pulses of depolarizing (upward-going pulses) or hyperpolarizing (downward-going pulses) current across its cell membrane. The injection of positive charge is depolarizing because it makes the cell less negative (i.e., decreases the potential difference across the cell membrane). Conversely, the injection of negative charge makes the membrane potential more negative, and this change in potential is called hyperpolarization. The larger the current that is injected, the greater the change in the membrane potential will be. The responses to hyperpolarizing and small-amplitude depolarizing current pulses (see Fig. 5.1 A ) all have the same fundamental shape because of the passive properties of the membrane. In contrast, the shapes of the responses to the larger depolarizing stimulus pulses differ from those to hyperpolarizing and small-amplitude depolarizing current pulses because the larger stimuli activate nonpassive elements in the membrane.

For the responses to hyperpolarizing current pulses, once a long enough time has elapsed from the start of the current pulse to allow the membrane voltage to plateau (essentially several times τ), virtually all of the injected current is flowing through the membrane resistance. If the difference between the initial and steady-state voltages is plotted against the amplitude of the current pulse (see Fig. 5.1 B ), a linear relationship is observed for the hyperpolarizing pulses, which is exactly what is expected from Ohm’s law (V = I × R) for current flowing through a resistor. The slope of this line (ΔV/ΔI) is referred to as the input resistance of the cell (R _in ) and is determined experimentally, exactly as just described. R _in is related to the membrane resistance (r _m ) of the cell, but the exact relationship depends on the geometry of the cell and is complex in most cases.

Next, note that although the current is injected as rectangular pulses, with vertical rising and falling edges, the shape of the membrane voltage responses just after the starts and ends of the pulses has slower rises and falls. Moreover, with regard to only the responses to hyperpolarizing and small-amplitude depolarizing current pulses (see Fig. 5.1 A ), the fall and rise in the membrane voltage have exponential shapes. This shows that the membrane is responding to these current pulses as a parallel RC circuit would; that is, the stimulus causes no change in membrane resistance or capacitance (c _m ), and thus the time course of the rise and fall in voltage is the same in all cases because it is governed by the same membrane time constant (τ).

The relationships between voltage and current just described show that within a certain range of stimulation, the cell membrane in one region of the axon can be modeled by a passive RC circuit. However, this model circuit, with only a single resistor and capacitor, takes no account of the fact that axons are spatially extended structures and that because of this, the resistance of the intracellular space is a significant factor in how electrical events in one region affect other regions. That is, if axons had no intracellular resistance, their intracellular space would be isoelectric, and voltage changes, like those just described, across one part of the axonal membrane would occur across all regions instantaneously. In this case, there would be no need for a special mechanism (i.e., the action potential) to propagate signals actively down the axon. In actuality, axons (and neurons in general) are spatially extended structures with significant resistance to current flow between different regions (this is one reason the relationship of R _in and r _m is complicated). Therefore, it is important to understand how current injected at one point along the axon affects the membrane potential at other points because this both helps explain why action potentials are needed and helps explain some of their characteristics.

When current pulses that elicit only passive responses are passed across the plasma membrane, the size of the change in potential recorded depends on the distance of the recording electrode from the point of passage of the current ( Fig. 5.2 ). The closer the recording electrode is to the site of current passage, the larger and steeper the change in potential is. The magnitude of the change in potential decreases exponentially with distance from the site of passage of the current, and the change in potential is said to reflect passive or electrotonic conduction. Such passively conducted changes in potential do not spread very far along the membrane before they become insignificant. As shown in Fig. 5.2 , an electrotonically conducted signal dies away over a distance of a few millimeters. The distance over which the change in potential decreases to 1/e (37%) of its maximal value is called the length constant or space constant (where e is the base of natural logarithms and is equal to 2.7182). A length constant of 1 to 3 mm is typical for mammalian axons, which can be more than a meter long, which makes obvious the need for a mechanism to propagate information about electrical events generated at the soma to the far end of the axon.

The length constant can be related to the electrical properties of the axon according to cable theory because nerve fibers have many of the properties of an electrical cable. In a perfect cable, the insulation surrounding the core conductor prevents all loss of current to the surrounding medium, so that a signal is transmitted along the cable with undiminished strength. If an unmyelinated nerve fiber (discussed later) is compared to an electrical cable, the plasma membrane equates to the insulation and the cytoplasm as the core conductor, but the plasma membrane is not a perfect insulator. Thus the spread of signals depends on the ratio of the membrane resistance to the axial resistance of the axonal cytoplasm (r _a ) . When the ratio of r _m to r _a is high, less current is lost across the plasma membrane per unit of axonal length, the axon can function better as a cable, and the distance that a signal can be conveyed electrotonically without significant decrement is longer. A useful analogy is to think of the axon as a garden hose with holes poked in it. The more holes there are in the hose, the more water leaks out along its length (analogous to more loss of current when r _m is low) and the less water is delivered to its nozzle.

According to cable theory, the length constant can be related to axonal resistance and is equal to $\sqrt{r_m/r_a}$ . This relationship can be used to determine how changes in axonal diameter affect the length constant and, hence, how the decay of electrotonic potentials varies. An increase in the diameter of the axon reduces both r _a and r _m . However, r _m is inversely proportional to diameter (because it is related to the circumference of the axon), whereas r _a varies inversely to the diameter squared (because it is related to the cross-sectional area of the axon). Therefore, r _a decreases more rapidly than r _m does as axonal diameter increases, and the length constant increases ( Fig. 5.3 ).

In sum, in the passive domain, the membrane response to electrical stimuli is essentially identical to that of a circuit composed of passive electrical elements, and it can thus be characterized by the length and time constants of the membrane, which will determine how far and how rapidly electrical signals at one point in the cell spread to other parts.

The Local Response

With regard to the experiment shown in Fig. 5.1 , if larger depolarizing current pulses are injected, the voltage response of the membrane no longer resembles that of a passive RC circuit. This is most easily observed with pulses that elicit depolarizations either just below or to the threshold membrane potential for an action potential but fail to evoke an action potential (tracings 0.89 and 1.0; the threshold membrane potential can be defined as the voltage at which the probability of evoking an action potential is 50%). In these cases, the voltage response shape is altered from that of the passive responses because the stimulus has changed the membrane potential sufficiently to cause the opening of significant numbers of voltage-sensitive Na ⁺ channels (described later).

Also, note the upward deviation from linearity for the corresponding points in the I-V curve (see Fig. 5.1 B ). Opening of these voltage-sensitive channels changes the membrane’s resistance and allows Na ⁺ to enter more easily, driven by its electrochemical gradient. This entry of positive charge (Na ⁺ current) enhances the depolarization by adding to the current pulse delivered by the electrode. The resulting depolarization is called a local response. The local response results from active changes in membrane properties (specifically, its Na ⁺ conductance), whereas in a passive electrotonic response, the conductance to various ions remains constant. Nevertheless, the local response is not self-regenerating but, again, decreases in amplitude with distance. The change in membrane properties is insufficient for what is needed to generate an action potential.