MEMBRANE POTENTIALS

Observations of Membrane Potentials

All cells, including neurons, have a resting potential that is typically around −70 mV, as detailed in Chapter 1. One of the signature features of neurons is their ability to change their membrane potential rapidly in response to an appropriate stimulus, and the most significant of these responses is the action potential. Our current knowledge about the ionic mechanisms of action potentials comes from experiments with many species. One of the most studied, however, is the squid because the large diameter (up to 0.5 mm) of the squid giant axon makes it a convenient model for electrophysiological research with intracellular electrodes. When a microelectrode (tip diameter <0.5 μm) is inserted through the plasma membrane of the squid giant axon, a potential difference 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 respect to the external electrode. This 70-mV potential difference is the resting membrane potential of the axon. By convention, membrane potentials are expressed as the intracellular potential minus the extracellular potential; therefore, the resting potential of squid giant axons, as well as many mammalian neurons, is about −70 mV. In the absence of perturbing influences, the resting membrane potential remains at −70 mV.

The Passive Response

Figure 5-1 illustrates the results of an experiment in which the membrane potential of an axon is perturbed by passing rectangular pulses of depolarizing or hyperpolarizing current across the plasma membrane. The injection of positive charge, which changes the membrane potential from −70 mV to −60 mV, is depolarizing because it makes the cell more positive (i.e., decreases the potential difference across the cell membrane). Conversely, a change in the membrane potential from −70 mV to −80 mV as a result of the injection of negative charge increases the polarization of the membrane; this change in potential is called hyperpolarization. The more current that passes across the plasma membrane, the larger the change in the membrane potential.

Figure 5-1 Responses of an axon to rectangular pulses of hyperpolarizing (a) or depolarizing (b to d) current. The change in transmembrane current and potential as recorded by an intracellular electrode is shown as a function of time. Note that when stimulated to threshold (d), the axon fires an action potential. For clarity, only the rising phase of the action potential is shown. RMP, resting membrane potential.

(Redrawn from Blankenship J: Neurophysiology. Philadelphia, Mosby, 2002.)

Note that although the current is injected as rectangular pulses, with vertical rising and falling edges, the shape of the membrane response to smallamplitude current pulses has a slower rise and fall. For hyperpolarizing and small-amplitude depolarizing current pulses, the rise and fall in the membrane voltage response has an exponential shape because the membrane is responding to the current as would a passive RC circuit. That is, the stimulus causes no change in membrane resistance or capacitance, and thus the time course of the rise and fall simply reflects the time required to discharge or charge the membrane capacitance. Recall that because there is an excess of negative ions inside the axon in comparison to outside, those negative ions will attract some positive ions to the outside of the membrane. These charges remain separated from each other by the cell membrane, similar to the storage of charge in a capacitor. Thus, at least in this passive domain, the membrane response to electrical stimuli closely follows the same laws that govern an electric circuit composed of a resistor and capacitor connected in parallel.

When current pulses that elicit only passive responses are passed across the plasma membrane, the size of the potential change 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 to the site of current passage, the larger and steeper the potential change. The magnitude of the potential change decreases exponentially with distance from the site of passage of the current, and the potential change is said to reflect passive or electrotonic conduction. Such changes do not spread very far along the membrane before they become insignificant. As shown in Figure 5-2, an electrotonically conducted signal dies away over a distance of a few millimeters. The distance over which the potential change decreases to 1/e (37%) of its maximal value is called the length constant or space constant (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.

Figure 5-2 Responses of an axon of a shore crab to a subthreshold rectangular current pulse by an extracellular electrode applied closely to its surface and located at different distances from the current-passing electrode. As the recording electrode is moved farther from the point of stimulation, the response of the membrane potential is slower and smaller.

(Redrawn from Hodgkin AL, Rushton WAH: Proc R Soc ser B 133:444-479, 1946.)

The length constant can be related to the electrical properties of the axon via 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 we compare an unmyelinated (see later) nerve fiber with an electrical cable, the plasma membrane equates to the insulation and the cytoplasm to 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 (r_m) and the axial resistance of the axonal cytoplasm (r_a). The higher the ratio of r_m to r_a, the less current lost across the plasma membrane per unit of axonal length, the better the axon can function as a cable, and the longer the distance that a signal can be transmitted electrotonically without significant decrement. A useful analogy is to think of the axon as a garden hose with holes poked in it. The more holes in the hose, the more water will leak out along its length (analogous to more loss of current when r_m is low) and the less water delivered to its nozzle.

Based on cable theory, the length constant can be related to axonal resistance and is equal to . By using this relationship we can determine how changes in axonal diameter will affect the length constant and hence how the decay of electrotonic potentials will vary. An increase in diameter of the axon will reduce 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). Thus, r_adecreases more rapidly than r_m does as axonal diameter increases, and therefore the length constant increases (Fig. 5-3).

Figure 5-3 Comparison of the length constant, λ, in relation to axon diameter. Note that the increase in diameter is associated with a decrease in r_i and an increase in the length constant.

(Redrawn from Blankenship J: Neurophysiology. Philadelphia, Mosby, 2002.)

Membrane capacitance is a major factor that shapes the time course of passive responses. To depolarize an adjacent portion of axon, the injected depolarizing positive charges must draw the inner negative charges from the membrane and thereby free the external positive charges (Fig. 5-4). The time that this process takes increases with the amount of axon membrane to be depolarized.

Figure 5-4 Mechanism of electrotonic spread of depolarization. A, The reversal of membrane polarity that occurs with local depolarization. B, The local currents that flow to depolarize adjacent areas of the membrane and allow conduction of the depolarization.

The Local (Subthreshold) Response

If a somewhat larger depolarizing current pulse is applied to a small portion of the membrane of an axon (Fig. 5-1, c), the voltage response no longer looks like that of a passive RC circuit (e.g., the tail does not decay exponentially). The shape is altered because the stimulus has changed the membrane potential sufficiently to cause the opening of significant numbers of voltage-sensitive Na⁺ channels (see later). Opening of these channels changes the membrane’s resistance and allows Na⁺ to enter, driven by its electrochemical gradient. This entry of positive charge enhances the depolarization by adding to the current pulse. The resulting depolarization is called a local or subthreshold response. The local response results from active changes in membrane properties (specifically r_m), which distinguishes it from the passive electrotonic response. Nevertheless, it is not self-regenerating and does not propagate down the axon but, again, decreases in amplitude with distance. The change in membrane properties is insufficient for what is needed to generate an action potential.

SUPRATHRESHOLD RESPONSE: THE ACTION POTENTIAL

Somewhat larger local responses are observed with still larger depolarizing current pulses until a threshold membrane potential is reached at which a different sort of response, the action potential (or spike), occurs (Fig. 5-5; see also Fig. 5-1, d). For example, the threshold value for the squid giant axon is near −55 mV. When the membrane potential exceeds this value, an action potential is triggered. Thus, the threshold can be defined as the membrane voltage at which there is a 50 : 50 chance of generating an action potential.

Figure 5-5 Components of the action potential with respect to time and voltage. Note that the time scale for the first few milliseconds has been expanded for clarity. RMP, resting membrane potential.

(Redrawn from Blankenship J: Neurophysiology. Philadelphia, Mosby, 2002.)

The action potential differs from the subthreshold and passive responses in three important ways: (1) it is a much larger response in which the polarity of the membrane potential actually overshoots (the cell interior becomes positive with respect to the exterior), (2) the action potential is propagated down the entire length of the nerve fiber, and (3) the action potential is propagated without decrement (i.e., it maintains its size and shape as it is regenerated along the axon). In addition, when a stimulus even larger than the threshold stimulus is applied, the action potential remains the same and does not increase with greater stimulus strength. A stimulus either produces a full-sized action potential or fails to do so. For this reason, the action potential is described as an all-or-none response.

Action potentials can be generated in other parts of the nerve cell membrane, but their most prominent role is signal conduction along the axon. When the membrane is depolarized to threshold, the depolarization becomes explosive (Fig. 5-5). The depolarization completely depolarizes the membrane and even overshoots such that the membrane potential reverses from negative to positive. The peak of the action potential approaches +50 mV. The membrane potential then returns toward the resting membrane potential almost as rapidly as it was depolarized. After repolarization, a variable hyperpolarization occurs that is known as the afterhyperpolarization. The action potential’s depolarization has a duration of 1 to 2 msec, but the hyperpolarizing afterpotential can persist from a few to 100 msec, depending on the particular type of neuron.

Ionic Basis of Action Potentials

An action potential is the result of successive, rapid, and transient changes in plasma membrane conductance to sodium and potassium ions. In the squid giant axon, the resting membrane potential (V_m) is about −70 mV, and the equilibrium potential of K⁺ (E_K) is about −100 mV. An increase in g_K would therefore hyperpolarize the membrane, whereas a decrease in g_K would tend to depolarize the membrane (see Chapter 2). Conversely, an increase in g_Na would cause depolarization and, if of sufficient magnitude, even a reversal in membrane polarity because E_Na is about +65 mV in the squid giant axon.

As with the resting membrane potential, the action potential depends on the opposing tendencies of (1) the Na⁺ gradient to bring the resting membrane potential toward the equilibrium potential for Na⁺ and (2) the K⁺ gradient to bring the resting membrane potential toward the equilibrium potential for K⁺. The relationship between potential, conductance, and ion current during an action potential includes the following (Fig. 5-6):

1. A rapid increase in g_Na and I_Na during the early phase of the action potential causes the membrane potential to move toward the equilibrium potential for Na⁺ (+65 mV). The peak of the action potential does not reach +65 mV because the Na⁺ channels quickly inactivate, thereby reducing g_Na and I_Na, and because the slower increase in g_K and I_K provides mounting opposition to depolarization.

2. The rapid return of the membrane potential toward the resting potential is caused by the continuing increase in g_K, as well as by the decrease in g_Na. The result is that the membrane potential is driven toward E_K.

3. During the hyperpolarizing afterpotential, the membrane potential is actually more negative than the resting potential because g_Na has returned to baseline levels but g_K remains elevated. Thus, the resting membrane potential is pulled even closer to the K⁺ equilibrium potential (-100 mV), and the membrane remains hyperpolarized as long as g_K remains elevated.

Figure 5-6 The action potential and the conductance and currents that underlie the action potential with respect to time. Note that the increased conductance for Na⁺ (and its inward flow) is associated with the rising phase of the action potential, whereas the slower increase in conductance for K⁺ (and its outward flow) is associated with repolarization of the membrane and with afterhyperpolarization. The reduction in I_Na before the peak of the action potential (even though G_Na is still high) is due to inactivation of the Na⁺ channels.

(Redrawn from Squires LR et al: Fundamental Neuroscience, 2nd ed. San Diego, CA, Academic Press, 2002.)

Ion Channels and Gates

Early studies on the mechanism underlying action potentials proposed that ion currents pass through separate Na⁺ and K⁺ channels, each with distinct characteristics, in the plasma membrane. Subsequent research has supported this interpretation. The amino acid sequences of the channel proteins and many of the functional and structural characteristics of the channels are now known in detail.

The structure of a voltage-gated Na⁺ channel (Fig. 5-7) consists of a single α subunit in association with a β₁ and a β₂ subunit. The α subunit has four repeated motifs of six transmembrane helices that surround a central ion channel or pore. The channel’s walls are partly formed by the number 6 helices in each motif. The functional channels of most voltage-gated K⁺ channels are comprised of four separate subunits, each consisting of a polypeptide with six membrane-spanning segments and similar to the motifs which make up the single α subunit of the Na⁺ channel.