Generation and propagation of the action potential

Properties of action potentials can be studied with intracellular microelectrodes

Many properties of the AP in a nerve axon can be illustrated by use of the experimental arrangement shown in Fig. 7.1 A. One intracellular electrode is used to pass current across the membrane. A second electrode (the “recording electrode”) is used to monitor the resulting changes in V _m . When a hyperpolarizing, or small depolarizing, current step is passed across the membrane, V _m exponentially approaches a new steady-state level ( Chapter 6 ). If a depolarizing stimulus exceeds a critical level (termed threshold ), an AP is generated ( Fig. 7.1 B). During an axonal AP, V _m depolarizes to a value near E _Na in approximately 1 msec (1/1000 of a second). The V _m then returns to the resting value in the next 1 to 2 msec. Further increases in stimulus intensity beyond the threshold level have no additional effect on the AP. If an AP is generated, its time course and amplitude are independent of the stimulus intensity; therefore the response is said to be “all-or-none.” Because of the sharp, pointy appearance of an AP, it is often referred to as a “spike.”

To examine the characteristics of AP propagation along the nerve axon, a second recording electrode can be placed in the axon at a position that is 3 to 4 length constants away from the stimulating electrode ( Fig. 7.1 A). Subthreshold V _m changes are not observed at the second recording electrode ( Fig. 7.1 C) because of the electrotonic decay of these signals caused by the passive properties of the axon ( Chapter 6 ). In contrast, the AP is transmitted at full amplitude to the second recording electrode ( Fig. 7.1 D). Thus the AP is propagated along the axon without decrement in size despite the passive properties of the axon.

If a pair of just-threshold stimuli is given with a long enough interval between them, both produce APs ( Fig. 7.2 A). If the interval between stimuli is short enough, however, the second stimulus fails to evoke an AP. The nerve is said to be refractory . The interval of time after an AP during which a second stimulus, regardless of its amplitude, is unable to evoke a response is called the absolute refractory period ( Fig. 7.2 B). The relative refractory period is the interval of time after an AP during which the second stimulus must be increased in intensity to evoke a second AP ( Fig. 7.2 B).

Ionic currents are measured at a constant membrane potential with a voltage clamp

In the late 1940s, Hodgkin and Huxley pioneered the study of ion channels using a technique called the voltage clamp to study the ionic basis of the AP in squid giant axons. ^a

a Alan Hodgkin and Andrew Huxley were awarded the Nobel Prize in Physiology or Medicine in 1963 for this work.

With this technique they could measure the ionic currents that flow across a membrane at a constant V _m . To appreciate the advantages of a voltage clamp, consider the following parameters that have complex interdependencies during a propagated AP in an axon: current, voltage, distance, and time. As illustrated in Fig. 7.1 , V _m changes as a function of distance during propagation. The ionic and capacitive currents that flow during the AP must also change as a function of distance. Furthermore, both the currents and V _m change as a function of time. By eliminating some of these variables while controlling others ( Box 7.1 ), the voltage clamp simplifies the situation in the following ways. First, distance is eliminated as a variable when the voltage clamp ensures that V _m is the same over the entire membrane surface under study; this condition is called “space-clamp.” Second, the voltage clamp apparatus allows V _m to be held, or clamped, at a constant level. Thus

BOX 7.1

The Voltage Clamp Is Used to Maintain a Constant Membrane Potential

The voltage clamp, which uses an electronic device that allows control, or “clamping,” of V _m at a desired level, is an example of a negative feedback control system. In this type of system, like the thermostat controlling the temperature in your home, a variable (temperature) is measured and compared with a “command level,” or set point (the temperature setting of the thermostat). The difference between the measured variable and the set point creates an “error signal.” The error signal activates an effector system (heater or air conditioner) that decreases the magnitude of the error (i.e., brings the temperature closer to the set point).

A schematic of the squid giant axon axial wire voltage clamp is shown in Fig. 7.3 . An amplifier measures the potential difference between an intracellular electrode ( V _in ) and an extracellular electrode ( V _out ). The output of this amplifier ( V _m ) is the controlled variable and is compared with the command potential ( V _command ), or set point, by an amplifier called the control amplifier. If V _m is not equal to V _command , an error signal causes a current to flow through an axial wire that is connected to the output of the control amplifier and inserted longitudinally through the axon. The current then flows out through the membrane to a grounded electrode to complete the circuit. The current passing through the axial wire rapidly and continuously causes V _m to remain equal to V _command . One way to measure the membrane current ( I _m ) is simply to measure the current flowing out of the control amplifier.

An important benefit of the low-resistance axial wire is that it greatly reduces the internal, axial resistance of the axoplasm. Thus the length constant

$\text{λ=}\sqrt{\frac{r_{\text{m}}}{r_{\text{i}}}}$

is greatly increased. The result is that V _m is constant over the membrane surface under study, or in other words, V _m is “space clamped.”

so the capacitive current

is zero. Third, elimination of the capacitive current leaves only the ionic current, which can now be measured as a function of time at a constant V _m . Because the ionic current flows through open ion channels, we can investigate the functional properties of the channels by analyzing the current.

Ionic currents are dependent on voltage and time

In a typical voltage clamp experiment V _m is changed in stepwise fashion from a negative “holding” potential near the cell’s resting potential (−70 mV) to a new level. When V _m is stepped to a more negative potential (e.g., −100 mV), the current shown in Fig. 7.4 A is recorded. The current consists of an initial very brief spike of inward current followed by a steady (time-independent) inward current. The spike is capacitive current, which reflects the addition of negative charges at the inside membrane surface as V _m goes from −70 to −100 mV. The steady inward current is ionic current that flows through ion channels, called leak channels, that are open under resting conditions. The leak current is a linear function of V _m ( Fig. 7.4 B); that is, it obeys Ohm’s Law and is said to be ohmic . For small depolarizations from −70 mV, the membrane behaves in an analogous fashion; that is, a spike of outward capacitive current is followed by a steady outward ionic leak current. This is consistent with the result shown in Fig. 6.3 , which was obtained by injecting current and measuring the change in V _m .

For larger depolarizations, however, the current pattern is strikingly different, as illustrated by the current recorded during a voltage clamp step to 0 mV ( Fig. 7.5 A). Shortly after the spike of outward capacitive current, an inward current develops and reaches a maximum in approximately 1 msec. This inward current then declines in amplitude and is followed by an outward current that reaches a maximum and is maintained through the remainder of the voltage clamp step. This total membrane current recording ( Fig. 7.5 A) contains three separable components of current ( Box 7.2 ):

• 1.

  A linear component, similar to that shown in Fig. 7.4 A, contains capacitive current and ionic leak current ( Fig. 7.5 B).

• 2.

  A time-dependent inward ionic current is carried by Na ⁺ ions flowing through voltage-gated Na ⁺ channels ( Fig. 7.5 C).

• 3.

  A time-dependent outward ionic current is carried by K ⁺ ions flowing through voltage-gated K ⁺ channels ( Fig. 7.5 D).

BOX 7.2

Current Components in Axons Are Separated and Identified With Ionic Substitutions

The most straightforward way to separate the ionic currents is to perform ionic substitution experiments, in which permeant ions are replaced by larger, impermeant ions. In the isolated squid giant axon the axoplasm can be removed and the axon interior perfused with a solution of known composition. Thus the ionic composition of both the internal and external solutions is under experimental control. If Na ⁺ is replaced with the larger, impermeant cation choline, the early inward current carried by Na ⁺ ions is eliminated ( Fig. 7.6 B), and if the remaining current is subtracted from the total current ( Fig. 7.6 A), the isolated Na ⁺ current is obtained ( Fig. 7.6 C). If cesium ions (Cs ⁺ ) are then substituted for intracellular and extracellular K ⁺ , the outward K ⁺ current is abolished and only linear capacitive and leakage currents remain ( Fig.7.6 D). By subtracting the linear current ( Fig. 7.6 D) from the current shown in Fig. 7.6 B, the isolated K ⁺ current is obtained ( Fig. 7.6 E).

The total current flowing through multiple channels is commonly referred to as a macroscopic current. The macroscopic Na ⁺ and K ⁺ currents shown in Fig. 7.5 can be described in terms of channel gating (opening and closing) kinetics and current flow through a single channel. Because the size of the current flowing through a single open channel is constant at a constant V _m (see later), the size of the macroscopic current is proportional to the number of open channels. The inward macroscopic Na ⁺ current ( Fig. 7.5 C) increases shortly after the depolarization, because Na ⁺ channels rapidly open and Na ⁺ flows into the cell down its electrochemical gradient (at 0 mV, the net driving force on Na ⁺ is inward and therefore the Na ⁺ current is inward). The Na ⁺ current reaches a maximum in approximately 1 msec and then becomes smaller as the Na ⁺ channels close. This closure of the Na ⁺ channels during maintained depolarization is called inactivation . The macroscopic K ⁺ current ( Fig. 7.5 D) shows that the gates on K ⁺ channels open more slowly than the Na ⁺ channel gates and they stay open during the remainder of the depolarization.

Voltage-gated channels exhibit voltage-dependent conductances

Permeability and conductance both provide a measure of the ease with which ions cross cell membranes ( Chapter 4 ). Conductance is the more appropriate measure of ease of ion movement when electrical measurements are used, such as with the voltage clamp. By analogy to the permeability ( P = J /Δ C ), according to Ohm’s Law ( Chapter 6 , Equation 6.1 ), conductance is the ratio between the rate of charge movement (current) and the potential difference across the membrane (i.e., g = I /Δ V ). The unit of conductance is siemens: a 1-siemen conductor passes 1 ampere of current per volt of potential difference.

Conductance can be calculated using Ohm’s Law and the Na ⁺ and K ⁺ ionic currents ( I _Na and I _K ) measured in a voltage clamp:

The V _m is known (it is controlled by the voltage clamp). E _Na and E _K can be calculated from the Nernst equation. The time courses of Na ⁺ and K ⁺ conductances ( g _Na and g _K ) at 0 mV, calculated from the currents at 0 mV using Equations 7.3 and 7.4 , are shown in Fig. 7.7 . Note that the conductances are always positive. After a brief delay, g _Na rapidly rises to a peak and then declines back toward zero, even though the membrane is still depolarized. The rising phase of the conductance is termed activation , and the declining phase is termed inactivation. The K ⁺ conductance, g _K , begins to increase (or activate) after a longer delay and rises more slowly than g _Na . After reaching a plateau, g _K remains at that level during the remainder of the depolarization (i.e., it does not inactivate).

At the molecular level, open ion channels are responsible for the conductance of the membrane, so the macroscopic conductance, g _Na or g _K , is proportional to the number of open channels:

where N _o is the number of open Na ⁺ channels and γ _Na is the conductance of a single Na ⁺ channel. If all Na ⁺ channels have the same average open probability and they behave independently of one another, it follows that

where N _T is the total number of Na ⁺ channels and p _o is the probability that a channel is open. Because N _T and γ _Na are constants, the fact that g _Na varies as a function of time (and voltage, as described later) means that the probability that a Na ⁺ channel is open must also be a function of time and voltage. The traces at the bottom of Fig. 7.7 show the probability of channel opening as a function of time during a voltage clamp step to 0 mV. The fact that Na ⁺ channels activate and then inactivate during maintained depolarization suggests that two gates are controlling the open and closed states of the channel: an activation gate and an inactivation gate.

For voltage-gated ion channels, the probability that a gate is in the open configuration depends on V _m . For Na ⁺ channels the fraction of open activation gates (i.e., p _o for the activation gate) in the steady state begins to increase at approximately −40 mV, then increases rapidly with small increments in voltage, and reaches a maximum at approximately 0 mV ( Fig. 7.8 ). This is one of the most important, fundamental properties of the voltage-gated Na ⁺ (and K ⁺ ) channels found in nerve axons and other excitable cells: the probability that a channel’s activation gate is open increases as V _m becomes more positive. The Na ⁺ channel inactivation gate has the opposite voltage dependence: as V _m is made more positive, p _o for the inactivation gate decreases ( Fig. 7.8 ). In other words, Na ⁺ channel inactivation gates close on depolarization.