An important early insight into how action potentials are generated came from an experiment performed by Kenneth Cole and Howard Curtis. While recording from the giant axon of the squid they found that ion conductance across the membrane increases dramatically during the action potential (Figure 7–1). This discovery provided the first evidence that the action potential results from changes in the flux of ions through channels in the membrane. It also raised two central questions: Which ions are responsible for the action potential, and how is the conductance of the membrane regulated?
The action potential results from an increase in ionic conductance of the axon membrane.
This historic recording from an experiment conducted in 1939 by Kenneth Cole and Howard Curtis shows the oscilloscope record of an action potential superimposed on a simultaneous record of membrane conductance.
A key insight into this problem was provided by Alan Hodgkin and Bernard Katz, who found that the amplitude of the action potential is reduced when the external Na+ concentration is lowered, indicating that Na+ influx is responsible for the rising phase of the action potential. They proposed that depolarization of the cell above threshold causes a brief increase in the cell membrane's permeability to Na+, during which Na+ permeability overwhelms the dominant K+ permeability of the resting cell membrane, thereby driving the membrane potential towards ENa. Their data also suggested that the falling phase of the action potential was caused by a later increase in K+ permeability.
Sodium and Potassium Currents Through Voltage-Gated Channels Are Recorded with the Voltage Clamp
This insight of Hodgkin and Katz raised a further question. What mechanism is responsible for regulating the changes in the Na+ and K+ permeabilities of the membrane? Hodgkin and Andrew Huxley reasoned that the Na+ and K+ permeabilities were regulated directly by the membrane voltage. To test this hypothesis they systematically varied the membrane potential in the squid giant axon and measured the resulting changes in the conductance of voltage-gated Na+ and K+ channels. To do this they made use of a new apparatus, the voltage clamp, developed by Kenneth Cole.
Prior to the availability of the voltage-clamp technique, attempts to measure Na+ and K+ conductance as a function of membrane potential had been limited by the strong interdependence of the membrane potential and the gating of Na+ and K+ channels. For example, if the membrane is depolarized sufficiently to open some of the voltage-gated Na+ channels, the influx of Na+ through these channels causes further depolarization. The additional depolarization causes still more Na+ channels to open and consequently induces more inward Na+ current:
This positive feedback cycle, which eventually drives the membrane potential to the peak of the action potential, makes it impossible to achieve a stable membrane potential. A similar coupling between current and membrane potential complicates the study of the voltage-gated K+ channels.
The voltage clamp interrupts the interaction between the membrane potential and the opening and closing of voltage-gated ion channels. It does so by adding or withdrawing a current from the axon that is equal to the current flowing through the voltage-gated membrane channels. In this way the voltage clamp prevents the membrane potential from changing. The amount of current that must be generated by the voltage clamp to keep the membrane potential constant provides a direct measure of the current flowing across the membrane (Box 7–1). Using the voltage-clamp technique, Hodgkin and Huxley provided the first complete description of the ionic mechanisms underlying the action potential.
Box 7–1 Voltage-Clamp Technique
The voltage-clamp technique was developed by Kenneth Cole in 1949 to stabilize the membrane potential of neurons for experimental purposes. It was used by Alan Hodgkin and Andrew Huxley in the early 1950s in a series of experiments that revealed the ionic mechanisms underlying the action potential.
The voltage clamp permits the experimenter to "clamp" the membrane potential at predetermined levels, preventing changes in membrane current from influencing the membrane potential. By controlling the membrane potential one can measure the effect of changes in membrane potential on the membrane's conductance of individual ion species.
The voltage clamp consists of one intracellular and extracellular pair of electrodes used to measure the membrane potential and one intracellular and extracellular pair of electrodes used to pass current across the membrane (Figure 7–2). Through the use of a negative feedback amplifier, the voltage clamp is able to pass the correct amount of current across the cell membrane to rapidly step the membrane to a constant predetermined potential.
Depolarization opens voltage-gated Na+ and K+ channels, initiating movement of Na+ and K+ across the membrane. This change in membrane current ordinarily would change the membrane potential, but the voltage clamp maintains the membrane potential at a predetermined (commanded) level.
When Na+ channels open in response to a moderate depolarizing voltage step, an inward ionic current develops because Na+ ions are driven through these channels by their electrochemical driving force. This Na+ influx would normally depolarize the membrane by increasing the positive charge on the inside of the membrane and reducing the positive charge on the outside.
The voltage clamp intervenes in this process by simultaneously withdrawing positive charges from the cell and depositing them in the external solution. By generating a current that is equal and opposite to the ionic current through the membrane, the voltage-clamp circuit automatically prevents the ionic current from changing the membrane potential from the commanded value. As a result, the net amount of charge separated by the membrane does not change and therefore no significant change in Vm can occur.
The voltage clamp is a negative feedback system. A negative feedback system is one in which the value of the output of the system (Vm in this case) is fed back as the input to a system and compared to a reference value (the command signal). Any difference between the command signal and the output signal activates a "controller" (the feedback amplifier in this case) that automatically reduces the difference. Thus the actual membrane potential automatically and precisely follows the command potential.
For example, assume that an inward Na+ current through the voltage-gated Na+ channels ordinarily causes the membrane potential to become more positive than the command potential. The input to the feedback amplifier is equal to (Vcommand – Vm). The amplifier generates an output voltage equal to this error signal multiplied by the gain of the amplifier. Thus, both the input and the resulting output voltage at the feedback amplifier will be negative.
This negative output voltage will make the internal current electrode negative, withdrawing net positive charge from the cell through the voltage-clamp circuit. As the current flows around the circuit, an equal amount of net positive charge will be deposited into the external solution through the other current electrode.
A refinement of the voltage clamp, the patch-clamp technique, allows the functional properties of single ion channels to be analyzed (see Box 5–1).
The negative feedback mechanism of the voltage clamp.
Membrane potential (Vm) is measured by one amplifier connected to an intracellular electrode and an extracellular electrode in the bath. The membrane potential signal is displayed on an oscilloscope and is also fed into the negative terminal of the voltage-clamp feedback amplifier. The command potential, which is selected by the experimenter and can be of any desired amplitude and waveform, is fed into the positive terminal of the feedback amplifier. The feedback amplifier then subtracts the membrane potential from the command potential and amplifies any difference between these two signals. The voltage output of the amplifier is connected to the internal current electrode, a thin wire that runs the length of the axon core. The negative feedback ensures that the voltage output of the amplifier drives a current across the resistance of the current electrode that alters the membrane voltage to minimize any difference between Vm and the command potential. To accurately measure the current-voltage relationship of the cell membrane, the membrane potential must be uniform along the entire surface of the axon. This is made possible by the highly conductive internal current electrode, which short-circuits the axoplasmic resistance, reducing axial resistance to zero (see Chapter 6). This low-resistance pathway eliminates all variations in electrical potential along the axon core.
One advantage of the voltage clamp is that it readily allows the ionic and capacitive components of membrane current to be analyzed separately. As described in Chapter 6, the membrane potential Vm is proportional to the charge Qm on the membrane capacitance Cm. When Vm is not changing, Qm is constant, and no capacitive current (ΔQm / Δt) flows. Capacitive current flows only when Vm is changing. Therefore when the membrane potential changes in response to a very rapid step of command potential, capacitive current flows only at the beginning and end of the step. Because the capacitive current is essentially instantaneous, the ionic currents that subsequently flow through the voltage-gated channels can be analyzed separately.
Measurements of these ionic currents can be used to calculate the voltage and time dependence of changes in membrane conductance caused by the opening and closing of Na+ and K+ channels. This information provides insights into the properties of these two types of channels.
A typical voltage-clamp experiment starts with the membrane potential clamped at its resting value. When a 10 mV depolarizing step is applied, a very brief outward current instantaneously discharges the membrane capacitance by the amount required for a 10 mV depolarization. This capacitive current (Ic) is followed by a smaller outward current that persists for the duration of the voltage step. This steady ionic current flows through the nongated resting ion channels of the membrane, which we refer to here as leakage channels (see Box 6–2). The current through these channels is called the leakage current, Il. The total conductance of this population of channels is called the leakage conductance (gl). At the end of the step a brief inward capacitive current repolarizes the membrane to its initial voltage and the total membrane current returns to zero (Figure 7–3A).
A voltage-clamp experiment demonstrates the sequential activation of two types of voltage-gated channels.
A. A small depolarization (10 mV) elicits capacitive and leakage currents (Ic and Il, respectively), the components of the total membrane current (Im).
B. A larger depolarization (60 mV) results in larger capacitive and leakage currents, plus a time-dependent inward ionic current followed by a time-dependent outward ionic current.
Top: Total (net) current in response to the depolarization. Middle: Individual Na+ and K+ currents. Depolarizing the cell in the presence of tetrodotoxin (TTX), which blocks the Na+ current, or in the presence of tetraethylammonium (TEA), which blocks the K+ current, reveals the pure K+ and Na+ currents (IK and INa, respectively) after subtracting Ic and Il. Bottom: Voltage step.
If a large depolarizing step is commanded, the current record is more complicated. The capacitive and leakage currents both increase in amplitude. In addition, shortly after the end of the capacitive current and the start of the leakage current, an inward (negative) current develops; it reaches a peak within a few milliseconds, declines, and gives way to an outward current. This outward current reaches a plateau that is maintained for the duration of the voltage step (Figure 7–3B).
A simple interpretation of these results is that the depolarizing voltage step sequentially turns on two types of voltage-gated channels that select for two distinct ions. One type of channel conducts ions that generate an inward current, while the other conducts ions that generate an outward current. Because these two oppositely directed currents partially overlap in time, the most difficult task in analyzing voltage-clamp experiments is to determine their separate time courses.
Hodgkin and Huxley achieved this separation by changing ions in the bathing solution. By replacing Na+ with a larger, impermeant cation (choline · H+), they eliminated the inward Na+ current. Later, the task of separating inward and outward currents was made easier by the discovery of drugs or toxins that selectively block the different classes of voltage-gated channels (Figure 7–4). Tetrodotoxin, a poison from a certain Pacific puffer fish, blocks the voltage-gated Na+ channel with a very high potency in the nanomolar range of concentration. (Ingestion of only a few milligrams of tetrodotoxin from improperly prepared puffer fish, consumed as the Japanese sushi delicacy fugu, can be fatal.) The cation tetraethylammonium specifically blocks the squid axon voltage-gated K+ channel.
Drugs that block voltage-gated Na+ and K+ channels.
A. Tetrodotoxin and saxitoxin both bind to Na+ channels with a very high affinity. Tetrodotoxin is produced by certain puffer fish, newts, and frogs. Saxitoxin is synthesized by the dinoflagellates Gonyaulax, which are responsible for red tides. Consumption of clams or other shellfish that have fed on the dinoflagellates during a red tide causes paralytic shellfish poisoning.
B. Tetraethylammonium is a cation that blocks certain voltage-gated K+ channels with a relatively low affinity. The plus signs represent positive charge. 4-Aminopyridine is another blocker of K+ channels. It is used to improve conduction of nerve impulses in patients with multiple sclerosis.
When tetraethylammonium is applied to the axon to block the K+ channels, the total membrane current (Im) consists of Ic, Il, and INa. The leakage conductance, gl, is constant; it does not vary with Vm or with time. Therefore the leakage current Il can be readily calculated and subtracted from Im, leaving INa and Ic. Because Ic occurs only briefly at the beginning and end of the pulse, it is easily isolated by visual inspection, revealing the pure INa. Similarly, IK can be measured when the Na+ channels are blocked by tetrodotoxin (Figure 7–3B).
By stepping the membrane to a wide range of potentials, Hodgkin and Huxley were able to measure the Na+ and K+ currents over the entire voltage extent of the action potential (Figure 7–5). They found that the Na+ and K+ currents vary as a graded function of the membrane potential. As the membrane voltage is made more positive, the outward K+ current becomes larger. The inward Na+ current also becomes larger with increases in depolarization, up to a certain extent. However, as the voltage becomes more and more positive, the Na+ current eventually declines in amplitude. When the membrane potential is +55 mV, the Na+ current is zero. Positive to +55 mV, the Na+ current reverses direction and becomes outward.
The magnitude and polarity of the Na+ and K+ membrane currents vary with the amplitude of membrane depolarization. Left:
With progressive depolarization the voltage-clamped membrane K+ current increases monotonically, because both gK and (Vm − EK), the driving force for K+, increase with increasing depolarization. The voltage during the depolarization is indicated at left. The direction and magnitude of the chemical (EK) and electrical driving force on K+, as well as the net driving force, is given by arrows at the right of each trace. (Up arrows = outward force; down arrows = inward force.) Right: At first the Na+ current becomes increasingly inward with increasing depolarization due to the increase in gNa. However, as the membrane potential approaches ENa (+55 mV) the magnitude of the inward Na+ current begins to decrease due to the decrease in inward driving force (Vm − ENa). Eventually, INa goes to zero when the membrane potential reaches ENa. At depolarizations positive to ENa, the sign of (Vm– ENa) reverses, and INa becomes outward. Arrows at the right of each trace show chemical (ENa) and electrical driving forces and net Na+ driving force.
Hodgkin and Huxley explained this behavior by a very simple model in which the size of the Na+ and K+ currents is determined by two factors. The first is the magnitude of the Na+ or K+ conductance, gNa or gK, which reflects the number of Na+ or K+ channels open at any instant (see Chapter 6). The second factor is the electrochemical driving force on Na+ ions (Vm − ENa) or K+ ions (Vm − EK). The model is thus expressed as:
According to this model the amplitudes of INa and IK change as the voltage is made more positive because there is an increase in gNa and gK. The Na+ and K+ conductances increase because the opening of the Na+ and K+ channels is voltage-dependent. The currents also change in response to changes in the electrochemical driving forces.
Both INa and IK initially increase in amplitude as the membrane is made more positive because gNa and gK increase steeply with voltage. However, as the membrane potential approaches ENa (+55 mV), INa declines because of the decrease in inward driving force, even though gNa is large. That is, the positive membrane voltage now opposes the influx of Na+ down its chemical concentration gradient. At +55 mV the chemical and electrical driving forces are in balance so there is no net INa, even though gNa is quite large. As the membrane is made positive to ENa, the driving force on Na+ becomes positive. That is, the electrical driving force pushing Na+ out is now greater than the chemical driving force pulling Na+ in, and hence INa becomes outward. The behavior of IK is simpler; because EK is quite negative (−75 mV), both gK and the outward driving force on K+ become larger as the membrane is made more positive, thereby increasing the outward K+ current.
Voltage-Gated Sodium and Potassium Conductances Are Calculated from Their Currents
From the two preceding equations Hodgkin and Huxley were able to calculate gNa and gK by dividing measured Na+ and K+ currents by the known Na+ and K+ electrochemical driving forces. Their results provide direct insight into how membrane voltage controls channel opening because the values of gNa and gK reflect the number of open Na+ and K+ channels (Box 7–2).
Box 7–2 Calculation of Membrane Conductances from Voltage-Clamp Data
Membrane conductances can be calculated from voltage-clamp currents using equations derived from an equivalent circuit (Figure 7–6) that includes the membrane capacitance (Cm); the leakage conductance (gl), representing the conductance of all of the resting (nongated) K+, Na+, and Cl– channels (see Chapter 6); and gNa and gK, the conductances of the voltage-gated Na+ and K+ channels.
In the equivalent circuit the ionic battery of the leakage channels, El, is equal to the resting membrane potential, and gNa and gK are in series with their appropriate ionic batteries.
The current through each class of voltage-gated channel may be calculated from a modified version of Ohm's law that takes into account both the electrical (Vm) and chemical (ENa or EK) driving forces on Na+ and K+:
IK = gK(Vm − EK)
INa = gNa(Vm − ENa).
Rearranging and solving for g gives two equations that can be used to compute the conductances of the active Na+ and K+ channel populations:
In these equations the independent variable Vm is set by the experimenter. The dependent variables IK and INa can be calculated from the records of voltage-clamp experiments (see Figure 7–5). The parameters EK and ENa can be determined empirically by finding the values of Vm at which IK and INa reverse their polarities, that is, their reversal potentials.
Equivalent circuit of a voltage-clamped neuron.
The voltage-gated conductance pathways (gK and gNa) are represented by the symbol for a variable conductance —a conductor (resistor) with an arrow through it. The conductance is variable because of its dependence on time and voltage. These conductances are in series with batteries representing the chemical gradients for Na+ and K+. In addition there are parallel pathways for leakage current (gl and El) and capacitative current (Cm). Arrows indicate current flow during a depolarizing step that has activated gK and gNa.
Measurements of gNa and gK at various levels of membrane potential reveal two functional similarities and two differences between the Na+ and K+ channels. Both types of channels open in response to depolarization. Also, as the size of the depolarization increases, the probability and rate of opening increase for both types of channels. The Na+ and K+ channels differ, however, in the rate at which they open and in their responses to prolonged depolarization. At all levels of depolarization the Na+ channels open more rapidly than K+ channels (Figure 7–7). When the depolarization is maintained for some time, the Na+ channels begin to close, leading to a decrease of inward current. The process by which Na+ channels close during a prolonged depolarization is termed inactivation.
The responses of K+ and Na+ channels to prolonged depolarization.
Increasing depolarizations elicit graded increases in K+ and Na+ conductance (gNa and gK), which reflect the proportional opening of thousands of voltage-gated K+ and Na+ channels. The Na+ channels open more rapidly than the K+ channels. During a maintained depolarization the Na+ channels close after opening because of the closure of an inactivation gate. The K+ channels remain open because they lack a fast inactivation process.
Thus depolarization causes Na+ channels to switch between three different states —resting, activated, or inactivated —which represent three different conformations of the Na+ channel protein (see Figure 5–7). In contrast, squid axon K+ channels do not inactivate; they remain open as long as the membrane is depolarized, at least for voltage-clamp depolarizations lasting up to tens of milliseconds (Figure 7–7).
In the inactivated state the Na+ channel cannot be opened by further membrane depolarization. The inactivation can be reversed only by repolarizing the membrane to its negative resting potential, whereupon the channel switches to the resting state. This switch takes some time because channels leave the inactivated state relatively slowly (Figure 7–8).
Sodium channels remain inactivated for a few milliseconds after a depolarizing current.
If the interval (Δt) between two depolarizing pulses (P1 and P2) is brief, the second pulse produces a smaller increase in gNa because many of the Na+ channels remain inactivated after the first pulse. The longer the interval between pulses, the greater the increase in gNa during the second pulse, because a greater fraction of channels will have recovered from inactivation during the period of repolarization and returned to the resting state when the second pulse begins. The time course of recovery from inactivation following repolarization contributes to determining the time course of the refractory period of an action potential.
These variable, time-dependent effects of depolarization on gNa are determined by the kinetics of two gating mechanisms in Na+ channels. Each Na+ channel has an activation gate that is closed while the membrane is at the resting potential and opened by depolarization. An inactivation gate is open at the resting potential and closes after the channel opens in response to depolarization. The channel conducts Na+ only for the brief period during depolarization when both gates are open (Figure 7–9). Repolarization reverses the two processes, closing the activation gate and then opening the inactivation gate.
Voltage-gated Na+ channels have two gates that respond in opposite ways to depolarization.
In the resting state the activation gate is closed and the inactivation gate is open (1). A depolarizing stimulus results in opening of the activation gate, allowing Na+ to flow through the channel, followed by closing of the inactivation gate (2). Once the inactivation gate has closed, the channel enters the inactivated state (3). On repolarization the inactivation gate opens and the activation gate closes as the channel returns to the resting state (1). The channel is only open during the brief period when both the activation and inactivation gates are open (2).
The Action Potential Can Be Reconstructed from the Properties of Sodium and Potassium Channels
Hodgkin and Huxley were able to fit their measurements of membrane conductance to a set of empirical equations that completely describe the Na+ and K+ conductances as a function of membrane potential and time. Using these equations and measured values for the passive properties of the axon, they computed the shape and conduction velocity of the action potential.
The calculated waveform of the action potential matched the waveform recorded in the unclamped axon almost perfectly. This close agreement indicates that the mathematical model developed by Hodgkin and Huxley accurately describes the properties of the channels that are essential for generating and propagating the action potential. More than a half-century later the Hodgkin-Huxley model stands as the most successful quantitative model in neural science if not in all of biology.
According to the Hodgkin-Huxley model an action potential involves the following sequence of events. Depolarization of the membrane causes Na+ channels to open rapidly (an increase in gNa), resulting in an inward Na+ current. This current, by discharging the membrane capacitance, causes further depolarization, thereby opening more Na+ channels, resulting in a further increase in inward current. This regenerative process drives the membrane potential toward ENa, causing the rising phase of the action potential.2 The depolarization limits the duration of the action potential in two ways: (1) It gradually inactivates the voltage-gated Na+ channels, thus reducing gNa, and (2) it opens, with some delay, the voltage-gated K+ channels, thereby increasing gK. Consequently, the inward Na+ current is followed by an outward K+ current that tends to repolarize the membrane (Figure 7–10).
The sequential opening of voltage-gated Na+ and K+ channels generates the action potential.
One of Hodgkin and Huxley's great achievements was to dissect the change in conductance during an action potential into separate components attributable to the opening of Na+ and K+ channels. The shape of the action potential and the underlying conductance changes can be calculated from the properties of the voltage-gated Na+ and K+ channels. (Adapted, with permission, from Hodgkin and Huxley 1952.)
In most nerve cells the action potential is followed by a hyperpolarizing after-potential, a transient shift of the membrane potential to values more negative than the resting potential. This brief negative change in Vm occurs because the K+ channels that open during the repolarizing phase of the action potential remain open for some time after Vm has returned to its resting value. It takes a few milliseconds for all of the K+ channels to return to the closed state. During this time, when the permeability of the membrane to K+ is greater than during the resting state, Vm is slightly greater (more negative) than its normal resting value, resulting in a Vm closer to EK (Figure 7–10).
The combined effect of this transient increase in K+ conductance and the residual inactivation of the Na+ channels (see Figure 7–10) underlies the absolute refractory period, the brief period of time following an action potential when it is impossible to elicit another action potential. As some K+ channels begin to close and some Na+ channels recover from inactivation, the membrane enters the relative refractory period, during which it is possible to trigger an action potential, but only by applying stimuli that are stronger than those normally required to reach threshold. Together, these refractory periods typically last just 5–10 ms.
Two features of the action potential predicted by the Hodgkin-Huxley model are its threshold and all-or-none behavior. A fraction of a millivolt can be the difference between a subthreshold stimulus and a stimulus that generates a full-sized action potential. This all-or-none phenomenon may seem surprising when one considers that gNa increases in a strictly graded manner as depolarization increases (see Figure 7–7). Each increment of depolarization increases the number of voltage-gated Na+ channels that open, thereby gradually increasing INa. How then can there be a discrete threshold for generating an action potential?
Although a small subthreshold depolarization increases the inward INa, it also increases two outward currents, IK and Il, by increasing the electrochemical driving forces acting on K+ and Cl–. In addition, the depolarization augments gK by gradually opening more voltage-gated K+ channels (Figure 7–7). As the outward IK and Il increase with depolarization they repolarize the membrane and resist the depolarizing action of the Na+ influx. However, because of the high voltage sensitivity and more rapid kinetics of activation of the Na+ channels, the depolarization eventually reaches a point where the increase in inward INa exceeds the increase in outward IK and Il. At this point there is a net inward ionic current. This produces a further depolarization, opening even more Na+ channels, so that the depolarization becomes regenerative, driving the membrane potential all the way to the peak of the action potential. The specific value of Vm at which the net ionic current (INa + IK + Il) just changes from outward to inward, depositing a net positive charge on the inside of the membrane capacitance, is the threshold.