Axonal Na ⁺ Channels

These membrane-spanning protein molecules contain a pore through which Na ⁺ ions can diffuse almost freely in the open state. In myelinated axons from peripheral nerve, voltage-sensitive Na ⁺ channels are clustered at high densities (up to 1,000/μm ) in the nodal axon, compared to the internodal region (25/μm ). The high density of Na ⁺ channels at the node reflects the need of saltatory conduction for a large inward current at the node ( Fig. 15-1 ).

Saltatory conduction (upper panel) is dependent on the specialized structure of the axonal membrane (lower panel). Different channels are distributed unevenly along the axonal membrane; sodium (Na ⁺ ) channels are found in high concentrations at the node, as are slow potassium (K ⁺ ) channels (Ks). Fast potassium channels (Kf) are almost exclusively paranodal. Inward rectifier channels ( I _H ), permeable to both K ⁺ and Na ⁺ ions, act to limit axonal hyperpolarization, whereas the Na ⁺ /K ⁺ pump serves to reverse ionic fluxes that may be generated through activity. Two classes of Na ⁺ channels are found at the node: transient (Na _t ) and persistent channels (Na _p ). Under physiologic conditions, the Na ⁺ –Ca ²⁺ exchanger assists in the restoration of the membrane potential by extruding Na ⁺ and Ca ²⁺ ions. The action potential is terminated by closure of the Na _t with the Na ⁺ /K ⁺ pump restoring the resting membrane potential by extruding 3 Na ⁺ ions for 2 K ⁺ ions.

When the nodal membrane is depolarized, an inward current is established, carried by Na ⁺ ions. This current is voltage-sensitive and regenerative; it increases with depolarization, and this in turn leads to depolarization of the next node. This potentially explosive process would end with the whole axon becoming depolarized, were it not for the fact that Na ⁺ channels immediately start closing again, due to channel inactivation.

Two functionally distinct types of Na ⁺ current can be distinguished. Classic transient Na ⁺ conductances account for about 98 percent of the total current . Persistent or non-inactivating Na ⁺ current is activated equally rapidly but at membrane potentials that are up to 20 mV more negative. At the most negative potentials over which these conductances operate, inactivation is minimal, giving rise to a persistent inward leak of Na ⁺ ions at resting potential, a potentially destabilizing property. This non-inactivating Na ⁺ current appears to have a greater expression in sensory axons than motor axons, likely to underlie the greater susceptibility for sensory nerves to become spontaneously active when damaged or diseased, leading to the sensation of paresthesias, dysesthesias, and pain.

Axonal K ⁺ Channels

Discussion of K ⁺ channels similarly may be simplified based on channel kinetics. Fast K ⁺ channels, found almost exclusively in the paranodal region, are responsible for limiting the re-excitation of the node that occurs following conduction of an action potential. Blockade of these channels by 4-aminopyridine, a treatment used to counter fatigue and weakness in patients with demyelinating neurologic diseases such as multiple sclerosis, may result in patients experiencing paresthesias as a result of removing the stabilizing influence of fast K ⁺ channels.

In contrast, slow K ⁺ channels are found in high density at the node. This nodal localization has been inferred from studies using tetraethylammonium, a selective K ⁺ channel blocker. Although slow K ⁺ channels are present at the node, they are not responsible for repolarization after conduction of single action potentials because of their slow activation time. However, these channels are open at resting membrane potential and so may contribute to its maintenance, whilst also acting to limit repetitive firing.

Inward Rectification ( I _h )

In addition to conventional K ⁺ channels, axons possess inwardly rectifying channels, permeable to K ⁺ ions and Na ⁺ ions. Inward rectification is widespread in excitable cells and is the basis, for instance, of cardiac rhythmicity, and consequently is referred to as the pacemaker current. This conductance is activated by membrane hyperpolarization, and attempts to limit excessive hyperpolarization. It seems likely that this conductance functions to maintain impulse transmission when the axon is hyperpolarized, as may occur following conduction of trains of impulses.

Axonal Na ⁺ /K ⁺ Pump

The Na ⁺ /K ⁺ pump, termed electrogenic because it generates a net outward flow of cations, is present on the axonal membrane. As initially demonstrated by Hodgkin and Huxley, the electrogenic Na ⁺ /K ⁺ pump drives three Na ⁺ ions out in exchange for two K ⁺ ions pumped in, with the process requiring metabolic energy from the hydrolysis of adenosine triphosphate. As the coupling ratio for Na ⁺ /K ⁺ exchange is unequal, a transmembrane current is produced by the operation of the pump. At rest and during activity, Na ⁺ ions enter the cell and K ⁺ ions leave by flowing down their concentration gradients. The axonal membrane Na ⁺ /K ⁺ pump may serve to reverse these fluxes and so maintain transmembrane ionic gradients. The role of restoring gradients of Na ⁺ and K ⁺ in axons is of particular importance following high-frequency impulse activity. The pump also participates in the regulation of the resting membrane potential. When the pump is blocked by cooling or application of a specific blocking agent such as ouabain or digitalis, the result is membrane depolarization.

Stimulus–Response Curve

Excitability testing is determined essentially by the stimulus–response properties of the axon. As the stimulus intensity increases, the size of the compound action potential will increase until it reaches a maximum peak response ( Fig. 15-2 ). Subsequently, the amount required to change the stimulus, following a change in the response, then can be predicted from the response error (i.e., the difference between the actual and target responses) and the slope of the stimulus–response curve (see Fig. 15-2 ). Therefore the stimulus–response relationship is integral in setting the target submaximal response (i.e., the steepest part of the curve) for threshold tracking, and the slope of this relationship then may be used in conjunction with the tracking error to optimize the subsequent threshold tracking.

Stimulus–response behavior of the axonal membrane: derivation of the stimulus–response curve, with the stimulus pattern depicted on the left. Middle: Stimulus–response curve plotted as the current required to achieve peak response. The responses to hyperpolarization are shifted to the right (higher stimulus strength), and with depolarization are shifted to the left (lower stimulus intensity).

Strength–Duration Properties

As the duration of a test stimulus increases, the strength of the current required to activate a single fiber or a specified fraction of a compound action potential decreases. Strength–duration time constant (or chronaxie) and rheobase are parameters that describe the strength–duration curve, i.e., the curve that relates the intensity of a threshold stimulus to its duration. Strength–duration time constant (SDTC) is an apparent membrane time constant inferred from the relationship between threshold current and stimulus duration, and provides a measure of the rate at which threshold current increases as the duration of the test stimulus is reduced to zero. In human peripheral nerve, the strength–duration relationship is described remarkably well by Weiss’s empirical law:

Weiss’s formula is used widely to calculate SDTC. In this formulation, SDTC equates to chronaxie (the stimulus duration corresponding to a threshold current that is twice rheobase). Rheobase is the threshold current (or estimated threshold current in mA) required if the stimulus is of infinitely long duration. Because there is a linear relationship between stimulus charge and stimulus duration, rheobase and SDTC can be calculated from a charge–stimulus duration plot with four different stimulus widths (0.2, 0.4, 0.8, and 1 msec). SDTC is derived from the x-intercept of the straight line fitted to the points representing different stimulus widths, whereby the slope of this relationship equates to the rheobase ( Fig. 15-3 ). Rheobase and SDTC are both properties of the nodal membrane. SDTC averages 0.46 msec in human motor axons and 0.67 msec in sensory axons of peripheral nerve. These values are much longer than the passive time constant of the nodes of Ranvier (approximately 50 μsec) because the effects of subthreshold current pulses are prolonged by the local response of low threshold Na ⁺ channels, particularly by persistent Na ⁺ channels. These channels are also important in determining repetitive and spontaneous activity, and this is the reason that SDTC is a clinically important excitability parameter.

Strength–duration properties derived from plots of stimulus strength versus stimulus duration, illustrating rheobase as the threshold current required for a stimulus of infinite duration, and chronaxie as the stimulus duration at which the threshold current is twice rheobase (left). Plot of threshold charge versus stimulus width, illustrating the determination of strength–duration time constant using Weiss’s Law (middle). Strength–duration time constant can be determined as the negative intercept on the x-axis of the line determined by only two stimulus widths.

Recovery Cycle of Excitability

Following conduction of a single nerve impulse, an axon undergoes a well-characterized and reproducible sequence of excitability changes before returning to its resting state, a process termed the recovery cycle ( Fig. 15-4 ). Initially, there is an absolute refractory period during which the axon is completely inexcitable and a propagated action potential cannot be generated, regardless of the strength of the stimulus. Subsequently, the axon becomes relatively refractory , during which period an action potential may be generated, but only if a stronger than normal stimulus is used. In human large myelinated axons the relative refractory period (RRP) is generally short, lasting less than 3 msec in most human studies. Adrian and Lucas in 1912 first observed that, following the relative refractory period, axons become excited more easily ( superexcitable period ) and also conduct impulses at a greater velocity than in the resting state. Following the superexcitable period, there is an additional period of decreased excitability ( subexcitable period ), before membrane potential settles back to its resting state.

The recovery cycle of excitability: stimulus patterns utilized to generate the recovery cycle waveforms (left) numbered to correspond to the relevant points on the recovery cycle curve. Recovery cycle plot illustrating the relative refractory period, superexcitability and subexcitability.

The mechanisms responsible for both the absolute and relative refractory periods are now well established; absolute refractoriness is due to inactivation of transient Na ⁺ channels, and the RRP is due to the gradual recovery of Na ⁺ channels from inactivation. The RRP increases with membrane depolarization and decreases with membrane hyperpolarization. Because of its sensitivity to polarization, refractoriness can be used as an indicator of membrane potential. However, the RRP is also sensitive to temperature and may be prolonged by cooling because of slowed channel kinetics at lower temperatures.

Superexcitability is due to a depolarizing afterpotential. During the action potential, there is a large influx of Na ⁺ ions at the node, which is not offset by an equal efflux of K ⁺ ions, so the axon as a whole is left with a net depolarizing charge, spread over nodal and internodal axolemma. During the action potential, the node depolarizes the internode, as the internode helps repolarize the node, both ending depolarized by a few millivolts. After the action potential, the large capacitance of the internode enables it to keep the node depolarized for tens of milliseconds. In myelinated axons, the superexcitability is strongly dependent on membrane potential; background depolarization reduces Na ⁺ influx and increases K ⁺ efflux, thus reducing the charge imbalance during the action potential; also, the opening of paranodal and internodal K ⁺ channels at rest short-circuits the afterpotential and reduces its duration. Conversely, hyperpolarization increases and prolongs the depolarizing afterpotential and superexcitability. Superexcitability therefore can also be used as an indicator of membrane potential.

Finally, the long-lasting phase of late subexcitability reflects hyperpolarization of the membrane potential, due to current through slow K ⁺ channels at the nodes of Ranvier. The channels are activated during the action potential (and also during the depolarizing afterpotential) and deactivate slowly. If an axon conducts a brief train of impulses, this late subexcitability becomes accentuated, producing the H ₁ phase of activity-dependent hypoexcitability, a hyperpolarization that therefore is also due to nodal slow K ⁺ channels. Late subexcitability is not simply sensitive to resting membrane potential ( E _R ), but to the electrochemical gradient for K ⁺ ions, i.e., to the difference between E _R and the potassium equilibrium potential ( E _K ), which is normally on the hyperpolarized side of E _R . This means that if axons are depolarized by polarizing currents (i.e., without changing E _K ), then the electrochemical gradient for K ⁺ ions is increased and subexcitability is increased. On the other hand, if axons are depolarized by raising extracellular K ⁺ , as occurs during ischemia, E _K is depolarized towards or beyond E _R , and late subexcitability is abolished. Late subexcitability is therefore not such a good indicator of membrane potential as superexcitability, but it can provide information about extracellular K ⁺ levels.

Threshold Electrotonus

Changes in potential of the nodal membrane spread into the internode, but slowly because of the resistance of the myelin sheath and consequently the slow charging of the internodal capacitance. This process results in slow activation and deactivation of voltage-dependent channels on the internodal membrane. Although Na ⁺ channel density is insufficient for the internodal membrane to generate an action potential, the changes in resistance of the internodal membrane and in the current stored on it will affect the behaviour of the node.

The only physiologic method available to examine the behavior of internodal conductances in living patients is the technique of threshold electrotonus (TE) ( Fig. 15-5 ). The term electrotonus refers to changes in membrane potential evoked by subthreshold depolarizing or hyperpolarizing current pulses. The technique of threshold electrotonus measures the threshold changes produced by prolonged depolarizing or hyperpolarizing currents, which are too weak to trigger action potentials (subthreshold currents). The term threshold electrotonus reflects the fact that, under most circumstances, the threshold changes parallel the underlying electrotonic changes in membrane potential. The changes in threshold were produced by 100-msec polarizing currents with intensities set to 40 percent of the unconditioned threshold, using 1-msec test pulses. In contrast to the recovery cycle, threshold changes conventionally are plotted as threshold reductions, with depolarizing responses upwards, to match the conventional way of plotting changes in membrane potential induced by such currents (i.e., electrotonus).

The current utilized to produce the threshold electrotonus waveform, with numbered bars reflecting the corresponding points on the threshold electrotonus curve (left panel). Threshold electrotonus waveform (depolarizing direction plotted upwards, hyperpolarizing direction plotted downwards) illustrating the response of the axon to 100 msec subthreshold polarizing currents (± 40 percent of threshold). Fast (F) phases in response to initial polarization and slow (S1) phases due to the gradual spread of current into the internode are indicated on the figure.

There are different phases of threshold electrotonus. In response to depolarizing current pulses, there is an initial fast phase that corresponds to the applied current (the “F” phase). A polarizing current 40 percent of threshold unsurprisingly reduces threshold by 40 percent. This is followed by further depolarization that develops slowly over some tens of milliseconds, measured as TEd (10 to 20 msec), as the current spreads to and depolarizes the internodal membrane (the “S1” phase). The threshold decrease (i.e., the extent of depolarization) reaches a peak—TEd(peak)—about 20 msec after the onset of the current pulses, dependent on its strength, and threshold then starts to return slowly towards the control level, TEd (90 to 100 msec ) . This reduction in excitability is termed S2 accommodation , and is due to activation of a hyperpolarizing conductance with slow kinetics. The use of K ⁺ channel blocking agents indicates that the slow accommodative process is due to activation of slow K ⁺ channels, which are located on both the node and the internode. When the direct-current (DC) pulse is terminated, threshold increases rapidly and there is then a slow undershoot—TEd(undershoot)—before it gradually recovers to control level. This is due to persistence of the increase in slow K ⁺ conductance, which deactivates slowly.

With long-lasting hyperpolarizing DC pulses, there is a fast increase in threshold, proportional to the applied current, and analogous to the comparable phase with depolarizing currents (the “F” phase). Then threshold continues to increase as the hyperpolarizing spreads to the internode: TEh(10 to 20 msec). This “S1” phase starts as a mirror image of the S1 phase with depolarizing current but soon diverges, because hyperpolarization closes K ⁺ channels (slow nodal, and fast and slow internodal K ⁺ channels), and this increases the amplitude and time constant of S1, the TEh(90 to 100 ms). On termination of the hyperpolarizing DC pulses, threshold rapidly decreases and then undergoes a slow, depolarizing overshoot—the TEh(overshoot) —as I _H slowly deactivates and the slow K ⁺ conductance is reactivated.

Current–Voltage Relationship and Slope

Just as the activation of different voltage-dependent channels in a cell can be identified by plotting a current–voltage ( I/V ) relationship, it can be convenient to plot the threshold changes at the ends of a series of long current pulses (i.e., 200-msec) of different amplitudes as a current–threshold relationship. This is done conventionally with threshold increase (hyperpolarization) to the left, threshold decrease (depolarization) to the right, depolarizing current to the top and hyperpolarizing current to the bottom, to correspond to a conventional I/V plot. This current–threshold relationship therefore reflects the rectifying properties of the axon (both nodal and internodal axolemma).

Outward rectification due to K ⁺ channel activation causes a steepening of the curve in the top right quadrant, and the steepening of the relationship in the bottom left quadrant indicates inward rectification due to activation of I _H . The slope (i.e., hyperpolarizing I/V slope) of this curve can be used to provide an estimate of the threshold analog of input conductance ( Fig. 15-6 ). The two parameters, resting I/V slope and minimum I/V slope, are derived from the current – threshold plot. If I/V slope is shifted to the left, the threshold analog of the conductance changes to more negative potentials, consistent with axonal depolarization.

Stimulus pattern required to generate the current–voltage relationship (left). The currents utilized to produce the current–voltage relationship represent 200 msec polarizing stimuli, ranging from +50 to −100 percent of threshold current. The current–voltage relationship, with response to depolarizing current depicted in the upper right quadrant and response to hyperpolarizing current in the lower left quadrant (middle). Outward rectification shifts the upper curve to the left, related to the activity of K ⁺ channels. Inward rectification occurs in response to hyperpolarization, related to the activity of the cation conductance I _H and shifting the lower curve to the right.