Normal and Pathological Roles of K Channels in Myelinated Axons

1. Overview of K Channel Function in Axonal Tree

Between the neuronal cell soma and the nerve terminals lies a complex morphological landscape, commonly referred to as the axonal tree, that an action potential has to navigate to reach the nerve terminal (Fig. 2) (Waxman, 1972). The bulk of the journey for an action potential takes place along monotonous cables designed in a rushtonian fashion optimized geometrically for conduction velocity (Rushton, 1951). However, the axonal tree is capable of signal integration through differential routing and frequency modulation as action potentials pass through branch points and local variation in geometry collectively referred to as transition zones (Fig. 2) (Swadlow et al., 1980; Waxman, 1972). How might axonal K channels modulate nerve signaling in this complex axonal tree? Are K channels more important in transition zones than in the rest of the axons? Do specific types of axonal Kv channels subserve different functions? In this chapter, we focus on the juxtaparanodal Kv1.1, as the availability of various Kv1.1 mutants has made this axonal channel the best characterized in terms of functions in myelinated axons. As discussed in great detail later, a major conclusion of physiological analysis of Kv1 mutants is that juxtaparanodal Kv1 channels play an important role in stabilizing transition zones in an axonal tree. Before going into functional issues, we first discuss the nature of transition zones.

2. Transition Zones

Transition zones in general refer to the regions in an axonal tree where there is a local change in geometry because of certain functional requirements. Important examples are the branch points or the nerve terminal region where the myelinated segment ends and the nonmyelinated segment begins (Fig. 2). The safety factor for nerve conduction is altered at these sites as a result of impedance mismatch. Impedance mis-matching is normally minimized by local variation in fiber geometry. For example, the internodes shorten as the nerve terminal is approached (Fig. 2, arrow) (Quick et al., 1979), and this has been shown theoretically to facilitate invasion of the nerve terminal (Khodorov and Timin, 1975). In pathological situations, remyelination proceeds by forming short internodes preceding lesion sites, providing impedance matching that contributes to successful propagation (Waxman and Brill, 1978).

Other variations in local fiber geometry may also prove important. First, postbranching internodes are significantly smaller than the rest of the fiber (Pfeiffer and Friede, 1985). Second, in dorsal root ganglion (DRG) neurons, the first internode after the initial segment has an unusually thin myelin sheath (Spencer et al., 1973). At the branch point of DRG neurons, the caliber of the CNS-directed axon is different than the PNS-directed axon (Spencer et al., 1973).

Figure 2 Schematic drawing of an axonal tree. Arrows show presynaptic shortening of internodes. Existing immunohistochemistry suggests that Kv1.1 is present at the juxtaparanodes, but absent from the nerve terminals (Brew et al., 2003; Zhou et al., 1998). The major function of juxtaparanodal Kv1.1 is to stabilize transition zones (branch points and presynaptic regions) in the axonal tree. (Modified after Waxman, 1972, with permission.)

Figure 2 Schematic drawing of an axonal tree. Arrows show presynaptic shortening of internodes. Existing immunohistochemistry suggests that Kv1.1 is present at the juxtaparanodes, but absent from the nerve terminals (Brew et al., 2003; Zhou et al., 1998). The major function of juxtaparanodal Kv1.1 is to stabilize transition zones (branch points and presynaptic regions) in the axonal tree. (Modified after Waxman, 1972, with permission.)

Third, action potentials could fail at branch points, and frequency-dependent failures at branch points could act as safety measures to prevent an injurious level of axonal activity from permeating other regions of the axonal tree. Collectively, transition zone excitability has profound implications for signal integration in normal and pathological axonal trees. Analysis of Kv1.1 mutants suggests that juxtaparanodal Kv1.1 stabilizes transition zones at nerve terminals and branch points.

a. Stabilization of Axonal Segment before the Nerve Terminal The internodal shortening ahead of the nerve terminal (Fig. 2, arrow), while facilitating impulse invasion of the nerve terminal (Quick et al., 1979; Waxman and Brill, 1978), also raises the local excitability by increasing the Na channel content per unit fiber length (Chiu et al., 1999). Do Kv channels function to stabilize this region, and, if so, by what mechanisms? Genetic ablation of Kv1.1 results in no detectable change in the morphology of the myelinated nerves (Chiu et al., 1999). There is only a slight change in the action potential waveform and refractory period (Smart et al., 1998). However, the most dramatic excitability change is traced to a short nerve segment of probably not more than one to two internodal lengths just before neuromuscular junction, where a single action potential in the mutant elicits multiple action potentials (Fig. 3) (Zhou et al., 1998, 1999). This occurs only when the temperature is cooled below the physiological level, contributing to an intense myokymia seen in mutant mice forced to swim in cold water (Zhou et al., 1998).

Stabilization of branch points of myelinated axons Branch points (Fig. 2) represent another site of impedance mismatch where a propagating action potential can be rerouted, reflected backwards, blocked, or its frequency of transmission altered. Analysis of Kv1.1 mutant mice, in conjunction with computer modeling, has shed light on how Kv1.1 might modulate branch point transmission.

Figure 3 Ablation ofjuxtaparanodal Kv1.1 destabilizes the axonal segment before the nerve terminal. (A) Computer simulations of action potential propagation (from top to bottom) toward the nerve terminal with Kv1.1 deleted. (Top) 37°C. (Bottom) 20°C. Note that at the lower temperature, a single action potential elicits a second impulse at segment (*), causing a backfiring, as well as another forward firing. (B) In the wild-type, the segment before the nerve terminal is electrically stable, thus ensuring a faithful 1 -to-1 transmission irrespective of temperature changes. (Modified from Zhou et al., 1999, with permission.)

The excitability of the basket cell axon plexus that innervates the Purkinje cells in the cerebellum was examined in Kv1.1 null mice (Zhang et al., 1999). Kv1.1 deletion does not affect the spontaneous firing rate of the basket cell soma, suggesting that Kv1.1 does not alter the number of action potentials emitted down the axonal tree. Yet an increase in the inhibitory postsynaptic current (IPSC) is recorded in the Kv1.1 null mice. This increase in IPSP could not be explained by an increase in the excitability of the basket cell axon terminals (such as an increase in bouton density, in the spontaneous firing rate at the nerve terminal, or in the action potential duration at the nerve terminal), because both the miniature IPSP and the amplitude of the IPSP are unaffected in the mutants. The conclusion, by a process of elimination, is that Kv1.1 deletion elevates excitability by reducing the failure rates of action potential propagation through branch points. A similar conclusion was reached using a transgenic mouse in which point mutations were engineered in the Kv1.1 gene to reproduce the human neurological disorder episodic ataxia (Herson et al., 2003). Since basket cell axons are nonmyelinated, these studies do not address whether Kv1.1 is a stabilizer of branch points in myelinated axons.

That Kv1.1 destabilizes branch points in myelinated axons is evoked to explain alterations in the excitability of the auditory system in the Kv1.1 null mice (KoppScheinpflug et al., 2003). In a technically demanding study, in vivo single-unit recordings were made from bushy cells, their axonal endings, and the MNTB neurons (calyces of Held) the bushy cells innervate. Two interesting observations emerge. First, no apparent changes in the excitability were observed in cell body or the calyceal terminals of the bushy cells; the latter is consistent with the nondetectability of Kv1.1 proteins in the calyceal terminals (Brew et al., 2003). Rather, Kv1.1 deletion diminishes the ability of the bushy cell axons to follow high frequency, sound-driven stimulations. Second, the jitter of the first spike measured at the MNTB cells (innervated by the bushy cells) is significantly increased in the Kv1.1 null mice, leading to a degradation of the highly precise processing of temporal information required of the auditory system. The hypothesis is that these excitability changes in the auditory system result from destabilization of branch points of the bushy cell axonal tree (Kopp-Scheinpflug et al., 2003). This study provides the first empirical evidence to suggest a change in excitability of branch points in myelinated axons upon genetic ablation of Kv1.1.

b. Theoretical Considerations and Computer Simulations Why should transition zones be particularly sensitive to Kv1.1 deletion? One reason is the existence of internodal shortening before some transition zones (Quick et al., 1979), as in PNS neuromuscular junctions and in the vicinity of some branch points. Local internodal shortening ahead of a

Figure 3 Ablation ofjuxtaparanodal Kv1.1 destabilizes the axonal segment before the nerve terminal. (A) Computer simulations of action potential propagation (from top to bottom) toward the nerve terminal with Kv1.1 deleted. (Top) 37°C. (Bottom) 20°C. Note that at the lower temperature, a single action potential elicits a second impulse at segment (*), causing a backfiring, as well as another forward firing. (B) In the wild-type, the segment before the nerve terminal is electrically stable, thus ensuring a faithful 1 -to-1 transmission irrespective of temperature changes. (Modified from Zhou et al., 1999, with permission.)

transition zone translates into excitability augmentation due to an increase in the Na channel content per unit length. In a normal nerve, this augmentation of excitability is counteracted by juxtaparanodal Kv1.1 and a background K conductance. The countereffect of juxtaparanodal Kv1.1 also increases on a per unit length basis as a result of internodal shortening. However, if one assumes that the background K conductance per unit length remains constant, which would be true if the background conductance is distributed uniformly along the axons, and that the internodal portion of the myelinated axon contributes significantly to the background resting conductance (Chiu, 1982; Chiu and Ritchie, 1984), then it is immediately apparent that deletion ofjuxta-paranodal Kv1.1 would produce a disproportionately larger loss of counteracting force at the transition zone over the rest of the nerve. This theoretical consideration, therefore, corroborates the conclusion from physiological analysis of the Kv1.1 mutants that juxtaparanodal Kv1.1 is an important modifier of transition zone excitability. However the directionality of the excitability change observed in the mutants is complex. For example, the types of transition zones appear to be important: Kv1.1 deletion elevates the excitability of transition zones ahead of the nerve terminal (Zhou et al., 1999), but depresses the excitability in transition zones at branch points (Kopp-Scheinpflug et al., 2003).

c. Computer Modeling Because direct, empirical measurement of branch point transmission is notoriously difficult to achieve, theoretical modeling becomes an important complementary tool to address the role of juxtaparanodal Kv1 at branch points. Mathematical modeling of a single branch point for myelinated axons has been achieved in our laboratory (Zhou and Chiu, 2001), and extension to an axonal tree with multiple branch points is now under way (Chan and Chiu, unpublished observations). Computer simulations show that action potential propagation through a single branch point in a myelinated axon is very sensitive to the prebranch internodal lengths, minor changes in the paranodal junctions and potassium accumulations at vicinity of the branch point (Zhou and Chiu, 2001). Further, preliminary calculations show that deletion of juxtaparanodal Kv1 channels shifts the cut-off frequency of high-frequency trains through a branch point to a higher frequency level, effectively augmenting the excitability of the axonal tree (Chan and Chiu, unpublished observations). Further computer modeling of myelinated axonal trees with complex branch point distribution will be needed to shed light on how Kv1 affects global signaling processing in an axonal tree.

d. Mechanism of Stabilization of Transition Zones Even though analysis of Kv1.1 mutants suggests that transition zones are stabilized by juxtaparanodal Kv1.1, it is unclear by what mechanism the stabilization is achieved.

One mechanism of stabilization is prevention of reentrant excitation of the node of Ranvier (Chiu and Ritchie, 1981) by flanking the node with a high-density band of juxtaparanodal Kv1.1 channels. In this scheme, the juxtaparanodal Kv1.1 channels only interact dynamically with nodal currents during excitation to prevent re-excitation, but the Kv1.1 channels do not contribute to the steady-state resting potential. The other mechanism of stabilization is maintaining a resting potential for the axon under the myelin (Chiu, 1982; Chiu and Ritchie, 1984). Kv1.1 is a strong candidate in this later mechanism, as its low threshold for activation (Hopkins et al., 1994) allows this channel to be partially open at the resting potential and contributes to stabilizing it. In the first mechanism (dynamic prevention of reentrant excitation), the pattern of Kv1.1 distribution (i.e., juxtapara-nodal clustering) is important. In the second mechanism (maintaining a steady resting potential), the total Kv1.1 content per internode, rather than the pattern of channel distribution, is important. Recent studies of the Caspr-2 knockout mice lend credence to the second mechanism. The unique feature of Caspr-2 ablation (see Chapter 3) is that it desegregates Kv1.1 without altering the total Kv1.1 content per internode (Poliak et al., 2003). If Kv1.1 stabilizes transition zones primarily by maintaining a resting potential for the axons, then there should be no change in the excitability of transition zones in the Caspr-2 knockout mice because in these mice, Kv1.1 simply randomizes over the internode without a reduction in total channel numbers, which should not lead to any change in the steady resting potential. Transition zone analysis of this mouse has so far been restricted to the neuromuscular junction (Poliak et al., 2003), and the excitability there is normal. Other transition zones, such as branch points, have not been evaluated. Thus, the best current working hypothesis from studies of Kv1.1 (Zhou et al., 1998) and Caspr-2 mutants (Poliak et al., 2003) is that Kv1.1 stabilizes transition zones by a mechanism involving stabilization of the resting potential. Evidently, transition zones are highly vulnerable to resting potential perturbation than the rest of the axon.

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