This study was supported by the Bulgarian Science Fund (DMU 03/72).
Internodal mechanism of pathological afterdischarges in myelinated axons
Article first published online: 11 SEP 2013
Copyright © 2013 Wiley Periodicals, Inc.
Muscle & Nerve
Volume 49, Issue 1, pages 47–55, January 2014
How to Cite
Dimitrov, A. G. and Dimitrova, N. A. (2014), Internodal mechanism of pathological afterdischarges in myelinated axons. Muscle Nerve, 49: 47–55. doi: 10.1002/mus.23874
- Issue published online: 16 DEC 2013
- Article first published online: 11 SEP 2013
- Accepted manuscript online: 12 APR 2013 04:10AM EST
- Manuscript Accepted: 5 APR 2013
- Bulgarian Science Fund. Grant Number: DMU 03/72
- potassium channel;
Introduction: Recent optical recordings of transmembrane potentials in the axons of pyramidal neurons have shown that the internodal action potentials (APs) predicted in our previous studies do exist. These novel processes are not well understood. In this study we aim to clarify electrical phenomena in peripheral myelinated axons (MAs). Methods: We used a multi-cable Hodgkin–Huxley-type model to simulate MAs with potassium channels that were either normal or inhibited along a short region of the internodal membrane. A brief stimulus was applied to the first node. Results: We demonstrated peculiarities in the internodal APs induced by a saltatory AP: They existed across internodal membranes, were detectable in periaxonal space but not in intracellular space, propagated continuously, collided near the mid-internodes, and produced internodal sources of afterdischarges. Conclusions: These results highlight the importance of the MA internodal regions as new therapeutic targets for avoiding afterdischarges provoked by reduced axonal fast potassium channel expression. Muscle Nerve 49: 47–55, 2014
amyotrophic lateral sclerosis
internodal action potential
internodal action potential that back-propagates from an internode toward the closest node
internodal action potential induced by a saltatory action potential
saltatory action potential
Afterdischarges, that is, continued spiking after a brief stimulus, are known to occur under normal and pathological conditions.[1-3] The nature of these afterdischarges remains poorly understood. Under certain conditions, neurons generate single action potentials (APs) at the initial segment of the axon. For neuronal burst firing, the axonal sodium channels at the first node of Ranvier are also essential. However, afterdischarges can originate within peripheral myelinated axons (MAs),[4-8] even though these MAs generally function in rapid signal conduction. What could a brief stimulus or single spike be altering in a peripheral axon to induce the afterdischarge regimen generally interpreted as a sign of axonal hyperexcitability9–11? Because the excitability of a cell is related to sodium channel activity, research into the source of new spikes or afterdischarges is generally focused on sites with high concentrations of sodium channels. Nodes of Ranvier are such candidate sites in peripheral MAs. Regions of excitable structures with low densities of sodium channels are usually ignored.
Our earlier theoretical studies predicted that a source of afterdischarges could be created in the internodal region of MAs, where the density of sodium channels is only 2–6% of the sodium channel density in nodal regions.[13-17] If the width of the periaxonal space in a large-diameter MA is <400 nm, a saltatory AP (sAP) can induce internodal APs (iAPs). This condition is easily satisfied, because the periaxonal space is usually only a few nanometers wide in a peripheral MA with normal myelination. When the internodal regions are devoid of potassium channels, the iAPs can create internodal sources of afterdischarges.
Experimental detection of the active internodal processes predicted in our theoretical studies is potentially problematic. The iAPs may be detected along with periaxonal or transmembrane potentials, which are undetectable with classical microelectrode techniques used to record intracellular potentials. A high-sensitivity transmembrane potential imaging technique was recently used by Popovic et al. to directly determine the location and length of the spike trigger zone in layer 5 pyramidal neurons. The high spatial resolution of the technique allowed them to simultaneously record transmembrane potentials as a function of time at numerous points along the proximal axon. Although iAPs were outside the main scope of their study, the investigators recorded internodal transmembrane APs with temporal characteristics similar to those of nodal APs. To verify that the recorded signals were from an MA, they demonstrated differences in propagation of APs in myelinated and unmyelinated axons. The nature of the iAPs was not discussed.
Better understanding of these processes is important for comprehension of MA function and discovery of new therapeutic targets. Therefore, we aimed to clarify the sequence of electrical phenomena in peripheral MAs induced by a brief stimulus and discuss their importance in terms of health and disease. We have already described some peculiarities in the processes activated during the production of afterdischarges in MAs lacking potassium channels along the internodes and related them to neuromyotonia. Signs of axonal hyperexcitability related to the presence of antibodies to potassium channels are also found in patients with amyotrophic lateral sclerosis (ALS).[21-23] MAs can also produce pathological afterdischarges even when only a short region of an internode is devoid of potassium channels, as in the case of side effects induced by oxaliplatin. The mechanism of afterdischarge production in such cases is described and demonstrated in this study. We emphasize the differences in sensitivities of intracellular, periaxonal, and transmembrane voltages detected in MAs to iAPs and sAPs. We will also draw parallels between the processes found experimentally in the proximal axon and those predicted by our current and previous[12, 18] theoretical results.
We used a multi-cable Hodgkin–Huxley-type model to simulate the electrophysiological processes occurring in a large-diameter peripheral MA. The axis cylinder of the MA had a radius of 12 μm. The MA had 21 nodes of Ranvier and 20 internodes. The density of the internodal sodium channels was 1/30 of the density of the nodal sodium channels.[13-17] A suprathreshold rectangular current pulse was applied to the first node of Ranvier for 50 μs at an intensity of 14 nA. The width of the narrow periaxonal space was 4 nm, which was much smaller than the limiting value (400 nm) for producing iAPs by an sAP. In simulations, the nodes and paranodes, with lengths of 1.5 μm and 79 μm, were represented with 1 and 79 segments, respectively. The uniform middle region of each internode, with a length of 1600 μm, was represented with 160 segments. Thus, the length of each segment was 1 μm and 10 μm in simulations of paranodes and middle portions of the internodes, respectively. Our MA segmentation is much finer than that used in other models where the paranodes and internodes were represented with only 2 and 5 segments, respectively.[25, 26] This enabled us to notice and study the internodal active processes whose spatial length along the internodal membrane was about 100 μm.
To demonstrate the mechanism of afterdischarges, we simulated the case when fast potassium channels were inhibited; that is, their density was equal to zero, along a certain internodal region. This corresponded to reduced potassium channel expression, which could be expected as a result of application of oxaliplatin or the presence of antibodies against potassium channels, as in the case of neuromyotonia or ALS.[21-23] In this study, a short (150-μm-long) central portion of the 11th internode was devoid of potassium channels. According to our recent study, 1 afterdischarge was produced in this case. We then examined differences in manifestations of iAPs and sAPs in the intracellular, periaxonal, and transmembrane (i.e., the difference between intracellular and periaxonal) voltages at different moments after the stimulus onset. Description of the model details and other specific parameters can be found in our recent reports.[12, 24]
To highlight the differences in the manner of propagation of the 2 types of APs (sAP and iAP) in an MA and to demonstrate the similarity of the processes obtained between our simulations and the experiments of Popovic et al., we estimated the latencies of the transmembrane sAPs and iAPs along the MA. The latencies were defined with respect to the onset of the brief current stimulus. The characteristic point in the transmembrane APs for latency estimation was at −40 mV of the AP rising phase.
To better clarify the internodal mechanism of pathological afterdischarges, we first examined APs in a normal MA.
Electrophysiological Events after Activation of a Normal Myelinated Axon
Stimulation of an MA resulted in generation of an sAP that quickly propagated along the axon by “jumping” from node to node, as expected (Fig. 1, black rectangles and solid arrows). The narrow periaxonal space allowed the sAP to produce iAPs. An iAP induced by the sAP, that is, iAP(s), was produced in each of the 2 internodes located adjacent to the active node (Fig. 1A, hatched rectangles, iAP(s)). Both of these iAP(s) slowly propagated in opposite directions, away from the active node (Fig. 1B, hatched rectangles and dashed arrows) and toward the middle of each adjacent internode, where they collided with the internodal waves produced by other neighboring nodes (Fig. 1C, the internode between nodes j and j + 1).
Delays in Action Potentials of a Myelinated Axon with Normal Potassium Channels
The differences in the appearance and propagation of sAP and iAPs(s) could be seen from the pattern of AP delays along the MA. After stimulation at the first node, an sAP propagated rapidly, with only a short delay, by jumping from node to node (Fig. 2A, open circles). In contrast, the 2 iAPs(s) induced by the sAP propagated continuously and more slowly away from each active node and toward the middle region of the internode (mid-internode) (Fig. 2B). iAPs(s) traversed this short distance (about 900 μm) in approximately 5 ms (Fig. 2B, solid lines between any open circle and the nearest maxima). The processes of iAP(s) propagation away from the activated node and extinction near the corresponding mid-internode were identical everywhere along the MA. They differed only by the exact moments of initiation (Fig. 2B, local minima) and extinction (Fig. 2B, local maxima), which were related to the delay in onset of the sAP at the parent nodes.
Time-Dependent Changes in Intracellular, Periaxonal, and Transmembrane Voltages after Onset of Saltatory Action Potential at Parent Node
The iAPs(s) appeared and began their continuous internodal propagation toward the mid-internode almost simultaneously with generation of the parent sAP. Thus, during the lifetime of the sAP, the iAPs(s) coexisted with the parent sAP in the region near the node. Large-diameter axons have long internodes. Therefore, the iAPs(s) continued their slow internodal propagation (Fig. 2B) after extinction of the short-lived sAP. As a result, depending on the distance from the parent node, the interrelations between sAP and iAP(s) differed. Three regions were distinguished in each node–internode complex: the node; the paranode; and the middle portion of the internode (Fig. 3, dashed rectangles in the schematic drawings at the top). We compared manifestations of the iAPs(s) and sAPs across the axonal membrane (Fig. 3, top row), in the periaxonal space (Fig. 3, middle row), and in the intracellular space (Fig. 3, bottom row) at several points at different distances from the node (Fig. 3, different curves) in these 3 axonal regions (Fig. 3, different columns).
The sAP was generated by the nodal membrane and thus existed across it (Fig. 3A). The electrical potential in the extracellular space and thus on the outer edge of the nodal membrane was close to zero (Fig. 3B); therefore, the sAP was also manifested in the intracellular space (Fig. 3C). Moreover, the sAP was detected almost simultaneously everywhere within the intracellular space because of passive distribution of the sAP along this space of relatively large volume (note the almost simultaneous curves of sAP in Fig. 3F and I). The sAP was also detectable at any point within the periaxonal space covered by myelin (Fig. 3E and H). In the mid-internode, the sAP was clearly manifested (asterisk in Fig. 3H). However, in the paranodal region of the periaxonal space, simultaneous existence of the iAPs(s) masked the sAP (asterisk in Fig. 3E). Nevertheless, the sAP (Fig. 3F and I) was not detected across the internodal membrane (Fig. 3D and asterisk in 3G).
In contrast to the sAP, the iAPs(s) were well pronounced in the internodal transmembrane voltages (Fig. 3D and G), but were absent from the potentials detected in the intracellular space (Fig. 3, bottom row). Although masked by the sAP in the paranodal region of the MA, the iAPs(s) were detectable in the periaxonal space covered by myelin (Fig. 3E and H). An explanation of differences in the manifestations of the sAP and iAPs(s) is given in the Discussion section.
Collision of Internodal Waves in Mid-Internode Area
Figure 4 shows the potential profiles along a portion of an MA for several time-points (t) after extinction of the sAP. Propagation of the iAPs(s) along the internodes was non-decrementing (Fig. 4, t1–t4). During the collision of iAPs(s) near the mid-internode, the amplitude of the iAPs(s) initially increased slightly (Fig. 4, t5), but then decreased continuously until full extinction (Fig. 4, t6–t9). Note that the solid lines in Figure 4 represent the spatial profiles of the iAPs(s) produced in the periaxonal space. The iAP(s) could not be detected in the intracellular space (Fig. 4, t = t1, dashed line).
Electrophysiological Events after Activation of an Abnormal Myelinated Axon
In contrast to the full extinction of the iAP(s) observed near the mid-internodes of normal MAs (Fig. 4, t9), the region of internodal membrane devoid of fast potassium channels could not repolarize in full. It remained depolarized to a certain degree after propagation and collision of the iAPs(s) (Fig. 5A, t1) in spite of inactivation of sodium channels and leakage currents in the internode.
Generation of Back-Propagating Internodal Action Potentials, iAP(b)
The boundary between the depolarized and normally repolarized regions forms the so-called “transition zone,” which can exist for a prolonged period of time (Fig. 5, t1–t9). The internodal membrane entered a refractory period after the iAP(s) passed. After the refractory period, the transition zones on both sides of the depolarized region became sources of follow-up iAPs called “back-propagating internodal APs” (iAP(b)), because they emerged (Fig. 5A, t2) and back-propagated (Fig. 5A, t3, t4) slowly and continuously from the transition zones in the abnormal internode toward the adjacent nodes. Similar to the iAPs(s), the iAPs(b) were also non-decrementing during their propagation along the abnormal internode. They were pronounced in amplitude in the very narrow periaxonal space (Fig. 5A, solid lines) and were practically undetectable in the intracellular space (Fig. 5A, dashed line in the top subplot, which shows the potentials produced during 4 moments of time, t1–t4).
Upon reaching the nodes, the back-propagating iAPs(b) activated them and produced an afterdischarge that propagated in a saltatory fashion in both directions along the MA (Fig. 5B, t5–t9). During the lifetime of the afterdischarge, the new iAPs were also induced and propagated along the paranodal regions of the corresponding internodal membranes; that is, the afterdischarge and iAPs coexisted. This finding can be seen in Figure 5B, where the envelopes of the periaxonal potentials along the MA changed simultaneously with the intracellular potentials (Fig. 5B, t6–t9, dashed lines). Thus, the processes induced by the afterdischarge were similar to those induced by the initial sAP (Figs. 3 and 4). The main difference between them was the direction of AP propagation (compare Fig. 2A and Fig. 5B, t6–t7). Importantly, the depolarized zone and transition zones continued to exist after extinction of the afterdischarge (Fig. 5B, t8–t9). The depolarized zone in the axonal region devoid of potassium channels became narrower over time and eventually disappeared. Until that moment, however, the internodal source and conditions for generating additional afterdischarges existed.
In contrast to the new internodal waves induced by the afterdischarge in all normal internodes (Fig. 5B, t5–t9, arrows point to these iAP(s) waves at t = t7, t8, t9), no new internodal waves were initiated in the abnormal internodes devoid of potassium channels (Fig. 5B, t6–t9, the internode between nodes 11 and 12). This finding was expected, because the iAP(b) leaves the paranodal regions of the abnormal internode in an absolute refractory period that makes the internode insensitive to the afterdischarge.
Delays in Action Potentials of a Myelinated Axon with Abnormal Potassium Channels
Delays in the APs of the normal and abnormal МАs were identical between generation of the sAP at the first node and extinction of the iAPs(s) in the last mid-internode (compare Fig. 2B and Fig. 6, bottom row). Figure 6 shows that, when a section of the internodal membrane was deprived of potassium channels (hatched rectangles), electrophysiological processes in the abnormal MA continued. The internodal membrane near the transition zones needed approximately 2 ms to overcome the refractory period. Then, the iAP(b) that arose near the depolarized internodal region propagated continuously to the nearest nodes (Fig. 6, schematic drawing and dashed lines of the delay curve between nodes n11 and n12). The range of the delays in the iAP(b) along the 11th internode was slightly greater than the range of delays in the iAP(s). The node-to-node delays of the saltatory afterdischarge (filled circles) during propagation toward the first and last nodes of the MA were similar to those of the initial sAP, with the only difference being the direction of propagation.
Mechanism of Afterdischarge Production
The appearance of peripheral nerve afterdischarges or muscle afteractivity is taken as evidence of axonal hyperexcitability,[9-11] which is often accompanied by potassium channel pathology. However, some studies did not find increased MA excitability in patients with neuromyotonia, irrespective of the presence of autoantibodies to potassium channels. The results of our study demonstrate the existence of a mechanism for producing axonal afterdischarges that does not require increased excitability of the MA. Our model required that a single MA internode contains at least a short region (<10% of its length) with inhibited potassium channels. Then, after initiation of a single sAP, the sAP induced an iAP(s) that propagated along the internode and left the internodal region with inhibited potassium channels more depolarized (i.e., less repolarized) than the rest of the internode (Fig. 5). This spatial difference in electrical potentials along the internode formed a transition zone that became an internodal source of afterdischarges (Fig. 5). The small width of the periaxonal space and thus its high electrical resistance ensured prolonged existence of the internodal source, which is a prerequisite for the production of new afterdischarges.
Our mechanism of afterdischarge production supports the idea of “differential repolarization” reported by Burns and Burns et al. over 55 years ago. They realized that the presence of an AP afterpotential was not sufficient for afterdischarge generation. Instead, a depolarization gradient that was somehow induced by a different rate of repolarization down the length of the cell was required. The gradient would be associated with current flow between these regions, which could induce afterdischarges. The transition zone described in our study (Fig. 5) represents the potential gradient along the cell, as suggested by Burns and Burns et al. The main difference between our ideas and theirs regarding the mechanism of afterdischarge production is that they[30, 31] considered only different portions of a muscle fiber or the dendrites and soma of a neuron, with no possible role for the internodes of the MA. It is natural that researchers and clinicians have overlooked the idea of an internodal source of afterdischarges, because the low density of sodium channels in the internodal region seems paradoxical as a source of axonal hyperexcitability. However, with adequate modeling, one can discover processes that are difficult to imagine.
For simplicity, we have considered only the case where 1 afterdischarge was produced by a source formed at the center of an internode by a short region with inhibited potassium channels. Although it was not demonstrated here or in our previous study, similar internodal sources were formed at the boundaries of all MA regions without potassium channels. The length and position of these regions defined the number of afterdischarges produced after a single sAP.
Where and Why Saltatory or Internodal Action Potentials Were Observed
The active electrophysiological processes in an MA occur across the membranes that generate them. The MA may be considered to be an electrical circuit with regions that act as resistors and capacitors. Passive distribution of the sAP between neighboring nodes results in only a slight displacement of the sAP curves detected at different points along the intracellular space, which has relatively low resistance (Fig. 3F and I). The passive distribution in the radial direction of the short-duration and thus rather high-frequency intracellular sAP is defined primarily by the relationship between the capacitances of the internodal membrane and myelin. In an axon with normal myelination, the capacitance of the membrane is much higher than that of myelin. This difference makes the amplitude of the sAP across the myelin, and thus in the periaxonal space (curves marked with asterisks in Fig. 3E and H), close to that in the intracellular space (Fig. 3, bottom row). As a result, reflecting the difference between the intracellular and periaxonal potentials, the internodal transmembrane AP contained no sign of the original sAP (Fig. 3D and G).
In contrast, the iAP(s) exists across the internodal membrane where it was generated (Fig. 3D and G). In an axon with normal myelination, the width of the periaxonal space is much smaller than the width of the intracellular space; therefore, the resistance of the periaxonal space is much greater than that of the intracellular space. For this reason, passive distribution of the iAP(s) was not observed in the intracellular space (Fig. 3, bottom row), which makes this space an inappropriate site for studies of iAP(s). The iAP(s) was also not detected clearly in the paranodal periaxonal region where it coexisted with the sAP (Fig. 3E). The sAP and iAP(s) could be distinguished clearly in the periaxonal space of a large-diameter MA in the central region of the internode (Fig. 3H). However, in the case of small-diameter MAs of the central nervous system, in which the internode is short (approximately 75–120 μm as shown in Fig. 9 in the study by Popovic et al.) and the sAP duration is comparable to the time elapsed until the iAP reaches the mid-internode, the sAP and iAP(s) would not be distinguishable in the periaxonal space. Thus, to study internodal processes, one should give preference to studies of internodal transmembrane AP detection, because the iAP(s) in such recordings is not contaminated by sAP throughout the internode (Fig. 3D and G).
The microelectrode technique for AP detection is an effective tool for discovering and understanding intimate mechanisms of cellular activity. However, this technique is not appropriate for detecting transmembrane iAP(s), because the electrodes would destroy the very thin periaxonal space and thus the MA internodal processes and iAP(s). In contrast, the high sensitivity and high spatial resolution of the transmembrane potential imaging technique provides experimental tools for studying the internodal processes. Thus, different manifestations of hyperexcitability based on internodal processes could be studied experimentally.
The results of our study suggest that nodal (Fig. 3A) and internodal (Fig. 3D and G) APs are of similar shape, duration, and amplitude. Popovic et al. also reported the generation of iAPs after the nodal sAP was initiated, and their sAP and iAP findings had similar characteristics (their Fig. 5F). The “wavelike” pattern of the delays in the APs along the MA is also similar to the findings by Popvic et al. (compare our Fig. 2B with their Figs. 5D and 9A). However, the absolute delays of the theoretical and experimental APs probably differed because the diameter of the simulated peripheral MA was much larger than that of the central MA. The detection of internodal potentials was not natural to Popovic et al., and therefore they verified experimentally that such a wavelike pattern of delays was typical for MAs only. In contrast to MAs, in unmyelinated axons, the delay in APs that propagated continuously along the fiber increased gradually with time (their Fig. 11). This process in unmyelinated fibers is identical to the case of continuous iAPs propagating from each node toward the corresponding mid-internode in our simulations (Figs. 2B and 6, lines between any circle and the adjacent maximum).
One disadvantage of the transmembrane potential imaging technique is that the amplitude of the AP is not calibrated on an absolute scale (i.e., millivolts). However, determination of the exact AP amplitudes is not a necessary condition for assessing the existence of internodal processes. Figure 3D shows that the iAP amplitude could depend on the position of the assessment point relative to the node. Our previous study showed that iAP production is a very robust process that continues to exist in MAs whose periaxonal space widths (and thus the electrical load on the node and internode that affects the sAP and iAP amplitudes) vary over a wide range, from a couple of nanometers up to 400 nm.
Thus, Popovic et al. detected experimentally: (1) the production of iAPs after activation of the nodal AP; (2) continuous propagation of the 2 iAPs from the neighboring nodes toward the mid-internode; (3) similarities in the shape of the iAPs and sAP; and (4) the AP delay pattern specific to MAs. Their findings are similar to those obtained with our simulations, which convinces us that the internodal processes predicted and described in this study and our earlier theoretical studies[12, 18] do exist!
Application of Results
The results of this study demonstrate a mechanism by which oxaliplatin, which is used to treat digestive tract tumors, could induce acute neurotoxic side effects when the drug penetrates the myelin and affects the fiber membrane (or at least its short portion), as proposed by Kagiava et al. A similar mechanism could explain the appearance of neuromyotonia in patients whose autoreactive antibodies cannot access the majority of axonal voltage-gated potassium channels. If suppression of the axonal potassium channels is massive or genetic, as in patients with episodic ataxia type 1, then the afterdischarges could be generated by every internode practically simultaneously along the entire length of the MA, as described by Dimitrov.
The elevated potassium channel antibodies, markedly reduced fast axonal potassium channel expression, and reduced potassium currents have also been reported in patients with ALS. Thus, the generally overlooked internodal processes could be useful for elucidating the pathophysiology of axonal excitability in ALS. Moreover, according to previous publications,[21-23] axonal hyperexcitability in ALS would lead to generation of fasciculations and may contribute to motor neuron death.
In conclusion, we hope that the results of our study will direct the attention of researchers and clinicians interested in understanding the mechanisms of afterdischarge production or axonal hyperexcitability provoked by inhibition of fast potassium channels to the internodal regions of the MA, which should become new targets for experimental studies and therapies. We agree with Debanne et al., who stated, “There are good reasons to believe that after the decade of the dendrites in the 1990s, a new era of axon physiology is now beginning.”
- 15Action potential conduction recorded optically in normal, demyelinated, and remyelinated axons. In: Waxman SG, Kocsis JD, Stys PK, editors. Axon. New York: Oxford University Press; 1995..
- 19Morphology of normal peripheral axons. In: Waxman SG, Kocsis JD, Stys PK, editors. Axon. New York: Oxford University Press; 1995. p 13–48., .