Subtle Paranodal Injury Slows Impulse Conduction in a Mathematical Model of Myelinated Axons

This study explores in detail the functional consequences of subtle retraction and detachment of myelin around the nodes of Ranvier following mild-to-moderate crush or stretch mediated injury. An equivalent electrical circuit model for a series of equally spaced nodes of Ranvier was created incorporating extracellular and axonal resistances, paranodal resistances, nodal capacitances, time varying sodium and potassium currents, and realistic resting and threshold membrane potentials in a myelinated axon segment of 21 successive nodes. Differential equations describing membrane potentials at each nodal region were solved numerically. Subtle injury was simulated by increasing the width of exposed nodal membrane in nodes 8 through 20 of the model. Such injury diminishes action potential amplitude and slows conduction velocity from 19.1 m/sec in the normal region to 7.8 m/sec in the crushed region. Detachment of paranodal myelin, exposing juxtaparanodal potassium channels, decreases conduction velocity further to 6.6 m/sec, an effect that is partially reversible with potassium ion channel blockade. Conduction velocity decreases as node width increases or as paranodal resistance falls. The calculated changes in conduction velocity with subtle paranodal injury agree with experimental observations. Nodes of Ranvier are highly effective but somewhat fragile devices for increasing nerve conduction velocity and decreasing reaction time in vertebrate animals. Their fundamental design limitation is that even small mechanical retractions of myelin from very narrow nodes or slight loosening of paranodal myelin, which are difficult to notice at the light microscopic level of observation, can cause large changes in myelinated nerve conduction velocity.     

The influence of an unmyelinated terminal on repetitive firing of a mammalian receptor afferent fiber

The distal end of a myelinated receptor afferent fiber consists of an unmyelinated terminal membrane which is assumed to be the site of sensory transduction, whereas the action potential encoding appears at a distal node of Ranvier. In the present paper a model of a mammalian myelinated nerve fiber was augmented by an unmyelinated terminal segment into which stimulating current was injected thus modelling the situation at a myelinated receptor afferent fiber. It was found that the introduction of the unmyelinated terminal reduces the repetitive firing rate shown by the model. However, also the amplitude of the spikes at the site of action potential generation diminishes through the large electrical load which the unmyelinated terminal imposes onto the active parts of the nerve fiber model. This "loss" of spike amplitude can abolish the ability of the model to show repetitive activity, if the unmyelinated terminal increases in size. On the other hand, the incorporation of sodium channels into the terminal membrane compensates the spike amplitude reduction introduced by the electrical load of that membrane. This allows repetitive firing at a lower frequency than would be possible for a model with an equivalent sodium-channel-free terminal. The results show that the unmyelinated terminal present at the distal end of myelinated receptor afferent fibers has not only the ability to provide sensory transduction but evokes also a reduction in the discharge rate of the encoding membrane.     

Contactin orchestrates assembly of the septate-like junctions at the paranode in myelinated peripheral nerve

Rapid nerve impulse conduction depends on specialized membrane domains in myelinated nerve, the node of Ranvier, the paranode, and the myelinated internodal region. We report that GPI-linked contactin enables the formation of the paranodal septate-like axo-glial junctions in myelinated peripheral nerve. Contactin clusters at the paranodal axolemma during Schwann cell myelination. Ablation of contactin in mutant mice disrupts junctional attachment at the paranode and reduces nerve conduction velocity 3-fold. The mutation impedes intracellular transport and surface expression of Caspr and leaves NF155 on apposing paranodal myelin disengaged. The contactin mutation does not affect sodium channel clustering at the nodes of Ranvier but alters the location of the Shaker-type Kv1.1 and Kv1.2 potassium channels. Thus, contactin is a crucial part in the machinery that controls junctional attachment at the paranode and ultimately the physiology of myelinated nerve.     

A distributed-parameter model of the myelinated human motor nerve fibre: temporal and spatial distributions of action potentials and ionic currents

 A double cable model of the myelinated human motor nerve fibre is presented. The model is based on the nodal and internodal channels in a previous, two-component model of human motor axons (Bostock et al. 1991), added to a complex extended cable structure of nodal, paranodal and internodal segments. The model assumes a high-resistance myelin sheath and a leakage pathway to the internodal axolemma via the paranodal seal resistance and periaxonal space. The parameter values of the model were adjusted to match the recordings of threshold electrotonus in human motor fibres from Bostock et al. (1991). Kirchoff ’s current law was used to derive a system of partial differential equations for the electrical equivalent circuit, and numerical integration was performed with a fixed time increment and non-uniform spatial step sizes, in accordance with the complex structure of the fibre. The model calculations provide estimates of the spatial and temporal distributions of action potentials and their transaxonal and transmyelin components, both in different segments of the fibre and at different moments during action potential propagation. The distribution of transaxonal and transmyelin currents along the fibre and their contributions from different ionic channels are also explored. Received: 14 July 1994/Accepted in revised form: 4 April 1995     

Comparison of morphological and physiological characteristics of the Ranvier node

Variations in the structure of Ranvier nodes and of the paranodal region of frog nerve fibers were examined in an intravital light-optical investigation. Several morphological characteristics of the degree of disturbance of the structures of the paranodal zone (myelin cones and bulbs of the node) are compared. Morphological characteristics for the same isolated nerve fibers were compared with electrophysiological characteristics obtained by the voltage clamp method. A definite parallel was found between the degree of morphological changes in the paranodal myelin and the fall in the maximal sodium and potassium conductances of the membrane, while the leakage conductance remained relatively constant. The lower resistance of the sodium and potassium systems to injurious factors evidently reflects the more complex molecular organization of the excitable (sodium and potassium) than of the leakage channels. Considerable changes in the properties of the sodium channels caused by batrachotoxin were not accompanied by any visible changes in the paranodal regions of the myelin sheath. The results are examined from the standpoint of modern views regarding the nature of axo-glial relations in the nerve fiber.A. V. Vishnevskii Institute of Surgery, Academy of Medical Sciences of the USSR, Moscow. I. P. Pavlov Institute of Physiology, Academy of Sciences of the USSR, Leningrad. Translated from Neirofiziologiya, Vol. 10, No. 4, pp. 400–406, July–August, 1978.     

Effects of a slow potassium permeability on repetitive activity of the frog node of ranvier

Adding a potassium permeability with slow kinetics to the Frankenhaeuser-Huxley equations describing action potential generation at a frog node of Ranvier has a twofold effect on the maintained repetitive firing the model can show. If the contribution of the slow to the total potassium permeability is increased, the maintained discharge frequency for a given stimulating current experiences a decrease. On the other hand, addition of the slow channel narrows the range of currents for which the model can generate repetitive activity. If as little as 6.2% of the total potassium permeability are provided by the slow channels, the Frankenhaeuser-Huxley equations completely lose the ability to show maintained firing. The introduction of the slow potassium current abolishes especially repetitive activity at low values of stimulating current. This effect is so marked that the minimal discharge frequency the model can maintain increases with increasing contribution of the slow channel. Therefore, an important purpose of the slow potassium channel present at the frog nodal membrane could consist of preventing the node of Ranvier from generating consistent firing on its own.     

The “Lillie Transition”: models of the onset of saltatory conduction in myelinating axons

Almost 90 years ago, Lillie reported that rapid saltatory conduction arose in an iron wire model of nerve impulse propagation when he covered the wire with insulating sections of glass tubing equivalent to myelinated internodes. This led to his suggestion of a similar mechanism explaining rapid conduction in myelinated nerve. In both their evolution and their development, myelinating axons must make a similar transition between continuous and saltatory conduction. Achieving a smooth transition is a potential challenge that we examined in computer models simulating a segmented insulating sheath surrounding an axon having Hodgkin-Huxley squid parameters. With a wide gap under the sheath, conduction was continuous. As the gap was reduced, conduction initially slowed, owing to the increased extra-axonal resistance, then increased (the “rise”) up to several times that of the unmyelinated fiber, as saltatory conduction set in. The conduction velocity slowdown was little affected by the number of myelin layers or modest changes in the size of the “node,” but strongly affected by the size of the “internode” and axon diameter. The steepness of the rise of rapid conduction was greatly affected by the number of myelin layers and axon diameter, variably affected by internode length and little affected by node length. The transition to saltatory conduction occurred at surprisingly wide gaps and the improvement in conduction speed persisted to surprisingly small gaps. The study demonstrates that the specialized paranodal seals between myelin and axon, and indeed even the clustering of sodium channels at the nodes, are not necessary for saltatory conduction.     

Internodal specializations of myelinated axons in the central nervous system

We have examined the localization of contactin-associated protein (Caspr), the Shaker-type potassium channels, Kv1.1 and Kv1.2, their associated beta subunit, Kvbeta2, and Caspr2 in the myelinated fibers of the CNS. Caspr is localized to the paranodal axonal membrane, and Kv1.1, Kv1.2, Kvbeta2 and Caspr2 to the juxtaparanodal membrane. In addition to the paranodal staining, an internodal strand of Caspr staining apposes the inner mesaxon of the myelin sheath. Unlike myelinated axons in the peripheral nervous system, there was no internodal strand of Kv1.1, Kv1.2, Kvbeta2, or Caspr2. Thus, the organization of the nodal, paranodal, and juxtaparanodal axonal membrane is similar in the central and peripheral nervous systems, but the lack of Kv1.1/Kv1.2/Kvbeta2/Caspr2 internodal strands indicates that the oligodendrocyte myelin sheaths lack a trans molecular interaction with axons, an interaction that is present in Schwann cell myelin sheaths.     

Membrane domain organization of myelinated axons requires βII spectrin

The precise and remarkable subdivision of myelinated axons into molecularly and functionally distinct membrane domains depends on axoglial junctions that function as barriers. However, the molecular basis of these barriers remains poorly understood. Here, we report that genetic ablation and loss of axonal βII spectrin eradicated the paranodal barrier that normally separates juxtaparanodal K⁺ channel protein complexes located beneath the myelin sheath from Na⁺ channels located at nodes of Ranvier. Surprisingly, the K⁺ channels and their associated proteins redistributed into paranodes where they colocalized with intact Caspr-labeled axoglial junctions. Furthermore, electron microscopic analysis of the junctions showed intact paranodal septate-like junctions. Thus, the paranodal spectrin-based submembranous cytoskeleton comprises the paranodal barriers required for myelinated axon domain organization.     

Real-time CARS imaging reveals a calpain-dependent pathway for paranodal myelin retraction during high-frequency stimulation

High-frequency electrical stimulation is becoming a promising therapy for neurological disorders, however the response of the central nervous system to stimulation remains poorly understood. The current work investigates the response of myelin to electrical stimulation by laser-scanning coherent anti-Stokes Raman scattering (CARS) imaging of myelin in live spinal tissues in real time. Paranodal myelin retraction at the nodes of Ranvier was observed during 200 Hz electrical stimulation. Retraction was seen to begin minutes after the onset of stimulation and continue for up to 10 min after stimulation was ceased, but was found to reverse after a 2 h recovery period. The myelin retraction resulted in exposure of Kv 1.2 potassium channels visualized by immunofluorescence. Accordingly, treating the stimulated tissue with a potassium channel blocker, 4-aminopyridine, led to the appearance of a shoulder peak in the compound action potential curve. Label-free CARS imaging of myelin coupled with multiphoton fluorescence imaging of immuno-labeled proteins at the nodes of Ranvier revealed that high-frequency stimulation induced paranodal myelin retraction via pathologic calcium influx into axons, calpain activation, and cytoskeleton degradation through spectrin break-down.     

Cytoskeletal transition at the paranodes: the Achilles' heel of myelinated axons

Myelination organizes axons into distinct domains that allow nerve impulses to propagate in a saltatory manner. The edges of the myelin sheath are sealed at the paranodes by axon-glial junctions that have a crucial role in organizing the axonal cytoskeleton. Here we propose a model in which the myelinated axons depend on the axon-glial junctions to stabilize the cytoskeletal transition at the paranodes. Thus paranodal regions are likely to be particularly susceptible to damage induced by demyelinating diseases such as multiple sclerosis.     

Localization of Phospholipid Synthesis to Schwann Cells and Axons

Quantitative electron microscopic autoradiography was used to detect and characterize endoneurial sites of lipid synthesis in mouse sciatic nerve. Six tritiated phospholipid precursors (choline, serine, methionine, inositol, glycerol, and ethanolamine) and a protein precursor (proline) were individually injected into exposed nerves and after 2 h the mice were perfused with buffered aldehyde. The labeled segments of nerve were prepared for autoradiography with procedures that selectively remove nonincorporated precursors and other aqueous metabolites, while preserving nerve lipids (and proteins). At both the light and electron microscope levels, the major site of phospholipid and protein synthesis was the crescent-shaped perinuclear cytoplasm of myelinating Schwann cells. Other internodal Schwann cell cytoplasm, including that in surface channels, Schmidt-Lanterman incisures, and paranodal regions, was less well labeled than the perinuclear region. Newly formed proteins were selectively located in the Schwann cell nucleus. Lipid and protein formation was also detected in unmyelinated fiber bundles and in endoneurial and perineurial cells. Tritiated inositol was selectively incorporated into phospholipids in both myelinated axons and unmyelinated fibers. Like inositol, glycerol incorporation appeared particularly active in unmyelinated fibers. Quantitative autoradiographic analyses substantiated the following points: myelinating Schwann cells dominate phospholipid and protein synthesis, myelinated axons selectively incorporate tritiated inositol, phospholipid precursors label myelin sheaths and myelinated axons better than proline.     

Developmental changes at the node and paranode in human sural nerves: morphometric and fine-structural evaluation

Developmental alterations of paranodal fiber segments have not been investigated systematically in human nerve fibers at the light- and electron-microscopic level. We have therefore analyzed developmental changes in the fine structure of the paranode in 43 human sural nerves during the axonal growth period up to 5 years of age, and during the subsequent myelin development up to 20 years and thereafter. The nodal, internodal, and paranodal axon diameters reach their adult values at 4–5 years of age. The ratio between internodal and paranodal axon diameters remains constant at 1.8–2.0. Despite a considerable increase in myelin sheath thickness, the length of the paranodal myelin sheath attachment zone at the axon does not increase correspondingly, because of attenuation, separation from the axolemma, and piling up of myelin loops in the paranode. Separation of variable numbers of terminal myelin loops from the underlying axolemma results in the formation of bracelets of Nageotte, whereas the transverse bands of these loops disappear. The adaptation of the paranodal myelin sheath to axonal expansion during development probably occurs by uneven gliding of the paranodal myelin loops simultaneously with internodal slippage of myelin lamellae. Since mechanically stabilizing structures (tight junctions and desmosomes between adjacent paranodal myelin processes; transverse bands between myelin loops and paranodal axolemma) are unevenly arranged, especially during rapid axonal growth, paranodal axonal growth with simultaneous adaptation of the myelin sheath is probably discontinuous with time.Presented in part at the 10th Biennial Meeting of the Peripheral Nerve Study Group at Arden House, Harriman, New York, USA, June 30th–July 3rd, 1991, and as a doctoral thesis (M. Bertram) at the RWTH Aachen in 1991     

Acrolein induces myelin damage in mammalian spinal cord

Myelin damage can lead to the loss of axonal conduction and paralysis in multiple sclerosis and spinal cord injury. Here, we show that acrolein, a lipid peroxidation product, can cause significant myelin damage in isolated guinea pig spinal cord segments. Acrolein-mediated myelin damage is particularly conspicuous in the paranodal region in both a calcium dependent (nodal lengthening) and a calcium-independent manner (paranodal myelin splitting). In addition, paranodal protein complexes can dissociate with acrolein incubation. Degraded myelin basic protein is also detected at the paranodal region. Acrolein-induced exposure and redistribution of paranodal potassium channels and the resulting axonal conduction failure can be partially reversed by 4-AP, a potassium channel blocker. From this data, it is clear that acrolein is capable of inflicting myelin damage as well as axonal degeneration, and may represent an important factor in the pathogenesis in multiple sclerosis and spinal cord injury.     

The role of fast and slow potassium currents in electrical activity of amphibian myelinated nerve fibres

The paper reviews the information about the role of fast and slow potassium currents in electrical activity of amphibian myelinated nerve fibres. It demonstrates the importance of discovering of fast and slow potassium currents and their following pharmacological separation (by potassium channels blockers 4-aminopyridine and tetraethylammonium) in investigation of mechanisms of biological potentials generation. The information about the existence of fast and slow potassium channels in the nerve membrane and about the properties of 4-aminopyridine and tetraethylammonium action served as a base for determination the nature of biological potentials and discovering the mechanism of potential-dependent action of 4-aminopyridine that for tens of years suffered from the lack of adequate explanation.     

Analysis of potassium channel functions in mammalian axons by gene knockouts

Mammalian axons express a rich repertoire of various K channel subtypes whose distribution is profoundly affected by myelination. In the past two decades, functional analysis of axonal K channels has been approached primarily through pharmacology. Recently, gene knockout techniques have been used to specifically delete a particular K channel subtype from axons. This is significant since the bulk of K channels in a myelinated nerve are covered by the myelin, making functional analysis of specific K channel subtypes by traditional means difficult. This review summarizes the first mutational analysis of this sort performed on an axonal fast K channel termed Kv1.1. This K channel is concealed by the myelin loops in the paranodes of all major myelinated fiber tracts, and exhibits highly heterogeneous distribution even in certain non-myelinated CNS axons. Physiological analysis of Kv1.1 null mutants suggest novel functions for this axonal K channel subtype, including modulation of conduction failures at branch points and stabilization of transition zones in myelinated nerves.     

A distributed-parameter model of the myelinated nerve fiber

This paper presents a new model for the characterization of electrical activity in the nodal, paranodal and internodal regions of isolated amphibian and mammalian myelinated nerve fibers. It differs from previous models in the following ways: (1) in its ability to incorporate detailed anatomical and electrophysiological data; (2) in its approach to the myelinated nerve fiber as a multi-axial cable; and (3) in the numerical algorithm used to obtain distributed model equation solutions for potential and current. The morphometric properties are taken from detailed electron microscopic anatomical studies (Berthold & Rydmark, 1983a, Experientia 39, 964-976). The internodal axolemma is characterized as an excitable membrane and model-generated nodal and internodal membrane action potentials are presented. A system of describing equations for the equivalent network model is derived, based on the application of Kirchoff's Current Law, which take the form of multiple cross-coupled parabolic partial differential equations. An implicit numerical integration method is developed and the numerical solution implemented on a parallel processor. Non-uniform spatial step sizes are used, enabling detailed representation of the nodal region while minimizing the number of total segments necessary to represent the overall fiber. Conduction velocities of 20.2 m sec-1 at 20 degrees C for a 15 microns diameter amphibian fiber and 57.6 m sec-1 at 37 degrees C for a 17.5 microns diameter mammalian fiber are achieved, which agrees qualitatively with published experimental data at similar temperatures (Huxley & St?mpfli, 1949, J. Physiol., Lond. 108, 315-339; Rasminsky, 1973, Arch, Neurol. 28, 287-292). The simulation results demonstrate the ability of this model to produce detailed representations of the transaxonal, transmyelin and transfiber potentials and currents, as well as the longitudinal extra-axonal, periaxonal and intra-axonal currents. Also indicated is the potential contribution of the paranodal axolemma to nodal activity as well as the presence of significant longitudinal currents in the periaxonal space adjacent to the node of Ranvier.     

Myelin as longitudinal conductor: a multi-layered model of the myelinated human motor nerve fibre

 The myelin sheath is normally regarded as an electrical insulator. Low values of radial conductance and capacitance have been measured, and in electrical models of myelinated axons the contribution of longitudinal conduction within the sheath has been ignored. According to X-ray diffraction studies, however, myelin sheaths comprise alternate lipid and aqueous layers, and the latter may be expected to have a low resistivity. We propose a new model of myelinated axons in which the aqueous layers within the myelin provide appreciable longitudinal and radial conductance, the latter via a spiral pathway. We have investigated the likely contribution of these conductive paths within the myelin to the electrical properties of a human motor nerve fibre by computer simulation, representing the myelin sheath as a series of interconnecting parallel lamellae. With this new model, action potential conduction has been simulated along a 20-node cable, and the electrotonic responses to 100-ms depolarizing and hyperpolarizing current pulses have been simulated for a uniformly polarized fibre. We have found that the hypothesis of a longitudinally conducting myelin sheath improves our previous model in two ways: it is no longer necessary to make implausible assumptions about the resistivity or width of the periaxonal space to simulate realistic electrotonus, and the conduction velocity is appreciably faster (by 8.6%). Received: 19 April 1999 / Accepted in revised form: 11 September 2000     

Pre- and postsynaptic effects of the calcium channel blocker verapamil in the nerve-muscle preparation

Verapamil did not change the amplitude of the miniature and multiquantal end-plate currents, synchronicity of the transmitter release and repetitive firing at the motor nerve endings. Verapamil shortened the decay of multiquantal currents, the effect being enhanced after acetylcholinesterase inhibition. In muscles with inhibited acetylcholinesterase, verapamil promoted the depression of successive end-late currents in rhythmic nerve stimulation. The data suggest that in skeletal muscles verapamil-sensitive calcium channels do not take part in physiological transmitter release or in chemical potentiation of the secretion after treatment with potassium channels blocking agents.     

Effects of KC 3791 on sodium and potassium channels in frog node of Ranvier

Effects of a new antiarrhytmic compound KC 3791 on sodium (INa) and potassium (IK) currents were studied in frog myelinated nerve fibres under voltage clamp conditions. When applied externally to the node of Ranvier, KC 3791 (KC) at concentrations of 10(-5)-10(-4) mol.l-1 produced both tonic and cumulative (use-dependent) inhibition of INa. An analysis of the frequency-, voltage- and time dependence of cumulative block by KC suggested that this block resulted from a voltage-dependent interaction of the drug with open Na channels. The progressive decrease in INa during repetitive pulsing was due to accumulation of Na channels in the resting-blocked state: closing of the activation gate after the end of each depolarizing pulse stabilized the KC-"receptor" complex. To unblock these channels a prolonged washing of the node had to be combined with a subsequent repetitive stimulation of the membrane; this suggested that channel could not become cleared of the blocker unless the activation gate has opened. KC also proved to be capable of blocking open K channels at outwardly directed potassium currents (IK). This block increased during membrane depolarization. Unblocking of K channels after the end of a depolarizing pulse proceeded much faster than unblocking of Na channels under identical conditions. Cumulative inhibition of outward IK during high-frequency membrane stimulation was therefore readily reversible upon a decrease in pulsing frequency.