Sensitivity of the electrical response of a node of Ranvier model to alterations of the myelin sheath geometry.

Nodes of Ranvier play critical roles in the generation and transmission of action potentials. Alterations in node properties during pathology and/or development are known to affect the speed and quality of electrical transmission. From a modelling standpoint, nodes of Ranvier are often described by systems of ordinary differential equations neglecting or greatly simplifying their geometric structure. These approaches fail to accurately describe how fine scale alteration in the node geometry or in myelin thickness in the paranode region will impact action potential generation and transmission. Here, we rely on a finite element approximation to describe the three dimensional geometry of a node of Ranvier. With this, we are able to investigate how sensitive is the electrical response to alterations in the myelin sheath and paranode geometry. We could in particular investigate irregular loss of myelin, which might be more physiologically relevant than the uniform loss often described through simpler modelling approaches.

Ultrafast and hypersensitive phase imaging of propagating internodal current flows in myelinated axons and electromagnetic pulses in dielectrics.

Many ultrafast phenomena in biology and physics are fundamental to our scientific understanding but have not yet been visualized owing to the extreme speed and sensitivity requirements in imaging modalities. Two examples are the propagation of passive current flows through myelinated axons and electromagnetic pulses through dielectrics, which are both key to information processing in living organisms and electronic devices. Here, we demonstrate differentially enhanced compressed ultrafast photography (Diff-CUP) to directly visualize propagations of passive current flows at approximately 100 m/s along internodes, i.e., continuous myelinated axons between nodes of Ranvier, from Xenopus laevis sciatic nerves and of electromagnetic pulses at approximately 5 × 107 m/s through lithium niobate. The spatiotemporal dynamics of both propagation processes are consistent with the results from computational models, demonstrating that Diff-CUP can span these two extreme timescales while maintaining high phase sensitivity. With its ultrahigh speed (picosecond resolution), high sensitivity, and noninvasiveness, Diff-CUP provides a powerful tool for investigating ultrafast biological and physical phenomena.

Microglia-neuron interaction at nodes of Ranvier depends on neuronal activity through potassium release and contributes to remyelination.

Microglia, the resident immune cells of the central nervous system, are key players in healthy brain homeostasis and plasticity. In neurological diseases, such as Multiple Sclerosis, activated microglia either promote tissue damage or favor neuroprotection and myelin regeneration. The mechanisms for microglia-neuron communication remain largely unkown. Here, we identify nodes of Ranvier as a direct site of interaction between microglia and axons, in both mouse and human tissues. Using dynamic imaging, we highlight the preferential interaction of microglial processes with nodes of Ranvier along myelinated fibers. We show that microglia-node interaction is modulated by neuronal activity and associated potassium release, with THIK-1 ensuring their microglial read-out. Altered axonal K+ flux following demyelination impairs the switch towards a pro-regenerative microglia phenotype and decreases remyelination rate. Taken together, these findings identify the node of Ranvier as a major site for microglia-neuron interaction, that may participate in microglia-neuron communication mediating pro-remyelinating effect of microglia after myelin injury.

Interactions among diameter, myelination, and the Na/K pump affect axonal resilience to high-frequency spiking.

Axons reliably conduct action potentials between neurons and/or other targets. Axons have widely variable diameters and can be myelinated or unmyelinated. Although the effect of these factors on propagation speed is well studied, how they constrain axonal resilience to high-frequency spiking is incompletely understood. Maximal firing frequencies range from ∼1 Hz to >300 Hz across neurons, but the process by which Na/K pumps counteract Na+ influx is slow, and the extent to which slow Na+ removal is compatible with high-frequency spiking is unclear. Modeling the process of Na+ removal shows that large-diameter axons are more resilient to high-frequency spikes than are small-diameter axons, because of their slow Na+ accumulation. In myelinated axons, the myelinated compartments between nodes of Ranvier act as a "reservoir" to slow Na+ accumulation and increase the reliability of axonal propagation. We now find that slowing the activation of K+ current can increase the Na+ influx rate, and the effect of minimizing the overlap between Na+ and K+ currents on spike propagation resilience depends on complex interactions among diameter, myelination, and the Na/K pump density. Our results suggest that, in neurons with different channel gating kinetic parameters, different strategies may be required to improve the reliability of axonal propagation.

Neuroinflammation in the normal-appearing white matter (NAWM) of the multiple sclerosis brain causes abnormalities at the nodes of Ranvier.

Changes to the structure of nodes of Ranvier in the normal-appearing white matter (NAWM) of multiple sclerosis (MS) brains are associated with chronic inflammation. We show that the paranodal domains in MS NAWM are longer on average than control, with Kv1.2 channels dislocated into the paranode. These pathological features are reproduced in a model of chronic meningeal inflammation generated by the injection of lentiviral vectors for the lymphotoxin-α (LTα) and interferon-γ (IFNγ) genes. We show that tumour necrosis factor (TNF), IFNγ, and glutamate can provoke paranodal elongation in cerebellar slice cultures, which could be reversed by an N-methyl-D-aspartate (NMDA) receptor blocker. When these changes were inserted into a computational model to simulate axonal conduction, a rapid decrease in velocity was observed, reaching conduction failure in small diameter axons. We suggest that glial cells activated by pro-inflammatory cytokines can produce high levels of glutamate, which triggers paranodal pathology, contributing to axonal damage and conduction deficits.

Nodes of Ranvier during development and repair in the CNS.

Saltatory conduction of action potentials along myelinated axons depends on the nodes of Ranvier - small unmyelinated axonal domains where voltage-gated sodium channels are concentrated. Our knowledge of the complex molecular composition of these axonal domains continues to accumulate, although the mechanisms of nodal assembly, which have been elucidated in the PNS, remain only partially understood in the CNS. Besides the key role of the nodes in accelerating conduction, nodal variations are thought to allow the fine tuning of axonal conduction speed to meet information processing needs. In addition, through their multiple glial contacts, nodes seem to be important for neuron-glia interactions. As we highlight in this Review, the disorganization of axonal domains has been implicated in the pathophysiology of various neurological diseases. In multiple sclerosis, for example, nodal and perinodal disruption following demyelination, with subsequent changes in ion channel distribution, leads to altered axonal conduction and integrity. The nodal clusters regenerate concurrently with but also prior to remyelination, allowing the restoration of axonal conduction. In this article, we review current knowledge of the organization and function of nodes of Ranvier in the CNS. We go on to discuss dynamic changes in the nodes during demyelination and remyelination, highlighting the impact of these changes on neuronal physiology in health and disease as well as the associated therapeutic implications.

Modelling the effects of ephaptic coupling on selectivity and response patterns during artificial stimulation of peripheral nerves.

Artificial electrical stimulation of peripheral nerves for sensory feedback restoration can greatly benefit from computational models for simulation-based neural implant design in order to reduce the trial-and-error approach usually taken, thus potentially significantly reducing research and development costs and time. To this end, we built a computational model of a peripheral nerve trunk in which the interstitial space between the fibers and the tissues was modelled using a resistor network, thus enabling distance-dependent ephaptic coupling between myelinated axons and between fascicles as well. We used the model to simulate a) the stimulation of a nerve trunk model with a cuff electrode, and b) the propagation of action potentials along the axons. Results were used to investigate the effect of ephaptic interactions on recruitment and selectivity stemming from artificial (i.e., neural implant) stimulation and on the relative timing between action potentials during propagation. Ephaptic coupling was found to increase the number of fibers that are activated by artificial stimulation, thus reducing the artificial currents required for axonal recruitment, and it was found to reduce and shift the range of optimal stimulation amplitudes for maximum inter-fascicular selectivity. During propagation, while fibers of similar diameters tended to lock their action potentials and reduce their conduction velocities, as expected from previous knowledge on bundles of identical axons, the presence of many other fibers of different diameters was found to make their interactions weaker and unstable.

Molecular organization and function of vertebrate septate-like junctions.

Septate-like junctions display characteristic ladder-like ultrastructure reminiscent of the invertebrate epithelial septate junctions and are present at the paranodes of myelinated axons. The paranodal junctions where the myelin loops attach to the axon at the borders of the node of Ranvier provide both a paracellular barrier to ion diffusion and a lateral fence along the axonal membrane. The septate-like junctions constrain the proper distribution of nodal Na+ channels and juxtaparanodal K+ channels, which are required for the safe propagation of the nerve influx and rapid saltatory conduction. The paranodal cell adhesion molecules have been identified as target antigens in peripheral demyelinating autoimmune diseases and the pathogenic mechanisms described. This review aims at presenting the recent knowledge on the molecular and structural organization of septate-like junctions, their formation and stabilization during development, and how they are involved in demyelinating diseases.

Local modulation of Neurofilament transport at Nodes of Ranvier.

Neurofilaments (NFs) are the most abundant cytoskeletal filaments undergoing 'slow axonal transport' in axons, and the population of NFs determines the axonal morphology. Both in vitro and ex-vivo experimental evidences show that the caliber of node is much thinner and the number of NFs in the node is much lower than the internode. Based on the Continuity equation, lower population of NFs indicates faster transport velocity. We propose that the local acceleration of NFs transport at node may result from the higher on-track rate [Formula: see text] or higher transition rate [Formula: see text] from pausing to running. We construct a segment of axon including both node and internode, and inject NFs by a fixed flux into it continuously. By upregulating transition rate of either [Formula: see text] or [Formula: see text] locally at the Node of Ranvier in the '6-state'model, we successfully accelerate NFs velocity and reproduce constriction of nodes. Our work demonstrates that local modulation of NF kinetics can change NFs distribution and shape the morphology of Node of Ranvier.

Saltatory Conduction along Myelinated Axons Involves a Periaxonal Nanocircuit.

The propagation of electrical impulses along axons is highly accelerated by the myelin sheath and produces saltating or "jumping" action potentials across internodes, from one node of Ranvier to the next. The underlying electrical circuit, as well as the existence and role of submyelin conduction in saltatory conduction remain, however, elusive. Here, we made patch-clamp and high-speed voltage-calibrated optical recordings of potentials across the nodal and internodal axolemma of myelinated neocortical pyramidal axons combined with electron microscopy and experimentally constrained cable modeling. Our results reveal a nanoscale yet conductive periaxonal space, incompletely sealed at the paranodes, which separates the potentials across the low-capacitance myelin sheath and internodal axolemma. The emerging double-cable model reproduces the recorded evolution of voltage waveforms across nodes and internodes, including rapid nodal potentials traveling in advance of attenuated waves in the internodal axolemma, revealing a mechanism for saltation across time and space.

Under the ECM Dome: The Physiological Role of the Perinodal Extracellular Matrix as an Ion Diffusion Barrier.

Enriched Na+ channel clustering allows for rapid saltatory conduction at a specialized structure in myelinated axons, the node of Ranvier, where cations are exchanged across the axon membrane. In the extracellular matrix (ECM), highly negatively charged molecules accumulate and wrap around the nodal gaps creating an ECM dome, called the perinodal ECM. The perinodal ECM has different molecular compositions in the central nervous system (CNS) and peripheral nervous system (PNS). Chondroitin sulfate proteoglycans are abundant in the ECM at the CNS nodes, whereas heparan sulfate proteoglycans are abundant at the PNS nodes. The proteoglycans have glycosaminoglycan chains on their core proteins, which makes them electrostatically negative. They associate with other ECM molecules and form a huge stable ECM complex at the nodal gaps. The polyanionic molecular complexes have high affinity to cations and potentially contribute to preventing cation diffusion at the nodes.In this chapter, we describe the molecular composition of the perinodal ECM in the CNS and PNS, and discuss their physiological role at the node of Ranvier.

Reduced order models of myelinated axonal compartments.

The paper presents a hierarchical series of computational models for myelinated axonal compartments. Three classes of models are considered, either with distributed parameters (2.5D EQS-ElectroQuasi Static, 1D TL-Transmission Lines) or with lumped parameters (0D). They are systematically analyzed with both analytical and numerical approaches, the main goal being to identify the best procedure for order reduction of each case. An appropriate error estimator is proposed in order to assess the accuracy of the models. This is the foundation of a procedure able to find the simplest reduced model having an imposed precision. The most computationally efficient model from the three geometries proved to be the analytical 1D one, which is able to have accuracy less than 0.1%. By order reduction with vector fitting, a finite model is generated with a relative difference of 10- 4 for order 5. The dynamical models thus extracted allow an efficient simulation of neurons and, consequently, of neuronal circuits. In such situations, the linear models of the myelinated compartments coupled with the dynamical, non-linear models of the Ranvier nodes, neuronal body (soma) and dendritic tree give global reduced models. In order to ease the simulation of large-scale neuronal systems, the sub-models at each level, including those of myelinated compartments should have the lowest possible order. The presented procedure is a first step in achieving simulations of neural systems with accuracy control.

Simulating perinodal changes observed in immune-mediated neuropathies: impact on conduction in a model of myelinated motor and sensory axons.

Immune-mediated neuropathies affect myelinated axons, resulting in conduction slowing or block that may affect motor and sensory axons differently. The underlying mechanisms of these neuropathies are not well understood. Using a myelinated axon model, we studied the impact of perinodal changes on conduction. We extended a longitudinal axon model (41 nodes of Ranvier) with biophysical properties unique to human myelinated motor and sensory axons. We simulated effects of temperature and axonal diameter on conduction and strength-duration properties. We then studied effects of impaired nodal sodium channel conductance and paranodal myelin detachment by reducing periaxonal resistance, as well as their interaction, on conduction in the 9 middle nodes and enclosed paranodes. Finally, we assessed the impact of reducing the affected region (5 nodes) and adding nodal widening. Physiological motor and sensory conduction velocities and changes to axonal diameter and temperature were observed. The sensory axon had a longer strength-duration time constant. Reducing sodium channel conductance and paranodal periaxonal resistance induced progressive conduction slowing. In motor axons, conduction block occurred with a 4-fold drop in sodium channel conductance or a 7.7-fold drop in periaxonal resistance. In sensory axons, block arose with a 4.8-fold drop in sodium channel conductance or a 9-fold drop in periaxonal resistance. This indicated that motor axons are more vulnerable to developing block. A boundary of block emerged when the two mechanisms interacted. This boundary shifted in opposite directions for a smaller affected region and nodal widening. These differences may contribute to the predominance of motor deficits observed in some immune-mediated neuropathies.NEW & NOTEWORTHY Immune-mediated neuropathies may affect myelinated motor and sensory axons differently. By the development of a computational model, we quantitatively studied the impact of perinodal changes on conduction in motor and sensory axons. Simulations of increasing nodal sodium channel dysfunction and paranodal myelin detachment induced progressive conduction slowing. Sensory axons were more resistant to block than motor axons. This could explain the greater predisposition of motor axons to functional deficits observed in some immune-mediated neuropathies.

Imaging Peripheral Nerve Regeneration: A New Technique for 3D Visualization of Axonal Behavior.

BACKGROUND: Peripheral nerve assessment has traditionally been studied through histological and immunological staining techniques in a limited cross-sectional modality, making detailed analysis difficult. A new application of serial section electron microscopy is presented to overcome these limitations. METHODS: Direct nerve repairs were performed on the posterior auricular nerve of transgenic YFP-H mice. Six weeks postoperatively the nerves were imaged using confocal fluorescent microscopy then excised and embedded in resin. Resin blocks were sequentially sectioned at 100 nm, and sections were serially imaged with an electron microscope. Images were aligned and autosegmented to allow for 3D reconstruction. RESULTS: Basic morphometry and axonal counts were fully automated. Using full 3D reconstructions, the relationships between the axons, the Nodes of Ranvier, and Schwann cells could be fully appreciated. Interactions of individual axons with their surrounding environment could be visualized and explored in a virtual three-dimensional space. CONCLUSIONS: Serial section electron microscopy allows the detailed pathway of the regenerating axon to be visualized in a 3D virtual space in comparison to isolated individual traditional histological techniques. Fully automated histo-morphometry can now give accurate axonal counts, provide information regarding the quality of nerve regeneration, and reveal the cell-to-cell interaction at a super-resolution scale. It is possible to fully visualize and "fly-through" the nerve to help understand the behavior of a regenerating axon within its environment. This technique provides future opportunities to evaluate the effect different treatment modalities have on the neuroregenerative potential and help us understand the impact different surgical techniques have when treating nerve injuries.

Normal audiogram but poor sensitivity to brief sounds in mice with compromised voltage-gated sodium channels (Scn8amedJ).

The Scn8amedJ mutation of the gene for sodium channels at the nodes of Ranvier slows nerve conduction, resulting in motor abnormalities. This mutation is also associated with loss of spontaneous bursting activity in the dorsal cochlear nucleus. However initial tests of auditory sensitivity in mice homozygous for this mutation, using standard 400-ms tones, demonstrated normal hearing sensitivity. Further testing, reported here, revealed a severely compromised sensitivity to short-duration tones of 10 and 2 ms durations. Such a deficit might be expected to interfere with auditory functions that depend on rapid processing of auditory signals.

Glial Sulfatides and Neuronal Complex Gangliosides Are Functionally Interdependent in Maintaining Myelinating Axon Integrity.

Sulfatides and gangliosides are raft-associated glycolipids essential for maintaining myelinated nerve integrity. Mice deficient in sulfatide (cerebroside sulfotransferase knock-out, CST-/-) or complex gangliosides (ß-1,4-N-acetylegalactosaminyltransferase1 knock-out, GalNAc-T-/-) display prominent disorganization of proteins at the node of Ranvier (NoR) in early life and age-dependent neurodegeneration. Loss of neuronal rather than glial complex gangliosides underpins the GalNAc-T-/- phenotype, as shown by neuron- or glial-specific rescue, whereas sulfatide is principally expressed and functional in glial membranes. The similarities in NoR phenotype of CST-/-, GalNAc-T-/-, and axo-glial protein-deficient mice suggests that these glycolipids stabilize membrane proteins including neurofascin155 (NF155) and myelin-associated glycoprotein (MAG) at axo-glial junctions. To assess the functional interactions between sulfatide and gangliosides, CST-/- and GalNAc-T-/- genotypes were interbred. CST-/-× GalNAc-T-/- mice develop normally to postnatal day 10 (P10), but all die between P20 and P25, coinciding with peak myelination. Ultrastructural, immunohistological, and biochemical analysis of either sex revealed widespread axonal degeneration and disruption to the axo-glial junction at the NoR. In addition to sulfatide-dependent loss of NF155, CST-/- × GalNAc-T-/- mice exhibited a major reduction in MAG protein levels in CNS myelin compared with WT and single-lipid-deficient mice. The CST-/- × GalNAc-T-/- phenotype was fully restored to that of CST-/- mice by neuron-specific expression of complex gangliosides, but not by their glial-specific expression nor by the global expression of a-series gangliosides. These data indicate that sulfatide and complex b-series gangliosides on the glial and neuronal membranes, respectively, act in concert to promote NF155 and MAG in maintaining the stable axo-glial interactions essential for normal nerve function.SIGNIFICANCE STATEMENT Sulfatides and complex gangliosides are membrane glycolipids with important roles in maintaining nervous system integrity. Node of Ranvier maintenance in particular requires stable compartmentalization of multiple membrane proteins. The axo-glial adhesion molecules neurofascin155 (NF155) and myelin-associated glycoprotein (MAG) require membrane microdomains containing either sulfatides or complex gangliosides to localize and function effectively. The cooperative roles of these microdomains and associated proteins are unknown. Here, we show vital interdependent roles for sulfatides and complex gangliosides because double (but not single) deficiency causes a rapidly lethal phenotype at an early age. These findings suggest that sulfatides and complex gangliosides on opposing axo-glial membranes are responsible for essential tethering of the axo-glial junction proteins NF155 and MAG, which interact to maintain the nodal complex.

Sensitivity analysis of the Poisson Nernst-Planck equations: a finite element approximation for the sensitive analysis of an electrodiffusion model.

Biological structures exhibiting electric potential fluctuations such as neuron and neural structures with complex geometries are modelled using an electrodiffusion or Poisson Nernst-Planck system of equations. These structures typically depend upon several parameters displaying a large degree of variation or that cannot be precisely inferred experimentally. It is crucial to understand how the mathematical model (and resulting simulations) depend on specific values of these parameters. Here we develop a rigorous approach based on the sensitivity equation for the electrodiffusion model. To illustrate the proposed methodology, we investigate the sensitivity of the electrical response of a node of Ranvier with respect to ionic diffusion coefficients and the membrane dielectric permittivity.

Strain partitioning between nerves and axons: Estimating axonal strain using sodium channel staining in intact peripheral nerves.

BACKGROUND: Peripheral nerves carry afferent and efferent signals between the central nervous system and the periphery of the body. When nerves are strained above physiological levels, conduction blocks occur, resulting in debilitating loss of motor and sensory function. Understanding the effects of strain on nerve function requires knowledge of the multi-scale mechanical behaviour of the tissue, and how this is transferred to the cellular environment. NEW METHOD: The aim of this work was to establish a technique to measure the partitioning of strain between tissue and axons in axially loaded peripheral nerves. This was achieved by staining extracellular domains of sodium channels clustered at nodes of Ranvier, without altering tissue mechanical properties by fixation or permeabilisation. RESULTS: Stained nerves were imaged by multi-photon microscopy during in situ tensile straining, and digital image correlation was used to measure axonal strain with increasing tissue strain. Strain was partitioned between tissue and axon scales by an average factor of 0.55. COMPARISONS WITH EXISTING METHODS: This technique allows non-invasive probing of cell-level strain within the physiological tissue environment. CONCLUSIONS: This technique can help understand the mechanisms behind the onset of conduction blocks in injured peripheral nerves, as well as to evaluate changes in multi-scale mechanical properties in diseased nerves.

Nodes of Ranvier in Glaucoma.

Retinal ganglion cell axons of the DBA/2J mouse model of glaucoma, a model characterized by extensive neuroinflammation, preserve synaptic contacts with their subcortical targets for a time after onset of anterograde axonal transport deficits, axon terminal hypertrophy, and cytoskeletal alterations. Though retrograde axonal transport is still evident in these axons, it is unknown if they retain their ability to transmit visual information to the brain. Using a combination of in vivo multiunit electrophysiology, neuronal tract tracing, multichannel immunofluorescence, and transmission electron microscopy, we report that eye-brain signaling deficits precede transport loss and axonal degeneration in the DBA/2J retinal projection. These deficits are accompanied by node of Ranvier pathology - consisting of increased node length and redistribution of the voltage-gated sodium channel Nav1.6 that parallel changes seen early in multiple sclerosis (MS) axonopathy. Further, with age, axon caliber and neurofilament density increase without corresponding changes in myelin thickness. In contrast to these findings in DBA/2J mice, node pathologies were not observed in the induced microbead occlusion model of glaucoma - a model that lacks pre-existing inflammation. After one week of systemic treatment with fingolimod, an immunosuppressant therapy for relapsing-remitting MS, DBA/2J mice showed a substantial reduction in node pathology and mild effects on axon morphology. These data suggest that neurophysiological deficits in the DBA/2J may be due to defects in intact axons and targeting node pathology may be a promising intervention for some types of glaucoma.

A model of motor and sensory axon activation in the median nerve using surface electrical stimulation.

Surface electrical stimulation has the potential to be a powerful and non-invasive treatment for a variety of medical conditions but currently it is difficult to obtain consistent evoked responses. A viable clinical system must be able to adapt to variations in individuals to produce repeatable results. To more fully study the effect of these variations without performing exhaustive testing on human subjects, a system of computer models was created to predict motor and sensory axon activation in the median nerve due to surface electrical stimulation at the elbow. An anatomically-based finite element model of the arm was built to accurately predict voltages resulting from surface electrical stimulation. In addition, two axon models were developed based on previously published models to incorporate physiological differences between sensory and motor axons. This resulted in axon models that could reproduce experimental results for conduction velocity, strength-duration curves and activation threshold. Differences in experimentally obtained action potential shape between the motor and sensory axons were reflected in the models. The models predicted a lower threshold for sensory axons than motor axons of the same diameter, allowing a range of sensory axons to be activated before any motor axons. This system of models will be a useful tool for development of surface electrical stimulation as a method to target specific neural functions.