Nicotinic acetylcholine receptors in mouse and rat optic nerves

Receptor-mediated calcium signaling in axons of mouse and rat optic nerves was examined by selectively staining the axonal population with a calcium indicator. Nicotine (1-50 microM) induced an axonal calcium elevation that was eliminated when calcium was removed from the bath, suggesting that nicotine induces calcium influx into axons. The nicotine response was blocked by d-tubocurarine and mecamylamine but not alpha-bungarotoxin, indicating the presence of calcium permeable, non-alpha7 nicotinic acetylcholine receptor (nAChR) subtype. Agonist efficacy order for eliciting the axonal nAChR calcium response was cytisine approximately nicotine > acetylcholine. The nicotine-mediated calcium response was attenuated during the process of normal myelination, decreasing by approximately 10-fold from P1 (premyelinated) to P30 (myelinated). Nicotine also caused a rapid reduction in the compound action potential in neonatal optic nerves, consistent with a shunting of the membrane after opening of the nonspecific cationic nicotinic channels. Voltagegated calcium channels contributed little to the axonal calcium elevation during nAChR activation. During repetitive stimulations, the compound action potential in neonatal mouse optic nerves underwent a gradual reduction in amplitude that could be partially prevented by d-tubocurarine, suggesting an activity-dependent release of acetylcholine that activates axonal AChRs. We conclude that mammalian optic nerve axons express nAChRs and suggest that these receptors are activated in an activity-dependent fashion during optic nerve development to modulate axon excitability and biology.     

Ephaptic transmission in squid giant axons.

Some characteristics of ephaptic transmission of action potentials were investigated with squid giant axons. For these studies two isolated axons were placed side by side or, on occasion, a single long axon was looped to form an "ephapse" between the axon trunk and one of its main branches. Extracellular potentials measured adjacent to axons surrounded by a very restricted volume of liquid ranged up to 80 mV in magnitude and had a shape similar to that of the membrane current. Intracellular records of the same axon regions show small voltage deflections; however, the transmembrane voltage (Vm = Vi - Vo) has the appearance of normally propagated action potentials. Ephaptic transmission of action potentials is possible when the ephaptic region is submerged in oil, as well as when the region is immersed in low-calcium solutions. When the speed of the propagated action potential is lowered by replacing the normal artifical seawater (ASW) with low-sodium ASW, some ephaptic effects are enhanced. It is concluded that in regions in which axons are confined by restricted extracellular volume, the large extracellular voltage changes arising during the passage of an action potential in one can cause ephaptic excitation in another.     

Coupling of calcium homeostasis to axonal sodium in axons of mouse optic nerve

Axonal populations in neonatal and mature optic nerves were selectively stained with calcium dyes for analysis of calcium homeostasis and its possible coupling to axonal Na. Repetitive nerve stimulation causes a rise in axonal [Ca(2+)](i) the posttetanus recovery of which is impeded by increasing the number of action potentials in the tetanus. This effect is augmented in 4-aminopyridine (4-AP; 1 mM), which dramatically increases the calcium and presumably sodium load during the tetanus. Increasing axonal [Na](i) with the Na-ionophore monensin (4-50 microM) and ouabain (30 microM) retards posttetanus calcium decline, suggesting that efficient calcium clearance depends on a low level of axonal [Na](i). Posttetanus calcium clearance is not affected by K-mediated depolarization. To further examine coupling between axonal [Na](i) and [Ca(2+)](i), the resting axonal [Ca(2+)](i) was monitored as axonal [Na(+)](i) was elevated with ouabain, veratridine, and monensin. In all cases, elevation of axonal [Na(+)](i) evokes a calcium influx into axons. This influx is unrelated to activation of calcium channels but is consistent with calcium influx via reversal of the Na/Ca exchanger expected as a consequence of axonal [Na(+)](i) elevation. In conclusion, this study demonstrates that calcium homeostasis in the axons of the optic nerve is strongly coupled to axonal [Na(+)](i) in a manner consistent with the Na/Ca exchanger playing a major role in extruding calcium following nerve activity.     

Cytochemical evidence for redistribution of membrane pump calcium-ATPase and ecto-Ca-ATPase activity, and calcium influx in myelinated nerve fibres of the optic nerve after stretch injury

Summary There has been controversy for some time as to whether a posttraumatic influx of calcium ions occurs in stretch/non-disruptively injured axons within the central nervous system in both human diffuse axonal injury and a variety of models of such injury. We have used the oxalate/pyroantimonate technique to provide cytochemical evidence in support of such an ionic influx after focal axonal injury to normoxic guinea pig optic nerve axons, a model for human diffuse axonal injury. We present evidence for morphological changes within 15 min of injury where aggregates of pyroantimonate precipitate occur in nodal blebs at nodes of Ranvier, in focal swellings within axonal mitochondria, and at localized sites of separation of myelin lamellae. In parallel with these studies, we have used cytochemical techniques for localization of membrane pump Ca²⁺-ATPase and ecto-Ca-ATPase activity. There is loss of labelling for membrane pump Ca²⁺-ATPase activity on the nodal axolemma, together with loss of ecto-Ca-ATPase from the external aspect of the myelin sheath at sites of focal separation of myelin lamellae. Disruption of myelin lamellae and loss of ecto-Ca-ATPase activity becomes widespread between 1 and 4 h after injury. This is correlated with both infolding and retraction of the axolemma from the internal aspect of the myelin sheath to form periaxonal spaces which are characterized by aggregates of pyroantimonate precipitate, and the development of myelin intrusions into invaginations of the axolemma such that the regular profile of the axon is lost. There is novel labelling of membrane pump Ca²⁺-ATPase on the cytoplasmic aspect of the internodal axolemma between 1 and 4 h after injury. There is loss of an organized axonal cytoskeleton in a proportion of nerve fibres by 4–6 h after injury. We suggest that these changes demonstrate a progressive pathology linked to calcium ion influx after stretch (non-disruptive) axonal injury to optic nerve myelinated fibres. We posit that calcium influx, linked to or correlated with changes in Ca²⁺-ATPase activities, results in dissolution of the axonal cytoskeleton and axotomy between 4 and 6 h after the initial insult to axons.     

Surviving anoxia: a tale of two white matter tracts

Successful axon function is vital to the overall performance of the central nervous system (CNS). White matter (WM) axons are dependent on constant supply of oxygen and glucose to transmit signals with high fidelity. The optic nerve is a pure WM tract composed of completely myelinated axons while corpus callosum (CC) slices contain both gray and WM portions of the brain with a mixture of myelinated and unmyelinated axons. Axon function in both WM tracts is resistant to anoxia with a subset of axons able to survive exclusively on energy generated by glycolysis. In mouse optic nerves (MONs), removal of glucose during anoxia causes complete loss of axon function, implicating glucose as the sole source of energy. In contrast, in rat optic nerve (RON), anoxia causes rapid and complete loss of function. Because RON is about twice the diameter of MON, glucose diffusion during anoxia is inadequate. Increasing bath glucose concentration restores the ability of RON axons to persist during anoxia. Although in 10 mM glucose, MONs and CC slices exhibit identical resistance to anoxia, 30 mM glucose unmasks the greater resistance of CC axons suggesting unmyelinated axons and/or the smallest axons with the thinnest myelin sheath are resistant to anoxia. These results reveal that CNS WM is remarkably tolerant of anoxia although there is regional variability in their ability to function and survive anoxia. To achieve optimal protection of the CNS in various neurological diseases, it is critical to understand the properties of regional energy metabolisms and injury mechanisms for successful therapeutic approaches.     

Retrograde degeneration of myelinated axons and re-organization in the optic nerves of adult frogs (Xenopus laevis) following nerve injury or tectal ablation

Summary The optic nerve proximal to the lesion (toward the retina) was examined by light and electron microscopy in adultXenopus laevis after various types of injury to optic nerve fibres. Intraorbital resection, transection or crush of the optic nerve or ablation of the contralateral optic tectum all resulted in marked alterations in the myelinated axon population and in the overall appearance of the nerve proximal to the site of injury. Examination of the nerves from 3 days to 6 months postoperatively indicated that a progressive, retrograde degeneration of myelin and loss of large-diameter axons occurred throughout the retinal nerve stump regardless of the type of injury or distance of the injury from the retina. The retinal stump of nerves receiving resection or transection showed a nearly complete loss of myelin and large-diameter axons while the degree of degeneration was subtotal in nerves receiving crush injury or after lesions farther from the retina (i.e. tectal ablation). In addition, the entire retinal nerve stump after all types of injury was characterized by the appearance of an actively growing axon population situated circumferentially under the glia limitans. The latter fibres are believed to represent regrowing axons which are being added onto the nerve, external to the original axon population and are suspected to modify actively the glial terrain and glia limitans.     

Mechanisms for differential block among single myelinated and non-myelinated axons by procaine

1. The differential sensitivity of saphenous nerve fibres in the cat to block by procaine HCl was re-examined by recording identifiable unit action potentials from small nerve filaments.2. Small myelinated axons were blocked more quickly than large myelinated axons, but this differential effect could not be accounted for by differences in anaesthetic concentration requirements.3. The onset of block in non-myelinated axons was slower than or equal to that of small myelinated axons depending on anaesthetic concentration.4. Absolute differential block of non-myelinated and small myelinated axons was obtained by limiting the length of axons exposed to procaine to 2 mm.5. Differential rates of blocking among myelinated axons appear to depend on differences in the length of axons that must be exposed to blocking concentrations of procaine and to arise from the irregular distribution of such concentrations within an exposed nerve.     

Morphological and electrophysiological characterization of the adult Siberian hamster optic nerve

Electrophysiological recordings and transmission electron microscopy were used to characterize the compound action potential (CAP) and morphology, respectively, of the optic nerve in the Siberian hamster. The CAP was polyphasic in nature, comprising four separate but overlapping peaks, thereby implying that four sub-populations of axons defined by conduction velocity are present in the nerve. The histological analysis of nerves from four animals revealed a cross-sectional area of 128,171 μm² containing 78,109 axons. All of the axons were myelinated, and measurements of axon surface area revealed values ranging from 0.09 to 9.92 μm², although 68.3% were <1 μm². In the regions of the nerve sampled, the area occupied by axons varied from 10.2 to 80.1%, but in 72.5% of these regions the axons occupied between 50 and 70% of the total cross-sectional area. All regions of the nerve expressed small axons, but larger axons (>2.5 μm²) were selectively distributed throughout the nerve. We conclude that the CAP recorded from hamster optic nerve displays four distinct peaks; however, morphological analysis failed to reveal a similar distribution of axon sizes.     

Modulation of axonal excitability mediated by surround electric activity: An intra-axonal study

Summary Intra-axonal recordings were obtained in vitro from frog sciatic nerve axons. Adjusting whole nerve stimulation current to just subthreshold for the impaled axon elicited triphasic threshold changes in that axon. Threshold changes were determined by direct intra-axonal current application. Graded subthreshold depolarizations were present in many axons during the passage of action potentials in surrounding axons. When nerve branches were stimulated and axon recordings were obtained from the main nerve trunk, both branches, the one that activated the impaled axon and the one that did not, elicited threshold changes in the impaled axon. These data indicate on a cellular level that impulse activity in an intact nerve bundle can modulate the excitability of adjacent nonactivated fibers.Supported by the Medical Research Service of the Veterans Administration, a grant from the National Multiple Sclerosis Society (RG 1365), and the Culpeper Foundation     

Electron microscopic study of the interaction of axons and glia at the site of anastomosis between the optic nerve and cellular or acellular sciatic nerve grafts

Summary The interactions between retinal ganglion cell (RGC) axons and glia at the site of optic nerve section and at the junctional zone between optic nerve and cellular or acellular peripheral nerve (PN) grafts have been studied electron microscopically. After transection, RGC axons, accompanied by processes of astrocyte cytoplasm, grew out from the proximal optic nerve stump into the scar tissue that developed between proximal and distal stumps. However, axons failed to cross the scar, and none entered the distal stump. By 3 days post lesion (DPL), bundles of RGC axons, accompanied by astrocytes and oligodendrocytes, grew out from the proximal optic nerve stump into the junctional zone between optic nerve and either type of PN graft. The bundles of RGC axons and growth cones that grew towards acellular PN grafts degenerated within 10–20 DPL; by 30 DPL a small number of axons persisted within the end of the proximal optic nerve stump. No axons were seen within the acellular PN grafts. These results suggest that reactive axonal sprouting, axon outgrowth and glial migration from the proximal optic nerve stump are events that occur during an acute response to injury, and that they are independent of the presence of Schwann cells. However, it would appear that few axons entered either scar or junctional zone unless accompanied by glia. There was little evidence that axon outgrowth was laminin-dependent.The bundles that grew towards cellular PN grafts encountered cells that we have identified as Schwann cells within the junctional zone: the axons in these bundles survived and entered the cellular grafts. Schwann cells migrated into the junctional zone from the cellular PN graft. It is probable that Schwann cells facilitated RGC axon entry into the graft directly by both cell contact and the secretion of neuronotrophic factors, and indirectly by modifying the CNS glia in the junctional zone.     

Nicotinic control of axon excitability regulates thalamocortical transmission

The thalamocortical pathway, a bundle of myelinated axons that arises from thalamic relay neurons, carries sensory information to the neocortex. Because axon excitation is an obligatory step in the relay of information from the thalamus to the cortex, it represents a potential point of control. We now show that, in adult mice, the activation of nicotinic acetylcholine receptors (nAChRs) in the initial portion of the auditory thalamocortical pathway modulates thalamocortical transmission of information by regulating axon excitability. Exogenous nicotine enhanced the probability and synchrony of evoked action potential discharges along thalamocortical axons in vitro, but had little effect on synaptic release mechanisms. In vivo, the blockade of nAChRs in the thalamocortical pathway reduced sound-evoked cortical responses, especially those evoked by sounds near the acoustic threshold. These data indicate that endogenous acetylcholine activates nAChRs in the thalamocortical pathway to lower the threshold for thalamocortical transmission and to increase the magnitude of sensory-evoked cortical responses. Our results show that a neurotransmitter can modulate sensory processing by regulating conduction along myelinated thalamocortical axons.     

Localization of the excitable membrane in the myelinated giant fiber of shrimp Penaeus japonicus

A significant DC-potential was recorded from the axon of shrimp myelinated giant nerve fiber, using a dye-filled microelectrode. Tracing of the dye assured that the source of the potential was the axonal membrane. All-or-none action potentials were obtained in the same preparation from which the ends of the axon were removed except for the synaptic region. It was concluded that the functionally excitable membrane is localized only in the synaptic region.     

The distribution of axons according to diameter in the optic nerve and optic tract of the rat

The distribution of axons according to diameter was examined in the optic nerve and optic tract of adult hooded rats. Observations were made on semithin sections, and measurements of axonal diameters were made on electron micrographs taken from various locations across thin sections through the optic nerve and tract. The distribution of axons by size differs markedly in the optic nerve and tract. Coarse (greater than 2 microns) and fine (less than or equal to 2 microns) axons are distributed throughout all regions of the optic nerve. In the optic tract, in contrast, coarse axons are especially dense dorsally, at the deep border of the tract, while they are absent ventrally, subjacent to the pial surface. No regions of the optic nerve contain densities of coarse axons as high as the deep nor as low as the superficial extremes of the optic tract. Nevertheless, even at the deep (dorsal) border of the optic tract, the coarse axons make up only a small minority (roughly 15%) of the total number of axons in that region. The axons 2 microns or smaller may be divisible into two overlapping, fine and intermediate, diameter classes, that are partially segregated within the optic tract, but not in the optic nerve: the distributions of axon diameters smaller than 2 microns are skewed to distinctly smaller diameters at the dorsal and ventral extremes of the optic tract, while in between, at mid-positions along the deep-to-superficial axis of the optic tract, the axon size distributions contain many more axons greater than 1 micron in diameter. These different axon diameter groups may arise from the morphologically distinct retinal ganglion cell types, and may underlie the components of the trimodal compound axon potential seen in the rat's primary optic pathway. Their partial segregation within the tract anticipates the partial segregation of their terminal arborizations within the laminae of the dorsal lateral geniculate nucleus. The rearrangement of axons into a partial segregation by size within the optic tract may indicate a chronology of axonal arrival during early development, proximity to the pial surface being an index of recency of arrival. As axonal outgrowth and neurogenesis appear to be directly related within the retinal ganglion cell population in mammals, the relative birthdates of the retinal ganglion cell types giving rise to the axon diameter classes in the rat may be inferred from the present results.     

Reduced model and simulation of myelinated axon using eigenfunction expansion and singular perturbation

In a myelinated axon, there exist many nodes of Ranvier where myelin sheaths are absent and action potentials are actively regenerated. Hence, a myelinated axon is a nonuniform cable where myelinated parts and unmyelinated nodes of Ranvier are described by different cable equations. For the modelling of a myelinated axon, the compartment model based on finite volume or finite difference discretization was dominantly used. In this paper, we propose a hybrid approach where an eigenfunction expansion combined with singular perturbation is employed for myelinated parts, and demonstrate that the proposed scheme can achieve an order of magnitude accuracy improvement for low order models. Moreover, it is also shown that the proposed scheme converges faster to attain a given accuracy. Hence, for simulation of myelinated axons, the proposed scheme can be an attractive alternative to the compartment model, that leads to a low order model with much higher accuracy or that converges faster for a given accuracy.     

Conduction velocity groups in the cat's optic nerve classified according to their retinal origin

Summary By recording antidromic field potentials and unit responses generated in the retina by stimulation of the optic tract and optic disc, evidence was obtained which suggests the presence of four major conduction velocity groups in the cat's optic nerve. The axons from all peripheral retina appear to fall into two groups, fast and slow, which correspond to the two major velocity groups described by earlier workers. Evidence is presented that the axons which arise from the area centralis form two distinctly slower conduction velocity groups. For each conduction velocity group, and for 60 single units, conduction velocity was estimated for both the intraretinal (unmyelinated) and extraretinal (myelinated) segments of the axons. All axons encountered accelerated markedly on leaving the retina. An anatomical basis for the classification of conduction velocity groups is presented in an accompanying paper.     

Axon diameter distributions across the monkey's optic nerve

The distribution of axons according to diameter has been examined in the optic nerve of old world monkeys. Axon diameters were measured from electron micrographs, and histograms were constructed at regular intervals across a section through the optic nerve to reveal the local axon diameter distribution. The total axon diameter distribution was also estimated. Fine-calibre optic axons (less than 2.0 micron in diameter) are found at all locations across the optic nerve. They are most frequent centrotemporally, where very few coarse optic axons can be found, but also make up the majority at the optic nerve's periphery. Coarse optic axons (greater than 2.0 microns in diameter) are increasingly common at progressively peripheral positions in the nerve. Around the nerve's circumference, these coarse optic axons are least numerous temporally, and most common dorsonasally. The axon diameter distribution peaks around 1.25 microns at most locations across the optic nerve, but there are more, slightly larger (1.5-2.0 microns), optic axons dorsally than ventrally. The estimated total axon diameter distribution is unimodal, peaking at 1.0-1.25 microns, with an extended tail towards larger diameters. This centroperipheral gradient of increasing axon diameters across the optic nerve is not substantial enough to account for the partial segregation of axons by size in the monkey's optic tract: there, coarse optic axons form a conspicuously greater proportion of the local axon diameter distribution along the tract's superficial (sub-pial) border, and fine optic axons are the only axons present near the tract's deep border. Hence, the fibre distribution in the optic tract cannot be formed by a simple combination of the fibre distributions of the two respective half-nerves, as described in the classic neuro-ophthalmologic literature. Rather, the present results, in conjunction with previous results from the optic tract, demonstrate that there must be a reorganization of axons by size in or near the optic chiasm.     

The non-immunosuppressive immunophilin ligand GPI-1046 potently stimulates regenerating axon growth from adult mouse dorsal root ganglia cultured in Matrigel

We used explant cultures of adult mouse dorsal root ganglia with spinal nerve attached growing in Matrigel to assess the effects of the non-immunosuppressive immunophilin ligand GPI-1046 [Snyder et al. (1998) TIPS 19, 21-26] on the growth rate of regenerating sensory axons and found a potent stimulation of axon growth. In these explant cultures, naked, unfasciculated axons emerge from the cut end of the spinal nerve and continue to grow in the Matrigel for up to eight days [Tonge et al. (1996) Neuroscience 73, 541-551]. Some axons are entirely smooth whilst others show prominent varicosities. Some of the former express the phosphorylated neurofilament epitope recognised by monoclonal antibody RT97, a marker for large calibre, myelinated axons, whilst the latter express calcitonin gene-related peptide, predominantly a marker for unmyelinated, and small diameter myelinated sensory axons. Many of the axons in these cultures also express the low-affinity neurotrophin receptor p75. GPI-1046 has been shown to have striking stimulatory effects on embryonic primary sensory axons growing in vitro and it was therefore of interest to see whether it could also enhance regenerating sensory axon growth from the adult ganglia in our cultures. GPI-1046 potently stimulated axon growth in our cultures in a dose-dependent manner. The stimulatory effect was not dependent on the class of sensory axon. These observations show that GPI-1046 is a potent stimulator of regenerating axons from adult, primary sensory neurones. The cellular site of action of GPI-1046 is unknown. To distinguish between a direct effect of the drug on neurones and an indirect effect we compared the effects of GPI-1046 on explant and dissociated cultures. In confirmation of previous results, we found that GPI-1046 potently stimulated axon outgrowth from explants of embryonic chick dorsal root ganglia. However, the drug was without effect on dissociated embryonic dorsal root ganglion neurones, suggesting that non-neuronal cells are important for axon growth stimulation.     

The postnatal development of the optic nerve of a reptile (Vipera aspis): A quantitative ultrastructural study

The number of axons in the optic nerve of the ovoviviparous reptile Vipera aspis was estimated from electron micrographs taken during the first 5 weeks of postnatal life. One to two days after birth, the optic nerve contains about 170,000 fibres, of which about 9% are myelinated. At the end of the fifth postnatal week, the number of optic fibres has fallen to about 100,000, of which about 42% are myelinated. This fibre loss continues after the fifth postnatal week, since in the adult viper the nerve contains about 60,000 fibres, of which 85% are myelinated; overall, about 65% of the optic nerve fibres present at birth disappear before the number of axons stabilises at the adult level. This study shows, for the first time, that the mode of development of the visual axons of reptiles is not that of anamniote vertebrates but similar to that of birds and mammals.     

Suprathreshold excitation of frog tectal neurons by short spike trains of single retinal ganglion cell

It has been established that coincident inputs from multiple presynaptic axons are required to achieve a suprathreshold level of excitation for the most of central neurons. The present study, however, was designed to determine whether a train of spikes of an individual retinal ganglion cell (that is, input from a single presynaptic axon) targeting a frog tectum layer F could evoke suprathreshold excitation of tectal neurons. The lungs of immobilized frog were artificially ventilated during experiments. An individual ganglion cell was electrically stimulated in the retina through a multi-channel electrode. Responses evoked in the tectum by the stimulation were recorded extracellularly from a terminal arborization of the retinotectal fiber using the carbon-fiber microelectrode. Negative and negative-positive spikes (referred to as first type population responses) and polyphasic spikes followed by excitatory synaptic potentials (referred to as second type population responses) were observed in the recordings of retinotectal activity. Usually, the population responses have ensued after the frequency facilitated first and/or second testing individual retinotectal synaptic potential and disappeared in a threshold manner with a reduction of retinotectal transmission by an application of kynurenic acid. These observations have suggested that the population responses were a consequence of a suprathreshold excitation of tectal neurons and, therefore, could serve as the sign for such an excitation. Recordings have also demonstrated that sources of the first type population responses (likely, the hillocks of axons or somas of postsynaptic neurons) lie deeper than the optic fiber layer F of the tectum, whereas sources of the second type population responses (likely, axon terminal arborizations of these postsynaptic neurons) are scattered throughout the optic fiber layers. The findings have suggested: 1) a short train of action potentials of an individual retinal ganglion cell (likely darkness, also known as 5th, detector) can excite tectal neurons to suprathreshold level; 2) tectal and perhaps, nucleus isthmi neurons that make up recurrent connection circuits to the optic fiber layers of the tectum are also activated; 3) a suprathreshold level for an individual retinotectal input is achieved primarily due to the frequency facilitation of synaptic potentials; and 4) an artificial ventilation of the lungs of immobilized frog favors the eliciting of a suprathreshold excitation of tectal neurons, demonstrating that the ventilation certainly improves the physiological condition of a frog.     

Computer model for action potential propagation through branch point in myelinated nerves

A mathematical model is developed for simulation of action potential propagation through a single branch point of a myelinated nerve fiber with a parent branch bifurcating into two identical daughter branches. This model is based on a previously published multi-layer compartmental model for single unbranched myelinated nerve fibers. Essential modifications were made to couple both daughter branches to the parent branch. There are two major features in this model. First, the model could incorporate detailed geometrical parameters for the myelin sheath and the axon, accomplished by dividing both structures into many segments. Second, each segment has two layers, the myelin sheath and the axonal membrane, allowing voltages of intra-axonal space and periaxonal space to be calculated separately. In this model, K ion concentration in the periaxonal space is dynamically linked to the activity of axonal fast K channels underneath the myelin in the paranodal region. Our model demonstrates that the branch point acts like a low-pass filter, blocking high-frequency transmission from the parent to the daughter branches. Theoretical analysis showed that the cutoff frequency for transmission through the branch point is determined by temperature, local K ion accumulation, width of the periaxonal space, and internodal lengths at the vicinity of the branch point. Our result is consistent with empirical findings of irregular spacing of nodes of Ranvier at axon abors, suggesting that branch points of myelinated axons play important roles in signal integration in an axonal tree.