In general the manuscript is considerably improved, being more detailed and streamlined. The authors have addressed the initial comments in detail. Much of the in vivo relevance relies on the strength of the new data where individual axons have been labelled and along which node length has been measured to determine relative variability along and between axons. This is a very nice approach and the authors should be commended for this revision.
Although many of the concepts proposed will require extensive experimental investigation, this study in and of itself is important in that it provides numerous key hypotheses that can and will be tested in the future. Nevertheless, I feel that the language of the manuscript sometimes goes beyond what is demonstrated e. It is not shown that nodal length is modified during plasticity, or even that it varies between relevant axons in naturally occurring systems where adaptations need to be made to ensure synchrony such as in auditory brainstem circuits, where the authors have previously studied internode length and axonal diameter.
In the absence of such data, it should be made very clear in the Abstract that this paper identifies regulation of nodal length as a potential mechanism for neuroplasticity only. Indeed, the authors must make sure that also the superficial reader will not confuse fact and fiction. Still "fiction" is the idea that nodes can change in size with predictable consequences on axonal conduction velocity as a physiological mechanism, by which neurons adapt axonal conduction to the demands of a larger neuronal network.
For comparison, had the authors been the first to discover that axons differ in caliber — which of course is well known — we could have the same discussion. In fact, it might be easier for neurons to fine-tune their axonal calibers e. See below. One worries to what extent the increased variance between axons is driven by these two axons.
If the removal of the two axons with the larger nodes removes the differences between versus within axons then it would be reassuring to see a slightly larger number of axons such that one didn't worry about any outlier or sampling artifacts. How representative are the 3 axons shown in Figure 2B? However, cortical myelination may not be finished by 2 months either, because even at age 6 months NG2CreERT2-based OPC lineage tracing experiments revealed newly generated oligodendrocytes Dimou et al.
This should be discussed. We have now carried out an analysis of the length of nodes of Ranvier in the optic nerve using immunofluorescence to compare to the existing EM data.
We find that the mean node length is similar using fluorescence and EM, but the total range of lengths observed is twice as large in fluorescently labeled tissue as is seen in EM.
This probably reflects the larger sample size studied with immunofluorescence. In order to minimize the error induced by analyzing nodes that are in different orientations in the sections, only nodes that lay parallel to the plane of optical sections were measured. We thank the reviewer for this helpful suggestion. We have completely redesigned Figure 1 to include nodes of various lengths for both the optic nerve and the cortex, and an analysis of node length variation along single axons is presented in Figure 2.
As the development of myelin varies across cortical layers and in different regions of the cortex. We originally used different ages because those were the ages of suitably labelled tissue that were readily available to us. In order to show that the variation in node length is not due to imaging nodes at various stages of development, but due to an actual diversity in the length of mature nodes, we have now re-done all the immunocytochemistry in week old rats to match the age group used for the EM analysis of optic nerve.
Furthermore, we confirmed that all the nodes of Ranvier that were imaged and analysed were positive for the mature node marker NaV1.
These methodological points are stated in the main text NaV1. The authors should provide information about the regions of the cortex that were examined. We apologise that this was not made clear in the previous version of the manuscript. All cortical imaging was done in layer 5 of the motor cortex of frontoparietal cortex. As indicated above we have now only included in our analysis nodes which were positive for the mature node marker NaV1.
In addition, as suggested, we have now carried out an analysis of NaV1. Overall there is a strong positive correlation between node length and total NaV labelling, suggesting that NaV density is maintained constant in nodes of different length.
However, at any specific node length there is a large variability in NaV1. We apologise for confusing the referee.
In the original Figure 1D the node lengths were displayed on the y axis rather than the x axis as was employed in the original Figures 2 and 3 , and they did indeed cover the full observed range from 0.
However, in the light of our new data we have now completely redesigned Figure 1 , and in the plots displaying node lengths in optic nerve and cortex layer V Figure 1F, G, H node length is now plotted on the x axis. We thank the reviewer for this suggestion. We now indicate the range of observed node lengths or internode lengths in all the graphs displaying the results of the simulations Figure 3A-F.
Figure 3 has now changed significantly compared to our previous submission. This is similar to that observed in the literature e. Chong et al.
Furthermore, as observed by Tomassy et al. The new Figure 3 shows how the effect of node length variation changes depending on internode length. Importantly, with our new parameters we find that the greatest effect on conduction velocity occurs in nodes with lengths between 0.
We appreciate the suggestion of validating the prediction about the length of successive nodes. Available serial EM datasets, however, do not cover a range long enough for us to be able to follow axons for the length of several long internodes. In order to overcome this difficulty, we have now added new experiments which combine single axon tracing using a fluorescent dextran tracer with immunohistochemical labelling of nodal NaV1. This approach enabled us to analyse the length of up to 13 consecutive nodes of Ranvier along individual axons over 1 mm long see new Figure 2.
Remarkably, our new data demonstrate that node length is similar along individual axons but different between axons, which strongly suggests that individual axons independently adjust their node lengths to tune conduction speed. Changing the number of ion channels on the membrane might be difficult without altering the amount of membrane at the node, as their insertion would be dependent on membrane trafficking.
It is because of this that we have simulated two scenarios: one in which the node elongates as more NaV channels are inserted i. For our simulations, internode length was maintained constant in order to isolate clearly for the reader the effect of node length on conduction velocity. It is unclear whether the sub-micron node length changes postulated in our calculation of the membrane areas changing would actually require remodelling of the adjacent myelin sheath — conceivably, slackness in the somewhat non-straight internode would allow the change of node length to be accommodated without a change of internode length, and furthermore node length might change by an eversion of the paranodal loops closest to the node without any other significant change to the myelin sheath reviewed by Arancibia-Carcamo and Attwell, , see Figure 3B and associated text.
In our revised manuscript we have now collected new data, and have measured the diameter of the axon at the paranodes as well as the nodes for all the nodes measured nodes for the cortex and nodes for the optic nerve.
These parameters given in Table 1 were included in the model when carrying out the new simulations presented in this manuscript. There is of course some variability in the ratio of the internode diameter to node diameter, but the focus of this paper is on the effect of node length, and diversifying the discussion to consider every parameter of the axon will detract from our main message.
The language has now been changed throughout to unequivocally distinguish our experimental conclusions and our theoretical conclusions.
For Figure 2 we traced 18 axons and measured the node length of as many nodes as we could find along those axons. The 3 axons shown were chosen to illustrate different mean node lengths.
As the reviewer points out, the majority of axons had nodes that fell within the 0. We found 2 axons in which the nodes were of longer lengths We find that, even with these two axons excluded, the mean coefficient of variation for the node length along single axons is We agree that cortical, or even optic nerve Young et al.
However, it is well established that Nav1. The funders had no role in study design, data collection and interpretation, or the decision to submit the work for publication. This article is distributed under the terms of the Creative Commons Attribution License , which permits unrestricted use and redistribution provided that the original author and source are credited. Article citation count generated by polling the highest count across the following sources: Scopus , Crossref , PubMed Central.
Here, we first establish that the spectral exponent of non-invasive electroencephalography EEG recordings is highly sensitive to general i. Building on the EEG spectral exponent as a viable marker of E:I, we then demonstrate its sensitivity to the focus of selective attention in an EEG experiment during which participants detected targets in simultaneous audio-visual noise. In addition to these endogenous changes in E:I balance, EEG spectral exponents over auditory and visual sensory cortices also tracked auditory and visual stimulus spectral exponents, respectively.
Mutations in RLBP1 are associated with recessively inherited clinical phenotypes, including Bothnia dystrophy, retinitis pigmentosa, retinitis punctata albescens, fundus albipunctatus, and Newfoundland rod—cone dystrophy.
However, the etiology of these retinal disorders is not well understood. Here, we generated homologous zebrafish models to bridge this knowledge gap. Using rlbp1a and rlbp1b single and double mutants, we investigated the pathological effects on visual function. Our analyses revealed that rlbp1a was essential for cone photoreceptor function and chromophore metabolism in the fish eyes. They accumulated cis and all- trans -retinyl esters which displayed as enlarged lipid droplets in the RPE reminiscent of the subretinal yellow-white lesions in patients with RLBP1 mutations.
During aging, these fish developed retinal thinning and cone and rod photoreceptor dystrophy. In contrast, rlbp1b mutants did not display impaired vision. The double mutant essentially replicated the phenotype of the rlbp1a single mutant. In Loligo there is a graded series of fibres with the larger in the longer nerves, and this is apparently a further device for ensuring more nearly simultaneous contraction. A similar compensatory delay function was demonstrated in the barn owl for ipsilateral and contralateral inputs from cochlear nucleus to brainstem neurons that are sensitive to interaural time delays Carr and Konishi, Similarly, different conduction delays in the diverging branches of a single axon can generate near-simultaneous responses in postsynaptic targets that lie at different conduction distance.
Such "isochronic" delivery of spikes generated by neurons with multiple distant targets could serve to synchronize spatially separate members of functional ensembles Chomiak et al. Isochronicity appears to be important in ensuring synchronous delivery of impulses from the inferior olivary nucleus in the brainstem to Purkinje neurons in the cerebellum , where longer branches have thicker diameters than shorter branches, indicating higher conduction velocities Sugihara et.
The observed diversity in axonal conduction delays also bear on whether synchronous firing of presynaptic neuronal ensembles would enhance the activation of postsynaptic targets Binding by Synchrony , Scholarpedia. Such ideas often assume that conduction delays are negligible, and such synchronous firing will result in synchronous arrival of impulses at postsynaptic targets. The broad spectrum of conduction times observed in many corticocortical systems indicates, however, that this is not always the case.
Izhikevich has demonstrated that different conduction delays in the divergent axonal branches of a small group of presynaptic neurons could serve to activate a very large number of distinct postsynaptic ensembles, depending on the order of firing of the presynaptic neurons.
The firing of the postsynaptic neurons would depend critically on the match between the spike timing in the presynaptic neurons and the axonal delays in their branches, such that only synchronously arriving inputs would generate spikes, and different spatiotemporal patterns of presynaptic activity would activate different postsynaptic ensembles. Through this mechanism, different spatiotemporal patterns of firing in the presynaptic neurons could generate time-locked "polychronic" firing patterns in groups of neurons, reminiscent of synfire braids Bienenstock, , also see Schuz and Preibl, Notably, these connections could be strengthened through mechanisms of spike-timing dependent plasticity Izhikevich, ; Lubenov and Siapas, ; Paugam-Moisey et al.
Diversity in signal transmission delays could also serve to shift oscillation dynamics and stabilize neural networks Omi and Shinomoto, One caveat for theoretical proposals employing long conduction delays to generate synchronous postsynaptic spiking is that very slowly conducting central axons may not "drive" postsynaptic targets using fast ionotropic postsynaptic receptors, as fast-conducting axons generally do.
An important distinction has been made between neurons that synaptically "drive" their targets vs. Given the considerable biological costs of fast-conducting axons above , it is reasonable to suppose that presynaptic axonal conduction delays may be matched to the requirements and time course of postsynaptic events. For example, the axons that mediate dopaminergic and noradrenergic synapses are very slowly conducting Table 1 and these transmitters utilize metabotropic receptor mechanisms, which have time courses that are orders of magnitude greater than those seen in ionotropic synaptic transmission.
Axons can be affected by a host of pathological conditions, most of which cause conduction delays, temporal dispersion of impulses and, ultimately, conduction failure. This topic has been the subject of many clinical reviews e. It is well-established that demyelination, or loss of the myelin sheath, occurs in a multifocal manner, producing lesions or demyelinated plaques that affect multiple tracts within the CNS, in disorders such as multiple sclerosis MS.
Demyelination leads to a reduction of conduction velocity, and, in more severely affected fibers, block of high-frequency impulse conduction or even failure of single action potentials McDonald ; Smith and Hall ; Waxman Slowing of impulse conduction is largely due to damage to the myelin insulation, with loss of the capacitative shield and a consequent increase in the time required for the propagating impulse to depolarize downstream portions of the membrane.
Importantly, patients with MS can experience remissions, in which they recover previously lost functions such as vision or the ability to walk, in the absence of substantial remyelination. Recovery of clinical functions in these instances appears to depend on molecular reorganization of chronically demyelinated axons, which acquire a higher-than-normal density of sodium channels in demyelinated and previously sodium-channel-poor regions Craner et al.
This molecular remodeling permits the bared, demyelinated axon membrane to support continuous impulse conduction which, as in fibers that are normally non-myelinated, occurs with a low conduction velocity Bostock and Sears ; Smith and Waxman Interestingly, patients can recover from episodes of optic neuritis inflammation and demyelination along the optic nerves, with a conduction delay of several tens of milliseconds in the visual evoked response this reflects the decreased conduction velocity along the chronically demyelinated optic nerve axons.
Visual acuity often recovers fully in these patients and, upon casual examination, they appear to have recovered fully. However, these patients often exhibit subtle abnormalities such as the Pulfrich phenomenon, in which patients perceive that a pendulum, swinging in front of them in a plane, to be swinging in a circular or elliptical trajectory , as a result of the delay in arrival of impulses from the affected eye.
Remyelination production of new myelin along demyelinated axons within the brain and spinal cord , occurs either by occasional endogenous myelin-forming cells Smith et. This observation has heightened interest in the development of reparative therapies, using any of a variety of cell types, including stem cells, as a therapeutic approach that might restore function in people with demyelinating diseases such has multiple sclerosis.
Less is known about the physiology of conduction in smaller, more slowly conducting axons, particularly the non-myelinated axons, in the diseased nervous system, since it is easier to record the activity of the larger myelinated axons, and since many of the available clinical tools, e. Table 1. Values for axonal conduction times and velocities for select axonal pathways in several mammalian species. Some axonal systems are very rapidly conducting, some are very slowly conducting, and some are characterized by a great diversity in axonal conduction delays.
Antic S and Zecevic D. Optical signals from neurons with internally applied voltage-sensitive dyes. Neuroscience , 15 2 : , Aston-Jones, G. Impulse conduction properties of noradrenergic locus coeruleus axons projecting to monkey cerebrocortex. Neuroscience , , Beloozerova, I. Activity of different classes of neurons of the motor cortex during locomotion. Neuroscience, , Bostock H, and Sears T. The intermodal axon membrane: electrical excitability and continuous conduction in segmental demyelination J.
Bienenstock, E. A model of neocortex , Network: Computation in neural systems, 6: , Briggs, F. Parallel processing in the corticogeniculate pathway of the macaque monkey. Neuron, , Budd, J. Neocortical axon arbors trade-off material and conduction delay conservation. Plos Comput Biol. Callaway, E.
In: The Visual Neurosciences Vol. Chalupa and J. Werner Editors , 68—, Carr, C. Axonal delay lines for time measurement in the owl's brainstem. USA, 85, , Cherniak, C. Local optimization of neuron arbors. Chklovskii, D. Schikorski, T. Wiring optimization in cortical circuits.
Chomiak, T. Functional architecture and spike timing properties of corticofugal projections from rat ventral temporal cortex. Cleland, B. Morstyn, R. Craner, M. Molecular changes in neurons in MS: altered axonal expression of Nav1. Evarts, E. Relation of discharge frequency to conduction velocity in pyramidal tract neurons. Assuming a traveling wave solution to this equation, Keener and Sneyd are able to relate, via approximation, the discrete cable equation to the cable equation describing a traveling wave along an unmyelinated fiber.
We summarize their argument below. Our discussion begins with the cable equation for the membrane potential V x , t in an unmyelinated axon 2 Here, C m is the membrane capacitance per unit area; d is the axon diameter; I ion is the membrane ionic current per unit area; and R c is the cytoplasmic resistivity in the axon.
We assume the extracellular space to be an isopotential. Given this ansatz, the cable equation, Eq 2 , takes the form 3. Moving to a myelinated axon, the cable equation is appropriate for the nodes of Ranvier, but given their diminutive size, we will approximate the nodes as isopotentials.
Because the internodes are wrapped with roughly extra layers of membrane, the membrane capacitance decreases by about a factor of while its resistance increases by the same factor. With the traveling wave ansatz, the discrete cable equation, Eq 5 , becomes a delay differential equation. In our simulations, we find a speed ratio of. We now adapt the arguments of Keener and Sneyd to a myelinated axon with non-uniform internodal length.
The transition between these two uniform regions occurs at node n. This equation is not on the same footing as the approximated delay differential equation, Eq 6 , for the uniformly myelinated fiber because there is no fixed delay relating the potential at adjacent nodes. But, perhaps the equation can still give us a qualitative hint as to how inhomogeneities can impact the propagation speed. In order to make some inroads on this problem, we will make two assumptions.
We anticipate that this time does not differ greatly from a naive estimate which can be justified post hoc ,. Before examining how well this fits with our model calculations, we make one qualitative observation about Eq The converse is also true. Through explicit computation, we qualitatively confirm these features; furthermore, we find good quantitative agreement with the change in conduction velocity implied by Eq Eq 12 predicts the deviations from the benchmark speeds with reasonable accuracy.
Though the deviations are small, they can compound in axons with a greater number of transitions between long and short internodes, as the ones considered in our computational study. The preceding discussion about the transition between two uniform regions with differing internodal lengths informs our calculations of the model neuron conduction velocities.
Referring to Fig 1 , for a given fraction of remyelinated segments, the spread in the conduction speeds for the model neurons is due to two effects. The first is merely statistical, a consequence of the inherent spread of the binomial distribution.
The second is due to relative ordering of short and long internodes in a model axon; this ordering determines the number of transitions between segments with different internode lengths. For the statistical aspect, given a fraction of remyelinated segments p and total number of initial normal internodes N , the binomial distribution on average yields Np segments which are demyelinated then remyelinated.
But, there is a spread in the distribution; its standard deviation is. This will result in lower higher propagation speed relative to the expected because there are greater fewer shorter internodes. If the model neuron contains fewer remyelinated segments, we expect a faster speed and vice versa. This spread in propagation speeds due to the sampling of the binomial distribution closely matches the spread in velocities for the model neurons.
Though the spread in propagation speeds, Fig 1 , is largely an issue of statistical sampling, the overall depression of the mean speed relative to the benchmark expectation is a consequence of the random distribution of inhomogeneous internodal lengths in the axon. In an axon which is randomly remyelinated with shorter internodes, then the number of transitions from shorter to longer internodes is, on average, balanced by those from long to short, but the overall impact of the transitions is a slowing of the AP propagation speed due to a slight asymmetry in the transition effect.
Of those 50 model neurons, we find that the conduction speed and standard deviation is In this restricted sample, on average the number of transitions from long to short internodes is roughly 17, and we find 18 short to long transitions. From our simulation of the semi-uniform axons, we estimate that the time for the conduction of an AP along the axon is increased by roughly For the average number of transitions observed in our restricted sample of model neurons, we then estimate that the propagation speed through such an axon should be Similar results hold for the other remyelinated neurons that we considered.
In Fig 2 , we plot, as black circles, the average CV for model neurons with given remyelination fraction p , assuming a g -ratio of 0. In Fig 2 , we also plot as the solid blue curve the benchmark velocity based purely upon the number of short and long internodes.
Qualitatively, the CV for the model neurons is much lower than naive expectations, consistent with the results derived from the McIntyre, et al. The black circles represent the average CV and standard deviation for model neurons with a given fraction of remyelinated segments with a g -ratio of 0. The purple diamonds represent the average CV and standard deviation for model neurons with a given fraction of remyelinated segments whose g -ratio is 0. For the same model neurons, we also explore the impact of tight junctions.
We ran our simulations for the Gow and Devaux model without TJs. We found that the CV was much lower than the model with TJs. Furthermore, the conduction velocity was relatively independent of the remyelination fraction.
For normal internodal lengths, the CV was 4. This is at odds with the analytical estimate, Eq 8 , that indicates that the velocity should scale as the square root of internode length.
In that analytical work, we assumed no transmembrane current in the internodal region. It is likely that the smaller axons lacking TJs violate this assumption, but tight junctions, at least in part, reduce current flow through the myelin which better approximates the idealized axon in the analytical work. Finally, with the Gow and Devaux model, we explore one further change in the myelin sheath that occurs during remyelination: thinner internodes.
This further suppresses the CV in the fully remyelinated fibers resulting in a CV of 4. In Fig 2 , we plot the CV for a given remyelination fraction, represented by purple diamonds, along with the benchmark speed, depicted by the solid red line.
The CVs for the inhomogeneous remyelinated fibers are qualitatively consistent with our previous results. As with the other cases, we find that the distribution of the inhomogeneities in internodal lengths impacts the conduction velocity. Generally, if a fiber has a large number of transitions between long and short internodal lengths, conduction velocity decreases relative to a semi-uniform fiber. Through this computational study, we were able to quantitatively assess the impact of progressive segmental demyelination and remyelination, simulated by shorter internodes with thinner myelin sheaths interspersed with normal internodes, on the conduction velocity of action potentials.
Previous computational studies have shown that shortened internodes reduce CV [ 13 , 24 ], consistent with experimental findings [ 17 , 18 , 23 , 24 ]. Our results confirm this, but we additionally find that the CV is sensitive to the distribution of shorter internodes relative to the standard longer internodes. In our simulations, we find CVs that are consistently lower than one might expect from an estimate of the CV based merely on the number of short and long internodes.
We find that an AP which travels from a shorter to longer internode speeds up relative to expectations, and one which travels from long to short slows.
Because of a slight asymmetry in the two cases, the net impact of such transitions is to slow the CV of an AP in an axon that has undergone random segmental demyelination and remyelination. Adapting the analysis of CV for myelinated neurons in Ref [ 2 ], we are able to mathematically trace this phenomena directly to the transitions between internodes of different lengths.
Based on these results, attention must be paid to the transitions between internodes of different lengths because this difference could be critical in accurately modeling a neural network of neurons with segmental demyelination and remyelination. We end with a brief comment on the limitations of our study. In our simulations, we study a large diameter PNS axon and a smaller diameter CNS axon with tight junctions that is geometrically similar.
It is heartening that both axons show qualitatively similar results in regards to the impact of partial remyelination on CV. Our analytical work suggests that the qualitative behavior observed with the model axons will persist for different geometries as long as the myelin is sufficiently insulating, but the actual quantitative details for different fibers can only be reliably accessed through simulation. One other limitation in our study is that our remyelinated segments did not account for the redistribution of ion channels that occurs with morphological changes.
In Ref [ 45 ], a study of demyelinated axons shows that new sodium channels are produced to meet the added demands of an increased number of nodes in remyelinated segments. After several weeks, the channel density in newly formed nodes is similar to that in established nodes, a result consistent with other studies [ 46 — 48 ].
While the re-establishment of normal channel densities progresses throughout the remyelination process [ 47 , 48 ], our study assumes completion of this process. As such, our results are only valid for mature remyelinated axons. Figure 2: The fate of demyelinated axons. The case in the CNS is illustrated. Research in Myelin Biology and Pathology. Figure 3. References and Recommended Reading Brinkmann, B. Waxman, S.
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