Abstract
Axons in the mammalian brain show significant diversity in myelination motifs, displaying spatial heterogeneity in sheathing along individual axons and across brain regions. However, its impact on neural signaling and susceptibility to injury remains poorly understood. To address this, we leveraged cable theory and developed model axons replicating the myelin sheath distributions observed experimentally in different regions of the mouse central nervous system. We examined how the spatial arrangement of myelin affects propagation and predisposition to conduction failure in axons with cortical versus callosal myelination motifs. Our results indicate that regional differences in myelination significantly influence conduction timing and signaling reliability. Sensitivity of action potential propagation to the specific positioning, lengths, and ordering of myelinated and exposed segments reveals non-linear and path-dependent conduction. Furthermore, myelination motifs impact signaling vulnerability to demyelination, with callosal motifs being particularly sensitive to myelin changes. These findings highlight the crucial role of myelinating glia in brain function and disease.
Significance Statement
This study highlights the importance of spatial heterogeneity of myelin sheathing in shaping nerve axonal conduction. Using model axons that faithfully replicate myelin distributions observed in the mouse central nervous system, our results revealed the impact of myelin patterns on the timing and reliability of neural signaling. Contrary to the conventional view in which uniform and equally spaced myelin segments imply linear conduction, our findings show that axonal conduction is a path-dependent, nonlinear process influenced by the specific distribution of myelinated and unmyelinated segments. Membrane potential propagation along model axons in the corpus callosum was found to be more vulnerable to myelin changes compared to those in the cortex, especially post-myelin injury, emphasizing the role of sheath locations in both health and disease.
Introduction
Myelinated axons play a pivotal role in supporting and facilitating the faithful conduction of action potentials (APs). Myelin-forming oligodendrocytes (OLs) engage in the synthesis of cellular membranes enwrapping axons through a multilamellar spiral configuration (Bradl and Lassmann, 2010; Simons and Nave, 2015), serving as an effective insulator for the axons and enabling saltatory conduction. Individual OLs have the capacity to generate multiple myelin sheaths, with each sheath potentially varying in length and enwrapping different axons (Chong et al., 2012; Tomassy et al., 2014). In contrast to the conventional depiction of axons, where myelin sheaths are uniformly distributed along their length, numerous investigations have shown that axonal myelin sheathing is, in fact, highly heterogeneous. Even when controlling for variations in length and overall myelin coverage (that is, the percentage of the axon covered by myelin, referred thereafter as PMC), internodes’ number, thickness, length and spatial arrangement do vary significantly between and along given axons (Sturrock, 1980; Bakiri et al., 2011; Tomassy et al., 2014; Ford et al., 2015; Micheva et al., 2016; Auer et al., 2018; Hill et al., 2018; Stedehouder et al., 2019; Benamer et al., 2020; Call and Bergles, 2021). Such diversity extends within and across brain regions (Glasser and Essen, 2011; Thornton et al., 2024). One of the most salient differences can be observed when comparing myelination motifs found in the white matter and cortex (Geurts and Barkhof, 2008; Glasser and Essen, 2011; Tomassy et al., 2014; Calabrese et al., 2015; Prins et al., 2015; Micheva et al., 2016; Timmler and Simons, 2019; Orthmann-Murphy et al., 2020; Call and Bergles, 2021; Corrigan et al., 2021; Lie et al., 2022; Thornton et al., 2024). Indeed, as axons traverse the corpus callosum, internode lengths exhibit greater variability, whereas, in the cerebral cortex, they tend to be more uniform (Chong et al., 2012). Myelination in the cortex and the corpus callosum follow independent developmental trajectories (Corrigan et al., 2021), further exhibiting distinct growth and regenerative responses following injury (Orthmann-Murphy et al., 2020; Thornton et al., 2024). Variability in myelin sheathing motifs also extends to brain regions and cell types (Micheva et al., 2016). Such striking differences are of prime functional significance, suggesting that precise sheath placement is important for cortical function (Orthmann-Murphy et al., 2020), reflecting regional differences in myelination strategies to support neural signaling (Chong et al., 2012; Tomassy et al., 2014; Thornton et al., 2024). Indeed, the spatial heterogeneity resulting from the particular positions and lengths of myelin sheaths, the molecular constitution of nodes, along with variations in the distribution and density of ion and/or leak channels, collectively influence axonal conduction and the reliable propagation of APs (Osso and Hughes, 2024). Such microstructural changes notably tune axonal conduction delays – the temporal interval required for an AP originating at the axon hillock to reach post-synaptic targets – which play an important role in neural circuits operation (Fields, 2008; Talidou et al., 2022) and to maintain brain function (Nagy et al., 2004; Bengtsson et al., 2005; Mabbott et al., 2006; Pujol et al., 2006; McKenzie et al., 2014; Pan et al., 2020; Steadman et al., 2020; Xin and Chan, 2020).
A crucial question that remains unanswered is the impact of such heterogeneity on the conduction of APs. Does spatial variation in myelin sheathing pattern affect conduction delays? If so, how much? Are these patterns equally resilient to variations in myelination, or are certain motifs more fragile and prone to conduction failure with changes in myelin coverage? Understanding the implications of regional myelination motifs diversity on axonal conduction would represent an important advancement in our understanding of the tactics employed by OLs to optimize neural trafficking, and in identifying which axons or part of these axons are more vulnerable to injury. An extensive corpus of scientific literature has developed mathematical models to investigate the propagation of APs along myelinated axons (Fitzhugh, 1962; Goldman and Albus, 1968; Grindrod and Sleeman, 1985; Basser, 1993; Nygren and Halter, 1999; McIntyre et al., 2002; Gow and Devaux, 2008; Babbs and Shi, 2013; Ashida and Nogueira, 2018; Scurfield and Latimer, 2018; Naud and Longtin, 2019; Schmidt and Knösche, 2019). Prevailing models oftentimes presuppose uniform, homogeneous myelin sheathing interspersed with exceedingly brief nodes of Ranvier. However, this convenient approximation severely limits the characterization of the effect of spatial heterogeneity in myelin sheathing along axons (Chong et al., 2012; Tomassy et al., 2014).
To circumvent this limitation, we developed model axons endowed with myelin sheath patterns closely matching those measured from the cerebral cortex and corpus callosum of mice (Chong et al., 2012). In vivo studies conducted in these regions (and others) by Chong et al. (2012) revealed considerable variability in the number, length and arrangement of myelin sheaths formed by individual OLs, representing ideal starting points to ground our explorations. We hence used these data to constrain our model axons, and compared how these distinct myelination motifs shape AP conduction reliability, as well as vulnerability to failure during demyelination. Our approach integrates variability in the lengths and number of myelin sheaths and exposed segments while keeping other parameters (e.g., axonal length, radius, g-ratio, biophysical parameters, etc) constant. This was done to ensure that any observed differences in axonal conduction can be attributed exclusively to myelin placement along the axons. We used and adapted cable theory, amenable to the representation of AP propagation across axons composed of myelin sheaths and exposed segments of arbitrary (and different) lengths. To face the challenging computational demands of analyzing such physiologically realistic axons, we leveraged a recent modeling framework (Grindrod and Sleeman, 1985; Ashida and Nogueira, 2018; Naud and Longtin, 2019; Schmidt and Knösche, 2019), in which a phenomenological model of membrane excitability is used to reproduce the rapid depolarization (spike) of the membrane potential along the exposed segments of the axon (Ashida and Nogueira, 2018), combined with diffusion accounting for the fast transmission of APs within myelin sheaths. This framework, shown to faithfully simulate propagation along myelinated axons (Ashida and Nogueira, 2018; Schmidt and Knösche, 2019), allowed us to quantify how spatial heterogeneity in myelin sheathing influences AP conduction, as well as the occurrence of conduction failures and susceptibility to conduction block.
Methods and Materials
Constructing axons with heterogeneous myelination motifs
We consider a cable of fixed length L, representing a bare axon. The cumulative length of the cable covered by myelin (Lmy) is determined by the formula Lmy = PMC · L, where PMC represents the percentage of myelin coverage. The remaining part of the axon constitutes the exposed length (Lexp), expressed as Lexp = L − Lmy. To construct a myelinated axon, we generate myelin sheaths, each of length
Cortical myelination motifs
To create an axon with cortical-like myelination we generate a set of Poisson-distributed numbers that sum to Lmy. Each element of the set corresponds to a myelin sheath with the value of the element denoting the length of the sheath
Callosal myelination motifs
To create an axon with callosal-like myelination we adopt a similar strategy, but use a different distribution compared to the one used above. We generate a set of Gamma-distributed numbers (Nmy in total) that sum to Lmy. The rationale underlying the selection of the Gamma distribution stems from the irregular sheath lengths generated per oligodendrocyte within the corpus callosum observed experimentally (Chong et al., 2012). Each element of a set following the Gamma distribution, Γ(k, θ), corresponds to a myelin sheath with the value of the element denoting the length of the sheath (
Modeling AP propagation along heterogeneously myelinated axons
To address the computational challenges of analyzing physiologically realistic axons, we combined elements from recent studies simulating AP conduction along myelinated axons (Grindrod and Sleeman, 1985; Ashida and Nogueira, 2018; Naud and Longtin, 2019; Schmidt and Knösche, 2019). These approaches, use simplified phenomenological models of rapid, standardized depolarization (spike) of the membrane potential along exposed segments, combined with the cable equation which describes the diffusion of AP along both exposed segments and myelin sheaths. Such models have repeatedly been shown to be in agreement with more detailed biophysical models relying on the Hodgkin-Huxley formalism (e.g., Arancibia-Cárcamo et al., 2017).
The membrane potential is determined by the properties and particular structure of myelinated and exposed segments along an axon. Due to high resistance along myelin sheaths, the membrane potential travels passively there and regenerates over exposed segments characterized by higher density of ion channels. Taking these properties into consideration, we built a model that governs the dynamics of the membrane potential along different segments of the axon. The model is defined by the following system of partial differential equations and conditions:
The solution ui of each differential equation involved in Equations 3–4 is the membrane potential within either an exposed segment/node of Ranvier (Eq. 3) or a myelin sheath (Eq. 4). We imposed matching conditions at the paranodes (see Eqs. 5–6), namely at the regions where the terminal myelin loops form septate-like junctions with the axolemma. Equation 5 indicates that the membrane potential u is continuous across a paranodal junction while Equation 6 assumes continuity in flux, that is, the longitudinal currents should match at the junction. Following Rall (1969), we assume zero Neumann boundary conditions at either end (Eqs. 7). For time t = 0 we set an initial condition equal to the leak reversal potential Eleak (Eq. 8). We analyze the resulting governing equations and define all the parameters below.
Exposed segments/nodes of Ranvier
Equation 3 models the membrane potential u along the unmyelinated parts of the axon. This model has been introduced in Table 5 in Ashida and Nogueira (2018) as a simplified version of the Hodgkin and Huxley (1952) and Wang–Buzaki models (Wang and Buzsáki, 1996). It accounts for spike generation and conduction, and has been inspired by the exponential integrate-and-fire model, which simulates the rapid growth of the membrane potential. In Equation 3, the membrane capacitance of the cable is denoted by Cc, a is the radius of the cable and rint is the intracellular resistivity. Three currents are lumped together into
To generate an AP, a brief external current Iinj is injected into the second exposed segment of the axon for a set duration TS:
List of model variables and parameters
Myelin sheaths
Turning to the parts of the axon covered by myelin, we assume that the myelin sheaths have infinite resistance. Consequently, in the absence of ionic currents, the membrane potential u along a myelin sheath satisfies the diffusion equation Equation 4 (cf. Dayan and Abbott, 2005). The capacitance of a myelin sheath Cmy is defined as follows:
Paranodal junctions
As the myelin loops bind to the axonal membrane, they form paranodal axoglial junctions at both ends of every myelin sheath. While there is a rich selection of dynamics and functions at the paranodal junctions to maintain reliable saltatory conduction (Rosenbluth, 2009) we exclude those details from our model. We apply the matching conditions given in Equations 5–6 at each paranodal junction, here denoted by
π. The diffusivities
κ in Equation 6 are defined by the diffusion coefficients of Equations 3–4. Specifically, from Equation 3 we have
Axonal conduction delays, CVs and conduction failure
For each segment (either myelinated or exposed/unmyelinated) along an axon, we compute the difference between the time the membrane potential spikes at the beginning and end of the segment. This difference gives the conduction delay along individual segments referred thereafter as segmental delay. We denote these delays by
Simulating myelin injury
We model demyelination along individual axons by removing
We compute axonal conduction delays (
τ) by summing the conduction delays across individual myelinated (
Numerical simulations
We modelled an axon as a medium composed of multiple layers, each representing the myelinated and exposed segments of the axon. Each segment was discretized into n + 1 equally spaced compartments, and second-order finite differences were used in space. Due to the varying lengths of the segments, the spatial step size dx differed for each segment. For temporal integration, we used the implicit Euler method.
To mitigate boundary effects at the beginning and end of the axon, we extend the axon at both ends, using copies of a portion of the axon with the same spatial and biophysical properties. This approach allowed us to compute the conduction delays and velocities along fixed axonal lengths without boundary artifacts. The numerical schemes used for the approximation of the solution of Equations 3–8 were based on the methods proposed by Carr and Turner (2016) and Hickson et al. (2011), which address the change of dynamics at the interfaces, namely at the paranodal junctions. The numerical scheme was implemented in MATLAB code, which is available online at https://github.com/atalidou/myelinPatterns.
Results
Modeling axons with spatially heterogeneous myelin sheathing
To characterize changes in AP conduction resulting from realistic and physiologically observed myelination motifs, we constructed nerve axon models incorporating myelin sheath heterogeneity that mirrors experimental observations (Chong et al., 2012) (see Methods). We sampled myelin sheath lengths matching those documented in the cerebral cortex and corpus callosum of mice (Chong et al., 2012) and used probabilistic tools to implement a framework that incrementally allocates these sampled sheaths to an initially fully unmyelinated (that is, bare) axon of a predetermined length (see Methods). A schematic illustrating differences between cortical and callosal myelination motifs is shown in Figure 1A–B.
Modeling axons of heterogeneous myelination motifs in grey and white matter. A, B, Schematic illustration of myelination motifs along individual axons in two different brain regions: in the cerebral cortex (blue, panel A) and corpus callosum (red, panel B). Callosal motifs are more spatially heterogeneous compared to those found in the cortex. C, Scatter plot of the mean values of myelin sheath lengths for axons featuring cortical and callosal myelin motifs for all cases of PMC examined. D, Scatter plot of the mean values of exposed segment lengths. E–F, Mean values of myelin sheath lengths, corresponding to cortical (panel E) and callosal (panel F) motifs, plotted separately for each PMC in the form of violin plots. G–H, Scatter plots of the number of myelin sheaths as a function of PMC (cortical motifs - panel G, callosal motifs - panel H). The lines indicate the median with interquartile range of the plotted data. I–J, Violin plots of the mean values of exposed segment lengths for each of the five cases of PMC. K–L, Nonlinear relation between the mean values of exposed segment lengths and their number. The geometrical parameters of the axons used are: axon length = 10 mm, radius = 2 μm and g-ratio = 0.6. The biophysical parameter values used are given in Table 1. The results shown are for K = 1000 independent axons for each PMC.
To broaden the applicability of our findings to axons with different levels of myelination, we examined five distinct scenarios, each representing varying PMC for a fixed total axonal length (that is, PMC values of
Geometrically, for a given axon length, any adjustments made to the number or lengths of myelin sheaths inevitably impact the corresponding number and lengths of exposed segments. The mean lengths of exposed segments are illustrated in Figure 1I–J. For the same value of PMC, callosal motifs exhibit significantly more variable and long exposed segments compared to cortical motifs (Fig. 1J). One may further notice that, as the PMC increases, the lengths of exposed segments decrease: as myelin covers an increasingly large portion of the axon, exposed segments become smaller and less variable. The relationship between the mean length and number of exposed segments is plotted in Figure 1K–L. There, one can see that cortical myelination motifs (Fig. 1K) are characterized by a smaller number of exposed segments compared to callosal motifs (Fig. 1L).
To isolate the impact (if any) of myelin sheath distribution heterogeneity on AP propagation and facilitate a meaningful comparison within and between cortical and callosal motifs, we deliberately kept constant the values of axonal length, radius/caliber and myelin sheath thickness (that is, g-ratio). The biophysical parameters used (see Table 1) also remain constant. This approach introduces variability solely in the length and placement of myelin sheaths and exposed segments along the axons while ensuring that any observed differences in axonal conduction are entirely the consequence of myelin heterogeneity.
We modelled the propagation of APs along these axons using cable theory (Dayan and Abbott, 2005), adapted to account for spatially heterogeneous myelination. To simulate spike generation and conduction within exposed segments, we used a spike-conducting integrate-and-fire model (Ashida and Nogueira, 2018). The rapid spread of APs along myelin sheaths was replicated assuming pure diffusion. The resulting system of equations is further supplemented by additional conditions that account for the current flow at the paranodal junctions, where the membrane potential transitions from myelinated to exposed segments, and vice versa (see Methods).
Influence of myelin sheath spatial heterogeneity on AP conduction
We started our analysis by exploring whether myelin sheathing heterogeneity influences AP propagation along individual axons. We first compared the conduction of APs along axons displaying a homogeneous myelin motif – characterized by myelin sheaths of uniform length periodically distributed along axons – with the conduction along axons featuring spatially heterogeneous myelin sheath distributions. For the purpose of this experiment, axons exhibiting callosal myelination motifs were used. Snapshots capturing the membrane potential’s evolution over time, accompanied by schematic representations of the axons, are illustrated in Figure 2A–D. Figure 2E–H present bar plots detailing the lengths of myelinated and exposed segments for each of the examined axons. For the axon with homogeneous myelination, both the lengths of myelin sheaths and exposed segments remain constant. Conversely, for the axons exhibiting heterogeneous myelination, one can see an important dispersion in those lengths. Differences could also be observed while comparing changes in APs waveform as they propagate along axons of either homogeneous or heterogeneous motifs. We characterized changes in AP waveform by quantifying the variability (i.e., standard deviation) of AP peak amplitudes computed between successive exposed segments of the axon. Specifically, we computed the AP peak within each discretized compartment of an exposed segment and calculated the standard deviation among those values. We repeated this process for each exposed segment along the axons. In the homogeneous case (Fig. 2A), the AP waveform remains unchanged as it propagates along the axon. This is corroborated by the near-zero variability in AP peak amplitude, as shown in Figure 2I. In contrast, heterogeneous myelination (Fig. 2B–D) introduces fluctuations in both the AP waveform and conduction time. Such variations in AP waveform are quantified in Figure 2J–L, where the standard deviation of AP peak amplitude along exposed segments is consistently observed, further varying along the same axon and exhibiting differing slopes across axons. These findings revealed that the particular location of myelin sheaths and exposed segments as well as their number and length lead to not only changes in AP waveform, but also instances of faster or slower conduction, as well as conduction failure (Fig. 2D).
Exemplar AP propagation along axons with spatially homogeneous and heterogeneous myelin sheathing. A, Snapshots illustrating the propagation of AP along an axon characterized by homogeneous myelination. B–D, Propagation of APs along axons exhibiting heterogeneous myelin motifs. For all four examples, the axonal length is L = 10 mm and PMC is 70%. A schematic representation of each axon is displayed at the top of these panels. E–H, Bar charts of the lengths of myelin sheaths and exposed segments for the four individual axons examined. Each bar in panels F–H represents the length of either a myelin sheath (red) or an exposed segment (black). As there is no variability in the lengths of sheaths and exposed segments along axons of homogeneous myelination, all those values are constant (panel E). The number of myelin sheaths varies for each axon and is denoted by Nmy. The number of exposed segments (Nexp) equals the number of myelin sheaths. In panel E, where the length of myelin sheaths is 56 μm, resulting in a total of 125 sheaths, assuming a uniform distribution of exposed segments, their individual length is 24 μm. Note, however, that the number and length of myelin sheaths and exposed segments vary across all three axons exhibiting heterogeneous myelin motifs. I-L, The standard deviation (std) of AP peaks along exposed segments is plotted as a function of the lengths of the exposed segments. In the homogeneous case (panel I), the variability of AP peaks is negligible compared to heterogeneous cases. In the heterogeneous cases (panels J–L), variability of AP peaks increases with respect to the lengths of exposed segments in a nonlinear way. M-P, The delays of APs along individual exposed segments are plotted as a function of the length of those segments. In the homogeneous case, these values remain constant, as depicted in panel I, whereas in the heterogeneous cases, they exhibit great variability. In panels H, L and P, the red arrows highlight the largest exposed segments, which result in significant delays and ultimately lead to conduction block.
These observations suggest that spatial heterogeneity of myelin sheaths and exposed segments influences axonal conduction delays. Indeed, segmental delays along exposed segments – that is the time required for an AP to traverse individual segments (see Methods) – were found to vary with the length of the segments in axons of heterogeneous motifs (axons 2, 3 and 4 in Figure 2N–P), while they remained constant for the axon of homogeneous myelination (axon 1 in Fig. 2M). The differing slopes in Figure 2N–P reflect the variations observed in the corresponding variability in AP waveform (Fig. 2J–L). Notably, the AP traverses short exposed segments rapidly and without significant waveform change, whereas, in longer segments, slower propagation is accompanied by significant changes in the AP peak amplitude. Additionally, APs propagated rapidly along myelinated regions, resulting in negligible delays and preserving the AP waveform (result not shown).
An important question remains: does the variability in AP propagation, as depicted in Figure 2, arise solely from the variability in segment lengths, or is this process also influenced by interactions between the AP dynamics in neighboring segments? To address this, we performed a detailed analysis of the conduction velocity (CV) in exposed segments, and explored whether AP conduction depends on neighboring segments. In the three axons with heterogeneous myelination shown in Figure 2 (axons 2, 3, and 4), segmental velocities decrease with exposed segment length (Fig. 3A–C). To better understand how CV is impacted by transitions from segment to segment, we calculated the change in segmental velocities, defined as the difference in CV between successive exposed segments. These changes were then plotted against the corresponding changes in exposed segment lengths (Fig. 3D–F). We denote the change by Δ. A positive Δ in exposed segment lengths indicates that a long segment is preceded by a shorter one, and vice versa. As shown in Figure 3D–F, the AP velocity increases (Δ of segmental velocities is positive) when transitioning from a long segment to a shorter one (Δ of exposed segment lengths is negative). Conversely, the AP velocity decreases (Δ of segmental velocities is negative) when transitioning from a short segment to a longer one (Δ of exposed segment lengths is positive).
Implications of myelin sheathing heterogeneity on axonal CV along exposed segments. A–C, AP velocities along exposed segments plotted with respect to the length of the segments for axons 2, 3 and 4 (of Fig. 2), respectively. The velocities decrease nonlinearly as the length of exposed segments increases. The slope is different for each of the three axons indicating the different dynamics the APs undergo when traveling along axons of heterogeneous myelin motifs. D–F, Change (denoted by Δ) of exposed segment lengths plotted as a function of the change in velocities along exposed segments for axons 2, 3 and 4. Despite the different segment lengths encountered between the three axons, the Δ of exposed segment lengths lies in the same range. Variability of Δ in segmental velocities is larger in axon 2 compared to axons 3 and 4. G–H, Lengths of myelinated and unmyelinated segments plotted in the order they appear along a section of axon 2 and axon 3. The lengths of sheaths and exposed segments are on average longer for axon 3 compared to axon 2. I–J, Velocities along the corresponding exposed segments of axons 2 and 3. Along axon 2, velocities are highly variable. K–L, Mean values of AP peaks along the myelin sheaths and exposed segments for axons 2 and 3. A sharp decrease of the AP peak in axon 2 occurs when the AP travels from a short segment to a much longer one. The dark grey shaded area highlights the two longest exposed segments that affect both the velocity and the mean of AP peaks. The light grey shaded areas and the arrows highlight other points of interest along the axons.
In Figure 3G–L, we analyzed selected sections of axons 2 and 3 from Figure 2. We plotted the segment lengths (both myelinated and unmyelinated) in the order they appear along the axons (Fig. 3G–H), the velocity along the exposed segments (Fig. 3I–J), and the mean value of the AP peaks for myelin sheaths and exposed segments (Fig. 3K–L). For axon 2, within the dark grey shaded area, we identified two exposed segments that are noticeably longer than the other exposed segments found within the same section of the axon. This caused a sharp decrease in the AP peak amplitude and segmental velocity. The subsequent second-longest exposed segment further slowed the velocity, while the AP peak amplitude remained low but showed an upward trend. The myelin sheath between the two long exposed segments played a critical role in preventing conduction failure. Without this myelin sheath, the AP would encounter a very long exposed segment, potentially leading to conduction failure (as in axon 4, Fig. 2). An interesting observation is evident for the exposed segments immediately before and after those in the dark grey shaded area (marked by black arrows). While these two segments have approximately the same length, the velocities differ significantly. This demonstrates that the velocity along an exposed segment is influenced not only by its length but also by the dynamics along neighboring segments. The exposed segment within the light grey shaded area is the shortest in the entire section. The AP traverses this segment quickly, maintaining its amplitude. For axon 3, both the myelinated and unmyelinated segments are, on average, longer than those in axon 2. This results in less variation in velocities along the exposed segments and smaller changes in the AP peak amplitudes. Taken together these insights hint at a nonlinear relationship between the axonal conduction delay and velocity and the spatial heterogeneity of myelin sheathing.
Heterogeneity of myelin sheathing impacts AP conduction reliability and susceptibility to failure
In light of the above observations, a natural question arises as to how spatial heterogeneity of myelin sheaths influences the reliability, propagation and efficacy of AP conduction. The distinct fluctuations of AP waveforms depicted in Figure 2J–L suggest that the time required for an AP to traverse axons is likely contingent upon the precise arrangement and lengths of myelin sheaths and exposed segments. To quantify this path-dependence, we calculated the conduction delays and the corresponding CVs of axons with identical biophysical properties, for a fixed axonal length and for each value of PMC. The lengths and number of myelin sheaths along these axons were randomly sampled from either cortical or callosal myelination motifs (see Fig. 1).
As expected, axonal conduction delays decreased with the addition of myelin (Fig. 4A), while axonal CVs increased (Fig. 4B). While the mean axonal CVs and delays were found to be comparable between cortical and callosal myelination motifs (Fig. 4C), the dispersion in axonal conduction delays and velocities did exhibit important differences, indicative of variability in AP propagation between and even within cortical and callosal myelination motifs. To quantify this variability, we computed the standard deviation of axonal conduction delays and velocities. We found that conduction delay variability was larger for callosal compared to cortical motifs, a trend that persisted across all PMC scenarios considered (bottom panel of Fig. 4D), despite being controlled for axonal length, PMC, and other physiological parameters (see Methods; Table 1). Furthermore, we observed a negative correlation between delay variability and PMC: as PMC increases, the dispersion of axonal conduction delays decreases. The associated axonal CVs also exhibited markedly lower variability in cortical compared to callosal motifs, whose CV was more variable across PMC values (top panel of Fig. 4D). Variability in conduction delays at low PMC values is also associated with variability in the number of exposed segments: as the number of exposed segments increases, the dispersion in conduction delays decreases (Fig. 4G–H). Consistent with the findings above, cortical motifs demonstrated smaller variability compared to the corpus callosum. Taken together, these results confirm that regional differences in myelination significantly influence AP propagation variability.
Axonal conduction variability as a result of spatially heterogeneous myelination along individual axons. A, Violin plots showing the distribution of axonal conduction delays (measured in ms) plotted for different myelin coverage marking the variability in axonal conduction caused by cortical and callosal myelin motifs. B, Violin plots of the corresponding distributions of axonal CVs (measured in m/s) for all five cases of PMC and for cortical and callosal myelin motifs. C, Mean values of axonal conduction delays (dark grey) and CVs (light gray) as a function of PMC. D, Bar plots of the standard deviation of axonal conduction delays (bottom) and axonal conduction velocities (top), for both cortical and callosal myelin motifs as a function of PMC. E, Rate of axonal conduction failures, that is, the number of failures over the total number of trials, for each PMC value. The top left intake plot is a representation of conduction success. The peak of the AP remains above the threshold at all times indicating that the AP reaches successfully the end-point of the axon. The top right intake plot is a representation of a conduction failure. The peak of the AP reaches a sub-threshold value making it unable to elicit a depolarization afterwards. F, Lengths of exposed segments in axons where we observe conduction failure. The left panel contains values of cortical axons and the right of callosal axons. For the cortical motifs, there are no values for
The consequences of myelination motifs extend beyond issues of conduction time reliability. Our analysis reveals that the faithful transmission of APs (that is, conduction success or failure) is also dependent on the distribution of myelin. Conduction failure can arise due to factors such as high stimulation frequency and/or reduced capacity of membrane potentials to depolarize in regions deprived of myelin (Schauf and Davis, 1974). This has important functional implications, including the inability to elicit depolarization in postsynaptic cells. In our model, conduction failures occur when the APs fail to reach the paranodal junction while traveling along longer exposed segments (see Methods). As a result, the amplitude of the AP falls below the threshold necessary for spike initiation, as depicted in the embedded plot of Figure 4E. An illustration of successful conduction is portrayed in Figure 4E, where the AP amplitude maintains supra-threshold values throughout the entire axon. By calculating the rate of conduction failures (see Methods), we found that both cortical and callosal motifs exhibited systematic failure in cases of low myelination (PMC=10%, Figure 4E). Figure 4F shows the lengths of exposed segments in axons where conduction failure occurs. These results clearly indicate that long exposed segments are complicit to AP conduction failure, and are especially salient in the callosal motifs. These segments provide more opportunities for ion leakage across the axonal membrane, which, among other factors, contributes to the gradual decrease in depolarization amplitude necessary for AP propagation. A considerably lower rate of conduction failures was observed in axons exhibiting higher degrees of myelination, with myelination motifs inherent to the corpus callosum showing slightly greater susceptibility to failures. Such differences can be linked to the larger representation of long unmyelinated segments in callosal motifs (Fig. 1J). In summary, these findings suggest that failure susceptibility might increase as axons traverse the corpus callosum, while grey matter myelination motifs – inherently less heterogeneous – may demonstrate heightened resilience to changes in PMC.
AP propagation is non-linear along heterogeneously myelinated axons
The results depicted in Figures 2⇑–4 suggest that axonal conduction delays are not solely determined by PMC or total axonal length; rather, conduction timing depends on the specific placement, ordering, and lengths of myelin sheaths and exposed segments. Indeed, even when controlling for differences in PMC and axonal length, conduction delays demonstrate important variability directly attributable to cortical or callosal myelin sheath arrangement (Fig. 4D). In Figure 5A–C, we plotted segmental delays against the length of the corresponding segment. Given that APs propagate rapidly along myelin sheaths through diffusion (see Methods), such delays are predominantly due to propagation along exposed segments. For axons with homogeneous myelin sheathing, conduction time scales linearly with the lengths of exposed segments, except for very long segments (Fig. 5A). The dispersion of segmental delays is zero, and the CV, reflected in the slope of the curve, remains constant. In contrast, axons with cortical and callosal motifs show increased segmental delay dispersion proportional to myelin sheath heterogeneity and PMC. The CVs fluctuate across segments and axons, as evidenced by the important variability in the slopes of the curves in Figure 5B–C. In line with our previous observations, callosal motifs did exhibit a more salient non-linearity combined with heightened variability of segmental delays, a feature directly linked to the statistical differences in exposed/myelinated segment lengths and number as well as the positioning of the segments on axons, compared to the cortical motifs (Fig. 1). These findings propose that axonal conduction is a path-dependent process, sensitive to cumulative transitions between myelinated and exposed segments of the axon, thereby confirming a dependence of AP propagation on myelination motifs.
Non-linearity and path-dependence of AP propagation along axons with heterogeneous myelin sheathing. A–C, Conduction delays along individual exposed segments (that is, segmental delays) are plotted as a function of their individual lengths. In panel A, the model axons feature homogeneous myelin sheathing, while in panels B (blue; cortical) and C (red; callosal) myelin sheaths are spatially heterogeneous. In each panel, color shading indicates PMC: light colors refer to low PMC values, and darker colors indicate high PMC values. The plotted data are for K = 1000 independent axons for each of the myelination motifs and PMC. D, (top panel) For a section of an individual axon with homogeneous myelination, we plotted how the propagation time of AP changes in space (that is, along successive segments of the axon). The black dots represent the time within exposed segments and the yellow dots the time within myelin sheaths. On the right side of the plot is a schematic representation of the section of the axon. (bottom panel) Corresponding CVs within each of the segments. The dashed yellow lines represent the asymptotic behavior of the CVs within myelin sheaths. E–F, Similarly, for an axon with cortical (panel E) and callosal (panel F) myelination motif. For panels D–F, simulations are for individual axons of length L =10 mm,
To better understand this nonlinear behavior, we examined in further detail AP propagation along individual segments (Fig. 5D–F). Along segments covered by myelin, transmission occurs instantaneously, as expected from saltatory conduction, while across exposed segments transmission slows down due to ionic currents (see Methods), leading to a nonlinear increase in AP propagation time. In a homogeneously myelinated axon, AP propagation time follows a periodic pattern across segments, repeated throughout the entire axon (Fig. 5D – top panel). However, for heterogeneously myelinated axons, delays were found to increase irregularly along successive exposed segments, with more pronounced changes observed for the callosal motif, which we recall is more heterogeneous (Fig. 5E–F – top panels). These trends are further reflected in the corresponding changes in CV experienced by the AP as it propagates along individual segments. Along myelin sheaths, CV is extremely high, reflecting the instantaneous spike timing. In contrast, within exposed segments, CV rapidly decreases as the AP enters the segments, and slightly increases before reaching the junction of the next myelin sheath (Fig. 5D–F – bottom panels). Mirroring the trend seen for the conduction delay, CV follows a periodic pattern in the homogeneously myelinated axon (Fig. 5D). However, fluctuations in CV were found to be especially irregular for the callosal motif (Fig. 5F). Taken together, these results suggest that APs are subjected to bouts of deceleration and acceleration along exposed segments. These collectively result in a deeply non-linear, path-dependent process, by which AP conduction becomes highly sensitive to the dynamics between neighboring segments (i.e., see Fig. 3), and thus myelin sheathing heterogeneity. It is interesting to consider the potential implications of the observed non-linearity in conduction delays and velocities, for instance when myelination motifs undergo demyelination.
Vulnerability of heterogeneous myelination motifs to demyelination
Upon the onset of demyelination, the integrity of myelin sheaths becomes compromised or completely breaks down, subsequently causing disruptions in the transmission of nerve impulses (Schauf and Davis, 1974). Such demyelination results from injury or loss of myelin sheaths and/or OLs, and occurs in numerous neurological (Duncan and Radcliff, 2016) and neuropsychiatric (Fields, 2008; Takahashi et al., 2011) disorders. Given the statistical differences in lengths, number and spatial distributions of myelin sheaths (Fig. 1), is AP conduction along axons with cortical or callosal motifs equally vulnerable to demyelination? To answer this question, we examined how cortical and callosal myelination motifs were impacted by myelin injury, and quantified their resulting predisposition to conduction failure. We modeled demyelination in two steps: (i) by systematically reducing the number of myelin sheaths, and (ii) by varying the excitability of the affected areas, specifically the demyelinated segment and the nodes adjacent to it. In other words, we varied the AP threshold along the newly formed exposed segments, while maintaining the baseline threshold value (−60.2 mV) in the unaffected segments. This was done to account for a pathological decrease in ion channel density (see Methods). A schematic illustration portraying the demyelination process described above is presented in Figure 6A. The reduction in the number of myelin sheaths naturally affects the PMC in damaged axons. Specifically, we initially set the PMC for axons before demyelination at
Vulnerability of cortical and callosal motifs to myelin injury. A, Schematic of the demyelination process. Axons of length L = 10 mm and initial
To measure vulnerability, we computed the rate of axonal conduction failures for various levels of excitability (i.e., AP threshold values, that change only along the newly exposed segments) and for successive application of myelin damage (Fig. 6E,H). We observed that callosal motifs were more vulnerable to demyelination, compared to cortical ones. This is confirmed by the higher rates of conduction failure (Fig. 6H). For both cortical and callosal motifs, conduction failures were expectedly found to be more prominent as the excitability of newly exposed segments decreases (that is, depolarization threshold increase, reflecting lower ion channel density). Next, we examined how demyelination affected the conduction delays along axons that did not experience failure in spite of experiencing extensive damage. Figure 6F,I showcases an increase in mean conduction delays as the axons become increasingly demyelinated. This trend was equally observed in both cortical and callosal motifs. At a fixed stage of demyelination, varying the AP threshold along the newly exposed segments affected only the rate of conduction failures, which increased with higher AP thresholds (Fig. 6E,H), while the mean conduction delays remained largely unchanged (Fig. 6F,I). This pattern was consistent across all stages of demyelination.
Figure 6J,M shows the amount of myelin coverage for each stage of demyelination. Comparing the mean conduction delays before (Fig. 4C) and after myelin damage (Fig. 6F,I) reveals a significant difference for axons with similar levels of myelin coverage. To investigate this further, we quantified the AP waveform by calculating the standard deviation of the AP peak amplitude as it propagated along the axons (Fig. 6K–L for cortical and Fig. 6N–O for callosal). Clearly, AP waveform demonstrates greater variability when traversing demyelinated axons. Such variability predisposes damaged axons to slower conduction or conduction block: demyelination-induced modulation of AP peak amplitude can be seen as interrogating both local excitability and myelin coverage, making the axon more susceptible to slow propagation or failure, particularly when the AP encounters long unmyelinated segments. We highlight that this is another salient manifestation of the path-dependent nature of axonal conduction along axons exhibiting heterogeneous myelin sheathing.
Discussion
Numerous experimental studies have revealed that mammalian axons display a wide diversity of myelination patterns. Significant heterogeneity in the number, thickness, length, and distribution of myelin sheaths along and between different axons, as well as across brain regions (Sturrock, 1980; Bakiri et al., 2011; Glasser and Essen, 2011; Chong et al., 2012; Tomassy et al., 2014; Ford et al., 2015; Micheva et al., 2016; Auer et al., 2018; Hill et al., 2018; Stedehouder et al., 2019; Benamer et al., 2020; Call and Bergles, 2021) has been observed. Notably, axons exhibit markedly different myelin sheathing motifs as they traverse the cortex and/or corpus callosum (Geurts and Barkhof, 2008; Glasser and Essen, 2011; Chong et al., 2012; Tomassy et al., 2014; Calabrese et al., 2015; Prins et al., 2015; Micheva et al., 2016; Timmler and Simons, 2019; Orthmann-Murphy et al., 2020; Call and Bergles, 2021; Corrigan et al., 2021; Lie et al., 2022; Thornton et al., 2024). However, how this variability influences neural signaling and susceptibility to injury remains poorly understood. Spatial heterogeneity in myelin sheathing is challenging to characterize with existing computational frameworks (Fitzhugh, 1962; Goldman and Albus, 1968; Grindrod and Sleeman, 1985; Basser, 1993; Nygren and Halter, 1999; McIntyre et al., 2002; Gow and Devaux, 2008; Babbs and Shi, 2013; Ashida and Nogueira, 2018; Scurfield and Latimer, 2018; Naud and Longtin, 2019; Schmidt and Knösche, 2019), often considering the axon as a cable with uniform myelin sheathing interspersed with exceedingly brief nodes of Ranvier. Motivated by the critical role played by myelin on AP conduction and its well-documented consequence on brain function (Nagy et al., 2004; Bengtsson et al., 2005; Mabbott et al., 2006; Pujol et al., 2006; McKenzie et al., 2014; Pan et al., 2020; Steadman et al., 2020; Xin and Chan, 2020), we here explored the influence of spatially heterogeneous myelin sheathing on axonal conduction reliability and predisposition to failure. Specifically, we developed a mathematical model of excitable axons displaying myelination motifs mirroring those observed experimentally in the cortex and corpus callosum of mice (Chong et al., 2012), brain areas known for their salient differences in myelin sheathing motifs (Geurts and Barkhof, 2008; Glasser and Essen, 2011; Chong et al., 2012; Tomassy et al., 2014; Calabrese et al., 2015; Prins et al., 2015; Micheva et al., 2016; Timmler and Simons, 2019; Orthmann-Murphy et al., 2020; Call and Bergles, 2021; Corrigan et al., 2021; Lie et al., 2022; Thornton et al., 2024). Leveraging experimental data (Chong et al., 2012), we systematically compared how such myelination motifs influence AP conduction delays, CVs as well as vulnerability to failure in these areas, for both healthy axons and those subjected to demyelination.
Our analysis revealed that variability in myelin patterns has an important impact on the reliability of axonal conduction. Indeed, axonal conduction was confirmed to be a nonlinear, path-dependent process, thereby sensitive to myelin sheath arrangement through the cumulative effect of AP propagating across myelinated and/or exposed segments of various lengths. Variability in conduction delays was found to correlate inversely with myelin coverage and differed between callosal and cortical motifs. This variability was however found to be more prominent amongst callosal motifs. We emulated demyelinating damage by selectively removing sheaths and quantifying resulting changes in AP conduction. Callosal myelination motifs, in particular, were found to display a greater sensitivity to demyelination, exhibiting increased failure rates compared to cortical motifs.
The diversity in myelin sheaths distribution along axons is the manifestation of highly plastic, area- and cell-type specific myelination processes, as well as the consolidation of signaling pathways by OLs. Through adaptive myelination and remodeling, myelin sheaths may retract and/or elongate (Gibson et al., 2014; Baraban et al., 2018; Krasnow et al., 2018), altering the lengths of exposed segments/nodes of Ranvier in an axon-specific manner (Arancibia-Cárcamo et al., 2017; Koskinen et al., 2023), thereby resulting in spatially heterogeneous myelination pattern. The manifest differences in myelin motifs (Chong et al., 2012; Tomassy et al., 2014; Timmler and Simons, 2019) and plasticity (Thornton et al., 2024) observed between grey and white matter axons suggest that precise sheath placement plays an important functional role (Timmler and Simons, 2019; Orthmann-Murphy et al., 2020). Myelin integrity has indeed been linked to a wide array of brain functions ranging from memory (Pan et al., 2020; Steadman et al., 2020) and learning (Bengtsson et al., 2005; McKenzie et al., 2014; Xin and Chan, 2020; Bacmeister et al., 2022) to executive functions (Nagy et al., 2004; Mabbott et al., 2006; Pujol et al., 2006).
In contrast, compromised myelin integrity, resulting from the loss of myelin sheaths and/or OLs impairment, is linked to an increasing range of neurological (Duncan and Radcliff, 2016; de Faria Jr et al., 2021) and neuropsychiatric conditions (Fields, 2008; Takahashi et al., 2011; de Faria Jr et al., 2021). Aberrant and/or maladaptive changes such as the lengthening of the nodes of Ranvier, breakdown of the electrically insulating barrier between the myelin sheath and the axonal membrane at the paranodal region, and shrinkage of the sheaths leading to the exposure of K+ channels in the juctaparanodes, are also potential contributors to the modulation of myelinated axon functionality. These changes could result in a slowdown of the AP propagation or even a conduction failure across a diverse spectrum of pathological conditions (Arancibia-Carcamo and Attwell, 2014; Freeman et al., 2016; Dolma and Joshi, 2023).
In line with multiple experimental studies (Geurts and Barkhof, 2008; Calabrese et al., 2015; Prins et al., 2015; Orthmann-Murphy et al., 2020; Call and Bergles, 2021; Lie et al., 2022; Thornton et al., 2024), our results identify a significant difference between myelination motifs in the cortex and corpus callosum in response to injury, with important potential implications in myelin disorders. This difference echoes a long-standing conundrum in the literature pertaining to the pathological manifestation, consequences and clinical relevance of grey versus white matter lesions observed across multiple sclerosis stages (Geurts and Barkhof, 2008; Prins et al., 2015; Lie et al., 2022). It is interesting to conjecture that variations in myelination patterns and resulting differences in vulnerability to demyelinating damage reported here may be involved in MS progression. For instance, the relatively higher resilience of cortical myelination motifs to damage (cf. Fig. 6) allows us to hypothesize that grey matter could involved in later stages of the disease compared to the white matter. Additionally, recent findings have linked aberrant myelination of the corpus callosum (but not the cortex) and epilepsy progression in mice (Knowles et al., 2022). These results indicate that maladaptive myelination in the corpus callosum may predispose brain networks to seizures by amplifying pathological oscillations. Our predictions pertaining to the heightened sensitivity of callosal motifs to changes in myelin suggest that the corpus callosum might represent a network of high vulnerability to maladaptive changes in myelin. Further research is required to delineate the respective contributions of grey and white matter axons in severity and progression of myelin-related disorders.
Recent advances in two- and three-photon fluorescence microscopy in vivo permit the imaging of myelin sheath patterns in mammalian circuits with unprecedented resolution (Hughes et al., 2018; Orthmann-Murphy et al., 2020; Thornton et al., 2024). Longitudinal changes in myelination have further recently been linked directly with perturbations in neural activity occurring in developmental, adaptive and/or remyelinating contexts (see Hughes et al., 2018; Bacmeister et al., 2022; Osso and Hughes, 2024 and references therein). We emphasize that these experimental approaches, combined with single cell electrophysiological recordings (e.g., spike timing, interspike-interval (ISI) distributions), could be used to test our model predictions, while informing further modeling work. Such experiments could provide novel insights as to the long debated relationship between myelination sheathing motifs and neural signaling (Salami et al., 2003; Mount and Monje, 2017), essential to understand the functional implications of the aforementioned differences in myelination observed between the grey and white matter.
While providing valuable insights, our study nonetheless faces limitations that should be acknowledged. First, our modeling framework balances physiological realism and computational tractability. To face the challenge of quantifying AP conduction along thousands of axons with different myelin sheathing placement patterns, we used a phenomenological model (Ashida and Nogueira, 2018). This approach relies on stereotyped models of axonal excitability (e.g., exponential integrate-and-fire model), combined with passive diffusion through the use of the cable equation. While good correspondence between the dynamics of such simplified models and more detailed biophysical models (e.g., Arancibia-Cárcamo et al., 2017) has been reported (Ashida and Nogueira, 2018; Schmidt and Knösche, 2019), future work should examine the combined effect of explicit ionic currents and myelin sheathing heterogeneity on conduction variability.
Second, we introduced variability exclusively to the longitudinal lengths of myelin sheaths and exposed segments, while keeping the axon radius constant and refraining from altering the myelin thickness. Introducing additional sources of variability, such as the g-ratio and/or axon diameter (Talidou et al., 2021) would provide a more comprehensive understanding of how these factors interact and influence axonal conduction, and could significantly expand the scope of our conclusions.
Third, we treated exposed segments of various lengths as nodes of Ranvier, assuming that ionic conductance does not change with length. Specifically, our model did not account for the different types of ion channels, their distribution along the exposed segments, or potential variation in their density within a given axon. These factors could affect the CV and variability of signal transmission. A detailed study incorporating ion channel dynamics and their spatial distribution could address this limitation.
Lastly, in characterizing the relationship between diverse myelination motifs and variability in axonal conduction delay, we used a phenomenological approach grounded in axonal geometry. This approach assumed infinite resistance along myelin sheaths and neglected the morphological structure of the paranodes. A more physiologically detailed model, incorporating additional features at the paranodal junctions, would significantly enhance the physiological relevance of our model, and would allow us to better understand the role played by paradonal junctions in AP conduction, providing a more accurate representation of signal transmission.
Footnotes
The authors declare no competing financial interests.
We thank the National Research Council of Canada (NSERC GRANT RGPIN-2017-06662) as well as the Canadian Institute of Health Research (CIHR GRANT NO PJT-156164) for funding. Special thanks to Ethan Hughes, Cristin Welle, Daniel Denman and Clara M Bacmeister for their insightful comments.
This is an open-access article distributed under the terms of the Creative Commons Attribution 4.0 International license, which permits unrestricted use, distribution and reproduction in any medium provided that the original work is properly attributed.
References
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