Myelin dystrophy impairs signal transmission and working memory in a multiscale model of the aging prefrontal cortex
- Department of Anatomy & Neurobiology, Boston University Chobanian & Avedisian School of Medicine, United States
- Centre de Recerca Matemàtica, Edifici C, Campus Bellaterra, Spain
- Departament de Matemàtiques, Universitat Autònoma de Barcelona, Edifici C, Spain
- Department of Mathematics, Franklin and Marshall College, United States
Figures
Figure 1
Electron photomicrographs (transverse sections) depicting age-related alterations in myelinated nerve fibers of area 46 of the rhesus monkey dorsolateral prefrontal cortex (dlPFC).
(A) Neuropil from a 10-year-old monkey. Healthy and compact myelin is visible as thick outlines surrounding nerve fibers which have been sectioned at their internodes. (B) Neuropil from a 27-year-old monkey. Arrows indicate dystrophic myelin surrounding nerve fibers, presenting a splitting of the major dense line of the myelin sheaths (left and right arrows) and balloons (left and middle arrows). Scale bar = 5 μm. Images are from the archives of Alan Peters and prepared as in Peters and Sethares, 2002.
Figure 2 with 1 supplement
Action potential (AP) transmission in the single neuron model.
(A) Cartoon of the model with a close-up view of unperturbed, demyelinated, and remyelinated segments (not to scale). The paranodes, juxtaparanodes, and internodes (shown in different shades of red) were insulated by myelin lamellae, adjacent to unmyelinated nodes (dark gray). During demyelination, lamellae were removed from a subset of segments; middle cartoon shows two lamellae remaining, indicating 50% lamellae removed relative to an unperturbed myelinated segment. During remyelination, select myelinated segments were replaced with two shorter myelinated segments separated by a new node; bottom cartoon shows remyelination with 50% of lamellae restored relative to unperturbed segments. At right are shown membrane potential traces simulated at the initial segment (top, dashed line) and near the distal end of one axon (here, 1.9 cm long) in the unperturbed, demyelinated, and remyelinated cases. Traces correspond to signals in a distal node and subsequent paranode, juxtaparanode, and internode respectively (colors indicating the axonal sections as in left panels). Demyelinating 75% of segments by removing 50% of their lamellae resulted in a 70% reduction in conduction velocity (CV), and failure of one AP. Remyelination of all affected segments with the same 50% of lamellae recovered the failed AP, and 98% of the CV delay relative to the demyelinated case (in 1 of the 30 simulated trials). (B) Close-up view of an AP simulated in the distal end of the unperturbed axon: suprathreshold in the node and subthreshold along the myelinated segment, indicating saltatory conduction. (C) Distribution of the 50 models of the cohort across two dimensions of parameter space: myelinated segment length and axon diameter. Grayscale shade of each model represents the mean CV change across three demyelination conditions: 25%, 50%, 75% of segments losing lamellae, averaged over 30 randomized trials and lamellae removal conditions.
Figure 2—figure supplement 1
Distribution of parameters and conduction velocities in the single neuron model cohort.
(A) Histograms of axon morphology parameters of models selected for the single neuron cohort (n=50). Top: axon diameter; middle: length of unperturbed myelinated segments; bottom: total myelin thickness in unperturbed segments, computed as the product of lamella thickness and number of lamellae. (B) Histograms of the conduction velocity (CV) for the 50 axons of the unperturbed model cohort (top), and representative demyelination and remyelination perturbations: mild demyelination (removing 25% of lamellae from 25% of the myelinated segments, second row); severe demyelination (removing all lamellae from 75% of the myelinated segments, third row); and complete (100%) remyelination (where the demyelinated segments from the third row were remyelinated by two shorter segments with 75% of lamellae). CVs averaged over 30 trials in each case. (C) Changes in CV (measured in %) in response to demyelination and remyelination versus the magnitude of current clamp step (+180, +280, or +380 pA). Shown are mean ± SEM (n=50) for demyelinating 50% of myelinated segments (removing all lamellae), and subsequent remyelination of those segments by shorter segments with 75% of lamellae.
Figure 3 with 1 supplement
Effects of demyelination on conduction velocity (CV) and action potential (AP) failures in the single neuron model.
(A) Heat maps showing CV change (reduction relative to the CV of the corresponding unperturbed models, measured in %) in response to select demyelination conditions across the 50 cohort axons (see Methods). Axons arranged vertically in increasing order of myelinated segment length (longest at the bottom). The three blocks from left to right show increasing numbers of demyelinated segments in each axon (25%, 50%, and 75% of segments respectively), illustrated by cartoons on top. Within each block, individual columns correspond to the percentage of myelin lamellae removed from each demyelinated segment (shown in cartoons below). Color of each box indicates the mean CV change across 30 trials of each condition, ranging from 0% (no effect) to –100% (AP failure). Overall, AP propagation was increasingly impaired with increasing levels of demyelination. Mean CV change (B) and percentage of AP failures (C) versus the percentage of lamellae removed for all demyelination conditions simulated. Colors represent the percentages of segments demyelinated, from 10% (light red) to 75% (black). Error bars represent mean ± SEM, averaged across all cohort axons (n=50) and 30 trials each.
Figure 3—figure supplement 1
Statistical analysis of parameters contributing to conduction velocity (CV) changes after demyelination and remyelination.
Coefficients of Lasso regression models with 10-fold cross-validation for demyelination (A) and remyelination (B). Parameters with non-zero coefficients are important factors underlying the response, critical in ascertaining the susceptibility of axons to respective perturbations. (C–D) The Lasso models effectively predicted how demyelination and remyelination affect CV. The models from (A–B) were applied to a novel test set (n=50 axons). Shown are predicted versus observed CV changes (z-scored; slowdown due to demyelination in (C), recovery due to remyelination in (D)) for the 50 novel axons. Adjusted R2=0.61 (C) and 0.87 (D) respectively.
Figure 4 with 2 supplements
Conduction velocity (CV) recovery in response to remyelination.
(A) Cartoons illustrating representative remyelination conditions after select segments were completely demyelinated. Top row shows an unperturbed axon with eight myelinated segments. Second row: 50% of segments are completely demyelinated. Third row: 25% of the demyelinated segments in second row (one in total) are remyelinated with two shorter segments, each with 25% of lamellae restored. Fourth row: 75% of the demyelinated segments in the second row (three in total) are remyelinated with two shorter segments, each with 50% of lamellae restored. Mean CV recovery (B) and percentage of action potential (AP) failures (C) versus the percentage of lamellae restored for all simulated remyelination conditions after complete demyelination. (D) Cartoons illustrating representative remyelination conditions after partial demyelination. Top row shows an unperturbed axon with eight myelinated segments. Second row: 50% of segments are partially demyelinated (with 50% of lamellae removed). Third row: 50% of the demyelinated segments in second row (two in total) are remyelinated with two shorter segments, each with 50% of lamellae restored. Mean CV recovery (E) and percentage of AP failures (F) versus the percentage of lamellae restored for all simulated remyelination conditions after partial demyelination. CV recovery in both cases (B and E) was calculated with respect to the CV change for the complete demyelination (see Methods). In panels (B, C, E, and F), the x-axis refers to the percentage of myelin lamellae restored relative to unperturbed segments, starting at 0% (no remyelination). Line styles represent the percentage of segments initially demyelinated, from 25% (dashed) to 75% (thick solid). Colors represent the extent of remyelination, from 25% (light red) to 100% (black). Shown are mean values, averaged across all cohort axons (n=50) and 30 trials each. For readability, error bars (representing ± SEM) are shown only for the condition of 50% demyelination of segments.
Figure 4—figure supplement 1
Conduction velocity (CV) recovery in response to remyelination across the model cohort.
Axons arranged vertically in increasing order of myelinated segment length (longest at the bottom). The three groups of heat maps from left to right represent how many segments were demyelinated initially (25%, 50%, and 75%, respectively). Within each group, the position in each of the four blocks indicates what proportion of demyelinated segments were remyelinated. Individual columns correspond to the percentage of lamellae restored to each remyelinated segment. Color of each box indicates the mean CV recovery from the corresponding demyelinated case across 30 trials (see Methods). (A) Recovery after complete demyelination, when all lamellae had been removed from affected segments. Columns highlighted in blue and green respectively correspond to the two remyelination cases shown in Figure 4A. CV recovery was positive, representing improvement, in all remyelination cases except one. For axon 22, the CV was worse for the mildest remyelination situation: when 25% of segments were initially demyelinated, then 25% of those segments were remyelinated by restoring just 25% of the myelin lamellae. A few axons showed recovery above 100%, suggesting faster conduction than in the unperturbed condition, when either 75% of the lamellae were restored. (B) Recovery after partial demyelination, when half of lamellae had been removed from affected segments. Column highlighted in green corresponds to the remyelination case shown in Figure 4D. CV recovery was positive, representing improvement, in all remyelination cases except one (axon 46, far left simulation condition).
Figure 4—figure supplement 2
Transitions between myelinated segments of dissimilar lengths affect response to perturbations.
(A) Mean conduction velocity (CV) change (measured in %) versus the number of transitions from unperturbed to demyelinated segments in 30 randomized trials for a given demyelination condition (50% of the segments affected, 50% of lamellae removed). (B) Mean CV change (measured in %) versus the number of transitions from unperturbed (long) to remyelinated (short) segments in 30 randomized trials for complete remyelination of 50% of the segments with 50% of lamellae restored. CV change was more severe as the number of transitions between segments of unequal lengths increased.
Figure 5 with 5 supplements
Action potential (AP) failures impair working memory performance in a spiking neural network model.
(A) Schematic of the delayed response task. Subjects fixate at the center of a computer screen and need to remember a cue stimulus, presented at one out of eight locations throughout the delay period, before indicating the remembered location with an eye movement. (B) Excitatory neuron activity for a cue stimulus presented at 135° of an (i) unperturbed control network, (ii) a network with demyelination, and (iii) a network with remyelination. Left: Single-trial raster plot showing the activity for each neuron (labeled by its preferred direction) during the precue (fixation), cue and delay periods of the task. The cue period is indicated by the gray shading. Middle: Average spike counts of the excitatory neurons during the delay period. The points show average spike rates of individual neurons and the solid line the average over 500 nearby neurons. Right: Trajectory of the bump center (i.e. the remembered cue location) read out from the neural activity across the cue and delay periods using a population vector (see Methods). Thin lines correspond to individual trials and the solid line to the trial average. (ii) Shows the effect of AP failure probabilities corresponding to demyelination of 25% of the myelinated segments by removing 75% of the myelin lamellae. (iii) Corresponds to AP failure probabilities for remyelination of 50% of the demyelinated segments by adding 75% of the myelin lamellae back, after previous partial demyelination of 25% of the segments. (C) Memory strength as a function of time and corresponding memory duration (horizontal bars; memory strength ≥0.4; see Methods). (D) Working memory diffusion (trial-to-trial variability of bump center) during the cue and delay periods. The inset shows a close-up of the diffusion for control networks. A similar increase of working memory diffusion with demyelination is also observed in networks with overall higher diffusion (Figure 5—figure supplement 1). When demyelination is restricted to a part of the network, diffusion only increases in the perturbed zone (Figure 5—figure supplement 3). (E) Working memory drift (systematic memory errors). Note that the remyelination curve (purple dotted line) in (E) superimposes the young curve (blue solid line). The red dashed line represents the demyelination case. The performance measures in (C–E) were obtained by averaging across 280 trials and 10 networks, either control (B, i) or perturbed (B, ii–iii).
Figure 5—figure supplement 1
Increased working memory diffusion in spiking networks with spatially correlated background inputs.
Bump position during the cue and delay periods for 280 trials and the eight possible cue directions for (A) a young, control network and (B) a perturbed network when remyelinating 50% of the segments after partial demyelination of 25% of the segments along the neuronal axons, by adding 75% of the myelin lamellae back. Simulations were done with spatially uncorrelated background inputs as in all other simulations in Figures 5—8 (left panels), and with spatially correlated background inputs (see Supplementary Methods; right panels). These simulations show that, as expected from theory, bump diffusion increases for spatially modulated noise correlations (Rosenbaum et al., 2017; Stein et al., 2021). Importantly, the effect of myelin alterations is an increase in diffusion in both cases, showing the robustness of our results (diffusion constant = 0.018 deg2/s in (A) left panel; 0.957 deg2/s in (B) left panel; 3.115 deg2/s in (A) right panel; and 9.605 deg2/s in (B) right panel).
Figure 5—figure supplement 2
Effect of propagation delays on control and perturbed networks.
(A) Memory strength (left panels) and diffusion (right panels) for the young, control networks with zero propagation delays (blue solid line), as in Figure 5, and with propagation delays from a uniform distribution with a range between 0 and 100 ms (yellow dashed line). (B) Memory strength and diffusion for perturbed networks when demyelinating 50% of the segments along the axons of model neurons, by removing 60% of the myelin lamellae without delays (red solid line), and with delays from a uniform distribution with a range between 0 and 40 ms (gray dashed line) and between 0 and 85 ms (black dash-dotted line). The measures of working memory performance were calculated by averaging across 20 networks and 280 trials for each network. Shaded areas indicate SEM for each case. For the young, control networks, there was no difference with and without propagation delays, even though the delays used in the network simulations were much larger than the delays quantified in the single neuron model (the longest delays found for the most extreme perturbation condition – demyelination of 75% of the segments by removing 100% of the myelin lamellae – were of 49.9 ms on average; A). Working memory performance was also unaffected in the perturbed network with action potential (AP) failures for delays ranging between 0 and 40 ms, also larger than the ones quantified in the single neuron model (for the case of 50% of the segments demyelinated by removing 60% of the myelin lamellae, the average delay in the cohort was 4.6 ms and the maximum delay was 15.7 ms; B). However, including extremely long delays of up to 85 ms did further impair memory compared to the impairment level introduced by AP failures alone (B).
Figure 5—figure supplement 3
Effect of spatially heterogeneous demyelination of the model neurons according to their preferred angle.
We also tested working memory performance in the network when demyelination affects only parts of the network. The figure shows the decoded bump center position during the cue and delay period for the eight possible cue directions when a fraction of neurons was perturbed and the rest of the neurons in the circuit were unaltered (Figure 5B). We perturbed 10% of the neurons around the neuron with preferred direction 90° (left panel), 25% of the neurons around –90° (middle panel), and 50% of the neurons around 180° (right panel). Bump traces for cues that lie inside the perturbed portion of the circuit are shown in blue. Network perturbation in the three cases consisted in demyelinating 25% of the segments along the axons of model neurons, by removing 70% of the myelin lamellae. In each case, 280 trials were simulated for one network. These simulations show an increased drift and diffusion inside the perturbed zone, consistent with the increased drift and diffusion when perturbing the entire network (Figure 6B and Figure 6—figure supplement 2). In particular, spatially heterogeneous demyelination in our network leads to a bias away from the affected zone and to increased trial-to-trial variability. Note that this is a model prediction, but we are not aware of empirical data showing heterogeneous demyelination with aging. Further, note that while our network model has a topological ring structure, neurons in PFC are not anatomically arranged depending on their preferred features. Thus, spatially heterogeneous demyelination would likely affect neurons with different feature preferences (i.e. neurons throughout our ring model).
Figure 5—figure supplement 4
Action potential (AP) failures impair working memory performance in a network model with activity-silent memory traces.
(A) Spiking and synaptic activity in an unperturbed, activity-silent working memory model. Top: Raster plot showing the activity for each excitatory neuron (labeled by its preferred direction) in a single trial with a cue stimulus presented at 180°. We modified our spiking neural network model such that it does not show elevated persistent firing throughout the delay period (see Figure 5B for comparison). In particular, we reduced the external background input to excitatory neurons by a factor of 3.61% and we increased the cue stimulus amplitude by 12.5%. Even though spiking activity decays to baseline (close to 0 Hz), a memory trace is imprinted in enhanced synaptic strength due to short-term synaptic facilitation (Mongillo et al., 2008). Selective spiking activity is recovered by a non-selective constant input applied during 300 ms to all excitatory neurons during the two reactivation periods (marked by yellow and green rectangles in the raster plot). The amplitude of the input was 11 mV during the first and 13 mV during the second reactivation period. Reactivation periods are marked in light gray shading in the remaining panels below and the cue period is indicated by dark gray shading. Firing rates (second row), synaptic facilitation variable u (third row), and synaptic depression variable x (bottom row) for the same trial, averaged for 500 neurons around the neuron with 180° as preferred direction (solid lines) and around the neuron with 0° as preferred direction (dashed lines). Note that reactivation recovers the activity bump (C) but also causes elevated firing and subsequent enhancement of synapses at all positions in the networks. (B) Activity in a network with demyelination of 50% of the myelinated segments by removing 60% of the myelin lamellae. AP failures lead to reduced firing rates in the cue and early delay periods and consequently to weaker synaptic enhancement. (C) Average spike counts of the excitatory neurons during the cue period (black lines), and the two reactivation periods indicated in the raster plots in (A) and (B) (yellow and green lines). Solid lines correspond to the control network and dashed lines to the perturbed network. (D) Memory strength as a function of time for the control and perturbed networks. (E–F) Trajectories of the bump center (i.e. remembered cue location) read-out from the neural activity across the cue and delay periods using a population vector (see Methods). Cue position was 180° in all trials. The perturbed network (F) shows larger working memory errors toward the end of the delay period compared to the control network (E).
Figure 5—figure supplement 5
Effect of propagation delays on control and perturbed activity-silent network models.
(A) Memory strength during the whole simulation time for the young, control networks relying on activity-silent working memory (Figure 5—figure supplement 4) with zero propagation delays (blue line), and with propagation delays from a uniform distribution with a range between 0 and 40 ms (yellow line) and between 0 and 100 ms (orange line). (B) Memory strength for perturbed networks when demyelinating 25% of the myelinated segments by removing 50% of the myelin lamellae, without delays (red line), and with uniformly distributed delays between 0 and 40 ms (light gray line) and between 0 and 100 ms (black line). The cue period is indicated by dark gray shading and reactivation periods are marked in light gray. Memory strength was calculated by averaging across 280 trials for one network. Shaded areas indicate SEM for each case. For the young, control networks (A), working memory was not affected by including delays of up to 40 ms. Unrealistically long delays ranging up to 100 ms did cause an impairment (the longest delays found for the most extreme perturbation condition – demyelination of 75% of the segments by removing 100% of the myelin lamellae – were of 49.9 ms on average). When also incorporating AP failures to the networks (B), we observed a similar trend. For this perturbation condition, delays of up to 40 ms were already much larger than the delays quantified in the single neuron model (for the case of 25% of the segments demyelinated by removing 50% of the myelin lamellae, the average delay in the cohort was 3.75 ms).
Figure 6 with 2 supplements
Working memory function in the network model is impaired by demyelination and recovered by sufficient remyelination.
(A) Memory duration and (B) diffusion constant for simulations of the delayed response task, as in Figure 5, for a systematic exploration of the effect of action potential (AP) failure probabilities corresponding to the different demyelination and remyelination conditions explored with the single neuron model. Left panel: Demyelination, realized by removing a fraction of myelin lamellae from a fraction of myelinated segments. Middle panel: Remyelination with two shorter and thinner myelin sheaths, with a node in between, of the previously completely demyelinated segments. Right panel: Same as the middle panel but for partial demyelination (removal of 50% of the myelin lamellae) rather than complete demyelination. In all cases, the performance measures were obtained by averaging across the 10 perturbed cohort networks and the 280 trials simulated for each network. The average memory duration for the 10 unperturbed, control networks in the cohort (averaged across 280 trials) was 4 s, and the average diffusion constant was 0.064 (both values corresponding to the case of 0% of myelin lamellae removed in the left panels of (A) and (B), respectively; not shown). Error bars represent mean ± SEM, averaged across all networks and trials.
Figure 6—figure supplement 1
Memory strength decreases for different degrees of demyelination and remyelination.
(A) Progressive memory strength reduction, due to higher degrees of demyelination (left panel) and lower degrees of remyelination (right panel), leads to a progressive shortening of the memory duration. Left panel: Demyelination of 25% of the myelinated segments by systematically removing myelin lamellae. Removing up to 50% of the lamellae causes no effect on the memory strength compared to the control networks (see Figure 5C; memory duration = 4 s). However, removing over 75% of the myelin lamellae progressively shortens memory duration (<2 s). Right panel: Systematic remyelination of the previously partially demyelinated 25% of the segments. Specially adding back more myelin lamellae recovers the memory strength and thus, the memory duration. Complete remyelination leads to control-like values (black lines; Figure 5C). (B) Memory strength at the end of the delay period for simulations of the delayed response task (DRT), for a systematic exploration of the effect of AP failure probabilities corresponding to the demyelination/remyelination conditions explored with the single neuron model (see Figure 6). Left panel: Demyelination. Middle panel: Remyelination of the previously completely (removal of 100% of the myelin lamellae) demyelinated segments. Right panel: Remyelination of the previously partially (removal of 50% of the myelin lamellae) demyelinated segments. In (A) and (B) memory strength was obtained by averaging across the 10 perturbed cohort networks and the 280 trials simulated for each network. The average memory strength for the 10 control networks in the cohort (averaged across 280 trials) was 0.765, corresponding to the case of 0% of lamellae removed in the left panel of (B). Error bars in (B) represent mean ± SEM, averaged across all networks and trials.
Figure 6—figure supplement 2
Increase of memory drift for different degrees of demyelination and remyelination.
Drift rate for simulations of the delayed response task (DRT), for a systematic exploration of the effect of action potential (AP) failure probabilities corresponding to the demyelination/remyelination conditions explored with the single neuron model (see Figure 6). Left panel: Demyelination. Middle panel: Remyelination of the previously completely (removal of 100% of the myelin lamellae) demyelinated segments. Right panel: Remyelination of the previously partially (removal of 50% of the myelin lamellae) demyelinated segments. Drift rate was obtained by averaging across the 10 perturbed cohort networks and the 280 trials simulated for each network. The average drift rate for the 10 control networks in the cohort (averaged across 280 trials) was 2.075 deg/s, corresponding to the case of 0% of lamellae removed in the left panel. Error bars represent mean ± SEM, averaged across all networks and trials.
Figure 7
Reduced normal myelin is associated with decreased working memory performance in the network model.
(A) Schematic of the quantification of unperturbed, normal myelin sheaths in groups of neurons containing intact and demyelinated axons with different proportions of demyelinated segments (see Methods). Vertical red lines indicate cross-sectional planes that mimic electron microscopy images capturing cross sections of different axonal parts. (B) Memory duration and (C) diffusion constant vs. the percentage of normal myelin sheaths. Linear regressions show significant positive correlations in both cases (memory duration: r=0.703, p=3.86 × 10–10; diffusion constant: r=–0.802, p=1.26 × 10–14). Circles: All the demyelinated segments in the perturbed axons in the groups were bare segments (all myelin lamellae removed). Squares: All the demyelinated segments in the perturbed axons had 75% of the myelin lamellae removed. Black horizontal bars indicate the percentage of normal sheaths observed in electron microscopy images from young and aged rhesus monkeys dorsolateral prefrontal cortex (dlPFC) (Peters and Sethares, 2002).
Figure 8
A higher proportion of new myelin sheaths impairs working memory in the network model.
(A) Schematic of the quantification of new myelin sheaths in groups of neurons containing intact and partly remyelinated axons. Vertical purple lines indicate cross-sectional planes that model electron microscopy images capturing cross sections of different axonal parts. (B) Memory duration and (C) diffusion constant vs the percentage of new myelin sheaths. Linear regressions show significant negative correlations in both cases (memory duration: r=–0.852, p=4.92 × 10–7; diffusion constant: r=0.607, p=0.003). The remyelinated axons in the groups have different proportions of segments remyelinated after partial demyelination, by adding 25% of the myelin lamellae back. Black horizontal bars indicate the percentage of paranodal profiles observed in electron microscopy images from young and aged rhesus monkeys dorsolateral prefrontal cortex (dlPFC) (Peters and Sethares, 2003).
Author response image 1
Action potential failures impair working memory performance in a network model with activity-silent memory traces.
(A) Spiking and synaptic activity in an unperturbed, activity-silent working memory model. Top: Raster plot showing the activity for each excitatory neuron (labeled by its preferred direction) in a single trial with a cue stimulus presented at 180°. We modified our spiking neural network model such that it does not show elevated persistent firing throughout the delay period (see Figure 5B for comparison). In particular, we reduced the external background input to excitatory neurons by a factor of 3.61% and we increased the cue stimulus amplitude by 12.5%. Even though spiking activity decays to baseline (close to 0 Hz), a memory trace is imprinted in enhanced synaptic strength due to short-term synaptic facilitation (Mongillo et al., 2008). Selective spiking activity is recovered by a non-selective constant input applied during 300 ms to all excitatory neurons during the two reactivation periods (marked by yellow and green rectangles in the raster plot). The amplitude of the input was 11 mV during the first and 13 mV during the second reactivation period. Reactivation periods are marked in light gray shading in the remaining panels below and the cue period is indicated by dark gray shading. Firing rates (second row), synaptic facilitation variable u (third row), and synaptic depression variable x (bottom row) for the same trial, averaged for 500 neurons around the neuron with 180° as preferred direction (solid lines) and around the neuron with 0° as preferred direction (dashed lines). Note that reactivation recovers the activity bump (C) but also causes elevated firing and subsequent enhancement of synapses at all positions in the networks. (B) Activity in a network with demyelination of 50% of the myelinated segments by removing 60% of the myelin lamellae. AP failures lead to reduced firing rates in the cue and early delay periods and consequently to weaker synaptic enhancement. (C) Average spike counts of the excitatory neurons during the cue period (black lines), and the two reactivation periods indicated in the raster plots in A and B (yellow and green lines). Solid lines correspond to the control network and dashed lines to the perturbed network. (D) Memory strength as a function of time for the control and perturbed networks. (E-F) Trajectories of the bump center (i.e., remembered cue location) read out from the neural activity across the cue and delay periods using a population vector (see Methods). Cue position was 180° in all trials. The perturbed network (F) shows larger working memory errors towards the end of the delay period compared to the control network (E).
Author response image 2
Effect of propagation delays on control and perturbed activity-silent network models.
(A) Memory strength during the whole simulation time for the young, control networks relying on activity-silent working memory (Supplementary Figure 8) with zero propagation delays (blue line), and with propagation delays from a uniform distribution with a range between 0 and 40 ms (yellow line) and between 0 and 100 ms (orange line). (B) Memory strength for perturbed networks when demyelinating 25% of the myelinated segments by removing 50% of the myelin lamellae, without delays (red line), and with uniformly distributed delays between 0 and 40 ms (light gray line) and between 0 and 100 ms (black line). The cue period is indicated by dark gray shading and reactivation periods are marked in light gray. Memory strength was calculated by averaging across 280 trials for one network. Shaded areas indicate SEM for each case. For the young, control networks (A), working memory was not affected by including delays of up to 40 ms. Unrealistically long delays ranging up to 100 ms did cause an impairment (the longest delays found for the most extreme perturbation condition – demyelination of 75% of the segments by removing 100% of the myelin lamellae – were of 49.9 ms on average). When also incorporating AP failures to the networks (B), we observed a similar trend. For this perturbation condition, delays of up to 40 ms were already much larger than the delays quantified in the single neuron model (for the case of 25% of the segments demyelinated by removing 50% of the myelin lamellae, the average delay in the cohort was 3.75 ms).
Author response image 3
Effect of localized myelin alterations on CV change.
Myelin alterations were either focused on the third of myelinated segments closest to the initial segment (‘proximally clustered’), the third of myelinated segments furthest from the initial segment (‘distally clustered’), or distributed according to a uniform distribution as in the current study. For demyelination, all lamellae were removed from 25% of myelinated segments (showing mean +/- SEM of all 50 cohort models, 30 randomized trials each). For remyelination, affected segments were replaced by two shorter segments with 75% of the original lamellae thickness and a node in between.
Author response image 4
Distribution of parameters and conduction velocities in the single neuron model cohort.
(A) Histograms of axon morphology parameters of models selected for the single neuron cohort. Top: axon diameter: middle, length of unperturbed myelin segments; bottom: total myelin thickness in unperturbed segments, computed as the product of lamella thickness and number of lamellae. (B) Histograms of the CV for the 50 axons of the unperturbed model cohort (top), and representative demyelination and remyelination perturbations: mild demyelination (removing 25% of lamellae from 25% of the myelinated segments, second row); severe demyelination (removing all lamellae from 75% of the myelinated segments, third row); and complete (100%) remyelination (where the demyelinated segments from the third row were remyelinated by two shorter segments with 75% of lamellae). CVs averaged over 30 trials in each case. (C) Changes in CV (measured in %) in response to demyelination and remyelination versus the magnitude of current clamp step (+180, +280, or +380 pA). Shown are mean +/- SEM for demyelinating 50% of myelinated segments (removing all lamellae), and subsequent remyelination of those segments by shorter segments with 75% of lamellae.
Author response image 5
Effect of spatially heterogeneous demyelination of the model neurons according to their preferred angle.
We also tested working memory performance in the network when demyelination affects only parts of the network. The figure shows the decoded bump center position during the cue and delay period for the eight possible cue directions when a fraction of neurons was perturbed and the rest of the neurons in the circuit were unaltered (Figure 5B). We perturbed 10% of the neurons around the neuron with preferred direction 90° (left panel), 25% of the neurons around -90° (middle panel), and 50% of the neurons around 180° (right panel). Bump traces for cues that lie inside the perturbed portion of the circuit are shown in blue. Network perturbation in the three cases consisted in demyelinating 25% of the segments along the axons of model neurons, by removing 70% of the myelin lamellae. In each case, 280 trials were simulated for one network. These simulations show an increased drift and diffusion inside the perturbed zone, consistent with the increased drift and diffusion when perturbing the entire network (Figure 6B and Supplementary Figure 11). In particular, spatially heterogeneous demyelination in our network leads to a bias away from the affected zone and to increased trial-to-trial variability. Note that this is a model prediction, but we are not aware of empirical data showing heterogeneous demyelination with aging. Further, note that while our network model has a topological ring structure, neurons in PFC are not anatomically arranged depending on their preferred features. Thus, spatially heterogeneous demyelination would likely affect neurons with different feature preferences (i.e., neurons throughout our ring model).
Author response image 6
Effect of propagation delays on control and perturbed networks.
(A) Memory strength (left panels) and diffusion (right panels) for the young, control networks with zero propagation delays (blue solid line), as in Figure 5, and with propagation delays from a uniform distribution with a range between 0 and 100 ms (yellow dashed line). (B) Memory strength and diffusion for perturbed networks when demyelinating 50% of the segments along the axons of model neurons, by removing 60% of the myelin lamellae without delays (red solid line), and with delays from a uniform distribution with a range between 0 and 40 ms (gray dashed line) and between 0 and 85 ms (black dash-dotted line). The measures of working memory performance were calculated by averaging across 20 networks and 280 trials for each network. Shaded areas indicate SEM for each case. For the young, control networks, there was no difference with and without propagation delays, even though the delays used in the network simulations were much larger than the delays quantified in the single neuron model (the longest delays found for the most extreme perturbation condition –demyelination of 75% of the segments by removing 100% of the myelin lamellae– were of 49.9 ms on average; A). Working memory performance was also unaffected in the perturbed network with AP failures for delays ranging between 0 and 40 ms, also larger than the ones quantified in the single neuron model (for the case of 50% of the segments demyelinated by removing 60% of the myelin lamellae, the average delay in the cohort was 4.6 ms and the maximum delay was 15.7 ms; B). However, including extremely long delays of up to 85 ms did further impair memory compared to the impairment level introduced by AP failures alone (B).
Tables
Table 1
Axon parameter ranges for Latin hypercube sampling (LHS) construction.
| Parameter | Values | |
|---|---|---|
| Minimum | Maximum | |
| Axon diameter (μm), measured at nodes | 0.5 | 1.02 |
| Node length (μm) | 0.25 | 2.02 |
| Myelinated segment length (μm) | 50 | 200 |
| Number of myelin lamellae | 5 | 20 |
| Lamella thickness (μm) | 0.013 | 0.019 |
| Scale factor for leak conductance | 0.1 | 1 |
| Scale factor for NaF maximal conductance | 0.1 | 1 |
| Scale factor for KDR maximal conductance | 0.1 | 1 |
Table 2
Network model parameters.
| Parameter | Value |
|---|---|
| 30° | |
| 35° | |
| 30° | |
| 30° | |
| 61.2° |
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Myelin dystrophy impairs signal transmission and working memory in a multiscale model of the aging prefrontal cortex
eLife 12:RP90964.
https://doi.org/10.7554/eLife.90964.3
