Electron photomicrographs (transverse sections) depicting age-related alterations in myelinated nerve fibers of area 46 of the rhesus monkey 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 microns. Images are from the archives of Alan Peters and prepared as in Peters and Sethares (2002).

Action potential 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, 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 one 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.

Effects of demyelination on CV and 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 high failure trials (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 and trials.

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 8 myelinated segments. Second row: 50% of segments are completely demyelinated. Third row: 25% of the demyelinated segments in second row (1 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 (3 in total) are remyelinated with two shorter segments, each with 50% of lamellae restored. Mean CV recovery (B) and percentage of high failure trials (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 8 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 (2 in total) are remyelinated with two shorter segments, each with 50% of lamellae restored. Mean CV recovery (E) and percentage of high failure trials (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 and trials. For readability, error bars (representing ± SEM) are shown only for the condition of 50% demyelination of segments.

Statistical analysis of parameters contributing to 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 from A-B were applied to a novel test set (50 axons) to predict effects of demyelination and remyelination. 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.

Action potential 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 through 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., 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. (E) Working memory drift (systematic memory errors). 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).

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 6, for a systematic exploration of the effect of AP failure probabilities corresponding to the different demyelination and remyelination conditions explored with the single neuron model. Left panel: demyelination of the different percentages of segments and lamellae. Middle panel: remyelination with two shorter and thinner myelin sheaths 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. See Figures 3-4 and Methods for details. 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 seconds, 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.

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 redlines 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, middle-aged and aged rhesus monkeys dlPFC (Peters and Sethares, 2002).

A higher proportion of new myelin sheaths impair working memory in the network model.

(A) Schematic of the quantification of new myelin sheaths in groups of neurons containing intact and 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 dlPFC (Peters and Sethares, 2003).

Axon parameter ranges for LHS construction

x and u are updated as xx (1 − u) and uu + U ∗ (1 − u), each time that there is a presynaptic spike. The variable x represents the amount of available neurotransmitter resources in the presynaptic terminal and u is the utilization parameter, indicating the residual calcium level (Bertram et al., 1996; Zucker and Regehr, 2002; Mongillo et al., 2008). With each spike, and amount ux of the available resources is used to produce the postsynaptic current. Thus, x is reduced, representing neurotransmitter depletion, and u is increased, representing the calcium influx into the presynaptic terminal and its effect on release probability. Between spikes, x and u recover to their baseline levels (x = 1 and u = U; 0 < x < 1) with time constants τdand τf. We set τf > τd so that they facilitate signal transmission (Tsodyks et al., 1998).

rj(t) is the firing rate of neuron j with preferred direction θj. Firing rates rj(t) were estimated as spike counts in a 250 ms window. A memory strength M(t) close to 0 indicates homogeneous activity of the network and M(t) close to 1 indicates a sharply modulated activity (Figure 6C).