Cortical waste clearance in normal and restricted sleep with potential runaway tau buildup in Alzheimer's disease

Abstract

Accumulation of waste in cortical tissue and glymphatic waste clearance via extracellular voids partly drives the sleep-wake cycle and modeling has reproduced much of its dynamics. Here, new modeling incorporates higher void volume and clearance in sleep, multiple waste compounds, and clearance obstruction by waste. This model reproduces normal sleep-wake cycles, sleep deprivation effects, and performance decreases under chronic sleep restriction (CSR). Once fitted to calibration data, it successfully predicts dynamics in further experiments on sleep deprivation, intermittent CSR, and recovery after restricted sleep. The results imply a central role for waste products with lifetimes similar to tau protein. Strong tau buildup is predicted if pathologically enhanced production or impaired clearance occur, with runaway buildup above a critical threshold. Predicted tau accumulation has timescales consistent with the development of Alzheimer's disease. The model unifies a wide sweep of phenomena, clarifying the role of glymphatic clearance and targets for interventions against waste buildup.

Figure 1

Model schematics. (a) Model of arousal dynamics incorporating key interactions between the homeostatic drive H, circadian drive C, and the sleep- and wake-active neuronal populations, VLPO and MA nuclei. Bar-headed lines indicate inhibitory connections, while the arrows show excitatory action. Dotted lines show relevant model outputs—sleep times and alertness. Constraints, such as sleep restriction are incorporated through action of the MA nuclei. See text for parameter descriptions. (b) Schematic cross section of an interstitial void during wake and during sleep with unobstructed flow (top) and obstructed flow (bottom) due to build up of waste products, shown shaded. The void radius increases during sleep by a factor of $\sqrt{\rho }$. In the absence of clearance, the area $\alpha H$ obstructed due to the effects of waste products is the same during wake and sleep.

Figure 2

Homeostatic dynamics with one and two species in a fixed arousal state with and without runaway. One species dynamics are shown in (a)–(f). (a) Rising $H_1$ and ${\beta }_{\sigma 1}=0$ for production rates $q_{\sigma 1}=7\times {10}^{-6},65\times {10}^{-6},$ and $140\times {10}^{-6}$ s${}^{-1}$, as labeled in units of ${10}^{-6}$. (b) Falling $H_1$ and ${\beta }_{\sigma 1}=0$ for $q_{\sigma 1}=20\times {10}^{-6},9\times {10}^{-6},$ and 0 s${}^{-1}$ from top to bottom. (c) Rising $H_1$ and ${\beta }_{\sigma 1}=0.1$ for the same values of $q_{\sigma 1}$ as in (a), with runaway case indicated with dot-dashed lines. (d) Falling $H_1$ for ${\beta }_{\sigma 1}=0.05,0.1,0$, from top to bottom. (e) Normalized clearance rate vs. t for the cases in (c), with runaway case indicated with dot-dashed lines. (f) Normalized clearance rate vs. t for the cases in (d); for ${\beta }_{\sigma 1}=0$ this ratio is 1 throughout so it is not shown. Homeostatic rise using two-species drive during wake is shown in (g)–(j). Fast clearance $H_1$ is shown in green, slow clearance $H_2$ in blue, and total H in red. (g) State with ${\beta }_1={\beta }_2=0$ and $H_1$ and $H_2$ starting from zero. (h) Same as in (g) but ${\beta }_1=0.05$ and ${\beta }_2=0.15$. (i) Overt runaway state with ${\beta }_1=0.15$ and ${\beta }_2=0.15$. (j) Covert runaway. (k) Clearance dynamics for two species with ${\beta }_1=0.15$ and ${\beta }_2=0.15$ in dot dashed line, ${\beta }_1=0.05$ and ${\beta }_2=0.15$ in solid line, and ${\beta }_1={\beta }_2=0$ in dashed line. In the covert runaway case $q_{\sigma 1}=65\times {10}^{-6}$ s${}^{-1}$ and $q_{\sigma 2}=30\times {10}^{-6}$ s${}^{-1}$; in all other cases $q_{\sigma 1}=65\times {10}^{-6}$ s${}^{-1}$ and $q_{\sigma 2}=7\times {10}^{-6}$ s${}^{-1}$.

Figure 3

One and two species dynamics of H and void blocking fraction for the best-fit parameters in Table 1 for the calibration experiments. One species dynamics for (a) normal sleep; (b) sleep deprivation; and (c) chronic sleep restriction, cycle-averaged and normalized to the baseline days with blue showing sleep deprivation, orange 4 h sleep opportunity, green 6 h, and purple 8 h. Two species dynamics for (d) normal sleep, (e) sleep deprivation, (f) chronic sleep restriction, cycle-averaged and normalized to the baseline days, plotted as in (c). Open symbols show PVT lapse data from Van Dongen et al.’s study. Void blockage fraction for two species: (g) during normal sleep-wake cycles, and (h) during chronic sleep restriction from. Blue, red, green, and purple indicate sleep deprivation, 4, 6, and 8 h sleep opportunity per day, respectively.

Figure 4

Model predictions for CSR protocols that were not used in parameter calibration. (a) Belenky et al. chronic sleep restriction and recovery, averaged across each cycle with two-species parameters from Table 1. Blue indicates 3 h of chronic sleep restriction, red 5 h, green 7 h, and purple 9 h. Filled circles show the experimental data. (b) St. Hilaire et al. chronic variable sleep restriction for two-species parameters from Table 1. Model prediction of H dynamics are shown with solid line. Experimental data are shown with gray circles.

Figure 5

Runaway predictions for the two species. (a)–(e) Demonstrate the case of a sudden change of one parameter at $t=100$ days, as labeled: (a) ${\eta }_2$ is 11.5 times higher than the best-fit value from Table 1, (b) ${\beta }_2$ is 11.5 times the best-fit value, (c) $\rho =1$, (d) $f_W$ is increased to 0.83 which indicates 20 h of wakefulness, and (e) ${\tau }_2$ is 11.5 times larger. In each case the dot-dashed line indicates $H_1$, the dashed line $H_2$, and the solid line, the total H. (f) Shows results for a gradual increase of ${\tau }_2$ over time, with an increase by a factor of 11.5 being reached at $t=3500$ days. (g) Comparison of total H for the conditions in (a)–(e), as labeled; dotted line shows case (f). (h) Corresponding void blockage fraction for the conditions in (a)–(f). All other parameters are set at their best-fit values from 1.