Fig. 1 Scaling of brain metabolism and connections with brain mass (kilogram) and age before transition. (A) Plot of the logarithm of cerebral metabolic rate versus the logarithm of brain mass before transition with measured slope of 1.60. (B) Plot of the logarithm of number of synapses versus the logarithm of brain mass before transition with measured slope of 1.23. (C) Plot of the logarithm of white matter volume versus the logarithm of brain mass before transition with measured slope of 1.21. Also, shown on the top horizontal axes is the corresponding age in years.
Fig. 2 Identification of transition from reorganization to repair. Plots of the sum of squared errors for the residuals of the two best-fit lines to data for (A) ln (tS/tA) and (B) ln (tNR/tA) on either side of a break point in the lines that corresponds to that value of the logarithm of brain mass (Mb). The minimum of each curve is identified as the transition point that divides sleep function into early and late developmental stages as described by our theory. These minima are unique and have values of Mb = 1.14 kg for the transition in tS/tA and Mb = 1.15 kg for the transition in tNR/tA, corresponding to ages of 2.4 to 2.5 years old, respectively. Also, shown on the top horizontal axes is the corresponding age in years. SSEs, sum of squared errors.
Fig. 3 Scaling and transition points for sleep time ratios. (A) Plot of the logarithm of the ratio of total sleep time to total awake time per day versus the logarithm of brain mass with measured slope of −0.33 before transition and −3.50 after. (B) Plot of the logarithm of the ratio of REM sleep time to total sleep time per day versus the logarithm of brain mass with measured slope of −0.60 before transition and −0.01 after. (C) Plot of the logarithm of the ratio of REM sleep time to total awake time per day versus the logarithm of brain mass with measured slope of −1.00 before transition and −5.10 after. (D) Plot of the logarithm of the ratio of NREM sleep time to total awake time per day versus the logarithm of brain mass with measured slope of 0.09 before transition and −3.16 after. Also, shown on the top horizontal axes is the corresponding age in years.
- Table 1 Early development (<2.4 years).
Summary of the key empirical results and theoretical tests of our model for the various ratios of sleep times in the first column during the period of early development (<2.4 years old). The second column contains the values and 95% confidence intervals for the scaling exponents as determined from direct empirical data, whereas the third through fifth columns contain the ranges of predicted values for the scaling exponents based on theories that sleep function is primarily for neural reorganization in either REM (third column) or NREM (fourth column) sleep or that it is primarily for neural repair (fifth column). The range of predicted values is calculated in each case using the three best-fit estimates for the scaling exponent α from Fig. 1. NA denotes that the corresponding theory makes no prediction for that specific variable. Predictions that match data are in bold. For these data, the predictions of the theory that sleep function during early development is primarily for neural reorganization in REM sleep are all supported, whereas the predictions of the theory that, during early development, sleep function is either primarily for neural repair or for neural reorganization during NREM sleep are all rejected.
Ratio Measured
exponentREM reorganization
predictionNREM reorganization
predictionRepair
predictiontS/tA −0.33 ± 0.07 NA NA 0.20 to 0.60 tR/tS −0.60 ± 0.06 −0.87 to −0.07 NA 0 tR/tA −1.00 ± 0.05 −1.20 to −0.40 NA NA tNR/tA 0.09 ± 0.09 NA −1.20 to −0.40 NA - Table 2 Late development (>2.4 years).
Summary of the key empirical results and theoretical tests of our model for the various ratios of sleep times in the first column during the period of late development (>2.4 years old). The second column contains the values and 95% confidence intervals of the scaling exponents as determined from direct empirical data, whereas the third through fifth columns contain the ranges of predicted values for the scaling exponents based on theories that sleep function is primarily for neural reorganization in either REM (third column) or NREM (fourth column) sleep or that it is primarily for neural repair (fifth column). The 95% confidence intervals for the predictions are derived from the confidence intervals determined for the scaling exponent α = − 1.70 ± 1.66 in later development (fig. S2). NA denotes that the corresponding theory makes no prediction for that specific variable. Predictions that match data are in bold. For these data, the predictions of the theory that sleep function during early development is primarily or neural repair and clearance are all supported, whereas the predictions of the theory that, during early development, sleep function is primarily for neural reorganization in REM sleep or NREM sleep are all rejected.
Ratio Measured
exponentREM reorganization
predictionNREM reorganization
predictionRepair
predictiontS/tA −3.50 ± 0.23 NA NA −2.70 ± 1.66 tR/tS −0.01 ± 0.52 8.90 ± 3.55 NA 0 tR/tA −5.10 ± 0.20 5.40 ± 3.32 NA NA tNR/tA −3.16 ± 0.26 NA 5.40 ± 3.32 NA
Supplementary Materials
Supplementary material for this article is available at http://advances.sciencemag.org/cgi/content/full/6/38/eaba0398/DC1
Additional Files
Supplementary Materials
Unraveling why we sleep: Quantitative analysis reveals abrupt transition from neural reorganization to repair in early development
Junyu Cao, Alexander B. Herman, Geoffrey B. West, Gina Poe, Van M. Savage
This PDF file includes:
- Sections S1 to S8
- Table S1
- Figs. S1 to S4
- References
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