Fig 1.
Correlation between REM sleep duration and inter-REM interval.
(A) Example EEG power spectrogram, EMG amplitude, and hypnogram with definitions of terms. REMpre, duration of the preceding REM sleep episode; inter-REM, duration of subsequent interval till next REM episode; |W|, sum of the durations of all wake episodes during the inter-REM interval; MA, microarousal (wake bouts ≤ 20 s); |N|, sum of the durations of all NREM episodes (including MAs) during the inter-REM interval. (B) Scatter plots with REMpre on the x-axis and subsequent inter-REM duration (left), |N| (middle), and |W| (right) on the y-axis. The results of linear regression fits are shown in red (P<0.00001 for all 3 slopes, n = 5098 sleep cycles from 72 mice recorded during the light phase).
Fig 2.
Conditional GMM to describe the relationship between REMpre and subsequent NREM.
(A) Scatter plot of REMpre vs. ln(|N|). Vertical dashed lines indicate consecutive 30 s bins of REMpre. Solid black lines represent the mean and standard deviation of ln(|N|) for each 30 s bin. (B) Histograms and probability density plots of ln(|N|) for consecutive REMpre bins as indicated on top. Probability densities were computed using a GMM. The notation [a, b) refers to the bin a ≤ REMpre < b. (C) Histogram of ln(|N|) for inter-REM intervals preceded by REM episodes in the range 30 s ≤ REMpre < 60 s. A GMM composed of two Gaussian distributions captures well the bimodal distribution of ln(|N|). The mean and standard deviation of the Gaussian for long and short cycles are referred to as μlong, σlong, and μshort, σshort, respectively. (D) Estimates of GMM parameters as a function of REMpre. The mixture parameter, klong, denotes the probability that a sleep cycle belongs to the long Gaussian distribution. For each parameter, we fitted a linear or logarithmic function describing its dependence on REMpre. (E) Heatmap in which each grid cell (x,y) represents the probability of transitioning from NREM to REM in between |N| - 25 s ≤ y ≤ |N| + 25 s following a REM episode of duration REMpre = x s for x in [10, 15, …, 250]. Each column of the heatmap sums up to 1. (F) Cumulative distribution function (CDF) of the GMM for 7 different values of REMpre. Each line represents, for the given REMpre value, the likelihood of entering the next REM period within |N| s of NREM sleep since the preceding REM episode.
Fig 3.
(A) (Left) Scatter plot of REMpre vs. ln(|N|) with color-coded single and sequential cycles. The threshold optimally separating sequential from single cycles is shown in black. (Right) Illustration of how the threshold was determined for REMpre = 30 s. The probability density functions (PDFs) for the two distributions of the GMM (for REMpre = 30 s) are plotted along the y-axis. The red asterisk indicates the value of ln(|N|) at which the two Gaussians intersect. Values of ln(|N|) below the intersection point are more likely to be drawn from the short distribution and are consequently labeled as sequential cycles. Gray points correspond to cycles with REMpre < 7.5 s for which the conditional GMM is not defined (S1B Fig and Methods). (B) Pie chart indicating the percentage of single and sequential cycles. (C) Box plot comparing REMpre for single and sequential cycles. For sequential cycles, REMpre was shorter than for single cycles (Welch’s t-test, t = -35.13, p = 2.59e-228, nsequential = 947, nsingle = 3961). (D) Histogram of |N| for sequential cycles. The vertical dashed line indicates the mean (85.46 s ± 40.92 s; mean ± s.d.). (E) Bar plot showing the percentage of the number of cycles within a REM sleep sequence. Over half of REM sleep sequences contain only one cycle (i.e. comprise two REM periods). (F) Spectral density of parietal (nsequential = 947, nsingle, = 3961) and prefrontal (nsequential = 936, nsingle = 3919) EEG during REM and NREM sleep for both sequential and single cycles. Horizontal lines indicate frequencies at which the spectral density of sequential and single cycles are statistically different at various ɑ levels; (Welch’s t-test, * p<0.05; ** p<0.01; *** p<0.001). One recording did not contain a prefrontal EEG channel. Shadings, 99% confidence interval (CI).
Fig 4.
Refractory and permissive periods during single cycles.
(A) (Left) Scatter plot of REMpre vs. ln(|N|) along with boundary (solid line) separating the refractory from the permissive period within single cycles. (Right) Illustration of how the threshold separating the refractory from the permissive period was determined for REMpre = 60 s. The CDF of the long Gaussian distribution is plotted along the y-axis. The value of |N| for which CDF(ln|N|) = 0.01 (indicated by the red asterisk) corresponds to the duration of the refractory period. (B) Scatter plot of REMpre vs. |N| along with the threshold separating the refractory from the permissive period. Of note, the refractory period is only defined for single cycles (red dots). The black line represents the threshold and the shading indicates the 99% confidence interval (CI) from 10,000 bootstrap iterations. (C) Spectral density of the prefrontal EEG for NREM sleep during the refractory and permissive period. The densities for both periods are statistically different for frequencies in the range 0–15 Hz (Welch’s t-test, *** p < 0.001, nrefractory = npermissive = 3892). Shadings, 99% CI. (D) Box plot comparing the rate of sleep spindles during the refractory and permissive period (Welch’s t-test, t = -36.96, p = 0.0, nrefractory = npermissive = 3908). The rate was calculated as the number of spindles per 1 min of NREM sleep. (E) Box plot comparing the rate of MAs during the refractory and permissive period (Welch’s t-test, t = 50.32, p = 0.0, nrefractory = npermissive = 3908). The rate was calculated as the number of MAs per 1 min of NREM sleep. (F) Progression of θ power, σ power, spindle rate, and MA rate throughout the refractory and permissive period for different values of REMpre. The refractory period is defined as outlined in A. The permissive period comprises the time from the end of the refractory period to the onset of the next REM period. The durations of both the refractory and permissive period were normalized to unit length and subdivided into quartiles of equal normalized duration. The average for all REMpre values is shown in black. Shadings, 99% CI. (G) Progression of θ power (Row 1) and σ power (Row 2) on non-normalized time scale during the first 600 s of NREM sleep during the inter-REM interval for different values of REMpre. The two vertical dashed lines indicate the lowest and highest threshold separating the refractory from the permissive period corresponding to the low and high bound of REMpre. Shadings, 99% CI.
Fig 5.
Relationship between wake episodes and NREM sleep during an inter-REM interval.
(A) (Left) Pie chart indicating the percentage of sequential cycles without (|W| = 0) and with wake episodes (|W| > 0). (Right) Box plot comparing |N| for sequential cycles with and without wake episodes (t-test, t = -3.22, p = 0.0012, n|W|>0 = 122, n|W| = 0 = 825 cycles). (B) (Left) Pie chart indicating the percentage of single cycles without and with wake episodes. (Right) Box plot comparing |N| for single cycles with and without wake episodes (Welch’s t-test, t = -28.64, p = 3.97e-163, n|W|>0 = 2259, n|W| = 0 = 1702). (C) Bar plot showing the distribution of the number of wake episodes during the inter-REM interval of single cycles. Note that 99.63% of single cycles had 8 or fewer wake episodes. (D) (Left) Box plot comparing total NREM duration, |N|, for single cycles with increasing values of total wake duration, |W| (Welch’s ANOVA, F(5,1233.21) = 301.99, p = 3.78e-211). The x-tick q0 corresponds to cycles without wake. The remaining cycles with |W| > 0 were subdivided into quintiles, labeled q1—q5, based on the distribution of |W| for single cycles. (Right) Box plot comparing |N| for single cycles based on the number of wake episodes occurring during the inter-REM interval (Welch’s ANOVA, F(5,475.26) = 246.53, p = 1.65e-129). Note that 97.61% of single cycles contained 5 or fewer wake episodes. (E) Progression of θ power, σ power, spindle rate, and MA rate during NREM sleep before and after a wake episode. Only sequences with at least 1 minute of NREM sleep both before and after wake during the inter-REM interval of single cycles were included. The duration of NREM episodes was normalized. ‘Before’ refers to all NREM sleep in between either the previous REM or wake episode and the current wake episode. ‘After’ refers to all NREM sleep in between the current wake episode and either the next wake or REM episode. Shadings, 99% CI. (F) Bar plot showing average drop (or increase) in θ power, σ power, spindle rate, and MA rate over wake episodes with different durations. All wake episodes for single cycles were divided into five quintiles based on the distribution of their durations. A drop or increase in each variable was calculated by subtracting the average value for 1 min of NREM after wake from the average value for 1 min of NREM before wake (θ: Welch’s ANOVA, F(4,899.90) = 10.48, p = 2.65e-08; σ: ANOVA, F(4,1901) = 1.99, p = 0.093; Spindles: ANOVA, F(4,1901) = 6.22, p = 5.70e-05; MAs: Welch’s ANOVA, F(4,895.63) = 9.13, p = 3.08e-07). Error bars, 95% CI from 1,000 bootstrap iterations.
Fig 6.
Effects of sleep history on REM episode duration.
(A) (Left) Box plot comparing the duration of REM sleep (REMpost) following sequential cycles for different values of REMpre. Red line, linear regression (slope = -0.22, R2 = 0.010, p = 0.0020). (Right) Box plot comparing REMpost following single cycles for different values of REMpre. Red line, linear regression (slope = -0.091, R2 = 0.0089, p = 5.07e-09). (B) Box plot comparing REMpost following single cycles with different values of |N|. Red line, linear regression (slope = 0.0041, R2 = 9.83e-04, p = 0.052). (C) Box plots comparing REMpost dependent on the CDF value at REM onset for single cycles. The left plot includes all REMpre values; the remaining plots show the correlation for increasing ranges of REMpre. Dashed lines, linear regression (All: slope = 22.82, R2 = 0.013, p = 1.01e-12; [7.5,60): slope = 8.58, R2 = 0.0013, p = 0.090; [60,120): slope = 29.42, R2 = 0.024, p = 1.57e-07; [120,180): slope = 29.64, R2 = 0.039, p = 3.12e-06; [180,240): slope = 43.28, R2 = 0.077, p = 0.0060). (D) Spectral density of prefrontal EEG during REM episodes following single cycles as a function of the CDF at REM onset (Welch’s ANOVA, δ: F(4,1078.85) = 16.18, p = 7.04e-13; θ: F(4,1084.95) = 6.06, p = 8.0e-05; σ: F(4,1089.74) = 9.46, p = 1.61e-07).
Fig 7.
Changes in REM sleep regulation between light and dark phase.
(A) Bar plots comparing the percentage of REM, NREM sleep, and wake during the light and dark phase (REM: Welch’s t-test, t = 16.14, p = 3.37e-30; NREM: t-test, t = 20.26, p = 4.53e-38; Wake: t-test, t = -20.79, p = 5.19e-39; nlight = 72, ndark = 35 mice). Error bars, 95% CIs from 1,000 bootstrap iterations. (B) Bar plot comparing the ratio REM/(REM+NREM) for the light and dark phase (t-test, t = 3.17, p = 0.0019, nlight = 72, ndark = 35 mice). Error bars, 95% CIs from 1,000 bootstrap iterations. (C) Pie chart showing the percentage of sequential and single cycles during the dark phase. (D) Comparison of GMM parameters for the light and dark phase (Welch’s t-test with Bootstrap, klong: t = -77.26, p = 0.0; μlong: t = -372.77, p = 0.0; σlong: t = -57.93, p = 0.0; Methods). (E) Comparison of μlong (solid lines), and threshold (Ref., dashed lines) separating the refractory from the permissive period for the light and dark phase. Shadings, 95% CIs obtained from 10,000 bootstrap iterations. (F) Comparison of the CDFs of the GMMs for the light and dark phase shown for 4 different values of REMpre.