A probabilistic model for the ultradian timing of REM sleep in mice
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.