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