Statistical properties of sleep-wake behavior in the rat and their relation to circadian and ultradian phases

Stephenson R, Famina S, Caron AM, Lim J

Sleep 2013 Sep;36(9):1377-90

PMID: 23997372


STUDY OBJECTIVES: To examine the statistical characteristics of short-term sleep-wake architecture and to evaluate their dependence on ultradian and circadian phase.

DESIGN: Observational, time series.

SETTING: Laboratory.

PARTICIPANTS: Ten male adult Sprague-Dawley rats.


MEASUREMENTS AND RESULTS: States of wakefulness (WAKE), rapid eye movement sleep (REM) and nonrapid eye movement sleep (NREM) were recorded in 5-sec epochs over 7 consecutive days. State bout durations were analyzed using parametric regression of survival curves, comparing exponential, biexponential, and power law models. WAKE survival curves were best fit by biexponential models, suggesting that there are two statistically distinct stochastic mechanisms generating two types of WAKE–“brief” WAKE and “long” WAKE. Exponential time constants varied as a function of circadian and ultradian phase, with “long” WAKE showing the largest effect. NREM survival curves exhibited biexponential and monoexponential distributions in light and dark, respectively, with weak effects of ultradian phase. REM survival curves approximated a monoexponential distribution that varied with circadian but not ultradian phase. χ(2) analysis was used in a three-state Markov model to evaluate whether conditional state transition probabilities exhibit the property of first-order dependence. This was partially confirmed, but only after accounting for heterogeneity associated with circadian and ultradian phase. However, there was evidence of residual second-order dependence indicating that additional sources of statistical heterogeneity may remain to be identified.

CONCLUSIONS: Sleep-wake state is regulated over short timescales by stochastic mechanisms. When the major sources of heterogeneity are taken into account, including two-component WAKE and NREM states, the sleep-wake system of the rat behaves, to a reasonable approximation, as a Markovian system that is modulated over ultradian and circadian timescales.

Sleep-wake behavior in the rat: ultradian rhythms in a light-dark cycle and continuous bright light

Stephenson R, Lim J, Famina S, Caron AM, Dowse HB

J. Biol. Rhythms 2012 Dec;27(6):490-501

PMID: 23223374


Ultradian rhythms are a prominent but little-studied feature of mammalian sleep-wake and rest-activity patterns. They are especially evident in long-term records of behavioral state in polyphasic animals such as rodents. However, few attempts have been made to incorporate ultradian rhythmicity into models of sleep-wake dynamics, and little is known about the physiological mechanisms that give rise to ultradian rhythms in sleep-wake state. This study investigated ultradian dynamics in sleep and wakefulness in rats entrained to a 12-h:12-h light-dark cycle (LD) and in rats whose circadian rhythms were suppressed and free-running following long-term exposure to uninterrupted bright light (LL). We recorded sleep-wake state continuously for 7 to 12 consecutive days and used time-series analysis to quantify the dynamics of net cumulative time in each state (wakefulness [WAKE], rapid eye movement sleep [REM], and non-REM sleep [NREM]) in each animal individually. Form estimates and autocorrelation confirmed the presence of significant ultradian and circadian rhythms; maximum entropy spectral analysis allowed high-resolution evaluation of multiple periods within the signal, and wave-by-wave analysis enabled a statistical evaluation of the instantaneous period, peak-trough range, and phase of each ultradian wave in the time series. Significant ultradian periodicities were present in all 3 states in all animals. In LD, ultradian range was approximately 28% of circadian range. In LL, ultradian range was slightly reduced relative to LD, and circadian range was strongly attenuated. Ultradian rhythms were found to be quasiperiodic in both LD and LL. That is, ultradian period varied randomly around a mean of approximately 4 h, with no relationship between ultradian period and time of day.

A simple model for the origin of quasiperiodic ultradian rhythms in sleep-wake state in the rat

Stephenson R

Commun Integr Biol 2013 Jan;6(1):e22433

PMID: 23802038


In a recent study,(1) ultradian rhythms of rat sleep-wake behavior were found, using several methods of time series analysis, to be “quasiperiodic.” That is, ultradian period varied apparently randomly around a mean of approximately 4 h, with no relationship between ultradian period and time of day. Here it is proposed that a simple two-oscillator model can explain the quasiperiodic characteristic of these rhythms. Specifically, in this model a periodic oscillator interacts with a stochastic oscillator to generate a behavioral pattern in which the period and amplitude of the simulated ultradian waves vary randomly around an average value. Preliminary simulations support the plausibility of the model; simulated waveforms were closely similar to behavior patterns observed in adult male rats. It is hypothesized that ultradian rhythms in sleep-wake behavior may arise from a periodic feedback loop (e.g., the sleep-wake homeostat) coupled to a stochastic sleep-wake “flip-flop” switch.