A Phase Dynamics Model of Human Circadian Rhythms

Abstract

Nonphotic entrainment of an overt sleep-wake rhythm and a circadian pacemaker-driving temperature/melatonin rhythm suggests existence of feedback mechanisms in the human circadian system. In this study, the authors constructed a phase dynamics model that consisted of two oscillators driving temperature/melatonin and sleep-wake rhythms, and an additional oscillator generating an overt sleep-wake rhythm. The feedback mechanism was implemented by modifying couplings between the constituent oscillators according to the history of correlations between them. The model successfully simulated the behavior of human circadian rhythms in response to forced rest-activity schedules under free-run situations: the sleep-wake rhythm is reentrained with the circadian pacemaker after release from the schedule, there is a critical period for the schedule to fully entrain the sleep-wake rhythm, and the forced rest-activity schedule can entrain the circadian pacemaker with the aid of exercise. The behavior of human circadian rhythms was reproduced with variations in only a few model parameters. Because conventional models are unable to reproduce the experimental results concerned here, it was suggested that the feedback mechanisms included in this model underlie nonphotic entrainment of human circadian rhythms.

Mathematical models of regulatory mechanisms of sleep-wake rhythms

“…Thanks to this adaptive mechanism, the rest-activity cycle comes to exert stronger effects on Osc I and II, and Osc I dominates Osc SW instead of Osc II, when the rest-activity cycle is forced to deviate from the mutually entrained phase position with Osc I and II. As shown in Figure 4, this model faithfully reproduces the behavior of sleepwake and melatonin rhythms observed in the experiment [5,34]. In addition, the behavior of circadian rhythms in transmeridian flights can also be simulated [6].…”

“…As shown in Figure 1b, the fundamental framework of a multioscillator model is two mutually interacting oscillators: one drives temperature and melatonin rhythms (tentatively called Osc I), generally reflecting the actions of the suprachiasmatic nucleus (SCN), and the other controls sleep-wake rhythm (tentatively called Osc II), which is often represented by plural oscillators [5,15]. In addition, Osc I is photoresponsive and exerts a stronger effect on Osc II than the opposite direction.…”

“…Multioscillator model with feedback from the rest-activity cycle to circadian oscillators[5,6]. C ij ði; j ¼ 1; 2; 3; i 6 ¼ jÞ denotes coupling strength, and h ij and sin denote functions of the phase angle between oscillators.…”

Modeling interactions between photic and nonphotic entrainment mechanisms in transmeridian flights

“…The model consists of three mutually coupled oscillators whose couplings are adaptively modified in association with correlations between oscillators. Our model successfully simulated the behavior of an overt sleep-wake and a melatonin rhythm during and after the forced rest-activity cycle (Nakao et al 2002). In addition, on the assumption that a physical exercise enhances effects of the forced rest-activity cycle on the pacemakers, the model simulated the experimental finding that the melatonin rhythm is accelerated even by the forced cycle with a period shorter than 24 h (Miyazaki et al 2001).…”

“…As a consequence, a feasible strategy to avoid serious jet lag is proposed. Figure 1 shows the model structure, which is the same as our previous model except for the photic entrainment mechanism (Nakao et al 2002). Therefore, the rationale of the model structure is only briefly described here for the reader's convenience.…”