Abstract
Circadian rhythms are established by the entrainment of our intrinsic body clock to periodic forcing signals provided by the external environment, primarily variation in light intensity across the day/night cycle. Loss of entrainment can cause a multitude of physiological difficulties associated with misalignment of circadian rhythms, including insomnia, excessive daytime sleepiness, gastrointestinal disturbances, and general malaise. This can occur after travel to different time zones, known as jet lag; when changing shift work patterns; or if the period of an individual’s body clock is too far from the 24 h period of environmental cycles. We consider the loss of entrainment and the dynamics of re-entrainment in a two-dimensional variant of the Forger-Jewett-Kronauer model of the human circadian pacemaker forced by a 24 h light/dark cycle. We explore the loss of entrainment by continuing bifurcations of one-to-one entrained orbits under variation of forcing parameters and the intrinsic clock period. We show that the severity of the loss of entrainment is dependent on the type of bifurcation inducing the change of stability of the entrained orbit, which is in turn dependent on the environmental light intensity. We further show that for certain perturbations, the model predicts counter-intuitive rapid re-entrainment if the light intensity is sufficiently high. We explain this phenomenon via computation of invariant manifolds of fixed points of a 24 h stroboscopic map and show how the manifolds organise re-entrainment times following transitions between day and night shift work.
Highlights
The function of the circadian timekeeping system is to align an organism’s physiology and behaviour with the daily environmental cycles conferred by Earth’s rotation
We compute invariant manifolds of fixed points for a 24 h stroboscopic map constructed from the model. We show that these manifolds are able to explain the dynamics of a rapid re-entrainment phenomenon that has been previously observed under certain conditions in simulations and experiments
The severity of the effect of such perturbations can be measured by the entrainment time, that is, the duration required for trajectories starting from arbitrary initial points to converge to the stable orbit as the phase of the circadian oscillator with respect to the external forcing is varied
Summary
The function of the circadian timekeeping system is to align an organism’s physiology and behaviour with the daily environmental cycles conferred by Earth’s rotation. Alignment is achieved by endogenous circadian oscillators with periods close to, but not exactly, 24 h synchronising to external 24 h periodic signals, such as the light/dark cycle, in a process called entrainment. Properties of both the internal oscillator and the external forcing signal, such as intrinsic period and light intensity, combine to determine the stable phase of entrainment. Circadian clocks with long intrinsic periods can lead to delayed sleep phase syndrome (DSPS), a disorder where patients tend to be unable to fall asleep until late at night and have difficulty waking up in the morning. Bright light therapy can help to advance the entrained phase of DSPS patients so that their hormonal rhythms, sleep-wake patterns, and peak performance times are more in line with societal norms [1].
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