1. Parametric models of the circadian pacemaker in controlled lighting conditions
- Author
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Usmani, Imran Masood, Skeldon, Anne, and Dijk, Derk-Jan
- Subjects
Circadian Rhythms ,circadian pacemaker ,zeitgebers ,controlled lighting conditions ,parametric models ,phase-only models ,two-dimensional models - Abstract
In mammals, the circadian pacemaker is a biological clock responsible for the timing of many of the body's circadian rhythms, including the sleep-wake cycle. Mathematical models of the circadian pacemaker could fi nd applications in the treatment of sleep disorders or in medical chronotherapy. Parametric models are phenomenological models that are widely used to model the circadian systems of diurnal animals. However, current models of the circadian pacemaker in humans are based on limited data, and they often produce inaccurate predictions when they are used in novel settings. We consider one- and two-dimensional parametric models, and we explore how the design of models is informed by experimental data. Our aim is to design models that accurately reproduce data from various experimental studies. The circadian pacemaker generates rhythms even in the absence of time cues, or zeitgebers. However, the pacemaker is responsive to light, which is how it synchronizes, or entrains, to the day-night cycle on the Earth's surface. In parametric models, the self-sustaining activity of the pacemaker is modelled by a clock with some intrinsic velocity and the effect of light is to modulate the velocity of the clock. The velocity response of the clock to light is the product of a tonic stimulus and a response function, which describes the sensitivity of the clock to light as a function of the state of the clock. In one-dimensional, or phase-only, parametric models, we show that it is necessary to make simplifying assumptions about the response function to design models based on data from studies in controlled lighting conditions. This motivates us to consider 'simple' clock models in which the response function is sinusoidal. We obtain two specific results in our study of phase-only models. Firstly, we show that the shorter period of sighted humans in forced desynchrony compared to the period of blind people can be explained by a model whose response function has a larger advance region than delay region. Secondly, we show that simple clock models with different response functions are required to reproduce the effects of light of different intensity in studies of humans in controlled lighting conditions. This challenges the prevailing view in circadian biology that the sensitivity of the pacemaker to light does not vary in different lighting conditions. We investigate how two-dimensional parametric models can reproduce the phenomena of type 0 phase resetting and after-effects. We show that the strength of attraction of the unperturbed limit cycle of the clock is a key feature of the models. We use a clock with a strongly attracting limit cycle to reproduce Khalsa's type 0 phase transition curve in humans. We use a clock with a weakly attracting limit cycle to reproduce after-effects in the four-striped grass mouse.
- Published
- 2022
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