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Mathematical modeling of endocrine regulation subject to circadian rhythm
Uppsala University, Disciplinary Domain of Science and Technology, Mathematics and Computer Science, Department of Information Technology, Automatic control.ORCID iD: 0000-0002-6608-250x
Delft Univ Technol, Delft Ctr Syst & Control, Mekelweg 2, NL-2628 CD Delft, Netherlands;RAS, IPME, St Petersburg, Russia.
Southwest State Univ, Dept Comp Sci, 50 Years October Str 94, Kursk 305040, Russia.
2018 (English)In: Annual Reviews in Control, ISSN 1367-5788, E-ISSN 1872-9088, Vol. 46, p. 148-164Article, review/survey (Refereed) Published
Abstract [en]

The 2017 Nobel Prize in Physiology or Medicine awarded for discoveries of molecular mechanisms controlling the circadian rhythm has called attention to the challenging area of nonlinear dynamics that deals with synchronization and entrainment of oscillations. Biological circadian clocks keep time in living organisms, orchestrating hormonal cycles and other periodic rhythms. The periodic oscillations of circadian pacemakers are self-sustained; at the same time, they are en trainable by external periodic signals that adjust characteristics of autonomous oscillations. Whereas modeling of biological oscillators is a well-established research topic, mathematical analysis of entrainment, i.e. the nonlinear phenomena imposed by periodic exogenous signals, remains an open problem. Along with sustained periodic rhythms, periodically forced oscillators can exhibit various "irregular" behaviors, such as quasiperiodic or chaotic trajectories. This paper presents an overview of the mathematical models of circadian rhythm with respect to endocrine regulation, as well as biological background. Dynamics of the human endocrine system, comprising numerous glands and hormones operating under neural control, are highly complex. Therefore, only endocrine subsystems (or axes) supporting certain biological functions are usually studied. Low-order dynamical models that capture the essential characteristics and interactions between a few hormones can than be derived. Goodwin's oscillator often serves as such a model and is widely regarded as a prototypical biological oscillator. A comparative analysis of forced dynamics arising in two versions of Goodwin's oscillator is provided in the present paper: the classical continuous oscillator and a more recent impulsive one, capturing e.g. pulsatile secretion of hormones due to neural regulation. The main finding of this study is that, while the continuous oscillator is always forced to a periodic solution by a sufficiently large exogenous signal amplitude, the impulsive one commonly exhibits a quasiperiodic or chaotic behavior due to non-smooth dynamics in entrainment.

Place, publisher, year, edition, pages
2018. Vol. 46, p. 148-164
Keywords [en]
Biomedical systems, Nonlinear dynamics, Synchronization, Entrainment, Hybrid systems, Impulse signals
National Category
Control Engineering
Identifiers
URN: urn:nbn:se:uu:diva-373086DOI: 10.1016/j.arcontrol.2018.08.002ISI: 000453618200010OAI: oai:DiVA.org:uu-373086DiVA, id: diva2:1277940
Funder
Swedish Research Council, 2015-05256Available from: 2019-01-11 Created: 2019-01-11 Last updated: 2019-01-11Bibliographically approved

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