Mathematical modeling of endocrine regulation subject to circadian rhythm

Mathematical modeling of endocrine regulation subject to circadian rhythm

Medvedev, Alexander (Uppsala University)
Proskurnikov, A.V. (TU Delft Team Tamas Keviczky; Russian Academy of Sciences)
Zhusubaliyev, Zhanybai T. (Southwest State University)

2018

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 entrainable 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.

Biomedical systems
Entrainment
Hybrid systems
Impulse signals
Nonlinear dynamics
Synchronization

http://resolver.tudelft.nl/uuid:84f48e81-3aca-466f-ac76-29a65101a543

https://doi.org/10.1016/j.arcontrol.2018.08.002

2020-09-22

1367-5788

Annual Reviews in Control, 46, 148-164

Institutional Repository

journal article

© 2018 Alexander Medvedev, A.V. Proskurnikov, Zhanybai T. Zhusubaliyev