Mathematical modeling of endocrine regulation subject to circadian rhythm |
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| Affiliation: | 1. Department of Information Technology, Uppsala University, Lägerhyddsvägen 2, Uppsala SE-751 05, Sweden;2. Delft Center for Systems and Control, Delft University of Technology, Mekelweg 2, Delft 2628 CD, The Netherlands;3. Institute for Problems in Mechanical Engineering of the Russian Academy of Sciences (IPME RAS), St. Petersburg, Russia;4. Department of Computer Science, Southwest State University, 50 Years of October Str. 94, Kursk 305040, Russia;1. Vellore Institute of Technology, Vellore, Tamilnadu, India;2. NMAM Institute of Technology, Nitte, Karnataka, India;1. Systems and Control Research Centre, School of Mathematics, Computer Science and Engineering, City, University of London, Northampton Square, London EC1V 0HB, UK;2. Department of Economics Section of Mathematics and Informatics, University of Athens, Pezmazoglou 8, Athens, Greece;1. Department of Industrial Engineering, DIEF University of Florence, Italy;2. Computer Science Department, University of Rome “La Sapienza”, Italy;3. WSENSE Srl, Rome, Italy;4. Interuniversity Center of Integrated Systems for the Marine Environment (ISME), Italy;1. Dipartimento di Ingegneria dell’Informazione (DII), Universita di Pisa, Via Girolamo Caruso 16, Pisa 56122, Italy;2. Interuniversity Center of Integrated Systems for the Marine Environment (ISME), Italy;3. Centro di Ricerca “E. Piaggio”, Università di Pisa, Largo Lucio Lazzarino 1, Pisa 56122, Italy;4. Marine Autonomous & Robotic Systems, National Oceanography Centre (NOC), Southampton, UK;5. Naval Experimentation and Support Center (CSSN), Italian Navy, Viale San Bartolomeo 400, La Spezia 19136, Italy;6. NATO Science & Technology Organization Centre for Maritime Research and Experimentation (STO CMRE), Viale San Bartolomeo 400, La Spezia 19136, Italy |
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| Abstract: | 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. |
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