Authors: Hedrih, Anđelka 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Biological Oscillators
Journal: Zbornik Radova : Dynamics of Hybrid Systems of Complex Structutes
Issue Date: 2022
Rank: M14
ISSN: 0351-9406
URL: http://elib.mi.sanu.ac.rs/files/journals/zr/27/zrn27p413-451.pdf
Abstract: 
There are many oscillatory processes within biological systems.
The whole human body is a complex system of coupled and synchronized
oscillators. The mode of coupling can be very different. Oscillatory
processes exist at almost every scale in human body: from systems of
organs to subcellular structures and molecules. Using knowledge from
several scientific fields (biology, medicine, theory of oscillations, theory
of elasticity, rheology, non-linear dynamics), a complex multidisciplinary
methodology for studying a wide class of oscillatory biodynamic models
has been set. The principle of phenomenological mapping has been used
in developing each of the oscillatory models of biological oscillators. In this
review, oscillatory models of three different structures will be presented:
the oscillatory model of double DNA chain helix, oscillatory model of zona
pellucida and conditions for successful fertilisation, and oscillatory model
of the mitotic spindle. These models are based on oscillations of chain
systems. The DNA double helix is considered as a molecular biological
oscillator, mitotic spindle as a subcellular system of coupled oscillators, and
zona pellucida as an oscillating spherical net of cross-chains of oscillators
that envelopes the female reproductive cell – the oocyte, at the surface of
which an interaction with male reproductive cell- spermatozoa occurs.
Assumptions of mathematical oscillatory models are presented as well as
conditions for resonance. Some numerical analysis are also presented.
Keywords: biological oscillators | zona pellucida | DNA double helix | mitotic spindle | free and forced oscillations
Publisher: Mathematical Institute of the SASA

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