Authors: Hedrih, Anđelka 
Hedrih, Katica (Stevanović) 
Affiliations: Mechanics 
Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: An Overview: About Three Models of Mitotic Spindle Oscillations and Their Mods
First page: 267
Last page: 274
Related Publication(s): Book of Proceedings
Conference: The Ninth International Congress of the Serbian Society of Mechanics, July 5-7, 2023, Vrnjačka Banja, Serbia
Issue Date: 2023
Rank: M33
ISBN: 978-86-909973-9-8
We present three oscillatory models of forced oscillating dynamics of mitotic spindle where
interconnections between sister chromatids and microtubules are represented by different types of
coupling: 1) ideally elastic elements, 2) viscoelastic elements and third model 3) connections
whose properties are expressed by fractional derivatives. Each model consists of a system of
oscillators. Each oscillator consists of sister chromatids of a certain chromosome that are
interconnected with centrosomes (represent a rheonomic centres of oscillations) through
microtubules. The rheonomic centers introduce kinematic excitation by external frequency force.
Each oscillator in all three models oscillates with two degrees of freedom.
Analytical expressions for the corresponding forced modes of oscillations for all three models
are determined. It is shown that the model of fractional properties is the most general, because for
the range of derivatives of non-integer order from zero to one, the primary modes were practically
obtained for all three models of mitotic spindle. For the limiting values of the derivative
parameter of fractional order, zero and one, the modes are transformed into the modes of the
ideally elastic model, or into the modes of the ideally viscous model, respectively.
Those modes, in each of the three models, are independent: there is neither interaction
between the modes, nor energy transfer from one mode to another.
Keywords: oscillatory model of the mitotic spindle | fractional modes | rheonomic system
Publisher: Serbian Society of Mechanics

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