An Overview: About Three Models of Mitotic Spindle Oscillations and Their Mods

Abstract

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.