Rayleigh function of energy dissipation in modelling oscillatory behaviour of moving sister chromatids in anaphase of mitosis

Abstract

Cell division is in the basis of the regeneration processes. The special and very complex structure named the mitotic spindle ensures movements of chromosomes during mitosis. During some parts of this process chromosomes have to move through the cytoplasm that is considered a viscous fluid with a low Reynolds number. A mathematical model of the mitotic spindle based on the theory of oscillations is used to study chromosome movements during anaphase. A mitotic spindle is considered as a system of coupled oscillators. The assumptions of the model are given. To describe the forced oscillations of moving chromosomes in the metaphase plate in the cytoplasm as a viscous fluid with a low Reynolds number, Rayleigh function of energy dissipation and a system of coupled ordinary differential equations were used. We analyzed this oscillatory process through energy analysis of moving sister chromatids. Numerical analyses were done for masses of mouse chromosomes, for different parameters of the mitotic spindle. The results show that the total energy of an oscillating pair of homologue chromosomes has an oscillatory character and is affected by the frequency of centrosome excitations and the spindle size. The obtained data could be of importance for understanding an asymmetric cell division and differentiating processes.