Kinetic energy of homologue chromosome pairs in biomechanical oscillatory model of mitotic spindle

Abstract

The ways in which chromosomes move within the cell during the cell division process is called functional genomic architecture. Weise et al (2016) postulate that functional genomic architecture is not only present in interphase but also in metaphase stage of cell division cycle. The aim of this work was to study how different oscillatory behavior of centrosomes as well as chromosomes’ mass arrangement affects kinetic energy of pairs of homologue chromosomes in the system of mitotic spindle during metaphase. The analyses were done through biomechanical oscillatory model of mitotic spindle. In biomechanical oscillatory model of mitotic spindle mitotic spindle is presented as a system of coupled oscillators where coupling is made over two rheonomic centers – centrosomes. One oscillatory pair consists of a centrosome, a microtubule and a related chromosome and these are interconnected with their homologous pair. Each element in the model has its mechanical counterpart. Analytical expressions for kinetic energy of oscillating pair of homologues chromosomes are given for the case that biomechanical system of mitotic spindle is conservative, linear and oscillate under external single frequency oscillation. Numerical analyses with some approximation for mouse chromosomes were done. Our numerical experiment reveals that kinetic energy of oscillating pair of homologue chromosomes has oscillatory character and is affected by chromosomes’ mass arrangement and frequency of centrosome excitation. If centrosomes oscillate with different frequencies, energy of pairs of homologue chromosomes has non-linear oscillatory character. Maximum value of amplitudes of kinetic energy of pair of same homologue chromosomes are equal in the case of equal frequency of forced centrosome excitation but differ over time in a case of different frequency of forced centrosome excitation. Regardless the distribution of chromosome masses (central or peripheral position of chromosomes with heavier masses) kinetic energy for each particular pair of homologue chromosomes are lower in the central zone of mitotic spindle, but amplitudes of kinetic energy for each pair of homologue chromosomes subsystems are lower when chromosomes with heavier masses are positioned in central zone of mitotic spindle compare to the case when they have peripheral positions in mitotic spindle. This difference in energy distribution regarding different centrosome oscillatory frequency in the same cell and mass chromosomes arrangement may carry additional epigenetic information and could be important for process of cell differentiation.