Oscillatory model of mitotic spindle

Mitotic spindle is a complex machinery that ensures the equal distribution of genetic material in two daughter cells. During the cell division cycle cells passes through different events and phases. Different mathematical models of separate events of cell division cycle exist in the literature. Mathematical models of mitotic spindle include modelling of: early spindle elongation, spindle assembly, search and capture models (proposed mechanisms how microtubules capture the exact chromosome), directional instability, kinetochore positioning, spindle positioning, mitotic spindle checkpoint, modelling metaphase spindle length, modelling electro-acoustic behaviour of the mitotic spindle. Here we are going to present an oscillatory model of mitotic spindle that is based on theory of oscillations and considered mitotic spindle as a system of coupled oscillators. The model is suitable to study the movements of chromosomes during metha- and ana- phase of cell division cycle. It takes into account the entire dynamics of the mitotic spindle –the dynamics of microtubules, centrosomes and chromosome arrangements. Each single oscillator consists of sister chromatid, corresponding microtubule and centrosome. The centrosomes are consider as a kinematic centres of oscillations. A forced oscillations of moving chromosomes in metaphase plate can be describe by system of coupled ordinary fractional order differential equation. The potential, kinetic and total oscillatory energy of single oscillator are study in the model. How different oscillatory behaviours of centrosomes and spindle size of the metaphase plate affect the energy of pairs of homologue chromosomes in the system of mitotic spindle will be discuss. The numerical results are discussed in the biological context of using oscillatory energy as physical parameter of a potential epigenetic coding.