Effects of the variation length, catastrophe and rescue on the dynamics of microtubules: machine learning approach

In this work, we investigate the effects of the variable length of the microtubule during the growth and shrink regimes, the cap length variations and the catastrophe phenomenon. The master equation and generating function were used to evaluate the mean length, the growth speed, the cap length probability and catastrophe probability of the microtubule. The results show that the growth of microtubules depends on the concentration of GTPs, of which we have two essential points of the growth speed. From a maximum concentration value, the concentration of GTPs no longer has a significant effect on length growth. The microtubule loses its cap when the length tends towards a maximum length and then, microtubule undergoes catastrophe phenomenon. The catastrophe probability increases with the microtubule length and decreases with the GTPs concentration. By applying Machine Learning techniques, we identified the MT characteristics that distinguish simultaneously all four kinetic states: growth, catastrophe, shortening, and rescue. At the cellular 25 M tubulin concentration, the most important quantities are the MT length L, average longitudinal curvature, MT tip width w, total energy of longitudinal interactions in MT lattice, and the energies of longitudinal and lateral interactions required to complete MT to full cylinder long and lat. These results allow greater insights into what brings about kinetic state stability and the transitions between states involved in MT dynamic instability behavior.