Effects of the GTPs concentration and variation length on the dynamics of microtubules

In this work, we investigate the effects of the variable length of the microtubule and the GTPs concentration 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. Results show that the microtubule growth with the GTPs concentration and exhibit two critical points 1.5 mol.l^-1 M and 8 mol.l^-1 M. After the critical concentration 8 mol.l^-1 M, the microtubule attains the maximum length. 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.