Modelling the role of spontaneous and collision induced catastrophe in the self organisation of cortical microtubules

Cortical microtubules form highly ordered structures through apparent self organisation. Two of the driving factors for this are believed to be the dynamic instability of the microtubules and the interactions that they have amongst themselves. In this paper we use a 3 state model to simulate the effect of the spontaneous growth to shrinkage rate and its relationship with the spontaneous shrinkage to growth rate. We find that the order of the microtubule is more sensitive to changes in the shrinkage to growth rate compared to its reverse. We also show that in microtubule collisions above the entrainment angle, in the absence of any other limiting factors, reducing the proportion of microtubules that undergo collision induced catastrophe (CIC) past 0.5 causes the array to rapidly lose order. This suggests that in cells with a low CIC, there exist additional mechanisms for controlling the microtubule growth direction.