Figure 2. Stochastic simulations demonstrate robustness of microtubule self-organization.

(A, top) Markov chain: each microtubule grows from the minus-end (blue) at the rescue rate ${\displaystyle {\alpha }^{\prime }}$, polymerizes at the rate ${\displaystyle \alpha }$ if it is stable with a T. GTP cap (green), undergoes catastrophe losing the T.GTP cap at the rate ${\beta }^{\prime }$, depolymerizes at the rate β, and regains the T.GTP cap with the rescue rate ${\alpha }^{\prime }$. (A, bottom) Parameterization of the effect of crosslinking proteins on microtubule-microtubule interactions, where the probability of an interaction scenario depends on the angle between microtubules. Here ${\theta }_c$ is the critical angle of zipping, and $p_{cat}$ is the probability of catastrophe. (B) Sensitivity analysis of the microtubule angle distribution. Left: Snapshots of zipping simulations in cells (magenta) of different eccentricities; for the base-level parameters $(\alpha ,\beta ,{\alpha }^{\prime },{\beta }^{\prime })=(1000,3500,4,1)$, ${\theta }_c=30$ and $p_{cat}=0.01$. Interacting microtubules form bundles, the colorbar indicates the number of microtubules in a bundle. Right: The microtubule angle distributions do not vary significantly in a wide parameter range, suggesting robustness of the microtubule self-organization. The distributions are shown for the variations of ${\displaystyle (\alpha ,\beta ,{\alpha }^{\prime },{\beta }^{\prime })}$ as compared to ${\displaystyle (1000,3500,4,1)}$, variable critical zipping angle ${\displaystyle {\theta }_c}$ and probability of catastrophe ${\displaystyle p_{cat}}$.