Microtubule angular and length PDF for three typical cases as indicated by the star symbols in Fig. 2. (a) Angular PDF counted by subunits for three typical cases in three different phases. Isotropic phase I in green, sharply aligned N_I phase in red, and aligned microtubules with broad angular distribution N_II phase in blue. The distribution is obtained by time average of samples. Each sample is rotated with its dominant distribution at 90°. The vertical axis breaks at 0.1–0.9 to show the sharp red peak clearer (N_I phase) which is about 20 times higher than the blue peak (N_II phase). Inset: the vertical axis in log scale. (b) Length probability PDF of number of microtubules. Both isotropic (green) and N_II (blue) phases demonstrate exponential decay in the length distributions. The N_I phase shows a very broad length distribution, which indicates that the system is dominated by extremely long microtubules. The analysis is performed in the steady state for a period 2× 10⁵ s with an interval of 10³s. Inset: microtubule length distribution in N_I phase with much broader range of length.