Length-dependent dynamics of microtubules

Certain regulatory proteins influence the polymerization dynamics of microtubules by inducing catastrophe with a rate that depends on the microtubule length. Using a discrete formulation, here we show that, for a catastrophe rate proportional to the microtubule length, the steady-state probability distributions of length decay much faster with length than an exponential decay as seen in the absence of these proteins.

Figure 1

Steady-state probability densities $p_n^{+}$ plotted for parameter values $r_a=10{\text{s}}^{-1}$, $r_d=40{\text{s}}^{-1}$, $r_{-+}=0.02{\text{s}}^{-1}$, and $r_{+-}=0.19{\text{s}}^{-1}$. Here and in Fig. 2, solid (dashed) lines correspond to length-independent (-dependent) catastrophe rates.

Figure 2

Steady-state probability densities $p_n^{-}$ plotted for parameter values the same as those of Fig. 1.

Figure 3

Steady-state probability densities $p_n^{+}$ plotted for parameter values $r_d=37.5{\text{s}}^{-1}$, $r_{+-}=0.014{\text{s}}^{-1}$, and $r_{-+}=0.044{\text{s}}^{-1}$.

Figure 4

Steady-state probability densities $p_n^{-}$ plotted for parameter values the same as those of Fig. 3.