Dynamic instability of microtubules: effect of catastrophe-suppressing drugs

Microtubules are stiff filamentary proteins that constitute an important component of the cytoskeleton of cells. These are known to exhibit a dynamic instability. A steadily growing microtubule can suddenly start depolymerizing very rapidly; this phenomenon is known as a "catastrophe." However, often a shrinking microtubule is "rescued" and starts polymerizing again. Here we develop a model for the polymerization-depolymerization dynamics of microtubules in the presence of catastrophe-suppressing drugs. Solving the dynamical equations in the steady state, we derive exact analytical expressions for the length distributions of the microtubules tipped with drug-bound tubulin subunits as well as those of the microtubules, in the growing and shrinking phases, tipped with drug-free pure tubulin subunits. We also examine the stability of the steady-state solutions.