Microtubules are stiff filamentary proteins that constitute an importantcomponent of the cytoskeleton of cells. These are known to exhibit a dynamicinstability. A steadily growing microtubule can suddenly start depolymerizingvery rapidly; this phenomenon is known as ``catastrophe''. However, often ashrinking microtubule is ``rescued'' and starts polymerizing again. Here wedevelope a model for the polymerization-depolymerization dynamics ofmicrotubules in the presence of {\it catastrophe-suppressing drugs}. Solvingthe dynamical equations in the steady-state, we derive exact analyticalexpressions for the length distributions of the microtubules tipped withdrug-bound tubulin subunits as well as those of the microtubules, in thegrowing and shrinking phases, tipped with drug-free pure tubulin subunits. Wealso examine the stability of the steady-state solutions.
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