Dynamic instability of microtubules: effect of catastrophe-suppressing drugs

TL;DR

This paper develops a mathematical model to analyze how catastrophe-suppressing drugs influence the dynamic instability and length distribution of microtubules, providing exact analytical solutions and stability analysis.

Contribution

It introduces a novel model for microtubule dynamics incorporating drugs that suppress catastrophe, deriving exact steady-state solutions and stability conditions.

Findings

Derived analytical expressions for microtubule length distributions.

Analyzed the stability of steady-state solutions.

Provided insights into drug effects on microtubule dynamics.

Abstract

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 ``catastrophe''. However, often a shrinking microtubule is ``rescued'' and starts polymerizing again. Here we develope a model for the polymerization-depolymerization dynamics of microtubules in the presence of {\it 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.