Mathematical Modeling of Dynamic Instability in Microtubules

Microtubules are biological polymers that have many functions in cells, such as support and structure in the cytoskeleton, providing avenues and mechanisms for intracellular transportation, and separating chromatids during cell division. Microtubule dynamic instability is an integral part of cell functioning, enabling microtubules to rapidly find and change spatial arrangements and interact with necessary biological components. Due to dynamic instability, microtubule ends switch randomly between phases of growth and depolymerization (subunits are being constantly added and removed from the ends of the various microtubules). The mechanisms of dynamic instability are not well understood, partially due to the complexity of microtubule structure. Experiments have shown that microtubules do not exhibit behavior consistent with the classical model of equilibrium polymer dynamics. Mathematical and computational models have been created to explore and better understand the phenomenon of dynamic instability. A coarse-grained stochastic model of a system of microtubules from Gregoretti et al. (JCS 2006) had previously been extended to simulate free microtubules in solution. To improve the model and make it more biologically realistic, a Monte Carlo algorithm was implemented that allows new microtubules to spontaneously form (nucleate) from the free subunits in the solution. Additional statistical output and analysis was also added to facilitate the investigation of the microtubule behavior. This enables the exploration of the effect of the ease of nucleation on the behavior of the system. The simulations will be compared with experimental results to attempt to better understand dynamic instability. The refinement of the understanding of dynamic instability has implications for the development of cancer treatments and the study of self-organized systems.