I formulate a dynamical model for microtubules interacting with a catastrophe-inducing boundary. In this model microtubules are either waiting to be nucleated, actively growing or shrinking, or stalled at the boundary. I first determine the steady-state occupation of these various states and the resultant length distribution. Next, I formulate the problem of the mean first-passage time to reach the boundary in terms of an appropriate set of splitting probabilities and conditional mean first-passage times and solve explicitly for these quantities using a differential equation approach. As an application, I revisit a recently proposed search-and-capture model for the interaction between microtubules and target chromosomes [M. Gopalakrishnan and B. S. Govindan, Bull. Math. Biol. 73, 2483 (2011)]. I show how my approach leads to a direct and compact solution of this problem.

Phys. Rev. E
Theory of Biomolecular Matter

Mulder, B. (2012). Microtubules interacting with a boundary : mean length and mean first-passage times. Phys. Rev. E, 86(1, Article number: 11902), 1–11. doi:10.1103/PhysRevE.86.011902