title: Microtubules interacting with a boundary: mean length and mean first-passage times.
abstract: 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.
authors.affiliation: FOM Institute AMOLF, Science Park 104, 1098XG Amsterdam, the Netherlands.
authors.forename: Bela M
authors.initials: BM
authors.lastname: Mulder
mesh_terms: D002875:Chromosomes / Q000737:chemistry* / Q000502:physiology*; D003198:Computer Simulation; D008870:Microtubules / Q000737:chemistry* / Q000502:physiology*; D008954:Models, Biological; D008956:Models, Chemical