Polymerization of microtubules in the presence of diffusing tubulins: a boundary layer analysis. (10th February 2015) - Yadav, Vandana; Mukherji, Sutapa
Abstract: Microtubules are biopolymers with an interesting growth dynamics that alternates between persistent phases of polymerization and depolymerization. The growth dynamics is expected to be influenced by the dynamics of the tubulin molecules around the microtubule. In this paper, we present a boundary layer based method that allows us to study systematically a nonlinear growth model coupling the growth dynamics of microtubule and the diffusive dynamics of free tubulins in the neighboring environment. Following previous experimental studies, we consider the growth and the rescue rates to be dependent on the tubulin density in the neighborhood of the microtubule tip. Considering the effect of various regulatory proteins that facilitate the motion of tubulin molecules along the direction of growth, we incorporate an effective biased diffusion of tubulin molecules. Based on the values of the bias velocity and other parameters, the boundary layer analysis shows two regions with distinct nature of microtubule length distributions. In order to show the wider applicability of the method, we briefly discuss the case of tubulin density dependent catastrophe rate. Some of our results are supported by numerical simulations.