Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation

We generalize the Dogterom-Leibler model for microtubule dynamics (Dogterom and Leibler in Phys Rev Lett 70(9):1347-1350, 1993) to the case where the rates of elongation as well as the lifetimes of the elongating shortening phases are a function of GTP-tubulin concentration. We analyze also the effect of nucleation rate in the form of a damping term which leads to new steady-states. For this model, we study existence and stability of steady states satisfying the boundary conditions at x=0. Our stability analysis introduces numerical and analytical Evans function computations as a new mathematical tool in the study of microtubule dynamics.