  We generalize the Dogterom-Leibler model for microtubule dynamics [DL] to the
case where the rates of elongation as well as the lifetimes of the elongating
and shortening phases are a function of GTP-tubulin concentration. We study
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.
