title: Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation.
abstract: 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.
authors.affiliation: Mississippi State University, Mississippi State, MS 39762, USA. syarahmadian@math.msstate.edu
authors.forename: Shantia
authors.initials: S
authors.lastname: Yarahmadian
authors.forename: Blake
authors.initials: B
authors.lastname: Barker
authors.forename: Kevin
authors.initials: K
authors.lastname: Zumbrun
authors.forename: Sidney L
authors.initials: SL
authors.lastname: Shaw
mesh_terms: D006160:Guanosine Triphosphate / Q000378:metabolism*; D007700:Kinetics; D008870:Microtubules / Q000378:metabolism*; D008954:Models, Biological; D009716:Numerical Analysis, Computer-Assisted; D058105:Polymerization; D013269:Stochastic Processes; D014404:Tubulin / Q000378:metabolism*
chemical_list: D014404:Tubulin; D006160:Guanosine Triphosphate