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.
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Research of S. Yarahmadian was partially supported under NSF grants number DMS-0070765 and DMS-0300487; Research of B. Barker was partially supported under NSF grants number DMS-0607721 and DMS-0300487; Research of K. Zumbrun was partially supported under NSF grants number DMS-0070765 and DMS-0300487; and Research of S. L. Shaw was partially supported by the Indiana Metacyte Institute at Indiana University, founded in part through a major grant from the Lily Endowment, INC.
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Yarahmadian, S., Barker, B., Zumbrun, K. et al. Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation. J. Math. Biol. 63, 459–492 (2011). https://doi.org/10.1007/s00285-010-0379-z
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DOI: https://doi.org/10.1007/s00285-010-0379-z