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- Title
Existence and stability of steady states of a reaction convection diffusion equation modeling microtubule formation.
- Authors
Yarahmadian, Shantia; Barker, Blake; Zumbrun, Kevin; Shaw, Sidney L.
- Abstract
We generalize the Dogterom-Leibler model for microtubule dynamics (Dogterom and Leibler in Phys Rev Lett 70(9):1347-1350, ) 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.
- Subjects
HEAT convection; HEAT equation; MICROTUBULES; DAMPING (Mechanics); BOUNDARY value problems; GUANOSINE triphosphate
- Publication
Journal of Mathematical Biology, 2011, Vol 63, Issue 3, p459
- ISSN
0303-6812
- Publication type
Article
- DOI
10.1007/s00285-010-0379-z