Math. Model. Nat. Phenom.
Volume 6, Number 1, 2011Instability and patterns. Issue dedicated to the memory of A. Golovin
|Page(s)||119 - 137|
|Published online||09 June 2010|
Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions
Department of Engineering Sciences & Applied Mathematics
Northwestern University, Evanston, IL 60208-3125 USA
2 Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439
3 Laboratoire de Physico-Chimie Théorique - UMR CNRS 7083, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
4 Mathematics & Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439
* Corresponding author. E-mail:
We study molecular motor-induced microtubule self-organization in dilute and semi-dilute filament solutions. In the dilute case, we use a probabilistic model of microtubule interaction via molecular motors to investigate microtubule bundle dynamics. Microtubules are modeled as polar rods interacting through fully inelastic, binary collisions. Our model indicates that initially disordered systems of interacting rods exhibit an orientational instability resulting in spontaneous ordering. We study the existence and dynamic interaction of microtubule bundles analytically and numerically. Our results reveal a long term attraction and coalescing of bundles indicating a clear coarsening in the system; microtubule bundles concentrate into fewer orientations on a slow logarithmic time scale. In semi-dilute filament solutions, multiple motors can bind a filament to several others and, for a critical motor density, induce a transition to an ordered phase with a nonzero mean orientation. Motors attach to a pair of filaments and walk along the pair bringing them into closer alignment. We develop a spatially homogenous, mean-field theory that explicitly accounts for a force-dependent detachment rate of motors, which in turn affects the mean and the fluctuations of the net force acting on a filament. We show that the transition to the oriented state can be both continuous and discontinuous when the force-dependent detachment of motors is important.
Mathematics Subject Classification: 35Q82 / 35Q84 / 35Q92 / 70F35 / 82C26 / 82C80
Key words: microtubule / molecular motor / stochastic / fokker-planck / mechanics / collision / kinetic / bifurcation / weakly nonlinear analysis / pattern formation / molecular dynamics / active temperature / multiplicative noise / brownian motion.
© EDP Sciences, 2010
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