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Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions

Published online by Cambridge University Press:  09 June 2010

S. Swaminathan ,
F. Ziebert ,
I. S. Aranson  and
D. Karpeev
S. Swaminathan
Affiliation:
Department of Engineering Sciences & Applied Mathematics Northwestern University, Evanston, IL 60208-3125 USA Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439
F. Ziebert
Affiliation:
Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439 Laboratoire de Physico-Chimie Théorique - UMR CNRS 7083, ESPCI, 10 rue Vauquelin, F-75231 Paris, France
I. S. Aranson
Affiliation:
Department of Engineering Sciences & Applied Mathematics Northwestern University, Evanston, IL 60208-3125 USA Materials Science Division, Argonne National Laboratory, Argonne, IL, 60439
D. Karpeev*
Affiliation:
Mathematics & Computer Science Division, Argonne National Laboratory, Argonne, IL, 60439
*
* Corresponding author. E-mail: s-swaminathan@northwestern.edu
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Abstract

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.

Keywords

microtubulemolecular motorstochasticfokker-planckmechanicscollisionkineticbifurcationweakly nonlinear analysispattern formationmolecular dynamicsactive temperaturemultiplicative noisebrownian motion.
Type
Research Article
Information
Mathematical Modelling of Natural Phenomena , Volume 6 , Issue 1: Instability and patterns. Issue dedicated to the memory of A. Golovin , 2011 , pp. 119 - 137
Copyright
© EDP Sciences, 2010

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