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Motor-Mediated Microtubule Self-Organization in Dilute andSemi-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-dilutefilament solutions. In the dilute case, we use a probabilistic model of microtubuleinteraction via molecular motors to investigate microtubule bundle dynamics. Microtubulesare modeled as polar rods interacting through fully inelastic, binary collisions. Ourmodel indicates that initially disordered systems of interacting rods exhibit anorientational instability resulting in spontaneous ordering. We study the existence anddynamic interaction of microtubule bundles analytically and numerically. Our resultsreveal a long term attraction and coalescing of bundles indicating a clear coarsening inthe system; microtubule bundles concentrate into fewer orientations on a slow logarithmictime scale. In semi-dilute filament solutions, multiple motors can bind a filament toseveral others and, for a critical motor density, induce a transition to an ordered phasewith a nonzero mean orientation. Motors attach to a pair of filaments and walk along thepair bringing them into closer alignment. We develop a spatially homogenous, mean-fieldtheory that explicitly accounts for a force-dependent detachment rate of motors, which inturn affects the mean and the fluctuations of the net force acting on a filament. We showthat the transition to the oriented state can be both continuous and discontinuous whenthe 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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