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

S. Swaminathan; F. Ziebert; I. S. Aranson; D. Karpeev

Mathematical Modelling of Natural Phenomena (2010)

- Volume: 6, Issue: 1, page 119-137
- ISSN: 0973-5348

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topSwaminathan, S., et al. "Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions." Mathematical Modelling of Natural Phenomena 6.1 (2010): 119-137. <http://eudml.org/doc/197693>.

@article{Swaminathan2010,

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.},

author = {Swaminathan, S., Ziebert, F., Aranson, I. S., Karpeev, D.},

journal = {Mathematical Modelling of Natural Phenomena},

keywords = {microtubule; molecular motor; stochastic; fokker-planck; mechanics; collision; kinetic; bifurcation; weakly nonlinear analysis; pattern formation; molecular dynamics; active temperature; multiplicative noise; brownian motion.; Fokker-Planck; Brownian motion.},

language = {eng},

month = {6},

number = {1},

pages = {119-137},

publisher = {EDP Sciences},

title = {Motor-Mediated Microtubule Self-Organization in Dilute and Semi-Dilute Filament Solutions},

url = {http://eudml.org/doc/197693},

volume = {6},

year = {2010},

}

TY - JOUR

AU - Swaminathan, S.

AU - Ziebert, F.

AU - Aranson, I. S.

AU - Karpeev, D.

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

JO - Mathematical Modelling of Natural Phenomena

DA - 2010/6//

PB - EDP Sciences

VL - 6

IS - 1

SP - 119

EP - 137

AB - 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.

LA - eng

KW - microtubule; molecular motor; stochastic; fokker-planck; mechanics; collision; kinetic; bifurcation; weakly nonlinear analysis; pattern formation; molecular dynamics; active temperature; multiplicative noise; brownian motion.; Fokker-Planck; Brownian motion.

UR - http://eudml.org/doc/197693

ER -

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