Nonlinear Phenomena in Complex Systems, 2006, Vol.9, No.2, pp.198-208

NONLINEAR PHENOMENA IN COMPLEX SYSTEMS
An Interdisciplinary Journal

2006, Vol.9, No.2, pp.198-208

On Cytoskeletal Patterns and Intrinsic Disorder Effects.
Falko Ziebert, Martin Hammele , and Walter Zimmermann

In a model for polar filaments, which are transported relative to each other by molecular motors, the homogeneous and isotropic filament distribution may become either unstable with respect to a stationary or oscillatory orientational instability of finite wavelength or with respect to a density instability, where the small wave numbers are not damped. Beyond these instabilities, in the weakly nonlinear regime, we find a competition between stripe patterns and asters where the asters are preferred in a larger parameter range. Besides the dynamic interactions via motors, filaments may also be connected persistently by crosslinker proteins like actinin. Clusters of permanently linked filaments are likely to be randomly distributed in space and such clusters are expected to affect the formation of patterns. As analyzed here in a simple case, the bifurcation is affected by the disorder in such a way that the onset of patterns becomes more likely, for instance by a reduction of the bifurcation threshold.
Key words: Pattern formation, Subcellular structure and processes, Complex systems, Disorder

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