Instabilities in a two-dimensional polar-filament-motor system
Theoretische Physik, Universität Bayreuth, D-95440, Bayreuth, Germany
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Revised: 22 July 2008
Published online: 29 October 2008
The dynamical interaction between filaments and motor proteins is known for their propensity to self-organize into spatio-temporal patterns. Since the filaments are polar in the sense that motors define a direction of motion on them, the system can display a spatially homogeneous polar-filament orientation. We show that the latter anisotropic state itself may become unstable with respect to inhomogeneous fluctuations. This scenario shares similarities with instabilities in planarly aligned nematic liquid crystals: in both cases the wave vector of the instability may be oriented either parallel or oblique to the polarity axis. However, the encountered instabilities here are long-wave instead of short-wave and the destabilizing modes are drifting ones due to the polar symmetry. Additionally a nonpropagating transverse instability is possible. The stability diagrams related to the various wave vector orientations relative to the polarity axis are determined and discussed for a specific model of motor-filament interactions.
PACS: 87.16.-b Subcellular structure and processes – / 47.54.-r Pattern selection; pattern formation – / 89.75.-k Complex systems –
© Springer, 2008