Self-Propagating Patterns in Active Filament Bundles

Abstract

Bundles of polar filaments which interact via active elements can exhibit complex dynamic behaviors. By using a simple and general description for the bundle dynamics, we find regimes for which density profiles propagate as solitary waves with a characteristic velocity along the bundle. These behaviors emerge from an interplay of local contractions in the bundle and relative sliding of oppositely oriented filaments. By introducing filament binding to and detachment from a substrate, the system is able to generate net motion as a self-organization phenomenon.

Active Brownian particles

“…[236]). It is a fascinating field of interdisciplinary research already for decades, which continues to thrive and continuously motivates theoretical investigations (see e.g [198,134,107] and recent reviews [121,178]). …”

Hydrodynamics of isotropic and liquid crystalline active polymer solutions

“…They are always diffusive and are given by 14) where 15) and φ is the angle between the wavevector k and the direction of the broken symmetry (ŷ). To gain some insight in the angular dependence of the modes it is useful to consider the behavior for special directions of the wavector.…”

“…These approaches have given valuable insights into the problem but are limited to small system sizes by computing power. A second very interesting development has been the proposal of 'mesoscopic' mean-field kinetic equations governing the dynamics of individual filaments where the effect of motors was incorporated via a motor-induced relative velocity of pairs of filaments, with the form of such velocity inferred from general symmetry considerations [11,12,13,14,15]. Finally, hydrodynamic equations have also been proposed where the large scale dynamics of the mixture is described in terms of a few coarse-grained fields whose dynamics is also inferred from symmetry considerations, [16,17,18,19,20,21,22,23].…”

Generic theory of active polar gels: a paradigm for cytoskeletal dynamics

“…In eukaryotic cells, the problem is however qualitatively new: the cross-links can be made of motor proteins which have their own dynamics driven by chemical energy. Experiments, simulations and analytical descriptions, have shown that such systems have a rich and complex behavior [8,9,10,11,12,13,14,15,16,17,18,19,20]. One can grasp the degree of complexity with the remark that cross-links define distances, in other words they define a metric.…”