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A general framework for the description of active bundles of polar filaments is presented. The activity of the bundle results from mobile cross-links that induce relative displacements between the aligned filaments. Our generic description is based on momentum conservation within the bundle. By specifying the internal forces, a simple minimal model for the bundle dynamics can be derived, capturing a rich variety of dynamic behaviors. In particular, contracted states as well as solitary and oscillatory waves appear through dynamic instabilities. We present the full bifurcation diagram of this model and study the effects of a dynamic motor distribution on the bundle dynamics. Furthermore, we discuss the mechanical properties of the bundle in the presence of externally applied forces. Our description is motivated by dynamic phenomena in the cytoskeleton and could apply to in vitro experiments as well as to stress fibers and to self-organization phenomena during cell locomotion.
Kruse et al. (2003) studied this question.