Effect of ambient fluid rheology on oscillatory instabilities in filament-motor systems

Filaments and filament bundles such as microtubules or actin interacting with molecular motors such as dynein or myosin constitute a common motif in biology. Synthetic mimics, examples being artificial muscles and reconstituted active networks, also feature active filaments. A common feature of these filament-motor systems is the emergence of stable oscillations as a collective dynamic response. Here, using a combination of classical linear stability analysis and non-linear numerical solutions, we study the dynamics of a minimal filament-motor system immersed in model viscoelastic fluids. We identify steady states, test the linear stability of these states, derive analytical stability boundaries, and investigate emergent oscillatory solutions and their properties. We show that the interplay between motor activity, aggregate elasticity and fluid viscoelasticity allows for stable oscillations or limit cycles to bifurcate from steady states. For highly viscous Newtonian media, frequencies at onset decay with viscosity as [Formula]. In viscoelastic fluids that have the same viscosity as the Newtonian fluid but additionally allow for temporary energy storage, emergent limit cycles are associated with higher frequencies. The magnitude of the increase in the frequency depends on motor mechanochemistry and the interplay between fluid relaxation time-scales and time-scales associated with motor binding and unbinding. Our results suggest that stability and dynamical response in filamentous active systems may be controlled by tailoring the rheology of the ambient environment.