A comparison of instabilities and dynamic states in active filament models

The motion of motor proteins along elastic biofilaments provides a means of fluid transport in and around living cells. Common modelling approaches for such active filaments involve a flexible filament subject to a combination of compressive follower forces and surface flows, both of which are meant to describe the effect of motor protein activity. In this study, we utilise tools from computational dynamical systems to identify filament states and their bifurcations for models that include and ignore surface flows. In addition, we explore the effect of the spatial distribution of activity on the resulting dynamics. Our computations reveal that filament states and bifurcations in all models are qualitatively similar at low actuation, though surface flows shift bifurcations to higher activity values. At higher actuation, however, the distribution of activity plays a key role in the transitions and resulting states. Importantly, actuation distributed uniformly along the filament length leads to a coherent, quasiperiodic state that remains stable even at very high values of actuation. When activity is concentrated near the free-end, however, the filament undergoes a complex series of bifurcations culminating in chaotic behaviour. We link and discuss these differences in dynamic states to the internal stress profiles that arise in the different models.