Spontaneous oscillations and hydrodynamics of active micro-filament

Cilia and flagella are thin hair-like cellular projections that play a variety of crucial roles from propulsion at low Reynolds number to long-range hydrodynamic transport. The movement of the cilium is produced by the bending of its core, known as the axoneme that consists of 9 pairs of microtubules. In presence of ATP, molecular motors carrying cargo undergo cycles of attachment and detachment generating sliding forces that are in turn converted to waving motion of the filaments. We present a microscopic bottom-up model that accounts for the detailed stochastic kinetics of molecular motors and as well as feedback from the geometry of the axoneme represented as an Euler elastica. Through direct numerical simulations that account for hydrodynamics, we find that beyond a critical activity of motors the elastica starts beating spontaneously resulting in propagating bending waves similar to those observed in sperm flagella. In the parameter space of the model, we are also able to observe whipping patterns of cilia and the breast stroke of Chlamydomonas. Using PCA, we construct reduced-order representations of the dynamics and flow fields in terms of fundamental singularities of Stokes flow. We also explore hydrodynamic interactions and collective behavior of interacting filaments.