Emergent Programmable Behavior and Chaos in Dynamically Driven Active Filaments*

How the behavior of biological systems emerges from its constituent parts is an outstanding challenge at the intersection of physics and biology. Single cells lacking neuro-muscular systems and having a direct connection between cell behavior and underlying biochemical and physical constituents, offer a unique opportunity to mechanistically understand behavior. A remarkable example of single-celled behavior is seen in the ciliate Lacrymaria olor, which uses rapid shape changes to an active, slender protrusion, many times the cell size, to hunt for prey. Here, inspired by these extreme behaviors in L. olor, we present an active filament model wherein behavior (filament shape dynamics) is mechanistically linked to the underlying physical properties and motile ciliary dynamics of the cell. Our model captures two key features of this system - dynamic activity patterns (extension and compression cycles) and active stresses that are uniquely aligned with the filament geometry - leading to a so-called "follower force" constraint. We show that active filaments under deterministic, time-varying follower forces display rich behaviors including periodic and aperiodic shape dynamics didover long times. We further show that aperiodic dynamics are due to a transition to chaos in regions of a biologically accessible parameter space. We further find a simple recurrence map of filament shape that predicts long-term behavior shedding light on the underlying nonlinearities in the dynamics. Lastly, using these maps as a design tool we demonstrate a few examples of “programming” filament behaviors by using frequency and amplitude modulated patterns of activity. Overall our work is a first step towards mechanistically understanding behavior in cells like L. olor and also inspires programmable active matter systems using filament geometries.