Emergent programmable behavior and chaos in dynamically driven active filaments

How the behavior of cells emerges from their constituent subcellular
biochemical and physical parts is an outstanding challenge at the
intersection of biology and physics. A remarkable example of single-cell
behavior occurs in the ciliate Lacrymaria olor, which hunts for its prey
via rapid movements and protrusions of a slender neck, many times the size
of the original cell body. The dynamics of this cell neck is powered by a
coat of cilia across its length and tip. How a cell can program this
active filamentous structure to produce desirable behaviors like search
and homing to a target remains unknown. Here, we present an active
filament model that allows us to uncover how a “program” (time sequence of
active forcing) leads to “behavior” (filament shape dynamics). Our model
captures two key features of this system—time-varying activity patterns
(extension and compression cycles) and active stresses that are uniquely
aligned with the filament geometry—a “follower force” constraint. We show
that active filaments under deterministic, time-varying follower forces
display rich behaviors including periodic and aperiodic dynamics over long
times. We further show that aperiodicity occurs due to a transition to
chaos in regions of a biologically accessible parameter space. We also
identify a simple nonlinear iterated map of filament shape that
approximately predicts long-term behavior suggesting simple, artificial
“programs” for filament functions such as homing and searching space.
Last, we directly measure the statistical properties of biological
programs in L. olor, enabling comparisons between model predictions and
experiments.