Emergent programmable behavior and chaos in dynamically driven active filaments
Krishnamurthy, D., & Prakash, M. (2023). Emergent programmable behavior and chaos in dynamically driven active filaments. Proceedings of the National Academy of Sciences, 120(28), e2304981120.
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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.
Significance:
Single-celled protozoa display remarkable animal-like behaviors without the aid of neurons. Mechanistically understanding how this behavior emerges from underlying physical and biochemical components remains a challenge. In this work, inspired by the rapid search and hunting behavior of Lacrymaria olor using its slender neck-like protrusion, we develop an active filament model toward understanding cell behavior from first principles. Using our model, we reveal how filament shape dynamics (“behavior”) emerge from time sequences of activity patterns (“programs”). We explore this idea further by designing simple activity motifs that lead to useful functions like homing and search. Finally, to close the loop, we measure the statistical properties of biological programs in L. olor and use these to directly compare model outputs and experiments.
