Emergent Programmable Behavior and Chaos in Dynamically Driven Active Filaments
Authors: Krishnamurthy Deepak , Prakash Manu 
Published: June 2022

Abstract

How the behavior of single cells emerges from their constituent sub-cellular biochemical and physical parts is an outstanding challenge at the intersection of biology and physics. A remarkable example of single-cell behavior is seen in the ciliateLacrymaria olor, which hunts by striking its prey via rapid movements and protrusions of a slender neck, many times the size of the original cell body. This dynamics of the cell neck is powered by active injection of energy into this slender filamentous structure via a coat of cilia across its length and specialized cilia at the tip. How a cell can program this dynamical active filament to produce desirable behaviors like search and homing to a target remains unknown. By constructing a coupled active-elastic and hydrodynamic model of a slender filament with activity at the tip, here we uncover how cell behavior (filament shape dynamics) can be controlled via activity dynamics. 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 over long times. We further show that aperiodic dynamics occur due to a transition to chaos in regions of a biologically accessible parameter space. By further dissecting the non-linear dynamics of this active filament system, we discover a simple iterative map of filament shape that predicts long-term behavior. Lastly, using these iterative maps as a design tool, we demonstrate examples of how a cell could “program” filament behaviors by using frequency and amplitude modulated activity patterns. Overall, our results serve as a framework to mechanistically understand behavior in single cells such asL. olorand present a novel chaotic dynamical system in active elastohydrodynamics. Our work also offers a direct framework for designing programmable active matter systems using filament geometries.

Significance statement

Single-celled protozoa display remarkable animal-like behaviors without the aid of neurons. Mechanistically understanding how this dynamic behavior emerges from underlying physical and biochemical components is an outstanding challenge. In this work, using an active filament model, we uncover the fundamental non-linear dynamics and non-variational mechanics that underlie the complex behaviors of single cells likeLacrymaria olor. In doing so we discover a novel route to chaos in active elastohydrodynamic systems and the first-ever description of how chaos can drive single-cell behaviors. Lastly, we present a framework for how filament behaviors can be “programmed” using dynamic, modulated activity patterns. Overall our work provides mechanistic insights into single-cell behaviors and offers a new framework for the design of filamentous active matter systems to achieve diverse functions.