Role of activity and dissipation in achieving precise beating in cilia: Insights from the rower model

Abstract

Cilia and flagella are micron-sized filaments that actively beat with remarkable precision in a viscous medium, driving microorganism movement and efficient flow. We study the rower model to uncover how cilia activity and dissipation enable this precise motion. In this model, cilia motion is represented by a micro-bead's Brownian movement between two distant harmonic potentials. At specific locations, energy pumps trigger potential switches, capturing cilia activity and generating oscillations. We quantify precision of oscillation using a quality factor, identifying its scaling with activity and oscillation amplitude, finding precision maximization at an optimal amplitude. The data collapse is not accurate for noisy oscillations. An exact analytic expression for the precision quality factor, based on first passage time fluctuations, and derived in the small noise approximation, explains its optimality and scaling. Energy budget analysis shows the quality factor's consistency with the thermodynamic uncertainty relation. Finally, we demonstrate that asymmetric beating reduces oscillation precision compared to the symmetric model: although the optimal amplitude remains unchanged, the overall scaling of the quality factor depends explicitly on the asymmetry parameter.