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

Abstract

Cilia and flagella are micron-sized slender filaments that actively beat in a viscous medium with remarkable accuracy despite thermal fluctuations and other uncertainties. Such precise beating is essential for swift locomotion for microorganisms and for generating an efficient flow in a carpet of cilia in fluid media. To understand the role of the interplay between dissipation and cilia activity in achieving such a precise oscillation, we study a minimal model of cilia known as the rower model. Here, the complex beating of a filament is simplified by a one-dimensional periodic motion of a micron-sized bead between two positions (the amplitude) immersed in a viscous fluid. The bead performs Brownian motion in one of the two harmonic potentials and switches to the other once it reaches two specific positions with a pump of energy which is a measure of cilia activity. We quantify the precision using the quality factor and find a scaling law for the precision with activity and dissipation. Interestingly, for an optimal amplitude where the precision becomes maximum. The scaling and optimal behavior in the quality factor can be explained by studying the noise in the first passage time. Finally, we discuss the energy budget in achieving precision.