Finding the ciliary beating pattern with optimal efficiency

TL;DR

This paper introduces a measure of energetic efficiency for cilia, determines optimal beating patterns, and finds that coordinated, antiplectic waves maximize efficiency, closely matching observed patterns in microorganisms like Paramecium.

Contribution

The study develops a new efficiency measure for cilia, identifies optimal beating patterns, and demonstrates their similarity to natural microorganism behaviors.

Findings

Optimal single cilium patterns are curly and symmetric.

Densely ciliated surfaces favor antiplectic wave coordination.

Paramecium's efficiency is near the theoretical maximum.

Abstract

We introduce a measure for energetic efficiency of biological cilia acting individually or collectively and numerically determine the optimal beating patterns according to this criterion. Maximizing the efficiency of a single cilium leads to curly, often symmetric and somewhat counterintuitive patterns. But when looking at a densely ciliated surface, the optimal patterns become remarkably similar to what is observed in microorganisms like Paramecium. The optimal beating pattern then consists of a fast effective stroke and a slow sweeping recovery stroke. Metachronal coordination is essential for efficient pumping and the highest efficiency is achieved with antiplectic waves. Efficiency also increases with an increasing density of cilia up to the point where crowding becomes a problem. We finally relate the pumping efficiency of cilia to the swimming efficiency of a spherical microorganism and show that the experimentally estimated efficiency of Paramecium is surprisingly close to the theoretically possible optimum.