Kinematics of the most efficient cilium

TL;DR

This paper numerically determines the most energy-efficient cilium kinematics, revealing dependence on bending rigidity and resembling natural two-stroke beating patterns, advancing understanding of biological fluid transport.

Contribution

It introduces a numerical method to find optimal cilium kinematics based on energetics, highlighting the role of the Sperm number in ciliary motion efficiency.

Findings

Optimal kinematics depend on the Sperm number.

Resemblance to natural two-stroke ciliary beating.

Provides a framework for understanding cilia efficiency.

Abstract

In a variety of biological processes, eukaryotic cells use cilia to transport flow. Although cilia have a remarkably conserved internal molecular structure, experimental observations report very diverse kinematics. To address this diversity, we determine numerically the kinematics and energetics of the most efficient cilium. Specifically, we compute the time-periodic deformation of a wall-bound elastic filament leading to transport of a surrounding fluid at minimum energetic cost, where the cost is taken to be the positive work done by all internal molecular motors. The optimal kinematics are found to strongly depend on the cilium bending rigidity through a single dimensionless number, the Sperm number, and closely resemble the two-stroke ciliary beating pattern observed experimentally.