Microscopic motility of isolated E. coli flagella

TL;DR

This study uses advanced microscopy to analyze the Brownian motion of isolated E. coli flagella, directly measuring their hydrodynamic properties and revealing their low propulsion efficiency, thus extending understanding of microscopic asymmetric particle dynamics.

Contribution

First direct experimental measurement of the hydrodynamic propulsion matrix of isolated E. coli flagella using volumetric microscopy and diffusion analysis.

Findings

Flagella are highly inefficient propellers with less than 5% maximum propulsion efficiency.

Validated theoretical models of flagellar hydrodynamics with experimental data.

Extended Brownian motion analysis techniques to asymmetric 3D particles.

Abstract

The fluctuation-dissipation theorem describes the intimate connection between the Brownian diffusion of thermal particles and their drag coefficients. In the simple case of spherical particles, it takes the form of the Stokes-Einstein relationship that links the particle geometry, fluid viscosity, and diffusive behavior. However, studying the fundamental properties of microscopic asymmetric particles, such as the helical-shaped propeller used by $\textit{E. coli}$, has remained out of reach for experimental approaches due to the need to quantify correlated translation and rotation simultaneously with sufficient spatial and temporal resolution. To solve this outstanding problem, we generated volumetric movies of fluorophore-labeled, freely diffusing, isolated $\textit{E. Coli}$ flagella using oblique plane microscopy. From these movies, we extracted trajectories and determined the hydrodynamic propulsion matrix directly from the diffusion of flagella via a generalized Einstein relation. Our results validate prior proposals, based on macroscopic wire helices and low Reynolds number scaling laws, that the average flagellum is a highly inefficient propeller. Specifically, we found the maximum propulsion efficiency of flagella is less than 5%. Beyond extending Brownian motion analysis to asymmetric 3D particles, our approach opens new avenues to study the propulsion matrix of particles in complex environments where direct hydrodynamic approaches are not feasible.