Computing the motor torque of Escherichia coli

TL;DR

This study uses numerical methods to accurately compute the motor torque of Escherichia coli, reconciling experimental data with theoretical models and highlighting the influence of cell-surface proximity.

Contribution

It introduces and compares two validated numerical approaches to estimate bacterial motor torque, providing more precise values aligned with experimental observations.

Findings

Motor torque ranges from 440 pNnm to 829 pNnm.

Torque depends critically on the distance to the nearby surface.

Numerical methods align well with experimental data.

Abstract

The rotary motor of bacteria is a natural nano-technological marvel that enables cell locomotion by powering the rotation of semi-rigid helical flagellar filaments in fluid environments. It is well known that the motor operates essentially at constant torque in counter-clockwise direction but past work have reported a large range of values of this torque. Focusing on Escherichia coli cells that are swimming and cells that are stuck on a glass surface for which all geometrical and environmental parameters are known (Darnton et al., J. Bacteriology, 2007, 189, 1756-1764), we use two validated numerical methods to compute the value of the motor torque consistent with experiments. Specifically, we use (and compare) a numerical method based on the boundary integral representation of Stokes flow and also develop a hybrid method combining boundary element and slender body theory to model the cell body and flagellar filament, respectively. Using measured rotation speed of the motor, our computations predict a value of the motor torque in the range 440 pNnm to 829 pNnm, depending critically on the distance between the flagellar filaments and the nearby surface.