Self-buckling and self-writhing of semi-flexible microorganisms

TL;DR

This paper models the mechanical behavior of semi-flexible microorganisms, revealing how buckling and writhing influence their motility, and identifies critical stiffness thresholds for effective movement.

Contribution

It introduces a Kirchhoff rod model coupled with flagellar dynamics to explain microbial buckling and writhing, providing new insights into their mechanical stability and motility.

Findings

Buckling and writhing depend on organism's mechanical properties.

Identified bifurcations leading to different equilibrium configurations.

Stiffness thresholds below which motility is compromised.

Abstract

The twisting and writhing of a cell body and associated mechanical stresses is an underappreciated constraint on microbial self-propulsion. Multi-flagellated bacteria can even buckle and writhe under their own activity as they swim through a viscous fluid. New equilibrium configurations and steady-state dynamics then emerge which depend on the organism's mechanical properties and on the oriented distribution of flagella along its surface. Modeling the cell body as a semi-flexible Kirchhoff rod and coupling the mechanics to a dynamically evolving flagellar orientation field, we derive the Euler-Poincar{\'e} equations governing dynamics of the system, and rationalize experimental observations of buckling and writhing of elongated swarmer cells of the bacterium {\it Proteus mirabilis}. A sequence of bifurcations is identified as the body is made more compliant, due to both buckling and torsional instabilities. These studies highlight a practical requirement for the stiffness of bacteria below which self-buckling occurs and cell motility becomes ineffective.