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

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{é} 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.

7 pages, 3 figures

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• The hydrodynamics of swimming microorganisms
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Cited by in corpus (2)

• Dynamics of Purcell-type microswimmers with active-elastic joints
• Instability and self-propulsion of flexible autophoretic filaments