Helical trajectories of swimming cells with a flexible flagellar hook

Zonghao Zou, Wilson Lough, and Saverio Spagnolie
Phys. Rev. Fluids 6, 103102 – Published 11 October 2021

Abstract

The flexibility of the bacterial flagellar hook is believed to have substantial consequences for microorganism locomotion. Using a simplified model of a rigid flagellum and a flexible hook, we show that the paths of axisymmetric cell bodies driven by a single flagellum in Stokes flow are generically helical. Phase-averaged resistance and mobility tensors are produced to describe the flagellar hydrodynamics, and a helical rod model which retains a coupling between translation and rotation is identified as a distinguished asymptotic limit. A supercritical Hopf bifurcation in the flagellar orientation beyond a critical ratio of flagellar motor torque to hook bending stiffness, which is set by the spontaneous curvature of the flexible hook, the shape of the cell body, and the flagellum geometry, can have a dramatic effect on the cell's trajectory through the fluid. Although the equilibrium hook angle can result in a wide variance in the trajectory's helical pitch, we find a very consistent prediction for the trajectory's helical amplitude using parameters relevant to swimming P. aeruginosa cells.

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  • Received 16 June 2021
  • Accepted 23 September 2021

DOI:https://doi.org/10.1103/PhysRevFluids.6.103102

©2021 American Physical Society

Physics Subject Headings (PhySH)

Physics of Living SystemsFluid Dynamics

Authors & Affiliations

Zonghao Zou, Wilson Lough, and Saverio Spagnolie*

  • Department of Mathematics, University of Wisconsin–Madison, 480 Lincoln Drive, Madison, Wisconsin 53706, USA

  • *spagnolie@math.wisc.edu

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Vol. 6, Iss. 10 — October 2021

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