Hydrodynamic model for Spiroplasma motility

Christian Esparza López and Eric Lauga
Phys. Rev. Fluids 5, 093102 – Published 8 September 2020
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Abstract

Spiroplasma is a small helical bacterium that swims and performs chemotaxis in a nonconventional way. Equipped with a flexible flat ribbon cytoskeleton, Spiroplasma deforms its body into a helix that periodically changes its chirality. The helical transformation produces a kink that propagates along the cell body and propels the microorganism in the opposite direction. Based on experimental observations, we develop a hydrodynamic model to describe Spiroplasma motility. We obtain expressions for the total linear and angular displacements of the cell body per swimming stroke. We show mathematically that the cell body does not reorient at the end of one period, which allows us to define an effective swimming speed, vs. We then use vs to calculate the energy dissipated in one stroke, Ẇ, and to define a hydrodynamic efficiency, η=Ẇ0/Ẇ, where Ẇ0 is the power spent by a straight filament moving at the same speed vs. We show that the helical shape of the cytoskeleton that maximizes both vs and η are helices of pitch angles ϕ close to that of Spiroplasma, ϕ35, in agreement with experimental observations and with previous numerical simulations.

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  • Received 4 April 2020
  • Accepted 31 July 2020

DOI:https://doi.org/10.1103/PhysRevFluids.5.093102

©2020 American Physical Society

Physics Subject Headings (PhySH)

Fluid DynamicsPhysics of Living Systems

Authors & Affiliations

Christian Esparza López and Eric Lauga*

  • Department of Applied Mathematics and Theoretical Physics, University of Cambridge, Cambridge CB3 0WA, United Kingdom

  • *e.lauga@damtp.cam.ac.uk

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Issue

Vol. 5, Iss. 9 — September 2020

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