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A study of bacterial flagellar bundling

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Abstract

Certain bacteria, such as Escherichia coli (E. coli) and Salmonella typhimurium (S. typhimurium), use multiple flagella often concentrated at one end of their bodies to induce locomotion. Each flagellum is formed in a left-handed helix and has a motor at the base that rotates the flagellum in a corkscrew motion.We present a computational model of the flagellar motion and their hydrodynamic interaction. The model is based on the equations of Stokes flow to describe the fluid motion. The elasticity of the flagella is modeled with a network of elastic springs while the motor is represented by a torque at the base of each flagellum. The fluid velocity due to the forces is described by regularized Stokeslets and the velocity due to the torques by the associated regularized rotlets. Their expressions are derived. The model is used to analyze the swimming motion of a single flagellum and of a group of three flagella in close proximity to one another. When all flagellar motors rotate counterclockwise, the hydrodynamic interaction can lead to bundling. We present an analysis of the flow surrounding the flagella. When at least one of the motors changes its direction of rotation, the same initial conditions lead to a tumbling behavior characterized by the separation of the flagella, changes in their orientation, and no net swimming motion. The analysis of the flow provides some intuition for these processes.

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Authors and Affiliations

  1. Department of Mathematics, University of Nebraska, 203 Avery Hall, P.O. Box 880130, Lincoln, NE, 68588, USA

    Heather Flores

  2. Department of Mathematics, University of California at Berkeley, 970 Evans Hall #3840, Berkeley, CA, 94720, USA

    Edgar Lobaton

  3. Department of Applied Mathematics and Scientific Computing, University of Maryland, 3103 Mathematics Building, College Park, MD, 20742, USA

    Stefan Méndez-Diez

  4. Department of Mathematics, Tulane University, 6823 St. Charles Avenue, #424, New Orleans, LA, 70118, USA

    Svetlana Tlupova & Ricardo Cortez

Authors
  1. Heather Flores
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  2. Edgar Lobaton
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  3. Stefan Méndez-Diez
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  4. Svetlana Tlupova
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  5. Ricardo Cortez
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Correspondence to Ricardo Cortez.

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Flores, H., Lobaton, E., Méndez-Diez, S. et al. A study of bacterial flagellar bundling. Bull. Math. Biol. 67, 137–168 (2005). https://doi.org/10.1016/j.bulm.2004.06.006

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  • DOI: https://doi.org/10.1016/j.bulm.2004.06.006

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