Skip to main content Accessibility help
×
×
Home

Locomotion of a single-flagellated bacterium

  • Yunyoung Park (a1), Yongsam Kim (a1) and Sookkyung Lim (a2)

Abstract

Single-flagellated bacteria propel themselves by rotating a flagellar motor, translating rotation to the filament through a compliant hook and subsequently driving the rotation of the flagellum. The flagellar motor alternates the direction of rotation between counterclockwise and clockwise, and this leads to the forward and backward directed swimming. Such bacteria can change the course of swimming as the hook experiences its buckling caused by the change of bending rigidity. In this paper, we present a comprehensive model of a monotrichous bacterium as a free swimmer in a viscous fluid. We describe a cell body as a rigid body using the penalty method and a flagellum as an elastic rod using Kirchhoff rod theory. The hydrodynamic interaction of the bacterium is described by the regularized Stokes formulation. Our model of a single-flagellated micro-organism is able to mimic a swimming pattern that is well matched with the experimental observation. Furthermore, we find the critical thresholds of the rotational frequency of the motor and the bending modulus of the hook for the buckling instability, and investigate the dependence of the buckling angle and the reorientation of the swimming cell after buckling on the physical and geometrical parameters of the model.

Copyright

Corresponding author

Email address for correspondence: kimy@cau.ac.kr

References

Hide All
Berg, H. C. 2003 The rotary motor of bacterial flagella. Annu. Rev. Biochem. 72 (1), 1954.
Berg, H. C. & Anderson, R. A. 1973 Bacteria swim by rotating their flagellar filaments. Nature 245, 380382.
Block, S. M., Blair, D. F. & Berg, H. C. 1989 Compliance of bacterial flagella measured with optical tweezers. Nature 338, 514518.
Block, S. M., Blair, D. F. & Berg, H. C. 1991 Compliance of bacterial polyhooks measured with optical tweezers. Cytometry 12 (6), 492496.
Chattopadhyay, S. & Wu, X. L. 2009 The effect of long-range hydrodynamic interaction on the swimming of a single bacterium. Biophys. J. 96 (5), 20232028.
Chwang, A. T. & Wu, T. Y. 1971 A note on the helical movement of micro-organisms. Proc. R. Soc. Lond. B 178 (1052), 327346.
Cortez, R. 2001 The method of regularized Stokeslets. SIAM J. Sci. Comput. 23 (4), 12041225.
Flynn, T. S. & Ma, J. 2004 Theoretical analysis of twist/bend ratio and mechanical moduli of bacterial flagellar hook and filament. Biophys. J. 86 (5), 32043210.
Fujita, T. & Kawai, T. 2001 Optimum shape of a flagellated microorganism. JSME Intl J. 44 (4), 952957.
Furuno, M., Atsumi, T., Yamada, T., Kojima, S., Nishioka, N., Kawagishi, I. & Homma, M. 1997 Characterization of polar-flagellar-length mutants in Vibrio alginolyticus . Microbiology 143 (5), 16151621.
Goto, T., Nakata, K., Baba, K., Nishimura, M. & Magariyama, Y. 2005 A fluid-dynamic interpretation of the asymmetric motion of singly flagellated bacteria swimming close to a boundary. Biophys. J. 89 (6), 37713779.
Hancock, G. J. 1953 The self-propulsion of microscopic organisms through liquids. Proc. R. Soc. Lond. A 217 (1128), 96121.
Higdon, J. J. L. 1979 The hydrodynamics of flagellar propulsion: helical waves. J. Fluid Mech. 94 (2), 331351.
Homma, M., Oota, H., Kojima, S., Kawagishi, I. & Imae, Y. 1996 Chemotactic responses to an attractant and a repellent by the polar and lateral flagellar systems of Vibrio alginolyticus . Microbiology 142, 27772783.
Hsu, C. & Dillon, R. 2009 A 3D motile rod-shaped monotrichous bacterial model. Bull. Math. Biol. 71 (5), 12281263.
Ishikawa, T. 2009 Suspension biomechanics of swimming microbes. J. R. Soc. Interface 6 (39), 815834.
Ishikawa, T., Sekiya, G., Imai, Y. & Yamaguchi, T. 2007 Hydrodynamic interactions between two swimming bacteria. Biol. J. 93 (6), 22172225.
Kawagishi, I., Imagawa, M., Imae, Y., McCarter, L. & Homma, M. 1996 The sodium-driven polar flagellar motor of marine Vibrio as the mechanosensor that regulates lateral flagellar expression. Mol. Microbiol. 20 (4), 693699.
Kim, M. J., Bird, J. C., Parys, A. J. V., Breuer, K. S. & Powers, T. R. 2003 A macroscopic scale model of bacterial flagellar bundling. Proc. Natl Acad. Sci. USA 100 (26), 1548115485.
Kim, Y. & Peskin, C. S. 2007 Penalty immersed boundary method for an elastic boundary with mass. Phys. Fluids 19 (5), 053103.
Kim, Y. & Peskin, C. S. 2016 A penalty immersed boundary method for a rigid body in fluids. Phys. Fluids 28 (3), 033603.
Ko, W., Lim, S., Lee, W., Kim, Y., Berg, H. C. & Peskin, C. S. 2017 Modeling polymorphic transformation of rotating bacterial flagella in a viscous fluid. Phys. Rev. E 95 (6), 063106.
Kudo, S., Imai, N., Nishitoba, M., Sugiyama, S. & Magariyama, Y. 2005 Asymmetric swimming pattern of Vibrio alginolyticus cells with single polar flagella. FEMS Microbiol. Lett. 242 (2), 221225.
Lauga, E. 2016 Bacterial hydrodynamics. Annu. Rev. Fluid Mech. 48, 105130.
Lauga, E. & Powers, T. R. 2009 The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72 (9), 096601.
Lee, W., Kim, Y., Olson, S. D. & Lim, S. 2014 Nonlinear dynamics of a rotating elastic rod in a viscous fluid. Phys. Rev. E 90 (3), 033012.
Lewis, C. L., Craig, C. C. & Senecal, A. G. 2014 Mass and density measurements of live and dead gram-negative and gram-positive bacterial populations. Appl. Environ. Microbiol. 80 (12), 36223631.
Lim, S., Ferent, A., Wang, X. S. & Peskin, C. S. 2008 Dynamics of a closed rod with twist and bend in fluid. SIAM J. Sci. Comput. 31 (1), 273302.
Lim, S. & Peskin, C. S. 2012 Fluid-mechanical interaction of flexible bacterial flagella by the immersed boundary method. Phys. Rev. E 85, 036307.
Magariyama, Y., Masuda, S., Takano, Y., Ohtani, T. & Kudo, S. 2001 Difference between forward and backward swimming speeds of the single polar-flagellated bacterium, Vibrio alginolyticus . FEMS Microbiol. Lett. 205 (2), 343347.
McCarter, L. L. 2001 Polar flagellar motility of the Vibrionaceae . Microbiol. Mol. Biol. Rev. 65 (3), 445462.
Olson, S., Lim, S. & Cortez, R. 2013 Modeling the dynamics of an elastic rod with intrinsic curvature and twist using a regularized Stokes formulation. J. Comput. Phys. 238, 169187.
Park, Y., Kim, Y., Ko, W. & Lim, S. 2017 Instabilities of a rotating helical rod in a viscous fluid. Phys. Rev. E 95 (2), 022410.
Phan-Thien, N., Tran-Cong, T. & Ramia, M. 1987 A boundary-element analysis of flagellar propulsion. J. Fluid Mech. 184, 533549.
Purcell, E. M. 1997 The efficiency of propulsion by rotating flagellum. Proc. Natl Acad. Sci. USA 94 (21), 1130711311.
Ramia, M., Tullock, K. L. & Phan-Thien, N. 1993 The role of hydrodynamic interaction in the locomotion of microorganisms. Biophys. J. 65 (2), 755778.
Rodenborn, B., Chen, C., Swinney, H. L., Liu, B. & Zhang, H. P. 2013 Propulsion of microorganisms by helical flagellum. Proc. Natl Acad. Sci. USA 110 (5), 338347.
Sen, A., Nandy, R. K. & Ghosh, A. N. 2004 Elasticity of flagellar hooks. J. Electron Microsc. 53 (3), 305309.
Shum, H. & Gaffney, E. A. 2012 The effects of flagellar hook compliance on motility of monotrichous bacteria: a modeling study. Phys. Fluids 24 (6), 061901.
Shum, H., Gaffney, E. A. & Smith, D. J. 2010 Modelling bacterial behaviour close to a no-slip plane boundary: the influence of bacterial geometry. Proc. R. Soc. Lond. A 466, 17251748.
Son, K., Guasto, J. S. & Stocher, R. 2013 Bacteria can exploit a flagellar buckling instability to change direction. Nat. Phys. 9, 494498.
Stocker, R. 2011 Reverse and flick: hybrid locomotion in bacteria. Proc. Natl Acad. Sci. USA 108 (7), 26352636.
Takano, Y., Yoshida, K., Kudo, S., Nishitoba, M. & Magariyama, Y. 2003 Analysis of small deformation of helical flagellum of swimming Vibrio alginolyticus . JSME. Intl J. 46 (4), 12411247.
Taylor, G. I. 1952 The action of waving cylindrical tails in propelling microscopic organisms. Proc. R. Soc. Lond. A 211 (1105), 225239.
Thawani, A. & Tirumkudulu, M. S. 2017 Trajectory of a model bacterium. J. Fluid Mech. 835, 252270.
Timoshenko, S. 1961 Theory of Elastic Stability, 2nd edn. McGraw-Hill.
Weng, Y., Delgado, F. F., Son, S., Burg, T. P., Wasserman, S. C. & Manalis, S. R. 2011 Mass sensors with mechanical traps for weighing single cells in different fluids. Lab on a Chip 11, 41744180.
Xie, L., Altindal, T., Chattopadhyay, S. & Wu, X. L. 2010 Bacterial flagellum as a propeller and as a rudder for efficient chemotaxis. Proc. R. Soc. Lond. A 108 (6), 22462251.
Recommend this journal

Email your librarian or administrator to recommend adding this journal to your organisation's collection.

Journal of Fluid Mechanics
  • ISSN: 0022-1120
  • EISSN: 1469-7645
  • URL: /core/journals/journal-of-fluid-mechanics
Please enter your name
Please enter a valid email address
Who would you like to send this to? *
×
MathJax

JFM classification

Metrics

Full text views

Total number of HTML views: 0
Total number of PDF views: 0 *
Loading metrics...

Abstract views

Total abstract views: 0 *
Loading metrics...

* Views captured on Cambridge Core between <date>. This data will be updated every 24 hours.

Usage data cannot currently be displayed