Bacteria can exploit a flagellar buckling instability to change direction

Journal name:
Nature Physics
Volume:
9,
Pages:
494–498
Year published:
DOI:
doi:10.1038/nphys2676
Received
Accepted
Published online

Bacteria swim by rotating rigid helical flagella and periodically reorienting to follow environmental cues1, 2. Despite the crucial role of reorientations, their underlying mechanism has remained unknown for most uni-flagellated bacteria3, 4. Here, we report that uni-flagellated bacteria turn by exploiting a finely tuned buckling instability of their hook, the 100-nm-long structure at the base of their flagellar filament5. Combining high-speed video microscopy and mechanical stability theory, we demonstrate that reorientations occur 10ms after the onset of forward swimming, when the hook undergoes compression, and that the associated hydrodynamic load triggers the buckling of the hook. Reducing the load on the hook below the buckling threshold by decreasing the swimming speed results in the suppression of reorientations, consistent with the critical nature of buckling. The mechanism of turning by buckling represents one of the smallest examples in nature of a biological function stemming from controlled mechanical failure6 and reveals a new role for flexibility in biological materials, which may inspire new microrobotic solutions in medicine and engineering7.

At a glance

Figures

  1. High-speed video microscopy of V. alginolyticus reveals that flicks occur after the onset of forward swimming.
    Figure 1: High-speed video microscopy of V. alginolyticus reveals that flicks occur after the onset of forward swimming.

    a, Image sequence captured with high-intensity dark-field microscopy at 420framess−1, showing the kinematics of the cell head and polar flagellum (tracked and coloured magenta; Methods) just before and during a flick (see also Supplementary Movie S1). The dashed orange line provides a reference for cell position. b, Cell trajectory containing a flick, captured with high-speed imaging (1,000framess−1, phase-contrast microscopy; see also Supplementary Movie S2). Cell head positions are shown by circular markers at 1ms intervals. A schematic of the head orientation at selected times is overlaid (not to scale). The inset shows the entire trajectory subsampled at a conventional frame rate of 30framess−1 (open circles). c, The alignment, q (directional cosine; Supplementary Information S2), between cell head and swimming direction, for the trajectory in b, reveals the distinct elements of the swimming cycle of V. alginolyticus, and in particular the short forward swimming segment (here, 18ms long; red) before the 60-ms-long flick (blue). The inset in b demonstrates that high-speed imaging is necessary to capture the short delay in the flick. d, Swimming speed during a flick (same colour scheme as in c). e, Transmission electron micrograph of V. alginolyticus, showing the single polar flagellum (mean head length 3.2μm, mean flagellar contour length 4.6μm; Supplementary Table S1), which has a sheath that covers it and prevents polymorphic transformations33. f,g, Schematics (not to scale) of the flagellar filament, hook and rotary motor during backward swimming (f), when the hook is in tension, and during forward swimming (g), when the hook is in compression.

  2. Reorientation dynamics depend on swimming speed.
    Figure 2: Reorientation dynamics depend on swimming speed.

    a, The mean swimming speed of V. alginolyticus decreases with the ambient sodium concentration, [Na+], allowing for a controlled reduction of the viscous load on cells, which depends linearly on swimming speed21. For each sodium concentration, >2,000 trajectories were analysed (error bars are standard deviations). Insets show typical trajectories at high ([Na+]=100mM, aqua) and low ([Na+]=3mM, magenta) sodium concentrations, illustrating the suppression of flicks at low swimming speeds (see also Supplementary Movie S4). b, Probability density function of V (left axis), showing the broad distribution of speeds in a population for any given sodium concentration. The grey histogram denotes the total number of trajectories analysed for each swimming speed (right axis), captured over a range of sodium concentrations ([Na+]=3–513mM). Coloured rectangles on the top axis represent speed ranges used in Fig. 3 and include >1,000 trajectories each.

  3. The probability of flicking shows a sharp increase with increasing load on the hook.
    Figure 3: The probability of flicking shows a sharp increase with increasing load on the hook.

    a, The probability PF that a cell flicks during a swimming cycle (the sequence of two runs and the two intervening reorientations) increases sharply with swimming speed V (open squares). Cell trajectories for all sodium concentrations, [Na+], from Fig. 2b are included and binned by swimming speed, with colours corresponding to the speed ranges in Fig. 2b. Cells that flick after the start of each forward run have PF=100%, whereas cells that never flick have PF=0%. The dashed magenta line indicates the mean swimming speed, V =47μms−1, for cells swimming at [Na+]=513mM, representative of natural marine conditions. The grey curve is a logistic fit, and horizontal and vertical error bars denote the standard deviation in cell speed and the error in classifying reorientations, respectively (Supplementary Information S4). The dependence of PF on V was confirmed by measuring PF for each individual [Na+] tested and binning each set by swimming speed (filled grey symbols, >300 trajectories each) by exploiting the natural variability in cell speed within a population. This rules out physiological effects associated with changes in [Na+] as a possible cause of the suppression of flicks. b, Stability diagram of the hook under combined axial and torsional loads. The hook is stable when the normalized viscous force (F/FCR) and torque (T/TCR) fall underneath the stability boundary (black curve) and is predicted to buckle otherwise. Symbols represent measurements for steady backward swimming (green diamonds), forward swimming (blue triangles), and short forward runs before flicks (red circles) from 135 trajectories recorded at 1,000framess−1 at a sodium concentration of [Na+]=513mM (Supplementary Information S6.1). Yellow filled symbols represent averages of the three cases and error bars denote standard deviations. Critical loads were computed on the basis of the bending stiffness for the loaded hook during steady swimming and for the relaxed hook during a flick (Supplementary Information S5). Open squares extend the same analysis to the data set from a, demonstrating the loss of stability as swimming speed increases.

  4. Turning by buckling is widespread among uni-flagellated bacteria.
    Figure 4: Turning by buckling is widespread among uni-flagellated bacteria.

    ac, Swimming trajectories of P. haloplanktis (a), V. coralliilyticus (b) and a natural bacterial community enriched from a seawater sample and exposed to a dead copepod (c; Supplementary Information S8). In all cases, trajectories exhibit the same alternation between 180° reversals (green circles) and large reorientations having a broad angular distribution centred about 90° (flicks; red squares) as for V. alginolyticus. Crosses are trajectory starting points and open circles denote cell head positions at 33ms intervals. Yellow trajectories in c are also captured at 33ms intervals and the white inset shows a magnified trajectory.

References

  1. Berg, H. C. E. coli in Motion (Springer, 2004).
  2. Berg, H. C. & Brown, D. A. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239, 500504 (1972).
  3. Leifson, E., Cosenza, B. J., Murchelano, R. & Cleverdon, R. C. Motile marine bacteria. I. Techniques, ecology, and general characteristics. J. Bact. 87, 652666 (1964).
  4. Xie, L., Altindal, T., Chattopadhyay, S. & Wu, X. L. Bacterial flagellum as a propeller and as a rudder for efficient chemotaxis. Proc. Natl Acad. Sci. USA 108, 22462251 (2011).
  5. Koike, M., Terashima, H., Kojima, S. & Homma, M. Isolation of basal bodies with C-ring components from the Na+-driven flagellar motor of Vibrio alginolyticus. J. Bact. 192, 375378 (2010).
  6. Krieger, K. Buckling down. Nature 488, 146147 (2012).
  7. Sitti, M. Miniature devices: Voyage of the microbots. Nature 458, 11211122 (2009).
  8. Li, J., Lykotrafitis, G., Dao, M. & Suresh, S. Cytoskeletal dynamics of human erythrocyte. Proc. Natl Acad. Sci. USA 104, 49374942 (2007).
  9. Gore, J. et al. DNA overwinds when stretched. Nature 442, 836839 (2006).
  10. Vogel, S. Life’s Devices: The Physical World of Animals and Plants (Princeton Univ. Press, 1988).
  11. Burrows, M. Biomechanics: Froghopper insects leap to new heights—An innovative leaping action propels these bugs to the top of the insect athletic league. Nature 424, 509509 (2003).
  12. Deegan, R. D. Finessing the fracture energy barrier in ballistic seed dispersal. Proc. Natl Acad. Sci. USA 109, 51665169 (2012).
  13. Singh, A. K., Prabhakar, S. & Sane, S. P. The biomechanics of fast prey capture in aquatic bladderworts. Biol. Lett. 7, 547550 (2011).
  14. Timoshenko, S. Theory of Elastic Stability 2nd edn (McGraw-Hill, 1961).
  15. Forterre, Y., Skotheim, J. M., Dumais, J. & Mahadevan, L. How the Venus flytrap snaps. Nature 433, 421425 (2005).
  16. Smith, M. L., Yanega, G. M. & Ruina, A. Elastic instability model of rapid beak closure in hummingbirds. J. Theor. Biol. 282, 4151 (2011).
  17. Sharon, E. et al. Mechanics: Buckling cascades in free sheets—Wavy leaves may not depend only on their genes to make their edges crinkle. Nature 419, 579579 (2002).
  18. Hedenstrom, A., Johansson, L. C. & Spedding, G. R. Bird or bat: Comparing airframe design and flight performance. Bioinspir. Biomim. 4, 015001 (2009).
  19. Lauder, G. V. & Madden, P. G. A. Fish locomotion: Kinematics and hydrodynamics of flexible foil-like fins. Exp. Fluids 43, 641653 (2007).
  20. Gaffney, E. A. et al. Mammalian sperm motility: Observation and theory. Annu. Rev. Fluid Mech. 43, 501528 (2011).
  21. Lauga, E. & Powers, T. R. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601 (2009).
  22. Brown, M. T. et al. Flagellar hook flexibility is essential for bundle formation in swimming Escherichia coli cells. J. Bact. 194, 34953501 (2012).
  23. Vogel, R. & Stark, H. Motor-driven bacterial flagella and buckling instabilities. Eur. Phys. J. E 35, 115 (2012).
  24. Sowa, Y., Hotta, H., Homma, M. & Ishijima, A. Torque–speed relationship of the Na+-driven flagellar motor of Vibrio alginolyticus. J. Mol. Biol. 327, 10431051 (2003).
  25. Block, S. M., Blair, D. F. & Berg, H. C. Compliance of bacterial flagella measured with optical tweezers. Nature 338, 514518 (1989).
  26. Block, S. M., Blair, D. F. & Berg, H. C. Compliance of bacterial polyhooks measured with optical tweezers. Cytometry 12, 492496 (1991).
  27. Samatey, F. A. et al. Structure of the bacterial flagellar hook and implication for the molecular universal joint mechanism. Nature 431, 10621068 (2004).
  28. Fujii, T., Kato, T. & Namba, K. Specific arrangement of alpha-helical coiled coils in the core domain of the bacterial flagellar hook for the universal joint function. Structure 17, 14851493 (2009).
  29. Stocker, R. et al. Rapid chemotactic response enables marine bacteria to exploit ephemeral microscale nutrient patches. Proc. Natl Acad. Sci. USA 105, 42094214 (2008).
  30. Rosenberg, E. et al. The role of microorganisms in coral health, disease and evolution. Nature Rev. Microbiol. 5, 355362 (2007).
  31. Darnton, N. C., Turner, L., Rojevsky, S. & Berg, H. C. On torque and tumbling in swimming Escherichia coli. J. Bact. 189, 17561764 (2007).
  32. Stocker, R. Marine microbes see a sea of gradients. Science 338, 628633 (2012).
  33. Goto, T. et al. A fluid-dynamic interpretation of the asymmetric motion of singly flagellated bacteria swimming close to a boundary. Biophys. J. 89, 37713779 (2005).

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Affiliations

  1. Department of Mechanical Engineering, MIT, Cambridge, Massachusetts 02139, USA

    • Kwangmin Son
  2. Ralph M. Parsons Laboratory, Department of Civil and Environmental Engineering, MIT, Cambridge, Massachusetts 02139, USA

    • Jeffrey S. Guasto &
    • Roman Stocker

Contributions

K.S. and J.S.G. performed experiments and analysed data. All authors designed experiments, discussed results and wrote the paper.

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The authors declare no competing financial interests.

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