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Enhanced bacterial swimming speeds in macromolecular polymer solutions

Nature Physics volume 15, pages 554–558 (2019)Cite this article

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Abstract

The locomotion of swimming bacteria in simple Newtonian fluids can successfully be described within the framework of low-Reynolds-number hydrodynamics1. The presence of polymers in biofluids generally increases the viscosity, which is expected to lead to slower swimming for a constant bacterial motor torque. Surprisingly, however, experiments have shown that bacterial speeds can increase in polymeric fluids2,3,4,5. Whereas, for example, artificial helical microswimmers in shear-thinning fluids6 or swimming Caenorhabditis elegans worms in wet granular media7,8 increase their speeds substantially, swimming Escherichia coli bacteria in polymeric fluids show just a small increase in speed at low polymer concentrations, followed by a decrease at higher concentrations2,4. The mechanisms behind this behaviour are currently unclear, and therefore we perform extensive coarse-grained simulations of a bacterium swimming in explicitly modelled solutions of macromolecular polymers of different lengths and densities. We observe an increase of up to 60% in swimming speed with polymer density and demonstrate that this is due to a non-uniform distribution of polymers in the vicinity of the bacterium, leading to an apparent slip. However, this in itself cannot predict the large increase in swimming velocity: coupling to the chirality of the bacterial flagellum is also necessary.

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Fig. 1: Simulations of a bacterium swimming in a dense macromolecular polymer solution.
Fig. 2: Fluid viscosity and swimming performance depend on polymer density.
Fig. 3: Flow fields and apparent slip velocities.
Fig. 4: Dependence of swimming speed on fluid properties.

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The data that support the plots within this paper and other findings of this study are available from the corresponding author upon request.

References

  1. Lauga, E. Bacterial hydrodynamics. Annu. Rev. Fluid Mech. 48, 105–130 (2016).

    Article  ADS  MathSciNet  Google Scholar 

  2. Schneider, W. R. & Doetsch, R. N. Effect of viscosity on bacterial motility. J. Bacteriol. 117, 696–701 (1974).

    Google Scholar 

  3. Berg, H. C. & Turner, L. Movement of microorganisms in viscous environments. Nature 278, 349–351 (1979).

    Article  ADS  Google Scholar 

  4. Martinez, V. A. et al. Flagellated bacterial motility in polymer solutions. Proc. Natl Acad. Sci. USA 111, 17771–17776 (2014).

    Article  ADS  Google Scholar 

  5. Patteson, A. E., Gopinath, A., Goulian, M. & Arratia, P. E. Running and tumbling with E. coli in polymeric solutions. Sci. Rep. 5, 15761 (2015).

    Article  ADS  Google Scholar 

  6. Gómez, S., Godínez, F. A., Lauga, E. & Zenit, R. Helical propulsion in shear-thinning fluids. J. Fluid Mech. 812, R3 (2017).

    Article  ADS  MathSciNet  Google Scholar 

  7. Juarez, G., Lu, K., Sznitman, J. & Arratia, P. E. Motility of small nematodes in wet granular media. Europhys. Lett. 92, 44002 (2010).

    Article  ADS  Google Scholar 

  8. Jung, S. Caenorhabditis elegans swimming in a saturated particulate system. Phys. Fluids 22, 031903 (2010).

    Article  ADS  Google Scholar 

  9. Azam, F. & Malfatti, F. Microbial structuring of marine ecosystems. Nat. Rev. Microbiol. 5, 782–791 (2007).

    Article  Google Scholar 

  10. McGuckin, M. A., Lindén, S. K., Sutton, P. & Florin, T. H. Mucin dynamics and enteric pathogens. Nat. Rev. Microbiol. 9, 265–278 (2011).

    Article  Google Scholar 

  11. Man, Y. & Lauga, E. Phase-separation models for swimming enhancement in complex fluids. Phys. Rev. E 92, 023004 (2015).

    Article  ADS  MathSciNet  Google Scholar 

  12. Magariyama, Y. & Kudo, S. A mathematical explanation of an increase in bacterial swimming speed with viscosity in linear-polymer solutions. Biophys. J. 83, 733–739 (2002).

    Article  ADS  Google Scholar 

  13. Leshansky, A. M. Enhanced low-Reynolds-number propulsion in heterogeneous viscous environments. Phys. Rev. E 80, 051911 (2009).

    Article  ADS  Google Scholar 

  14. Praprotnik, M., Delle Site, L. & Kremer, K. Multiscale simulation of soft matter: from scale bridging to adaptive resolution. Annu. Rev. Phys. Chem. 59, 545–571 (2008).

    Article  ADS  Google Scholar 

  15. Phan-Thien, N., Tran-Cong, T. & Ramia, M. A boundary-element analysis of flagellar propulsion. J. Fluid Mech. 184, 533–549 (1987).

    Article  ADS  Google Scholar 

  16. Watari, N. & Larson, R. G. The hydrodynamics of a run-and-tumble bacterium propelled by polymorphic helical flagella. Biophys. J. 98, 12–17 (2010).

    Article  ADS  Google Scholar 

  17. Vogel, R. & Stark, H. Rotation-induced polymorphic transitions in bacterial flagella. Phys. Rev. Lett. 110, 158104 (2013).

    Article  ADS  Google Scholar 

  18. Hu, J., Yang, M., Gompper, G. & Winkler, R. G. Modelling the mechanics and hydrodynamics of swimming E. coli. Soft Matter 11, 7867–7876 (2015).

    Article  ADS  Google Scholar 

  19. Drescher, K., Dunkel, J., Cisneros, L. H., Ganguly, S. & Goldstein, R. E. Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering. Proc. Natl Acad. Sci. USA 108, 10940–10945 (2011).

    Article  ADS  Google Scholar 

  20. Balin, A. K., Zöttl, A., Yeomans, J. M. & Shendruk, T. Biopolymer dynamics driven by helical flagella. Phys. Rev. Fluids 2, 113102 (2017).

    Article  ADS  Google Scholar 

  21. de Gennes, P. G. Polymers at an interface; a simplified view. Adv. Colloid Interface Sci. 27, 189–209 (1987).

    Article  Google Scholar 

  22. Tuinier, R., Dhont, J. K. G. & Fan, T.-H. How depletion affects sphere motion through solutions containing macromolecules. Europhys. Lett. 75, 929–935 (2006).

    Article  ADS  Google Scholar 

  23. Fan, T.-H., Dhont, J. K. G. & Tuinier, R. Motion of a sphere through a polymer solution. Phys. Rev. E 75, 011803 (2007).

    Article  ADS  Google Scholar 

  24. Gray, J. & Hancock, G. J. The propulsion of sea-urchin spermatozoa. J. Exp. Biol. 32, 802–814 (1955).

    Google Scholar 

  25. Chwang, A. T. & Wu, T. Y. A note on the helical movement of micro-organisms. Proc. R. Soc. Lond. B 178, 327–346 (1971).

    Article  ADS  Google Scholar 

  26. Rodenborn, B., Chen, C.-H., Swinney, H. L., Liu, B. & Zhang, H. P. Propulsion of microorganisms by a helical flagellum. Proc. Natl Acad. Sci. USA 110, E338–E347 (2013).

    Article  Google Scholar 

  27. Liu, B., Powers, T. R. & Breuer, K. S. Force-free swimming of a model helical flagellum in viscoelastic fluids. Proc. Natl Acad. Sci. USA 108, 19516–19520 (2011).

    Article  ADS  Google Scholar 

  28. Spagnolie, S. E., Liu, B. & Powers, T. R. Locomotion of helical bodies in viscoelastic fluids: enhanced swimming at large helical amplitudes. Phys. Rev. Lett. 111, 068101 (2013).

    Article  ADS  Google Scholar 

  29. Barr, A. H. Superquadrics and angle-preserving transformations. IEEE Comput. Graph. Appl. 1, 11–23 (1981).

    Article  Google Scholar 

  30. Higdon, J. J. L. A hydrodynamic analysis of flagellar propulsion. J. Fluid Mech. 90, 685–711 (1979).

    Article  ADS  MathSciNet  Google Scholar 

  31. Reigh, S. Y., Winkler, R. G. & Gompper, G. Synchronization and bundling of anchored bacterial flagella. Soft Matter 8, 4363–4372 (2012).

    Article  ADS  Google Scholar 

  32. Allen, M. P. & Tildesley, D. J. Computer Simulation of Liquids (Clarendon, Oxford, England, 1989).

    MATH  Google Scholar 

  33. Weeks, J. D., Chandler, D. & Andersen, H. C. Role of repulsive forces in determining the equilibrium structure of simple liquids. J. Chem. Phys. 54, 5237–5247 (1971).

    Article  ADS  Google Scholar 

  34. Kapral, R. Multiparticle collision dynamics: simulation of complex systems on mesoscales. Adv. Chem. Phys. 140, 89–146 (2008).

    Google Scholar 

  35. Gompper, G., Ihle, T., Kroll, D. M. & Winkler, R. G. Multi-particle collision dynamics: a particle-based mesoscale simulation approach to the hydrodynamics of complex fluids. Adv. Polym. Sci. 221, 1–87 (2009).

    Google Scholar 

  36. Malevanets, A. & Yeomans, J. M. Dynamics of short polymer chains in solution. Europhys. Lett. 52, 231–237 (2000).

    Article  ADS  Google Scholar 

  37. Backer, J. A., Lowe, C. P., Hoefsloot, H. C. J. & Iedema, P. D. Poiseuille flow to measure the viscosity of particle model fluids. J. Chem. Phys. 122, 154503 (2005).

    Article  ADS  Google Scholar 

  38. Saramito, P. Complex Fluid Modelling and Algorithms (Springer International, Cham, 2016).

  39. Rubinstein, M. & Colby, R. H. Polymer Physics. (Oxford University Press, Oxford, 2003).

  40. Chattopadhyay, S., Moldovan, R., Yeung, C. & Wu, X. L. Swimming efficiency of bacterium Escherichia coli. Proc. Natl Acad. Sci. USA 103, 13712–13717 (2006).

    Article  ADS  Google Scholar 

  41. Kim, S. & Karrila, J. S. Microhydrodynamics - Principles and Selected Applications (Dover, Mineola, 1991).

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Acknowledgements

We are grateful to T. Shendruk for helpful discussions and comments on the manuscript. We acknowledge discussions with W. Poon, V. Martinez, A. Morozov, A. Balin and A. Doostmohammadi. This project has received funding from the European Union’s Horizon 2020 research and innovation programme under the Marie Skłodowska-Curie grant agreement no. 653284. The authors would like to acknowledge the use of the University of Oxford Advanced Research Computing (ARC) facility in carrying out this work.

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  1. Rudolf Peierls Centre for Theoretical Physics, Clarendon Lab., Oxford, UK

    Andreas Zöttl & Julia M. Yeomans

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  1. Andreas Zöttl
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Contributions

A.Z. and J.M.Y. designed the research. A.Z. developed the MPCD simulation code, performed the simulations, analysed the data and developed the theory. A.Z. and J.M.Y. developed the results and wrote the paper.

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Correspondence to Andreas Zöttl.

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The authors declare no competing interests.

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Journal peer review information: Nature Physics thanks Alex Leshansky and other anonymous reviewer(s) for their contribution to the peer review of this work.

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Supplementary information

Supplementary Information

Supplementary Figures 1–10.

Supplementary Video 1

Dynamics and swimming performance of a bacterium in different fluids. Swimming in a Newtonian fluid in the absence of polymers (top), and in a semi-dilute (density ρ = 0.05, centre) and dense (density ρ = 0.2, bottom) polymer solution consisting of macromolecular semiflexible polymers (length N = 12, stiffness kb = 12kBT). Left: side view; middle: front view; right: back view. The colours of individual polymers are to aid visualization.

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Zöttl, A., Yeomans, J.M. Enhanced bacterial swimming speeds in macromolecular polymer solutions. Nat. Phys. 15, 554–558 (2019). https://doi.org/10.1038/s41567-019-0454-3

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