Celli, J. P. et al. Helicobacter pylori moves through mucus by reducing mucin viscoelasticity. Proc. Natl Acad. Sci. USA 106, 14321–14326 (2009).
Suarez, S. S. & Pacey, A. A. Sperm transport in the female reproductive tract. Hum. Reprod. Update 12, 23–37 (2006).
Wells, M. L. & Goldberg, E. D. Occurrence of small colloids in sea water. Nature 353, 342–344 (1991).
Verdugo, P. et al. The oceanic gel phase: a bridge in the DOM–POM continuum. Mar. Chem. 92, 67–85 (2004).
Azam, F. & Malfatti, F. Microbial structuring of marine ecosystems. Nat. Rev. Microbiol. 5, 782–791 (2007).
Lauga, E. & Powers, T. R. The hydrodynamics of swimming microorganisms. Rep. Prog. Phys. 72, 096601 (2009).
Childress, S. Mechanics of Swimming and Flying (Cambridge Univ. Press, 1981).
Berg, H. C. E. coli in Motion (Springer, 2004).
Lauga, E. Bacterial hydrodynamics. Annu. Rev. Fluid Mech. 48, 105–130 (2016).
Elfring, G. J. & Lauga, E. in Complex Fluids in Biological Systems (ed. Spagnolie, S.) 283–317 (Springer, 2015).
Patteson, A. E., Gopinath, A. & Arratia, P. E. Active colloids in complex fluids. Curr. Opin. Colloid Interf. Sci. 21, 86–96 (2016).
Shoesmith, J. G. The measurement of bacterial motility. Microbiology 22, 528–535 (1960).
Schneider, W. R. & Doetsch, R. N. Effect of viscosity on bacterial motility. J. Bacteriol. 117, 696–701 (1974).
Berg, H. C. & Turner, L. Movement of microorganisms in viscous environments. Nature 278, 349–351 (1979).
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).
Martinez, V. A. et al. Flagellated bacterial motility in polymer solutions. Proc. Natl Acad. Sci. USA 111, 17771–17776 (2014).
Zhang, Y., Li, G. & Ardekani, A. M. Reduced viscosity for flagella moving in a solution of long polymer chains. Phys. Rev. Fluids 3, 023101 (2018).
Patteson, A. E., Gopinath, A., Goulian, M. & Arratia, P. E. Running and tumbling with E. coli in polymeric solutions. Sci. Rep. 5, 15761 (2015).
Qu, Z., Temel, F. Z., Henderikx, R. & Breuer, K. S. Changes in the flagellar bundling time account for variations in swimming behavior of flagellated bacteria in viscous media. Proc. Natl Acad. Sci. USA 115, 1707–1712 (2018).
Qu, Z. & Breuer, K. S. Effects of shear-thinning viscosity and viscoelastic stresses on flagellated bacteria motility. Phys. Rev. Fluids 5, 073103 (2020).
Zöttl, A. & Yeomans, J. M. Enhanced bacterial swimming speeds in macromolecular polymer solutions. Nat. Phys. 15, 554–558 (2019).
Binagia, J. P., Phoa, A., Housiadas, K. D. & Shaqfeh, E. S. G. Swimming with swirl in a viscoelastic fluid. J. Fluid Mech. 900, A4 (2020).
Man, Y. & Lauga, E. Phase-separation models for swimming enhancement in complex fluids. Phys. Rev. E 92, 023004 (2015).
Hyon, Y., Marcos, Powers, T. R., Stocker, R. & Fu, H. C. The wiggling trajectories of bacteria. J. Fluid Mech. 705, 58–76 (2012).
Hibbing, M. E., Fuqua, C., Parsek, M. R. & Peterson, S. B. Bacterial competition: surviving and thriving in the microbial jungle. Nat. Rev. Microbiol. 8, 15–25 (2010).
Nelson, B. J., Kaliakatsos, I. K. & Abbott, J. J. Microrobots for minimally invasive medicine. Annu. Rev. Biomed. Eng. 12, 55–85 (2010).
Bechinger, C. et al. Active particles in complex and crowded environments. Rev. Mod. Phys. 88, 045006 (2016).
Peng, Y., Liu, Z. & Cheng, X. Imaging the emergence of bacterial turbulence: phase diagram and transition kinetics. Sci. Adv. 7, eabd1240 (2021).
Liu, Z., Zeng, W., Ma, X. & Cheng, X. Density fluctuations and energy spectra of 3D bacterial suspensions. Soft Matter 17, 10806–10817 (2021).
Lauga, E., DiLuzio, W. R., Whitesides, G. M. & Stone, H. A. Swimming in circles: motion of bacteria near solid boundaries. Biophys. J. 90, 400–412 (2006).
Hiemenz, P. C. & Lodge, T. Polymer Chemistry 2nd edn (CRC Press, 2007).
Darnton, N. C., Turner, L., Rojevsky, S. & Berg, H. C. On torque and tumbling in swimming Escherichia coli. J. Bacteriol. 189, 1756–1764 (2007).
Macosko, C. W. Rheology: Principles, Measurements, and Applications (VCH, 1994).
Jeffrey, D. J. & Onishi, Y. Calculation of the resistance and mobility functions for two unequal rigid spheres in low-Reynolds-number flow. J. Fluid Mech. 139, 261–290 (1984).
Zhang, B. K., Leishangthem, P. K., Ding, Y. & Xu, X. L. An effective and efficient model of the near-field hydrodynamic interactions for active suspensions of bacteria. Proc. Natl Acad. Sci. USA 118, e2100145118 (2021).
Li, G., Tam, L.-K. & Tang, J. X. Amplified effect of Brownian motion in bacterial near-surface swimming. Proc. Natl Acad. Sci. USA 105, 18355–18359 (2008).
Block, S. M., Blair, D. F. & Berg, H. C. Compliance of bacterial flagella measured with optical tweezers. Nature 338, 514–518 (1989).
Berg, H. C. & Brown, D. A. Chemotaxis in Escherichia coli analysed by three-dimensional tracking. Nature 239, 500–504 (1972).
Crenshaw, H. C. A new look at locomotion in microorganisms: rotating and translating. Am. Zool. 36, 608–618 (1996).
Rossi, M., Cicconofri, G., Beran, A., Noselli, G. & DeSimone, A. Kinematics of flagellar swimming in Euglena gracilis: helical trajectories and flagellar shapes. Proc. Natl Acad. Sci. USA 114, 13085–13090 (2017).
Cortese, D. & Wan, K. Y. Control of helical navigation by three-dimensional flagellar beating. Phys. Rev. Lett. 126, 088003 (2021).
Shimogonya, Y. et al. Torque-induced precession of bacterial flagella. Sci. Rep. 5, 18488 (2015).
Poon, W. C. K., Weeks, E. R. & Royall, C. P. On measuring colloidal volume fractions. Soft Matter 8, 21–30 (2012).
Crocker, J. C. & Grier, D. G. Methods of digital video microscopy for colloidal studies. J. Colloid Interf. Sci. 179, 298–310 (1996).