Propulsion contribution from individual filament in a flagellar bundle

Abstract

Flagellated microorganisms overcome the low-Reynolds-number time reversibility by rotating helical flagella [E. M. Purcell, Am. J. Phys. 45, 3–11 (1977); D. Bray, Cell Movements: From Molecules to Motility, 2nd ed. (Garland Publishing, New York, NY, 2001); Lauga and Powers, Rep. Prog. Phys. 72, 096601 (2009); and E. Lauga, Annu. Rev. Fluid Mech. 48, 105–130 (2016)]. For peritrichous bacteria, the randomly distributed flagellar filaments align in the same direction to form a bundle, facilitating complex locomotive strategies [Berg and Brown, Nature 239, 500–504 (1972); Turner et al., J. Bacteriol. 182, 2793–2801 (2000); and Darnton et al., J. Bacteriol. 189, 1756–1764 (2007)]. To understand the process of flagellar bundling, especially propulsion force generation, we develop a multi-functional macroscopic experimental system and employ advanced numerical simulations for verification. Flagellar arrangements and phase differences between helices are investigated, revealing the variation in propulsion contributions from individual helices. Numerically, we build a time-dependent model to match the bundling process and study the influence of hydrodynamic interactions. Surprisingly, it is found that the total propulsion generated by a bundle of two filaments is constant at various phase differences between the helices. However, the difference between the propulsion from each helix is significantly affected by a phase difference, and only one of the helices is responsible for the total propulsion when the phase difference is equal to π. Building on our experimental and computational results, we develop a theoretical model considering the propulsion contribution of each filament to better understand microbial locomotion mechanisms, especially the wobbling behavior of the cell. Our work also sheds light on the design and control of artificial microswimmers.