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Microorganism motility often takes place within complex, viscoelastic fluid environments, e.g. sperm in cervicovaginal mucus and bacteria in biofilms. In such complex fluids, strains and stresses generated by the microorganism are stored and relax across a spectrum of length and time scales and the complex fluid can be driven out of its linear response regime. Phenomena not possible in viscous media thereby arise from feedback between the swimmer and the complex fluid, making swimming efficiency co-dependent on the propulsion mechanism and fluid properties. Here, we parameterize a flagellar motor and filament properties together with elastic relaxation and nonlinear shear-thinning properties of the fluid in a computational immersed boundary model. We then explore swimming efficiency, defined as a particular flow rate divided by the torque required to spin the motor, over this parameter space. Our findings indicate that motor efficiency (measured by the volumetric flow rate) can be boosted or degraded by relatively moderate or strong shear thinning of the viscoelastic environment. 

We present a mathematical model of lophotrichous bacteria, motivated by Pseudomonas putida, which swim through fluid by rotating a cluster of multiple flagella extended from near one pole of the cell body. Although the flagella rotate individually, they are typically bundled together, enabling the bacterium to exhibit three primary modes of motility: push, pull, and wrapping. One key determinant of these modes is the coordination between motor torque and rotational direction of motors. The computational variations in this coordination reveal a wide spectrum of dynamical motion regimes, which are modulated by hydrodynamic interactions between flagellar filaments. These dynamic modes can be categorized into two groups based on the collective behavior of flagella, i.e., bundled and unbundled configurations. For some of these configurations, experimental examples from fluorescence microscopy recordings of swimming P. putida cells are also presented. Furthermore, we analyze the characteristics of stable bundles, such as push and pull, and investigate the dependence of swimming behaviors on the elastic properties of the flagella. 

To swim through a viscous fluid, a flagellated bacterium must overcome the fluid drag on its body by rotating a flagellum or a bundle of multiple flagella. Because the drag increases with the size of bacteria, it is expected theoretically that the swimming speed of a bacterium inversely correlates with its body length. Nevertheless, despite extensive research, the fundamental size–speed relation of flagellated bacteria remains unclear with different experiments reporting conflicting results. Here, by critically reviewing the existing evidence and synergizing our own experiments of large sample sizes, hydrodynamic modeling, and simulations, we demonstrate that the average swimming speed ofEscherichia coli, a premier model of peritrichous bacteria, is independent of their body length. Our quantitative analysis shows that such a counterintuitive relation is the consequence of the collective flagellar dynamics dictated by the linear correlation between the body length and the number of flagella of bacteria. Notably, our study reveals how bacteria utilize the increasing number of flagella to regulate the flagellar motor load. The collective load sharing among multiple flagella results in a lower load on each flagellar motor and therefore faster flagellar rotation, which compensates for the higher fluid drag on the longer bodies of bacteria. Without this balancing mechanism, the swimming speed of monotrichous bacteria generically decreases with increasing body length, a feature limiting the size variation of the bacteria. Altogether, our study resolves a long-standing controversy over the size–speed relation of flagellated bacteria and provides insights into the functional benefit of multiflagellarity in bacteria. 

We present an in silico microswimmer motivated by peritrichous bacteria, E. coli, which can run and tumble by spinning their flagellar motors counterclockwise (CCW) or clockwise (CW). Runs are the directed movement driven by a flagellar bundle, and tumbles are reorientations of cells caused by some motors' reversals from CCW to CW. In a viscous fluid without obstacles, our simulations reveal that material properties of the hook and the counterrotation of the cell body are important factors for efficient flagellar bundling and that longer hooks in mutant cell models create an instability and disrupt the bundling process, resulting in a limited range of movement. In the presence of a planar wall, we demonstrate that microswimmers can explore environment near surface by making various types of tumble events as they swim close to the surface. In particular, the variation of tumble duration can lead the microswimmer to run in a wide range of direction. However, we find that cells near surface stay close to the surface even after tumbles, which suggests that the tumble motion may not promote cells' escape from the confinement but promote biofilm formation. 

Abstract Lophotrichous bacteria swim through fluid by rotating their flagellar bundle extended collectively from one pole of the cell body. Cells experience modes of motility such as push, pull, and wrapping, accompanied by pauses of motor rotation in between. We present a mathematical model of a lophotrichous bacterium and investigate the hydrodynamic interaction of cells to understand their swimming mechanism. We classify the swimming modes which vary depending on the bending modulus of the hook and the magnitude of applied torques on the motor. Given the hook’s bending modulus, we find that there exist corresponding critical thresholds of the magnitude of applied torques that separate wrapping from pull in CW motor rotation, and overwhirling from push in CCW motor rotation, respectively. We also investigate reoriented directions of cells in three-dimensional perspectives as the cell experiences different series of swimming modes. Our simulations show that the transition from a wrapping mode to a push mode and pauses in between are key factors to determine a new path and that the reoriented direction depends upon the start time and duration of the pauses. It is also shown that the wrapping mode may help a cell to escape from the region where the cell is trapped near a wall. 

Swimming trajectories of bacteria can be altered by environmental conditions, such as background flow and physical barriers, that limit the free swimming of bacteria. We present a comprehensive model of a bacterium that consists of a rod-shaped cell body and a flagellum which is composed of a motor, a hook, and a filament. The elastic flagellum is modeled based on the Kirchhoff rod theory, the cell body is considered to be a rigid body, and the hydrodynamic interaction of a bacterium near a wall is described by regularized Stokeslet formulation combined with the image system. We consider three environmental conditions: (1) a rigid surface is placed horizontally and there is no shear flow, (2) a shear fluid flow is present and the bacterium is near the rigid surface, and (3) while the bacterium is near the rigid surface and is under shear flow, an additional sidewall which is perpendicular to the rigid surface is placed. Each environmental state modifies the swimming behavior. For the first condition, there are two modes of motility, trap and escape, whether the bacterium stays near the surface or moves away from the surface as we vary the physical and geometrical properties of the model bacterium. For the second condition, there exists a threshold of shear rate that classifies the motion into two types of paths in which the bacterium takes either a periodic coil trajectory or a linear trajectory. For the last condition, the bacterium takes upstream motility along the sidewall for lower shear rates and downstream motility for larger shear flow rates.