Force and torque on a cylinder rotating in a narrow gap at low Reynolds number: Scaling and lubrication analyses

From hydrodynamic lubrication to many-body interactions in dense suspensions of active swimmers

We study how hydrodynamic interactions affect the collective behaviour of active particles suspended in a fluid at high concentrations, with particular attention to lubrication forces which appear when the particles are very close to one another. We compute exactly the limiting behaviour of the hydrodynamic interactions between two spherical (circular) active swimmers in very close proximity to one another in the general setting in both three and (two) dimensions. Combining this with far-field interactions, we develop a novel numerical scheme which allows us to study the collective behaviour of large numbers of active particles with accurate hydrodynamic interactions when close to one another. We study active swimmers whose intrinsic flow fields are characterised by force dipoles and quadrupoles. Using this scheme, we are able to show that lubrication forces when the particles are very close to each other can play as important a role as long-range hydrodynamic interactions in determining their many-body behaviour. We find that when the swimmer force dipole is large, finite clusters and open gel-like clusters appear rather than complete phase separation. This suppression is due to near-field lubrication interactions. For swimmers with small force dipoles, we find surprisingly that a globally polar-ordered phase appears because near-field lubrication rather than long-range hydrodynamics dominates the alignment mechanism. Polar order is present for very large system sizes and is stable to fluctuations with a finite noise amplitude. We explain the emergence of polar order using a minimal model in which only the leading rotational effect of the near-field interaction is included. These phenomena are also reproduced in two dimensions.

Vancomycin Reduces Cell Wall Stiffness and Slows Swim Speed of the Lyme Disease Bacterium

Borrelia burgdorferi, the spirochete that causes Lyme disease, is a tick-transmitted pathogen that requires motility to invade and colonize mammalian and tick hosts. These bacteria use a unique undulating flat-wave shape to penetrate and propel themselves through host tissues. Previous mathematical modeling has suggested that the morphology and motility of these spirochetes depends crucially on the flagellar/cell wall stiffness ratio. Here, we test this prediction using the antibiotic vancomycin to weaken the cell wall. We found that low to moderate doses of vancomycin (≤2.0 μg/mL for 24 h) produced small alterations in cell shape and that as the dose was increased, cell speed decreased. Vancomycin concentrations >1.0 μg/mL also inhibited cell growth and led to bleb formation on a fraction of the cells. To quantitatively assess how vancomycin affects cell stiffness, we used optical traps to bend unflagellated mutants of B. burgdorferi. We found that in the presence of vancomycin, cell wall stiffness gradually decreased over time, with a 40% reduction in the bending stiffness after 36 h. Under the same conditions, the swimming speed of wild-type B. burgdorferi slowed by ∼15%, with only marginal changes to cell morphology. Interestingly, our biophysical model for the swimming dynamics of B. burgdorferi suggested that cell speed should increase with decreasing cell stiffness. We show that this discrepancy can be resolved if the periplasmic volume decreases as the cell wall becomes softer. These results provide a testable hypothesis for how alterations of cell wall stiffness affect periplasmic volume regulation. Furthermore, since motility is crucial to the virulence of B. burgdorferi, the results suggest that sublethal doses of antibiotics could negatively impact spirochete survival by impeding their swim speed, thereby enabling their capture and elimination by phagocytes.