Fluid dynamics and noise in bacterial cell–cell and cell–surface scattering

Abstract

Bacterial processes ranging from gene expression to motility and biofilm formation are constantly challenged by internal and external noise. While the importance of stochastic fluctuations has been appreciated for chemotaxis, it is currently believed that deterministic long-range fluid dynamical effects govern cell-cell and cellsurface scattering-the elementary events that lead to swarming and collective swimming in active suspensions and to the formation of biofilms. Here, we report direct measurements of the bacterial flow field generated by individual swimming Escherichia coli both far from and near to a solid surface. These experiments allowed us to examine the relative importance of fluid dynamics and rotational diffusion for bacteria. For cell-cell interactions it is shown that thermal and intrinsic stochasticity drown the effects of long-range fluid dynamics, implying that physical interactions between bacteria are determined by steric collisions and near-field lubrication forces. This dominance of short-range forces closely links collective motion in bacterial suspensions to self-organization in driven granular systems, assemblages of biofilaments, and animal flocks. For the scattering of bacteria with surfaces, long-range fluid dynamical interactions are also shown to be negligible before collisions; however, once the bacterium swims along the surface within a few microns after an aligning collision, hydrodynamic effects can contribute to the experimentally observed, long residence times. Because these results are based on purely mechanical properties, they apply to a wide range of microorganisms.low Reynolds number hydrodynamics | microswimmers C ollective behavior of bacteria, such as biofilm formation (1), swarming (2), and turbulence-like motion in concentrated suspensions (3, 4), has profound effects on foraging, signaling, and transport of metabolites (5, 6), and can be of great biomedical importance (7,8). Large-scale coherence in bacterial systems typically arises from a combination of biochemical signaling (9) and physical interactions. Recent theoretical models that focus on physical aspects of bacterial dynamics identify pairwise long-range hydrodynamic interactions (10-16) as a key ingredient for collective swimming. Such ''microscopic" approaches underpin continuum theories that aim to describe the phenomenology of microbial suspensions (17-23). An assumption underlying many of these theories is that a self-propelled bacterium can be modeled as a force dipole; its body exerts a drag force F on the fluid that is balanced by the rearward flagellar thrust −F. The leading-order fluid velocity field at distance r is therefore a dipolar ''pusher" flow of magnitude u ∝ Fℓ∕ηr 2 (see streamlines in Fig. 1B), where η is the viscosity, and ℓ the distance between the forces (24, 25). While higher order corrections may be due to force-quadrupole contributions (26), the hypothesis that the leading-order flow field around a bacterium is dipolar has not yet been verified experimentally.A closely related, c...

Batchelor Prize Lecture Fluid dynamics at the scale of the cell

“…Estimates suggest this requires volume fractions in the range of a few per cent, and indeed this is roughly the point at which collective behaviour begins to be seen, as discussed in § 5. The problem of cell-surface interactions with competing hydrodynamic effects and rotational Brownian motion leads to a non-trivial Kramers-like problem for escape from the surface that has only begun to be explored (Drescher et al 2011). It has been known for many years that swimming cells accumulate near surfaces.…”

“…This provides ex post facto justification for the use of Squires' result for the lateral advection of Stokeslets in explaining the infalling trajectories of colonies forming a hydrodynamic bound state. Measurements of the flow fields around individual freely swimming cells were then extended to the case of bacteria using a different method (Drescher et al 2010b(Drescher et al , 2011. Here, rather than using a tracking microscope, we adopted a fixed (horizontal) field of view on an inverted microscope, with a typically narrow focal plane width, and monitored swimming cells and advected tracer particles.…”

Bugs on a Slippery Plane

“…These flows can be compared with flow fields from numerical computations (O'Malley & Bees, 2012). Drescher et al (2010a) measured the flow around freely-swimming bacteria. These studies again revealed stresslet behaviour in the far-field (decaying approximately as the reciprocal of the radius squared) although they reported the overwhelming importance of stochastic effects in cell-cell and cell-boundary interactions over larger distances.…”

Effective viscosity of puller-like microswimmers: a renormalization approach

“…To calculate the enhancement ratio, we use the following parameters of the puller model (figure 2 [1,3]. Finally, the Stokes drag law holds: f p ¼ 6pbh 0 vN, where an expression for N can be found in [4].…”

“…Pullers typically propel themselves by executing a breaststroke-like motion with a pair of flagella attached at the front of the body (e.g. [3]). This should be compared to the propulsion of pushers such as Escherichia coli, which use a rotating flagellar bundle pushing the fluid behind the bacterial body (e.g.…”