Simultaneous Tracking of Pseudomonas aeruginosa Motility in Liquid and at the Solid-Liquid Interface Reveals Differential Roles for the Flagellar Stators

Bacteria sense chemicals, surfaces, and other cells and move toward some and away from others. Studying how single bacterial cells in a population move requires sophisticated tracking and imaging techniques. We have established quantitative methodology for label-free imaging and tracking of individual bacterial cells simultaneously within the bulk liquid and at solid-liquid interfaces by utilizing the imaging modes of digital holographic microscopy (DHM) in three dimensions (3D), differential interference contrast (DIC), and total internal reflectance microscopy (TIRM) in two dimensions (2D) combined with analysis protocols employing bespoke software. To exemplify and validate this methodology, we investigated the swimming behavior of a Pseudomonas aeruginosa wild-type strain and isogenic flagellar stator mutants (motAB and motCD) within the bulk liquid and at the surface at the single-cell and population levels. Multiple motile behaviors were observed that could be differentiated by speed and directionality. Both stator mutants swam slower and were unable to adjust to the near-surface environment as effectively as the wild type, highlighting differential roles for the stators in adapting to near-surface environments. A significant reduction in run speed was observed for the P. aeruginosa mot mutants, which decreased further on entering the near-surface environment. These results are consistent with the mot stators playing key roles in responding to the near-surface environment.IMPORTANCE We have established a methodology to enable the movement of individual bacterial cells to be followed within a 3D space without requiring any labeling. Such an approach is important to observe and understand how bacteria interact with surfaces and form biofilm. We investigated the swimming behavior of Pseudomonas aeruginosa, which has two flagellar stators that drive its swimming motion. Mutants that had only either one of the two stators swam slower and were unable to adjust to the near-surface environment as effectively as the wild type. These results are consistent with the mot stators playing key roles in responding to the near-surface environment and could be used by bacteria to sense via their flagella when they are near a surface.

A multi-mode digital holographic microscope

We present a transmission-mode digital holographic microscope that can switch easily between three different imaging modes: inline, dark field off-axis, and bright field off-axis. Our instrument can be used: to track through time in three dimensions microscopic dielectric objects, such as motile micro-organisms; localize brightly scattering nanoparticles, which cannot be seen under conventional bright field illumination; and recover topographic information and measure the refractive index and dry mass of samples via quantitative phase recovery. Holograms are captured on a digital camera capable of high-speed video recording of up to 2000 frames per second. The inline mode of operation can be easily configurable to a large range of magnifications. We demonstrate the efficacy of the inline mode in tracking motile bacteria in three dimensions in a 160 μm × 160 μm × 100 μm volume at 45× magnification. Through the use of a novel physical mask in a conjugate Fourier plane in the imaging path, we use our microscope for high magnification, dark field off-axis holography, demonstrated by localizing 100 nm gold nanoparticles at 225× magnification up to at least 16 μm from the imaging plane. Finally, the bright field off-axis mode facilitates quantitative phase microscopy, which we employ to measure the refractive index of a standard resolution test target and to measure the dry mass of human erythrocytes.

Bulk-mediated diffusion on a planar surface: full solution

We consider the effective surface motion of a particle that intermittently unbinds from a planar surface and performs bulk excursions. Based on a random-walk approach, we derive the diffusion equations for surface and bulk diffusion including the surface-bulk coupling. From these exact dynamic equations, we analytically obtain the propagator of the effective surface motion. This approach allows us to deduce a superdiffusive, Cauchy-type behavior on the surface, together with exact cutoffs limiting the Cauchy form. Moreover, we study the long-time dynamics for the surface motion.

Effective surface motion on a reactive cylinder of particles that perform intermittent bulk diffusion

In many biological and small scale technological applications particles may transiently bind to a cylindrical surface. In between two binding events the particles diffuse in the bulk, thus producing an effective translation on the cylindrical surface. We here derive the effective motion on the surface allowing for additional diffusion on the cylindrical surface itself. We find explicit solutions for the number of adsorbed particles at one given instant, the effective surface displacement, as well as the surface propagator. In particular sub- and superdiffusive regimes are found, as well as an effective stalling of diffusion visible as a plateau in the mean squared displacement. We also investigate the corresponding first passage problem.

Lévy fluctuations and mixing in dilute suspensions of algae and bacteria

Swimming micro-organisms rely on effective mixing strategies to achieve efficient nutrient influx. Recent experiments, probing the mixing capability of unicellular biflagellates, revealed that passive tracer particles exhibit anomalous non-Gaussian diffusion when immersed in a dilute suspension of self-motile Chlamydomonas reinhardtii algae. Qualitatively, this observation can be explained by the fact that the algae induce a fluid flow that may occasionally accelerate the colloidal tracers to relatively large velocities. A satisfactory quantitative theory of enhanced mixing in dilute active suspensions, however, is lacking at present. In particular, it is unclear how non-Gaussian signatures in the tracers' position distribution are linked to the self-propulsion mechanism of a micro-organism. Here, we develop a systematic theoretical description of anomalous tracer diffusion in active suspensions, based on a simplified tracer-swimmer interaction model that captures the typical distance scaling of a microswimmer's flow field. We show that the experimentally observed non-Gaussian tails are generic and arise owing to a combination of truncated Lévy statistics for the velocity field and algebraically decaying time correlations in the fluid. Our analytical considerations are illustrated through extensive simulations, implemented on graphics processing units to achieve the large sample sizes required for analysing the tails of the tracer distributions.

How subdiffusion changes the kinetics of binding to a surface

Under molecular crowding conditions, biopolymers have been reported to subdiffuse, (r(2)(t)) approximately = t(alpha), with 0 <alpha < 1. Here we study the exchange dynamics of such a subdiffusing particle with a reactive boundary using a continuous time random walk approach. We derive the generalized boundary condition and consider the unbinding from the boundary. An ensuing weak ergodicity breaking has profound consequences for material exchange between the boundary and bulk. We discuss the effects in biological contexts such as gene regulation or membrane-bulk exchange processes. We also suggest various methods to experimentally probe the subdiffusive behavior.

Noisy swimming at low Reynolds numbers

Small organisms (e.g., bacteria) and artificial microswimmers move due to a combination of active swimming and passive Brownian motion. Considering a simplified linear three-sphere swimmer, we study how the swimmer size regulates the interplay between self-driven and diffusive behavior at low Reynolds number. Starting from the Kirkwood-Smoluchowski equation and its corresponding Langevin equation, we derive formulas for the orientation correlation time, the mean velocity and the mean-square displacement in three space dimensions. The validity of the analytical results is illustrated through numerical simulations. Tuning the swimmer parameters to values that are typical of bacteria, we find three characteristic regimes: (i) Brownian motion at small times, (ii) quasiballistic behavior at intermediate time scales, and (iii) quasidiffusive behavior at large times due to noise-induced rotation. Our analytical results can be useful for a better quantitative understanding of optimal foraging strategies in bacterial systems, and they can help to construct more efficient artificial microswimmers in fluctuating fluids.

Bulk-mediated surface diffusion along a cylinder: Propagators and crossovers

We consider the effective motion along a cylinder of a particle that freely diffuses in the bulk and intermittently binds to the cylinder. From an exact approach we derive the different regimes of the effective motion along the cylinder characterized by physical rates for binding/unbinding and the bulk diffusivity. We obtain a transient regime of superdiffusion and, interestingly, a saturation regime characteristic for the cylindrical geometry. This saturation in a finite system is not terminal but eventually turns over to normal diffusion along the cylinder. The first passage behavior of particles to the cylinder surface is derived. Consequences for actual systems are discussed.

Subdiffusion and weak ergodicity breaking in the presence of a reactive boundary

We derive the boundary condition for a subdiffusive particle interacting with a reactive boundary with a finite reaction rate. Molecular crowding conditions, that are found to cause subdiffusion of larger molecules in biological cells, are shown to effect long-tailed distributions with an identical exponent for both the unbinding times from the boundary to the bulk and the rebinding times from the bulk. This causes a weak ergodicity breaking: typically, an individual particle either stays bound or remains in the bulk for very long times. We discuss why this may be beneficial for in vivo gene regulation by DNA-binding proteins, whose typical concentrations are nanomolar.