Effective interactions and dynamics of small passive particles in an active bacterial medium

Probing the out-of-equilibrium dynamics of driven colloids by X-ray photon correlation spectroscopy

The high brilliance of fourth-generation synchrotron sources coupled with advanced X-ray detectors enables a wide range of dynamic studies of colloids and other soft-matter systems. In particular, the higher fraction of coherent flux provided by these new sources is a major boost for X-ray photon correlation spectroscopy (XPCS). As a result, not only can equilibrium dynamics be accessed but also relatively fast out-of-equilibrium processes can be investigated by XPCS. This article briefly recalls the statistical properties of coherent scattering and then demonstrates a case study of non-equilibrium fluctuations in a driven colloidal system. A simple example is the resuspension of colloids by vigorous shaking, where the inhomogeneous flow generates local variations in number density of particles leading to strong velocity fluctuations. The Brownian motion of the particles homogenizes the suspension with time and the system gradually returns to pure diffusive dynamics. On the other hand, in a uniformly sheared suspension of particles, such concentration gradients do not form and upon cessation of shear the return to Brownian dynamics is rapid. These transient non-equilibrium effects can inadvertently influence micrometre-range particle size measurement by means of dynamic scattering methods.

Lipid vesicle pools studied by passive X-ray microrheology

Vesicle pools can form by attractive interaction in a solution, mediated by proteins or divalent ions such as calcium. The pools, which are alternatively also denoted as vesicle clusters, form by liquid-liquid phase separation (LLPS) from an initially homogeneous solution. Due to the short range liquid-like order of vesicles in the pool or cluster, the vesicle-rich phase can also be regarded as a condensate, and one would like to better understand not only the structure of these systems, but also their dynamics. The diffusion of vesicles, in particular, is expected to change when vesicles are arrested in a pool. Here we investigate whether passive microrheology based on X-ray photon correlation spectroscopy (XPCS) is a suitable tool to study model systems of artificial lipid vesicles exhibiting LLPS, and more generally also other heterogeneous biomolecular fluids. We show that by adding highly scattering tracer particles to the solution, valuable information on the single vesicle as well as collective dynamics can be inferred. While the correlation functions reveal freely diffusing tracer particles in solutions at low CaCl[Formula: see text] concentrations, the relaxation rate [Formula: see text] shows a nonlinear dependence on [Formula: see text] at a higher concentration of around 8 mM CaCl[Formula: see text], characterised by two linear regimes with a broad cross-over. We explain this finding based on arrested diffusion in percolating vesicle clusters.

Noncentral forces mediated between two inclusions in a bath of active Brownian rods

Using Brownian Dynamics simulations, we study effective interactions mediated between two identical and impermeable disks (inclusions) immersed in a bath of identical, active (self-propelled), Brownian rods in two spatial dimensions, by assuming that the self-propulsion axis of the rods may generally deviate from their longitudinal axis. When the self-propulsion is transverse (perpendicular to the rod axis), the accumulation of active rods around the inclusions is significantly enhanced, causing a more expansive steric layering (ring formation) of the rods around the inclusions, as compared with the reference case of longitudinally self-propelling rods. As a result, the transversally self-propelling rods also mediate a significantly longer ranged effective interaction between the inclusions. The bath-mediated interaction arises due to the overlaps between the active-rod rings formed around the inclusions, as they are brought into small separations. When the self-propulsion axis is tilted relative to the rod axis, we find an asymmetric imbalance of active-rod accumulation around the inclusion dimer. This leads to a noncentral interaction, featuring an anti-parallel pair of transverse force components and, hence, a bath-mediated torque on the dimer.

Mode-coupling theory for tagged-particle motion of active Brownian particles

We derive a mode-coupling theory (MCT) to describe the dynamics of a tracer particle that is embedded in a dense system of active Brownian particles (ABPs) in two spatial dimensions. The ABP undergo translational and rotational Brownian motion and are equipped with a fixed self-propulsion speed along their orientational vector that describes their active motility. The resulting equations of motion for the tagged-particle density-correlation functions describe the various cases of tracer dynamics close to the glass transition: that of a single active particle in a glass-forming passive host suspensions, that of a passive colloidal particle in a suspension of ABP, and that of active tracers in a bath of active particles. Numerical results are presented for these cases assuming hard-sphere interactions among the particles. The qualitative and quantitative accuracy of the theory is tested against event-driven Brownian dynamics (ED-BD) simulations of active and passive hard disks. Simulation and theory are found in quantitative agreement, provided one adjusts the overall density (as known from the passive description of glassy dynamics), and allows for a rescaling of self-propulsion velocities in the active host system. These adjustments account for the fact that ABP-MCT generally overestimates the tendency for kinetic arrest. We confirm in the simulations a peculiar feature of the transient and stationary dynamical density-correlation functions regarding their lack of symmetry under time reversal, demonstrating the nonequilibrium nature of the system and how it manifests itself in the theory.

Dynamic and mechanical evolution of an oil-water interface during bacterial biofilm formation

We present an experimental study combining particle tracking, active microrheology, and differential dynamic microscopy (DDM) to investigate the dynamics and rheology of an oil-water interface during biofilm formation by the bacteria Pseudomonas Aeruginosa PA14. The interface transitions from an active fluid dominated by the swimming motion of adsorbed bacteria at early age to an active viscoelastic system at late ages when the biofilm is established. The microrheology measurements using microscale magnetic rods indicate that the biofilm behaves as a viscoelastic solid at late age. The bacteria motility at the interface during the biofilm formation, which is characterized in the DDM measurements, evolves from diffusive motion at early age to constrained, quasi-localized motion at later age. Similarly, the mobility of passively moving colloidal spheres at the interface decreases significantly with increasing interface age and shows a dependence on sphere size after biofilm formation that is orders-of-magnitude larger than that expected in a homogeneous system in equilibrium. We attribute this anomalous size dependence to either length-scale-dependent rheology of the biofilm or widely differing effects of the bacteria activity on the motion of spheres of different sizes.

Evolution of the analytical scattering model of live Escherichia coli

A previously reported multi-scale model for (ultra-)small-angle X-ray (USAXS/SAXS) and (very) small-angle neutron scattering (VSANS/SANS) of live Escherichia coli was revised on the basis of compositional/metabolomic and ultrastructural constraints. The cellular body is modeled, as previously described, by an ellipsoid with multiple shells. However, scattering originating from flagella was replaced by a term accounting for the oligosaccharide cores of the lipopolysaccharide leaflet of the outer membrane including its cross-term with the cellular body. This was mainly motivated by (U)SAXS experiments showing indistinguishable scattering for bacteria in the presence and absence of flagella or fimbrae. The revised model succeeded in fitting USAXS/SAXS and differently contrasted VSANS/SANS data of E. coli ATCC 25922 over four orders of magnitude in length scale. Specifically, this approach provides detailed insight into structural features of the cellular envelope, including the distance of the inner and outer membranes, as well as the scattering length densities of all bacterial compartments. The model was also successfully applied to E. coli K12, used for the authors' original modeling, as well as for two other E. coli strains. Significant differences were detected between the different strains in terms of bacterial size, intermembrane distance and its positional fluctuations. These findings corroborate the general applicability of the approach outlined here to quantitatively study the effect of bactericidal compounds on ultrastructural features of Gram-negative bacteria without the need to resort to any invasive staining or labeling agents.

Confinement-induced alternating interactions between inclusions in an active fluid

In a system of colloidal inclusions suspended in an equilibrium bath of smaller particles, the particulate bath engenders effective, short-ranged, primarily attractive interactions between the inclusions, known as depletion interactions, that originate from the steric depletion of bath particles from the immediate vicinity of the inclusions. In a bath of active (self-propelled) particles, the nature of such bath-mediated interactions can qualitatively change from attraction to repulsion, and they become stronger in magnitude and range of action as compared with typical equilibrium depletion interactions, especially as the bath activity (particle self-propulsion) is increased. We study effective interactions mediated by a bath of active Brownian particles between two fixed, impenetrable, and disk-shaped inclusions in a planar (channel) confinement in two dimensions. Confinement is found to strongly influence the effective interaction between the inclusions, specifically by producing alternating interaction profiles with possible attractive and repulsive regions in sufficiently narrow channels. We study the dependence of the ensuing interactions on different system parameters and the orientational (parallel versus perpendicular) configuration of the inclusion pair relative to the channel walls. The confinement effects are largely regulated by the layering of active particles next to the surface boundaries, both of the inclusions and the channel walls that counteract one another in accumulating the active particles in their own proximities. In narrow channels, the combined effects due to the channel walls and the inclusions lead to peculiar structuring of active particles (reminiscent of wavelike interference patterns) within the channel.

Effective interactions mediated between two permeable disks in an active fluid

We study steady-state properties of a bath of active Brownian particles (ABPs) in two dimensions in the presence of two fixed, permeable (hollow) disklike inclusions, whose interior and exterior regions can exhibit mismatching motility (self-propulsion) strengths for the ABPs. We show that such a discontinuous motility field strongly affects spatial distribution of ABPs and thus also the effective interaction mediated between the inclusions through the active bath. Such net interactions arise from soft interfacial repulsions between ABPs that sterically interact with and/or pass through permeable membranes assumed to enclose the inclusions. Both regimes of repulsion and attractive (albeit with different mechanisms) are reported and summarized in overall phase diagrams.

Clusterization of self-propelled particles in a two-component system

We consider a mixture of active solute molecules in a suspension of passive solvent particles comprising a thermal bath. The solute molecules are considered to be extended objects with two chemically distinct heads, one head of which having chemical affinity towards the solvent particles. The coupled Langevin equations for the solvent particles along with the equations governing the dynamics of active molecules are numerically simulated to show how the active molecules self-assemble to form clusters which remain in dynamic equilibrium with the free solute molecules. We observe an interesting crossover at an intermediate time in the variation of the order parameter with time when the temperature of the bath is changed signifying the differential behavior of clusterization below and above the crossover time associated with a transition between a thermodynamic and a quasithermodynamic regime. Enthalpy-entropy compensation in the formation of clusters below the crossover is demonstrated.

Particle-resolved lattice Boltzmann simulations of 3-dimensional active turbulence

Collective behaviour in suspensions of microswimmers is often dominated by the impact of long-ranged hydrodynamic interactions. These phenomena include active turbulence, where suspensions of pusher bacteria at sufficient densities exhibit large-scale, chaotic flows. To study this collective phenomenon, we use large-scale (up to N = 3 × 106) particle-resolved lattice Boltzmann simulations of model microswimmers described by extended stresslets. Such system sizes enable us to obtain quantitative information about both the transition to active turbulence and characteristic features of the turbulent state itself. In the dilute limit, we test analytical predictions for a number of static and dynamic properties against our simulation results. For higher swimmer densities, where swimmer-swimmer interactions become significant, we numerically show that the length- and timescales of the turbulent flows increase steeply near the predicted finite-system transition density.