Jana Schwarz-Linek

Phase separation and rotor self-assembly in active particle suspensions.

Adding a nonadsorbing polymer to passive colloids induces an attraction between the particles via the “depletion” mechanism. High enough polymer concentrations lead to phase separation. We combine experiments, theory, and simulations to demonstrate that using active colloids (such as motile bacteria) dramatically changes the physics of such mixtures. First, significantly stronger interparticle attraction is needed to cause phase separation. Secondly, the finite size aggregates formed at lower interparticle attraction show unidirectional rotation. These micro-rotors demonstrate the self-assembly of functional structures using active particles. The angular speed of the rotating clusters scales approximately as the inverse of their size, which may be understood theoretically by assuming that the torques exerted by the outermost bacteria in a cluster add up randomly. Our simulations suggest that both the suppression of phase separation and the self-assembly of rotors are generic features of aggregating swimmers and should therefore occur in a variety of biological and synthetic active particle systems.

Differential Dynamic Microscopy of Bacterial Motility

We demonstrate a method for the fast, high-throughput characterization of the dynamics of active particles. Specifically, we measure the swimming speed distribution and motile cell fraction in Escherichia coli suspensions. By averaging over ∼10(4) cells, our method is highly accurate compared to conventional tracking, yielding a routine tool for motility characterization. We find that the diffusivity of nonmotile cells is enhanced in proportion to the concentration of motile cells.

Flagellated bacterial motility in polymer solutions

Significance The way microorganisms swim in concentrated polymer solutions has important biomedical implications, i.e., how pathogens invade the mucosal lining of mammal guts. Physicists are also fascinated by self-propulsion in such complex non-Newtonian fluids. The current standard model of how bacteria propelled by rotary helical flagella swim through concentrated polymer solutions postulates bacteria-sized pores, allowing them relative easy passage. Our experiments using high-throughput methods overturn this standard model. Instead, we show that the peculiarities of flagellated bacteria locomotion in concentrated polymer solutions are due to the fast-rotating flagellum, giving rise to a lower local viscosity in its vicinity. The bacterial flagellum is therefore a nano-rheometer for probing flows at the molecular level. It is widely believed that the swimming speed, v, of many flagellated bacteria is a nonmonotonic function of the concentration, c, of high-molecular-weight linear polymers in aqueous solution, showing peaked v(c) curves. Pores in the polymer solution were suggested as the explanation. Quantifying this picture led to a theory that predicted peaked v(c) curves. Using high-throughput methods for characterizing motility, we measured v and the angular frequency of cell body rotation, Ω, of motile Escherichia coli as a function of polymer concentration in polyvinylpyrrolidone (PVP) and Ficoll solutions of different molecular weights. We find that nonmonotonic v(c) curves are typically due to low-molecular-weight impurities. After purification by dialysis, the measured v(c) and Ω(c) relations for all but the highest-molecular-weight PVP can be described in detail by Newtonian hydrodynamics. There is clear evidence for non-Newtonian effects in the highest-molecular-weight PVP solution. Calculations suggest that this is due to the fast-rotating flagella seeing a lower viscosity than the cell body, so that flagella can be seen as nano-rheometers for probing the non-Newtonian behavior of high polymer solutions on a molecular scale.

Enhanced diffusion of nonswimmers in a three-dimensional bath of motile bacteria

We show, using differential dynamic microscopy, that the diffusivity of nonmotile cells in a three-dimensional (3D) population of motile E. coli is enhanced by an amount proportional to the active cell flux. While nonmotile mutants without flagella and mutants with paralyzed flagella have quite different thermal diffusivities and therefore hydrodynamic radii, their diffusivities are enhanced to the same extent by swimmers in the regime of cell densities explored here. Integrating the advective motion of nonswimmers caused by swimmers with finite persistence-length trajectories predicts our observations to within 2%, indicating that fluid entrainment is not relevant for diffusion enhancement in 3D.

Swimming in a crystal

We study catalytic Janus particles and Escherichia coli bacteria swimming in a two-dimensional colloidal crystal. The Janus particles orbit individual colloids and hop between colloids stochastically, with a hopping rate that varies inversely with fuel (hydrogen peroxide) concentration. At high fuel concentration, these orbits are stable for 100s of revolutions, and the orbital speed oscillates periodically as a result of hydrodynamic, and possibly also phoretic, interactions between the swimmer and the six neighbouring colloids. Motile E. coli bacteria behave very differently in the same colloidal crystal: their circular orbits on plain glass are rectified into long, straight runs, because the bacteria are unable to turn corners inside the crystal.

Switching of Swimming Modes in Magnetospirillium gryphiswaldense

The microaerophilic magnetotactic bacterium Magnetospirillum gryphiswaldense swims along magnetic field lines using a single flagellum at each cell pole. It is believed that this magnetotactic behavior enables cells to seek optimal oxygen concentration with maximal efficiency. We analyze the trajectories of swimming M. gryphiswaldense cells in external magnetic fields larger than the earths field, and show that each cell can switch very rapidly (in <0.2 s) between a fast and a slow swimming mode. Close to a glass surface, a variety of trajectories were observed, from straight swimming that systematically deviates from field lines to various helices. A model in which fast (slow) swimming is solely due to the rotation of the trailing (leading) flagellum can account for these observations. We determined the magnetic moment of this bacterium using a to our knowledge new method, and obtained a value of (2.0±0.6) × 10(-16) A · m(2). This value is found to be consistent with parameters emerging from quantitative fitting of trajectories to our model.

Polymer-induced phase separation in Escherichia coli suspensions

We studied aggregation and phase separation in suspensions of de-flagellated Escherichia coli (AB1157) in phosphate buffer induced by the anionic polyelectrolyte sodium polystyrene sulfonate. We also performed Monte Carlo simulations of this system based on the Asakura–Oosawa model of colloid–polymer mixtures. The results of these simulations, as well as comparison with previous work on synthetic colloid–polymer mixtures, demonstrate that the role of the polymer is to cause a depletion attraction between the E. coli cells. The implication of these results for understanding the role of (predominantly anionic) extracellular polymeric substances (EPS) secreted by bacteria in various natural phenomena such as biofilm formation is discussed.

Hook length of the bacterial flagellum is controlled to nanometer-scale for optimal motility performance

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal-body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer-scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook-length variants of Salmonella enterica. Measurements of plate-assay motility, single-cell swimming speed and directional persistence in quasi 2D and population-averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild type hook-length. We conclude that too short hooks may be too stiff to function as a junction and too long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant, but robust mechanisms to maximize their fitness under specific environmental constraints.Most bacteria swim in liquid environments by rotating one or several flagella. Each flagellum consists of a long external filament that is connected to a membrane-embedded basal-body by a short, curved structure: the hook. The length of the hook is controlled on a nanometer-scale by a sophisticated molecular ruler mechanism and it functions as a flexible universal joint allowing transmission of motor torque to the filament. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook length variants of Salmonella enterica. Measurements of plate-assay motility, single-cell swimming speed and directional persistence in quasi 2D and population-averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild type hook length. We conclude that too short hooks may be too stiff to function as a junction and too long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook length control mechanism is therefore a prime example of how bacteria evolved elegant, but robust mechanisms to maximize their fitness under specific environmental constraints. Significance statement Many bacteria use flagella for directed movement in liquid environments. The flexible hook connects the membrane-embedded basal-body of the flagellum to the long, external filament. Flagellar function relies on self-assembly processes that define or self-limit the lengths of major parts. The length of the hook is precisely controlled on a nanometer-scale by a molecular ruler mechanism. However, the physiological benefit of tight hook length control remains unclear. Here, we show that the molecular ruler mechanism evolved to control the optimal length of the flagellar hook, which is consistent with efficient motility performance. These results highlight the evolutionary forces that enable flagellated bacteria to optimize their fitness in diverse environments and might have important implications for the design of swimming micro-robots.

Bacteria as living patchy colloids: Phenotypic heterogeneity in surface adhesion

Genetically identical bacteria possess varying numbers of surface-adhering patches. Understanding and controlling the surface adhesion of pathogenic bacteria is of urgent biomedical importance. However, many aspects of this process remain unclear (for example, microscopic details of the initial adhesion and possible variations between individual cells). Using a new high-throughput method, we identify and follow many single cells within a clonal population of Escherichia coli near a glass surface. We find strong phenotypic heterogeneities: A fraction of the cells remain in the free (planktonic) state, whereas others adhere with an adhesion strength that itself exhibits phenotypic heterogeneity. We explain our observations using a patchy colloid model; cells bind with localized, adhesive patches, and the strength of adhesion is determined by the number of patches: Nonadherers have no patches, weak adherers bind with a single patch only, and strong adherers bind via a single or multiple patches. We discuss possible implications of our results for controlling bacterial adhesion in biomedical and other applications.

Hook length of the bacterial flagellum is optimized for maximal stability of the flagellar bundle

Most bacteria swim in liquid environments by rotating one or several flagella. The long external filament of the flagellum is connected to a membrane-embedded basal body by a flexible universal joint, the hook, which allows the transmission of motor torque to the filament. The length of the hook is controlled on a nanometer scale by a sophisticated molecular ruler mechanism. However, why its length is stringently controlled has remained elusive. We engineered and studied a diverse set of hook-length variants of Salmonella enterica. Measurements of plate-assay motility, single-cell swimming speed, and directional persistence in quasi-2D and population-averaged swimming speed and body angular velocity in 3D revealed that the motility performance is optimal around the wild-type hook length. We conclude that too-short hooks may be too stiff to function as a junction and too-long hooks may buckle and create instability in the flagellar bundle. Accordingly, peritrichously flagellated bacteria move most efficiently as the distance travelled per body rotation is maximal and body wobbling is minimized. Thus, our results suggest that the molecular ruler mechanism evolved to control flagellar hook growth to the optimal length consistent with efficient bundle formation. The hook-length control mechanism is therefore a prime example of how bacteria evolved elegant but robust mechanisms to maximize their fitness under specific environmental constraints.