Escherichia coli as a model active colloid: A practical introduction

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.

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 microrobots.

Probing the Spatiotemporal Dynamics of Catalytic Janus Particles with Single-Particle Tracking and Differential Dynamic Microscopy

We demonstrate differential dynamic microscopy and particle tracking for the characterization of the spatiotemporal behavior of active Janus colloids in terms of the intermediate scattering function (ISF). We provide an analytical solution for the ISF of the paradigmatic active Brownian particle model and find striking agreement with experimental results from the smallest length scales, where translational diffusion and self-propulsion dominate, up to the largest ones, which probe effective diffusion due to rotational Brownian motion. At intermediate length scales, characteristic oscillations resolve the crossover between directed motion to orientational relaxation and allow us to discriminate active Brownian motion from other reorientation processes, e.g., run-and-tumble motion. A direct comparison to theoretical predictions reliably yields the rotational and translational diffusion coefficients of the particles, the mean and width of their speed distribution, and the temporal evolution of these parameters.

Dynamic density shaping of photokinetic E. coli

Many motile microorganisms react to environmental light cues with a variety of motility responses guiding cells towards better conditions for survival and growth. The use of spatial light modulators could help to elucidate the mechanisms of photo-movements while, at the same time, providing an efficient strategy to achieve spatial and temporal control of cell concentration. Here we demonstrate that millions of bacteria, genetically modified to swim smoothly with a light controllable speed, can be arranged into complex and reconfigurable density patterns using a digital light projector. We show that a homogeneous sea of freely swimming bacteria can be made to morph between complex shapes. We model non-local effects arising from memory in light response and show how these can be mitigated by a feedback control strategy resulting in the detailed reproduction of grayscale density images.

Many bacteria can move in response to environmental signals. This helps guide them towards better conditions for growth and survival. Escherichia coli is a bacterium that can swim quickly through liquid, using tiny propeller-like structures that rotate many times per second. These ‘propellers’ are powered by a cellular motor, called the flagellar motor, which similar to an electric motor, requires an energy source to drive movement.

Proteorhodopsin, a protein originally isolated from free-swimming micro-organisms in the ocean, is an alternative energy source that helps bacteria move. The protein is located close to the surface of the cell, where it acts like a solar panel and captures energy from light. In cells powered by proteorhodopsin, the intensity of light from their environment determines their swimming speed: brighter light means faster movement, and less light, slower movement. Proteorhodopsin is now also a useful tool in the laboratory. For example, genetically engineering bacteria to produce proteorhodopsin provides a way to control their movement remotely, using a light source.

Swimming bacteria, much like cars in city traffic, are known to accumulate in areas where their speed decreases. By controlling swimming speed with proteorhodopsin, researchers can manipulate the local density of bacteria simply by projecting different patterns of light.

To study the factors influencing this phenomenon, Frangipane et al. used genetically modified E. coli that could respond to light via proteorhodopsin to make layers of cells that could then have light patterns projected onto them. The results showed that the bacteria responded slowly to these stimuli, which was the main factor limiting the resolution of the final pattern they formed. A simple feedback mechanism, which compared the pattern formed by the cells to the desired image and updated the projected light accordingly, was enough to solve this problem. This way, the layers of E.coli could be turned into a near-perfect copy of the original image.

This work allows us to control the movement of large populations of bacteria more precisely than ever before. This could be extremely valuable for building the next generation of microscopic devices. For example, bacteria could be made to surround a larger object such as a machine part or a drug carrier, and then used as living propellers to transport it where it is needed.

Motile bacteria in a critical fluid mixture

We studied the swimming of Escherichia coli bacteria in the vicinity of the critical point in a solution of the nonionic surfactant C_{12}E_{5} in buffer solution. In phase-contrast microscopy, each swimming cell produces a transient trail behind itself lasting several seconds. Comparing quantitative image analysis with simulations show that these trails are due to local phase reorganization triggered by differential adsorption. This contrasts with similar trails seen in bacteria swimming in liquid crystals, which are due to shear effects. We show how our trails are controlled, and use them to probe the structure and dynamics of critical fluctuations in the fluid medium.

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

This article presents an investigation of the interparticle interactions and dynamics of submicron silica colloids suspended in a bath of motile Escherichia coli bacteria. The colloidal microstructure and dynamics were probed by ultra-small-angle x-ray scattering and multi-speckles x-ray photon correlation spectroscopy, respectively. Both static and hydrodynamic interactions were obtained for different colloid volume fractions and bacteria concentrations as well as when the interparticle interaction potential was modified by the motility buffer. Results suggest that motile bacteria reduce the effective attractive interactions between passive colloids and enhance their dynamics at high colloid volume fractions. The enhanced dynamics under different static interparticle interactions can be rationalized in terms of an effective viscosity of the medium and unified by means of an empirical effective temperature of the system. While the influence of swimming bacteria on the colloid dynamics is significantly lower for small particles, the role of motility buffer on the static and dynamic interactions becomes more pronounced.

Phoretic interactions and oscillations in active suspensions of growing Escherichia coli

Bioluminescence imaging experiments were carried out to characterize spatio-temporal patterns of bacterial self-organization in active suspensions (cultures) of bioluminescent Escherichia coli and its mutants. An analysis of the effects of mutations shows that spatio-temporal patterns formed in standard microtitre plates are not related to the chemotaxis system of bacteria. In fact, these patterns are strongly dependent on the properties of mutants that characterize them as self-phoretic (non-flagellar) swimmers. In particular, the observed patterns are essentially dependent on the efficiency of proton translocation across membranes and the smoothness of the cell surface. These characteristics can be associated, respectively, with the surface activity and the phoretic mobility of a colloidal swimmer. An analysis of the experimental data together with mathematical modelling of pattern formation suggests the following: (1) pattern-forming processes can be described by Keller-Segel-type models of chemotaxis with logistic cell kinetics; (2) active cells can be seen as biochemical oscillators that exhibit phoretic drift and alignment; and (3) the spatio-temporal patterns in a suspension of growing E. coli form due to phoretic interactions between oscillating cells of high metabolic activity.

Bacteria as living patchy colloids: Phenotypic heterogeneity in surface adhesion

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.

Painting with light-powered bacteria

Self-assembly is a promising route for micro- and nano-fabrication with potential to revolutionise many areas of technology, including personalised medicine. Here we demonstrate that external control of the swimming speed of microswimmers can be used to self assemble reconfigurable designer structures in situ. We implement such ‘smart templated active self assembly’ in a fluid environment by using spatially patterned light fields to control photon-powered strains of motile Escherichia coli bacteria. The physics and biology governing the sharpness and formation speed of patterns is investigated using a bespoke strain designed to respond quickly to changes in light intensity. Our protocol provides a distinct paradigm for self-assembly of structures on the 10 μm to mm scale.

The ability to generate microscale patterns and control microswimmers may be useful for engineering smart materials. Here Arlt et al. use genetically modified bacteria with fast response to changes in light intensity to produce light-induced patterns.

Wall accumulation of bacteria with different motility patterns

We systematically investigate the role of different swimming patterns on the concentration distribution of bacterial suspensions confined between two flat walls, by considering wild-type motility Escherichia coli and Pseudomonas aeruginosa, which perform Run and Tumble and Run and Reverse patterns, respectively. The experiments count motile bacteria at different distances from the bottom wall. In agreement with previous studies, an accumulation of motile bacteria close to the walls is observed. Different wall separations, ranging from 100 to 250μm, are tested. The concentration profiles result to be independent on the motility pattern and on the walls' separation. These results are confirmed by numerical simulations, based on a collection of self-propelled dumbbells-like particles interacting only through steric interactions. The good agreement with the simulations suggests that the behavior of the investigated bacterial suspensions is determined mainly by steric collisions and self-propulsion, as well as hydrodynamic interactions.

Van't Hoff's law for active suspensions: the role of the solvent chemical potential

We extend Van't Hoff's law for the osmotic pressure to a suspension of active Brownian particles. The propelled particles exert a net reaction force on the solvent, and thereby either drive a measurable solvent flow from the connecting solvent reservoir through the semipermeable membrane, or increase the osmotic pressure and cause the suspension to rise to heights as large as micrometers for experimentally realized microswimmers described in the literature. The increase in osmotic pressure is caused by the background solvent being, in contrast to passive suspensions, no longer at the chemical potential of the solvent reservoir. The difference in solvent chemical potentials depends on the colloid-membrane interaction potential, which implies that the osmotic pressure is a state function of a state that itself is influenced by the membrane potential.

Osmotaxis in Escherichia coli through changes in motor speed

Bacterial motility, and in particular repulsion or attraction toward specific chemicals, has been a subject of investigation for over 100 years, resulting in detailed understanding of bacterial chemotaxis and the corresponding sensory network in many bacterial species. For Escherichia coli most of the current understanding comes from the experiments with low levels of chemotactically active ligands. However, chemotactically inactive chemical species at concentrations found in the human gastrointestinal tract produce significant changes in E. coli's osmotic pressure and have been shown to lead to taxis. To understand how these nonspecific physical signals influence motility, we look at the response of individual bacterial flagellar motors under stepwise changes in external osmolarity. We combine these measurements with a population swimming assay under the same conditions. Unlike for chemotactic response, a long-term increase in swimming/motor speeds is observed, and in the motor rotational bias, both of which scale with the osmotic shock magnitude. We discuss how the speed changes we observe can lead to steady-state bacterial accumulation.

Light controlled 3D micromotors powered by bacteria

Self-propelled bacteria can be integrated into synthetic micromachines and act as biological propellers. So far, proposed designs suffer from low reproducibility, large noise levels or lack of tunability. Here we demonstrate that fast, reliable and tunable bio-hybrid micromotors can be obtained by the self-assembly of synthetic structures with genetically engineered biological propellers. The synthetic components consist of 3D interconnected structures having a rotating unit that can capture individual bacteria into an array of microchambers so that cells contribute maximally to the applied torque. Bacterial cells are smooth swimmers expressing a light-driven proton pump that allows to optically control their swimming speed. Using a spatial light modulator, we can address individual motors with tunable light intensities allowing the dynamic control of their rotational speeds. Applying a real-time feedback control loop, we can also command a set of micromotors to rotate in unison with a prescribed angular speed.

Dynamic stabilization of Janus sphere trans-dimers

We experimentally investigated the self-assembly of chemically active colloidal Janus spheres into dimers. The trans-dimer conformation, in which the two active sites are oriented roughly in opposite directions and the particles are osculated at their equators, becomes dominant as the hydrogen peroxide fuel concentration increases. Our observations suggest high spinning frequency combined with little translational motion is at least partially responsible for the stabilization of the trans-dimer as activity increases.

Dynamics of ellipsoidal tracers in swimming algal suspensions

Enhanced diffusion of passive tracers immersed in active fluids is a universal feature of active fluids and has been extensively studied in recent years. Similar to microrheology for equilibrium complex fluids, the unusual enhanced particle dynamics reveal intrinsic properties of active fluids. Nevertheless, previous studies have shown that the translational dynamics of spherical tracers are qualitatively similar, independent of whether active particles are pushers or pullers-the two fundamental classes of active fluids. Is it possible to distinguish pushers from pullers by simply imaging the dynamics of passive tracers? Here, we investigated the diffusion of isolated ellipsoids in algal C. reinhardtii suspensions-a model for puller-type active fluids. In combination with our previous results on pusher-type E. coli suspensions [Peng et al., Phys. Rev. Lett. 116, 068303 (2016)PRLTAO0031-900710.1103/PhysRevLett.116.068303], we showed that the dynamics of asymmetric tracers show a profound difference in pushers and pullers due to their rotational degree of freedom. Although the laboratory-frame translation and rotation of ellipsoids are enhanced in both pushers and pullers, similar to spherical tracers, the anisotropic diffusion in the body frame of ellipsoids shows opposite trends in the two classes of active fluids. An ellipsoid diffuses fastest along its major axis when immersed in pullers, whereas it diffuses slowest along the major axis in pushers. This striking difference can be qualitatively explained using a simple hydrodynamic model. In addition, our study on algal suspensions reveals that the influence of the near-field advection of algal swimming flows on the translation and rotation of ellipsoids shows different ranges and strengths. Our work provides not only new insights into universal organizing principles of active fluids, but also a convenient tool for detecting the class of active particles.

Tracking E. coli runs and tumbles with scattering solutions and digital holographic microscopy

We use in-line digital holographic microscopy to image freely swimming E. coli. We show that fitting a light scattering model to E. coli holograms can yield quantitative information about the bacterium's body rotation and tumbles, offering a precise way to track fine details of bacterial motility. We are able to extract the cell's three-dimensional (3D) position and orientation and recover behavior such as body angle rotation during runs, tumbles, and pole reversal. Our technique is label-free and capable of frame rates limited only by the camera.

Intermediate scattering function of an anisotropic active Brownian particle

Various challenges are faced when animalcules such as bacteria, protozoa, algae, or sperms move autonomously in aqueous media at low Reynolds number. These active agents are subject to strong stochastic fluctuations, that compete with the directed motion. So far most studies consider the lowest order moments of the displacements only, while more general spatio-temporal information on the stochastic motion is provided in scattering experiments. Here we derive analytically exact expressions for the directly measurable intermediate scattering function for a mesoscopic model of a single, anisotropic active Brownian particle in three dimensions. The mean-square displacement and the non-Gaussian parameter of the stochastic process are obtained as derivatives of the intermediate scattering function. These display different temporal regimes dominated by effective diffusion and directed motion due to the interplay of translational and rotational diffusion which is rationalized within the theory. The most prominent feature of the intermediate scattering function is an oscillatory behavior at intermediate wavenumbers reflecting the persistent swimming motion, whereas at small length scales bare translational and at large length scales an enhanced effective diffusion emerges. We anticipate that our characterization of the motion of active agents will serve as a reference for more realistic models and experimental observations.

Phototaxis of synthetic microswimmers in optical landscapes

Many microorganisms, with phytoplankton and zooplankton as prominent examples, display phototactic behaviour, that is, the ability to perform directed motion within a light gradient. Here we experimentally demonstrate that sensing of light gradients can also be achieved in a system of synthetic photo-activated microparticles being exposed to an inhomogeneous laser field. We observe a strong orientational response of the particles because of diffusiophoretic torques, which in combination with an intensity-dependent particle motility eventually leads to phototaxis. Since the aligning torques saturate at high gradients, a strongly rectified particle motion is found even in periodic asymmetric intensity landscapes. Our results are in excellent agreement with numerical simulations of a minimal model and should similarly apply to other particle propulsion mechanisms. Because light fields can be easily adjusted in space and time, this also allows to extend our approach to dynamical environments.

Escherichia coli modulates its motor speed on sensing an attractant

It is well known that Escherichia coli achieves chemotaxis by modulating the bias of the flagellar motor. Recent experiments have shown that the bacteria vary their swimming speeds as well in presence of attractants. However, this increase in the swimming speed in response to the attractants has not been correlated with the increase in the flagellar motor speed. Using flickering dark-field microscopy, we measure the head-rotation speed of a large population of cells to correlate it with the flagellar motor speed. Experiments performed with wild-type and trg-deletion mutant strains suggest that the cells are capable of modulating the flagellar motor speed via mere sensing of a ligand. The motor speed can be further correlated with the swimming speed of the cells and was found to be linear. These results suggest the existence of a hitherto unknown intra-cellular pathway that modulates the flagellar motor speed in response to sensing of chemicals, thereby making chemotaxis more efficient than previously known.