Vincent Arnaud Martinez

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.

Differential Dynamic Microscopy for Anisotropic Colloidal Dynamics

Differential dynamic microscopy (DDM) is a low-cost, high-throughput technique recently developed for characterizing the isotropic diffusion of spherical colloids using white-light optical microscopy. (1) We develop the theory for applying DDM to probe the dynamics of anisotropic colloidal samples such as various ordered phases, or particles interacting with an external field. The q-dependent dynamics can be measured in any direction in the image plane. We demonstrate the method on a dilute aqueous dispersion of anisotropic magnetic particles (hematite) aligned in a magnetic field. The measured diffusion coefficients parallel and perpendicular to the field direction are in good agreement with theoretical values. We show how these measurements allow us to extract the orientational order parameter S(2) of the system.

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.

Arrest of Flow and Emergence of Activated Processes at the Glass Transition of a Suspension of Particles with Hard Spherelike Interactions

By combining aspects of the coherent and self-intermediate scattering functions, we show that the arrest of particle number density fluctuations spreads from the position of the main structure factor peak. We propose that this arrest impairs the systems ability to respond to diffusing momentum currents, leading to an enhanced resistance to flow. From the stretching of the coherent intermediate scattering functions in the glass, we read a manifestation of the undissipated thermal energy-the source of the ergodicity restoring processes that short-circuit the sharp transition to a perfect glass.

Scattering efficiency of aggregated clusters of spheres: dependence on configuration and composition.

We study the orientation average scattering cross section of various isolated aggregates of identical spherical particles as functions of their size, optical properties, and spatial configurations. Two kinds of aggregates are studied: latex particles in water and rutile titanium dioxide pigments in a polymeric resin, with size parameters varying from 0.6 to 2.3. Calculations are performed by using a recursive centered T-matrix algorithm solution of the multiple scattering equation that we previously developed [J. Quant. Spectrosc. Radiat. Transfer 79-80, 533 (2003)]. We show that for a specific size of the constituent spheres, their respective couplings apparently vanish, regardless of the aggregate configuration, and that the scattering cross section of the entire cluster behaves as if its constituents were isolated. We found that the particular radius for which this phenomenon occurs is a function of the relative refractive index of the system. We also study the correlations between the strength of the coupling among the constituent spheres, and the pseudofractal dimension of the aggregate as it varies from 1 to 30.

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.

Absorption and scattering properties of dense ensembles of nonspherical particles

The purpose of this work is to show that an appropriate multiple T-matrix formalism can be useful in performing qualitative studies of the optical properties of colloidal systems composed of nonspherical objects (despite limitations concerning nonspherical particle packing densities). In this work we have calculated the configuration averages of scattering and absorption cross sections of different clusters of dielectric particles. These clusters are characterized by their refraction index, particle shape, and filling fraction. Computations were performed with the recursive centered T-matrix algorithm (RCTMA), a previously established method for solving the multiple scattering equation of light from finite clusters of isotropic dielectric objects. Comparison of the average optical cross sections between the different systems highlights variations in the scattering and absorption properties due to the electromagnetic interactions, and we demonstrate that the magnitudes of these quantities are clearly modulated by the shape of the primary particles.

Dynamics of hard sphere suspensions using dynamic light scattering and X-ray photon correlation spectroscopy: Dynamics and scaling of the intermediate scattering function

Intermediate scattering functions are measured for colloidal hard sphere systems using both dynamic light scattering and x-ray photon correlation spectroscopy. We compare the techniques, and discuss the advantages and disadvantages of each. Both techniques agree in the overlapping range of scattering vectors. We investigate the scaling behavior found by Segré and Pusey [Phys. Rev. Lett. 77, 771 (1996)] but challenged by Lurio et al. [Phys. Rev. Lett. 84, 785 (2000)]. We observe a scaling behavior over several decades in time but not in the long-time regime. Moreover, we do not observe long-time diffusive regimes at scattering vectors away from the peak of the structure factor and so question the existence of long-time diffusion coefficients at these scattering vectors.

Painting with light-powered bacteria

External control of the swimming speed of ‘active particles’ can be used to self assemble designer structures in situ on the μm to mm scale. We demonstrate such reconfigurable templated active self assembly in a fluid environment using light powered strains of Escherichia coli. The physics and biology controlling the sharpness and formation speed of patterns is investigated using a bespoke fast-responding strain. Microand nano-fabrication can revolutionise many areas of technology, including personalised medicine. There are two conceptually distinct ways to construct structures on the 10 nm to 10 μm scale: lithography, which uses ‘scalpels’ such as chemical etching or electron beams, or self assembly[1], in which microscopic ‘Lego components’ move themselves into position. Both equilibrium phase transitions (e.g. crystallization) and nonequilibrium processes are exploited for self assembly. In either case, external templates can be used to direct the process, with reconfigurable templates offering programmability. Self assembly was originally inspired by chemistry and biology, where the components are individual molecules. Increasingly, colloidal building blocks are used, with bespoke particle shape, size and interaction, e.g. ‘patchy particles’ with heterogeneous surface chemistry[2]. Active, or self-propelled, colloids open up further opportunities. We show how to assemble structures on the μm to mm scale that are reconfigurable in real time using Escherichia coli bacteria – ‘living active colloids’ – that swim only when illuminated[3]. The process is directed by a smart, or programmable, external template applied by a spatial light modulator. Active colloids, or self-propelled micro-swimmers, are attracting significant recent attention[4] as ‘active matter’[5, 6]. They violate time-reversal symmetry[7], and may be used, e.g., to transport colloidal ‘cargos’[8]. For both fundamental physics and applications, external control of swimming, e.g. using particles with lightactivated self-propulsion[9, 10, 11, 12], opens up many new possibilities. Thus, e.g., light-activated motile bacteria can be used to actuate and control micro-machinery [13]. ∗Electronic address: j.arlt@ed.ac.uk; Corresponding author 1 ar X iv :1 71 0. 08 18 8v 1 [ co nd -m at .s of t] 2 3 O ct 2 01 7 The self assembly of micro-swimmers into clusters of tens of particles has already been demonstrated[14, 15, 12]. Recent simulations[16] suggest that the patterned illumination of light-activated swimmers can be used for the templated self assembly[1] of designer structures comprising 10-10 particles. Real-time reconfiguration of the light field then allows smart templated active self assembly (STASA), which we here implement for the first time using light-controlled motile bacteria. E. coli bacteria[17] (cell body ≈ 2 μm×1 μm) swim by turning ≈ 7-10 μm long helical flagella using membraneembedded rotary motors powered by a protonmotive force (PMF) that arises from active pumping of H to the extracellular medium[18]. Unlike all synthetic active colloids to date and most bacteria, E. coli can generate PMF in nutrient-free motility buffer[19] by utilising internal resources and oxygen (O2) to produce energetic electron pairs. These release their energy stepwise along an electrochemical potential ladder of respiratory enzymes located in the inner cell membrane, generating a PMF of ≈ −150 mV. The electron pair ultimately passes to and reduces O2 to water. Thus, with no O2, PMF = 0 and swimming ceases[17]. If cells under anaerobic conditions can express proteorhodopsin (PR)[3], a green-photon-driven proton pump[20], then they will swim only when suitably illuminated: these are living analogues of synthetic light-activated colloidal swimmers.[9, 10, 11, 12] We show below that the speed with which such cells respond to changes in illumination is crucial for successful bacterial STASA. For this work, we constructed a PR-bearing mutant (AD10) that stops much faster when illumination ceases than previously-reported[3, 21], by deleting the unc gene cluster[22] encoding the F1FoATPase membrane protein complex (see SI §1.1), so that these enzymes cannot act in reverse in darkness to continue to export protons and sustain a PMF[23]. We suspended cells in phosphate motility buffer at optical density OD . 8 (cell-body volume fraction ≈ 1.1%)[17] and sealed 2 μL into 20 μm high flat capillaries, where cells swim in two dimensions but have enough room to ‘overtake’ each other in all three spatial dimensions. Differential dynamic microscopy (DDM)[24] returned an averaged speed v̄ ≈ 30 μm s−1 and β ≈ 20% of non-motile organisms at OD=1 under fully-oxygenated conditions. (Note that ‘non-motile’ = cells that can never swim; ‘stationary’ = non-swimming cells capable of motility when illuminated.) Motile cells were allowed to swim until O2 was depleted and v̄ dropped abruptly to zero after a few minutes[17] (see SI §1.2 and Fig. S1(a)). After these cells were left in the dark for ≈ 10 min, green illumination was turned on (510 – 560 nm, intensity I ≈ 5 mW cm−2 at the sample). The stationary cells accelerated uniformly before saturating, Fig. 1. Fitting the data to v̄(t) = v̄satt/(t+τon) gives v̄sat = 9.5 μm s−1, τon = 30 s. When illumination ceased, v̄ dropped within τoff . 1 s, but never quite to zero – it is unclear why a few cells (< 1%) continued to swim. v̄sat increased with I, Fig. 1 (inset), up to . 27 μm s−1. {v̄, β, vsat, τon} changed over hours as cells aged. The discharging of the PMF through the membrane (capacitance C & 10−14 F) and rotary motors (total resistance R . 10 Ω) upon cessation of illumination should take RC ∼ 1 s (see SI §1.3 for details), which explains the observed τoff . Consistent with this interpretation, τoff is approximately independent of the starting speed of decelerating cells (see SI §1.2 and Fig. S2(a)). The observed τon ≈ 30 s is likely controlled by the rate constant[25] for stator units to come on and off motors, kstator ≈ 0.04 s−1 ∼ τ−1 on . In sustained darkness, motors disassemble in PR-bearing E. coli, and full ‘motor resurrection’ upon illumination takes[21] ∼ 200 s, in agreementSelf-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.