Correction: Sizing multimodal suspensions with differential dynamic microscopy.

Correction for 'Sizing multimodal suspensions with differential dynamic microscopy' by Joe J. Bradley et al., Soft Matter, 2023, 19, 8179-8192, https://doi.org/10.1039/D3SM00593C.

Quantitative characterization of run-and-tumble statistics in bulk bacterial suspensions.

We introduce a numerical method to extract the parameters of run-and-tumble dynamics from experimental measurements of the intermediate scattering function. We show that proceeding in Laplace space is unpractical and employ instead renewal processes to work directly in real time. We first validate our approach against data produced using agent-based simulations. This allows us to identify the length and time scales required for an accurate measurement of the motility parameters, including tumbling frequency and swim speed. We compare different models for the run-and-tumble dynamics by accounting for speed variability at the single-cell and population level, respectively. Finally, we apply our approach to experimental data on wild-type Escherichia coli obtained using differential dynamic microscopy.

Characterization and Control of the Run-and-Tumble Dynamics of Escherichia Coli.

We characterize the full spatiotemporal gait of populations of swimming Escherichia coli using renewal processes to analyze the measurements of intermediate scattering functions. This allows us to demonstrate quantitatively how the persistence length of an engineered strain can be controlled by a chemical inducer and to report a controlled transition from perpetual tumbling to smooth swimming. For wild-type E. coli, we measure simultaneously the microscopic motility parameters and the large-scale effective diffusivity, hence quantitatively bridging for the first time small-scale directed swimming and macroscopic diffusion.

Sizing multimodal suspensions with differential dynamic microscopy.

Differential dynamic microscopy (DDM) can be used to extract the mean particle size from videos of suspensions. However, many suspensions have multimodal particle size distributions, for which a single 'mean' is not a sufficient description. After clarifying how different particle sizes contribute to the signal in DDM, we show that standard DDM analysis can extract the mean sizes of two populations in a bimodal suspension given prior knowledge of the sample's bimodality. Further, the use of the CONTIN algorithm obviates the need for such prior knowledge. Finally, we show that by selectively analysing portions of the DDM images, we can size a trimodal suspension where the large particles would otherwise dominate the signal, again without prior knowledge of the trimodality.

Run-to-Tumble Variability Controls the Surface Residence Times of E. coli Bacteria.

Motile bacteria are known to accumulate at surfaces, eventually leading to changes in bacterial motility and biofilm formation. We use a novel two-color, three-dimensional Lagrangian tracking technique to follow simultaneously the body and the flagella of a wild-type Escherichia coli. We observe long surface residence times and surface escape corresponding mostly to immediately antecedent tumbling. A motility model accounting for a large behavioral variability in run-time duration reproduces all experimental findings and gives new insights into surface trapping efficiency.

In Situ Characterization of the Protein Corona of Nanoparticles In Vitro and In Vivo.

A new theoretical framework that enables the use of differential dynamic microscopy (DDM) in fluorescence imaging mode to quantify in situ protein adsorption onto nanoparticles (NP) while simultaneously monitoring for NP aggregation is proposed. This methodology is used to elucidate the thermodynamic and kinetic properties of the protein corona (PC) in vitro and in vivo. The results show that protein adsorption triggers particle aggregation over a wide concentration range and that the formed aggregate structures can be quantified using the proposed methodology. Protein affinity for polystyrene (PS) NPs is observed to be dependent on particle concentration. For complex protein mixtures, this methodology identifies that the PC composition changes with the dilution of serum proteins, demonstrating a Vroman effect never quantitatively assessed in situ on NPs. Finally, DDM allows monitoring of the evolution of the PC in vivo. This results show that the PC composition evolves significantly over time in zebrafish larvae, confirming the inherently dynamic nature of the PC. The performance of the developed methodology allows to obtain quantitative insights into nano-bio interactions in a vast array of physiologically relevant conditions that will serve to further improve the design of nanomedicine.

Probing the dynamics of turbid colloidal suspensions using differential dynamic microscopy.

Few techniques can reliably measure the dynamics of colloidal suspensions or other soft materials over a wide range of turbidities. Here we systematically investigate the capability of Differential Dynamic Microscopy (DDM) to characterise particle dynamics in turbid colloidal suspensions based on brightfield optical microscopy. We measure the Intermediate Scattering Function (ISF) of polystyrene microspheres suspended in water over a range of concentrations, turbidities, and up to 4 orders of magnitude in time-scales. These DDM results are compared to data obtained from both Dynamic Light Scattering (DLS) and Two-colour Dynamic Light Scattering (TCDLS). The latter allows for suppression of multiple scattering for moderately turbid suspensions. We find that DDM can obtain reliable diffusion coefficients at up to 10 and 1000 times higher particle concentrations than TCDLS and standard DLS, respectively. Additionally, we investigate the roles of the four length-scales relevant when imaging a suspension: the sample thickness L, the imaging depth z, the imaging depth of field DoF, and the photon mean free path . More detailed experiments and analysis reveal the appearance of a short-time process as turbidity is increased, which we associate with multiple scattering events within the imaging depth of the field. The long-time process corresponds to the particle dynamics from which particle-size can be estimated in the case of non-interacting particles. Finally, we provide a simple theoretical framework, ms-DDM, for turbid samples, which accounts for multiple scattering.

Characterising shear-induced dynamics in flowing complex fluids using differential dynamic microscopy.

Microscopic dynamics reveal the origin of the bulk rheological response in complex fluids. In model systems particle motion can be tracked, but for industrially relevant samples this is often impossible. Here we adapt differential dynamic microscopy (DDM) to study flowing highly-concentrated samples without particle resolution. By combining an investigation of oscillatory flow, using a novel "echo-DDM" analysis, and steady shear, through flow-DDM, we characterise the yielding of a silicone oil emulsion on both the microscopic and bulk level. Through measuring the rate of shear-induced droplet rearrangements and the flow velocity, the transition from a solid-like to liquid-like state is shown to occur in two steps: with droplet mobilisation marking the limit of linear visco-elasticity, followed by the development of shear localisation and macroscopic yielding. Using this suite of techniques, such insight could be developed for a wide variety of challenging complex fluids.

Particle sizing for flowing colloidal suspensions using flow-differential dynamic microscopy.

Particle size is a key variable in understanding the behaviour of the particulate products that underpin much of our modern lives. Typically obtained from suspensions at rest, measuring the particle size under flowing conditions would enable advances for in-line testing during manufacture and high-throughput testing during development. However, samples are often turbid, multiply scattering light and preventing the direct use of common sizing techniques. Differential dynamic microscopy (DDM) is a powerful technique for analysing video microscopy of such samples, measuring diffusion and hence particle size without the need to resolve individual particles while free of substantial user input. However, when applying DDM to a flowing sample, diffusive dynamics are rapidly dominated by flow effects, preventing particle sizing. Here, we develop "flow-DDM", a novel analysis scheme that combines optimised imaging conditions, a drift-velocity correction and modelling of the impact of flow. Flow-DDM allows a decoupling of flow from diffusive motion that facilitates successful particle size measurements at flow speeds an order of magnitude higher than for DDM. We demonstrate the generality of the technique by applying flow-DDM to two separate microscopy methods and flow geometries.

Anisotropic dynamics and kinetic arrest of dense colloidal ellipsoids in the presence of an external field studied by differential dynamic microscopy.

Anisotropic dynamics on the colloidal length scale is ubiquitous in nature. Of particular interest is the dynamics of systems approaching a kinetically arrested state. The failure of classical techniques for investigating the dynamics of highly turbid suspensions has contributed toward the limited experimental information available up until now. Exploiting the recent developments in the technique of differential dynamic microscopy (DDM), we report the first experimental study of the anisotropic collective dynamics of colloidal ellipsoids with a magnetic hematite core over a wide concentration range approaching kinetic arrest. In addition, we have investigated the effect of an external magnetic field on the resulting anisotropic collective diffusion. We combine DDM with small-angle x-ray scattering and rheological measurements to locate the glass transition and to relate the collective short- and long-time diffusion coefficients to the structural correlations and the evolution of the zero shear viscosity as the system approaches an arrested state.

Dynamic and static quenching of 2-aminopurine fluorescence by the natural DNA nucleotides in solution.

2-aminopurine (2AP) is a responsive fluorescent base analogue that is used widely as a probe of the local molecular environment in DNA. The ability of 2AP to report changes in local conformation and base-stacking interactions arises from the efficient quenching of its fluorescence by the natural DNA bases. However, the mechanism of this inter-base quenching remains imperfectly understood. Two previous studies of the collisional quenching of 2AP by the natural bases, in different buffer solutions, showed that dynamic quenching efficiency depends on the identity of the natural base, but disagreed on the relative quenching efficiencies of the bases. We report a comprehensive investigation of inter-base quenching of 2AP by the natural nucleoside monophosphates (NMPs), replicating the buffer conditions used in the previous studies. Using time-resolved fluorescence measurements to distinguish between dynamic and static quenching, we find that the dynamic quenching rate constants of the different bases show a consistent trend across both buffers, and this is in line with a charge-transfer mechanism. Time-resolved measurements also provide insight into static quenching, revealing formation of 2AP-NMP ground-state complexes in which 2AP displays a very short fluorescence lifetime, comparable to that seen in oligonucleotides. In these complexes, the dependence of the rate of quenching on the partner base also supports a charge-transfer mechanism.

A combined rheometry and imaging study of viscosity reduction in bacterial suspensions.

Suspending self-propelled "pushers" in a liquid lowers its viscosity. We study how this phenomenon depends on system size in bacterial suspensions using bulk rheometry and particle-tracking rheoimaging. Above the critical bacterial volume fraction needed to decrease the viscosity to zero, [Formula: see text], large-scale collective motion emerges in the quiescent state, and the flow becomes nonlinear. We confirm a theoretical prediction that such instability should be suppressed by confinement. Our results also show that a recent application of active liquid-crystal theory to such systems is untenable.

Spontaneous shrinking of soft nanoparticles boosts their diffusion in confined media.

Improving nanoparticles (NPs) transport across biological barriers is a significant challenge that could be addressed through understanding NPs diffusion in dense and confined media. Here, we report the ability of soft NPs to shrink in confined environments, therefore boosting their diffusion compared to hard, non-deformable particles. We demonstrate this behavior by embedding microgel NPs in agarose gels. The origin of the shrinking appears to be related to the overlap of the electrostatic double layers (EDL) surrounding the NPs and the agarose fibres. Indeed, it is shown that screening the EDL interactions, by increasing the ionic strength of the medium, prevents the soft particle shrinkage. The shrunken NPs diffuse up to 2 orders of magnitude faster in agarose gel than their hard NP counterparts. These findings provide valuable insights on the role of long range interactions on soft NPs dynamics in crowded environments, and help rationalize the design of more efficient NP-based transport systems.

Dynamic optical rectification and delivery of active particles.

We use moving light patterns to control the motion of Escherichia coli bacteria whose motility is photo-activated. Varying the pattern speed controls the magnitude and direction of the bacterial flux, and therefore the accumulation of cells in up- and down-stream reservoirs. We validate our results with two-dimensional simulations and a 1-dimensional analytic model, and use these to explore parameter space. We find that cell accumulation is controlled by a competition between directed flux and undirected, stochastic transport. Our results point to a number of design principles for using moving light patterns and light-activated micro-swimmers in a range of practical applications.

Dynamics-dependent density distribution in active suspensions.

Self-propelled colloids constitute an important class of intrinsically non-equilibrium matter. Typically, such a particle moves ballistically at short times, but eventually changes its orientation, and displays random-walk behaviour in the long-time limit. Theory predicts that if the velocity of non-interacting swimmers varies spatially in 1D, v(x), then their density ρ(x) satisfies ρ(x) = ρ(0)v(0)/v(x), where x = 0 is an arbitrary reference point. Such a dependence of steady-state ρ(x) on the particle dynamics, which was the qualitative basis of recent work demonstrating how to 'paint' with bacteria, is forbidden in thermal equilibrium. Here we verify this prediction quantitatively by constructing bacteria that swim with an intensity-dependent speed when illuminated and implementing spatially-resolved differential dynamic microscopy (sDDM) for quantitative analysis over millimeter length scales. Applying a spatial light pattern therefore creates a speed profile, along which we find that, indeed, ρ(x)v(x) = constant, provided that steady state is reached.

High-throughput characterisation of bull semen motility using differential dynamic microscopy.

We report a high-throughput technique for characterising the motility of spermatozoa using differential dynamic microscopy. A movie with large field of view (∼10mm2) records thousands of cells (e.g. ≈ 5000 cells even at a low cell density of 20 × 106 cells/ml) at once and yields averaged measurements of the mean ([Formula: see text]) and standard deviation (σ) of the swimming speed, head oscillation amplitude (A0) and frequency (f0), and the fraction of motile spermatozoa (α). Interestingly, we found that the measurement of α is facilitated because the swimming spermatozoa enhance the motion of the non-swimming population. We demonstrate the ease and rapidity of our method by performing on-farm characterisation of bull spermatozoa motility, and validate the technique by comparing laboratory measurements with tracking. Our results confirm the long-standing theoretical prediction that [Formula: see text] for swimming spermatozoa.

Tricarbocyanine N-triazoles: the scaffold-of-choice for long-term near-infrared imaging of immune cells in vivo.

Herein tricarbocyanine N-triazoles are first described as a rationally-designed near-infrared (NIR) structure overcoming the brightness and photostability limitations of tricarbocyanines for long-term in vivo imaging. The straightforward synthetic approach and the wide availability of alkynes makes this strategy a versatile methodology for the preparation of highly stable N-substituted tricarbocyanines. Furthermore, we validated CIR38M as a non-transferable marker to monitor the fate of therapeutic T cells non-invasively in vivo, showing enhanced performance over conventional NIR fluorophores (i.e. DiR, IR800CW and indocyanine green) as well as compatibility with human cells for translational studies. CIR38M is able to track over time smaller numbers of T cells than current NIR agents, and to visualise antigen-driven accumulation of immune cells at specific sites in vivo. This chemical technology will improve longitudinal imaging studies to assess the efficacy of cell-based immunotherapies in preclinical models and in human samples.

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.

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.