Differential Variance Analysis: a direct method to quantify and visualize dynamic heterogeneities

Emergence of bacterial glass

Densely packed, motile bacteria can adopt collective states not seen in conventional, passive materials. These states remain in many ways mysterious, and their physical characterization can aid our understanding of natural bacterial colonies and biofilms as well as materials in general. Here, we overcome challenges associated with generating uniformly growing, large, quasi-two-dimensional bacterial assemblies by a membrane-based microfluidic device and report the emergence of glassy states in two-dimensional suspension of Escherichia coli. As the number density increases by cell growth, populations of motile bacteria transition to a glassy state, where cells are packed and unable to move. This takes place in two steps, the first one suppressing only the orientational modes and the second one vitrifying the motion completely. Characterizing each phase through statistical analyses and investigations of individual motion of bacteria, we find not only characteristic features of glass such as rapid slowdown, dynamic heterogeneity, and cage effects, but also a few properties distinguished from those of thermal glass. These distinctive properties include the spontaneous formation of micro-domains of aligned cells with collective motion, the appearance of an unusual signal in the dynamic susceptibility, and the dynamic slowdown with a density dependence generally forbidden for thermal systems. Our results are expected to capture general characteristics of such active rod glass, which may serve as a physical mechanism underlying dense bacterial aggregates.

Mesoscopic Characterization of the Early Stage of the Glucono-δ-Lactone-Induced Gelation of Milk via Image Analysis Techniques

We provide a method for quantifying the kinetics of gelation in milk acidified with glucono-δ-lactone (GDL) using image analysis techniques, particle image velocimetry (PIV), differential variance analysis (DVA) and differential dynamic microscopy (DDM). The gelation of the milk acidified with GDL occurs through the aggregation and subsequent coagulation of the casein micelles as the pH approaches the isoelectric point of the caseins. The gelation of the acidified milk with GDL is an important step in the production of fermented dairy products. PIV qualitatively monitors the average mobility of fat globules during gelation. The gel point estimated by PIV is in good agreement with that obtained by rheological measurement. DVA and DDM methods reveal the relaxation behavior of fat globules during gelation. These two methods make it possible to calculate microscopic viscosity. We also extracted the mean square displacement (MSD) of the fat globules, without following their movement, using the DDM method. The MSD of fat globules shifts to sub-diffusive behavior as gelation progresses. The fat globules used as probes show the change in matrix viscoelasticity caused by the gelling of the casein micelles. Image analysis and rheology can be used complementarily to study the mesoscale dynamics of the milk gel.

Differential dynamic microscopy for the characterisation of motility in biological systems

Differential Dynamic Microscopy (DDM) is a relatively new technique which measures the dynamics of suspended particles using a dynamic light scattering formalism. Videos are recorded using standard light microscopy at moderate frame rates, and fluctuations in pixel intensity are measured as a function of time. As only pixel intensity is analysed, it is not necessary to resolve individual particles. This allows for low magnifications and wide fields of view, and therefore dynamics can be measured on tens of thousands of scattering objects, providing robust statistics. A decade ago the technique was successfully applied to measure bacterial motility. Since then, it has been applied to a range of motile systems, but has not yet reached the wider biological community. This perspective reviews the work done so far, and provides the basic background to enable the broader application of this promising technique.

Multiscale heterogeneous dynamics in two-dimensional glassy colloids

On approaching the glass transition, a dense colloid exhibits a dramatic slowdown with minute structural changes. Most microscopy experiments directly follow the motion of individual particles in real space, whereas scattering experiments typically probe the collective dynamics in reciprocal space, at variable wavevector q. Multiscale studies of glassy dynamics are experimentally demanding and thus seldom performed. By using two-dimensional hard-sphere colloids at various area fractions φ, we show here that Differential Dynamic Microscopy (DDM) can be effectively used to measure the collective dynamics of a glassy colloid in a range of q within a single experiment. As φ is increased, the single decay of the intermediate scattering functions is progressively replaced by a more complex relaxation that we fit to a sum of two stretched-exponential decays. The slowest process, corresponding to the long-time particle escapes from caging, has a characteristic time τs = 1/(DLq2 ) with diffusion coefficient DL ∼ (φc −φ)2.8 , and φc ≈ 0.81. The fast process exhibits, instead, a non-Brownian scaling of the characteristic time τf(q) and a relative amplitude a(q) that monotonically increases with q. Despite the non-Brownian nature of τf(q), we succeed in estimating the short-time diffusion coefficient Dcage, whose φ-dependence is practically negligible compared to the one of DL. Finally, we extend DDM to measure the q-dependent dynamical susceptibility χ4(q,t), a powerful yet hard-to-access multiscale indicator of dynamical heterogeneities. Our results show that DDM is a convenient tool to study the dynamics of colloidal glasses over a broad range of time and length-scales.

Elastic and Dynamic Heterogeneity in Aging Alginate Gels

Anomalous aging in soft glassy materials has generated a great deal of interest because of some intriguing features of the underlying relaxation process, including the emergence of "ultra-long-range" dynamical correlations. An intriguing possibility is that such a huge correlation length is reflected in detectable ensemble fluctuations of the macroscopic material properties. We tackle this issue by performing replicated mechanical and dynamic light scattering (DLS) experiments on alginate gels, which recently emerged as a good model-system of anomalous aging. Here we show that some of the monitored quantities display wide variability, including large fluctuations in the stress relaxation and the occasional presence of two-step decay in the DLS decorrelation functions. By quantifying elastic fluctuation through the standard deviation of the elastic modulus and dynamic heterogeneities through the dynamic susceptibility, we find that both quantities do increase with the gel age over a comparable range. Our results suggest that large elastic fluctuations are closely related to ultra-long-range dynamical correlation, and therefore may be a general feature of anomalous aging in gels.

Disentangling collective motion and local rearrangements in 2D and 3D cell assemblies

The accurate quantification of cellular motility and of the structural changes occurring in multicellular aggregates is critical in describing and understanding key biological processes, such as wound repair, embryogenesis and cancer invasion. Current methods based on cell tracking or velocimetry either suffer from limited spatial resolution or are challenging and time-consuming, especially for three-dimensional (3D) cell assemblies. Here we propose a conceptually simple, robust and tracking-free approach for the quantification of the dynamical activity of cells via a two-step procedure. We first characterise the global features of the collective cell migration by registering the temporal stack of the acquired images. As a second step, a map of the local cell motility is obtained by performing a mean squared amplitude analysis of the intensity fluctuations occurring when two registered image frames acquired at different times are subtracted. We successfully apply our approach to cell monolayers undergoing a jamming transition, as well as to monolayers and 3D aggregates that exhibit a cooperative unjamming-via-flocking transition. Our approach is capable of disentangling very efficiently and of assessing accurately the global and local contributions to cell motility.

Understanding charged vesicle suspensions as Wigner glasses: dynamical aspects

Suspensions of charged vesicles in water with added salt are widespread in nature and industrial production. Here we investigate, via Brownian dynamics simulations, a model that grasps the key features of these systems, with bidisperse colloidal beads interacting via a hard-core and an electrostatic double layer potential. Our goal is to focus on a set of interaction parameters that is not generic but measured in recent experiments, and relevant for a class of consumer products, such as liquid fabric softeners. On increasing the volume fraction in a range relevant to real formulation, we show that the dynamics become progressively slower and heterogeneous, displaying the typical signatures of an approaching glass transition. On lowering the salt concentration, which corresponds to increasing the strength and range of the electrostatic repulsion, the emergence of glassy dynamics becomes significantly steeper, and, remarkably, occurs at volume fractions well below the hard-sphere glass transition. The volume fraction dependence of the structural relaxation time at different salt concentration is well described through a functional law inspired by a recently proposed model (Krausser et al 2015 Proc. Natl Acad. Sci. USA 112 13762). According to our results, the investigated system may be thought of as a Wigner glass, i.e. a low-density glassy state stabilized by long-range repulsive interactions. Overall, our study suggests that glassy dynamics plays an important role in controlling the stability of these suspensions.

Unjamming overcomes kinetic and proliferation arrest in terminally differentiated cells and promotes collective motility of carcinoma

During wound repair, branching morphogenesis and carcinoma dissemination, cellular rearrangements are fostered by a solid-to-liquid transition, known as unjamming. The biomolecular machinery behind unjamming and its pathophysiological relevance remain, however, unclear. Here, we study unjamming in a variety of normal and tumorigenic epithelial two-dimensional (2D) and 3D collectives. Biologically, the increased level of the small GTPase RAB5A sparks unjamming by promoting non-clathrin-dependent internalization of epidermal growth factor receptor that leads to hyperactivation of the kinase ERK1/2 and phosphorylation of the actin nucleator WAVE2. This cascade triggers collective motility effects with striking biophysical consequences. Specifically, unjamming in tumour spheroids is accompanied by persistent and coordinated rotations that progressively remodel the extracellular matrix, while simultaneously fluidizing cells at the periphery. This concurrent action results in collective invasion, supporting the concept that the endo-ERK1/2 pathway is a physicochemical switch to initiate collective invasion and dissemination of otherwise jammed carcinoma.

Diffusion in agitated frictional granular matter near the jamming transition

We study agitated frictional disks in two dimensions with the aim of developing a scaling theory for their diffusion over time. As a function of the area fraction ϕ and mean-square velocity fluctuations 〈v^{2}〉 the mean-square displacement of the disks 〈d^{2}〉 spans four to five orders of magnitude. The motion evolves from a subdiffusive form to a complex diffusive behavior at long times. The statistics of 〈d^{n}〉 at all times are multiscaling, since the probability distribution function (PDF) of displacements has very broad wings. Even where a diffusion constant can be identified it is a complex function of ϕ and 〈v^{2}〉. By identifying the relevant length and time scales and their interdependence one can rescale the data for the mean-square displacement and the PDF of displacements into collapsed scaling functions for all ϕ and 〈v^{2}〉. These scaling functions provide a predictive tool, allowing one to infer from one set of measurements (at a given ϕ and 〈v^{2}〉) what are the expected results at any value of ϕ and 〈v^{2}〉 within the scaling range.

Emergence and percolation of rigid domains during the colloidal glass transition

Using video microscopy, we measure local spatial constraints in disordered binary colloidal samples, ranging from dilute fluids to jammed glasses, and probe their spatial and temporal correlations to local dynamics during the glass transition. We observe the emergence of significant correlations between constraints and local dynamics within the Lindemann criterion, which coincides with the onset of glassy dynamics in supercooled liquids. Rigid domains in fluids are identified based on local constraints and demonstrate a percolation transition near the glass transition, accompanied by the emergence of dynamical heterogeneities. Our results show that spatial constraint instead of the geometry of amorphous structures is the key that connects the complex spatial-temporal correlations in disordered materials.

The nature of collective excitations and their crossover at extreme supercritical conditions

Physical properties of an interacting system are governed by collective excitations, but their nature at extreme supercritical conditions is unknown. Here, we present direct evidence for propagating solid-like longitudinal phonon-like excitations with wavelengths extending to interatomic separations deep in the supercritical state at temperatures up to 3,300 times the critical temperature. We observe that the crossover of dispersion curves develops at k points reducing with temperature. We interpret this effect as the crossover from the collective phonon to the collisional mean-free path regime of particle dynamics and find that the crossover points are close to both the inverse of the shortest available wavelength in the system and to the particle mean free path inferred from experiments and theory. Notably, both the shortest wavelength and mean free path scale with temperature with the same power law, lending further support to our findings.

Influence of wall heterogeneity on nanoscopically confined polymers

We investigate via molecular dynamics simulations the behaviour of a polymer melt confined between surfaces with increasing spatial correlation (patchiness) of weakly and strongly interacting sites. Beyond a critical patchiness, we find a dramatic dynamic decoupling, characterized by a steep growth of the longest relaxation time and a constant diffusion coefficient. This arises from dynamic heterogeneities induced by the walls in the adjacent polymer layers, leading to the coexistence of fast and slow chain populations. Structural variations are also present, but they are not easy to detect. Our work opens the way to a better understanding of adhesion, friction, rubber reinforcement by fillers, and many other open issues involving the dynamics of polymeric materials on rough, chemically heterogeneous and possibly "dirty" surfaces.

Perspective: Differential dynamic microscopy extracts multi-scale activity in complex fluids and biological systems

Differential dynamic microscopy (DDM) is a technique that exploits optical microscopy to obtain local, multi-scale quantitative information about dynamic samples, in most cases without user intervention. It is proving extremely useful in understanding dynamics in liquid suspensions, soft materials, cells, and tissues. In DDM, image sequences are analyzed via a combination of image differences and spatial Fourier transforms to obtain information equivalent to that obtained by means of light scattering techniques. Compared to light scattering, DDM offers obvious advantages, principally (a) simplicity of the setup; (b) possibility of removing static contributions along the optical path; (c) power of simultaneous different microscopy contrast mechanisms; and (d) flexibility of choosing an analysis region, analogous to a scattering volume. For many questions, DDM has also advantages compared to segmentation/tracking approaches and to correlation techniques like particle image velocimetry. The very straightforward DDM approach, originally demonstrated with bright field microscopy of aqueous colloids, has lately been used to probe a variety of other complex fluids and biological systems with many different imaging methods, including dark-field, differential interference contrast, wide-field, light-sheet, and confocal microscopy. The number of adopting groups is rapidly increasing and so are the applications. Here, we briefly recall the working principles of DDM, we highlight its advantages and limitations, we outline recent experimental breakthroughs, and we provide a perspective on future challenges and directions. DDM can become a standard primary tool in every laboratory equipped with a microscope, at the very least as a first bias-free automated evaluation of the dynamics in a system.

Effects of chemically heterogeneous nanoparticles on polymer dynamics: insights from molecular dynamics simulations

The dispersion of solid nanoparticles within polymeric materials is widely used to enhance their performance. Many scientific and technological aspects of the resulting polymer nanocomposites have been studied, but the role of the structural and chemical heterogeneity of the nanoparticles has just started to be appreciated. For example, simulations of polymer films on planar heterogeneous surfaces revealed unexpected, non-monotonic activation energy to diffusion on varying the surface composition. Motivated by these intriguing results, here we simulate via molecular dynamics a different, fully three-dimensional system, in which the heterogeneous nanoparticles are incorporated in a polymer melt. The nanoparticles are roughly spherical assemblies of strongly and weakly attractive sites, in fractions of f and 1 - f, respectively. We show that the polymer diffusion is still characterized by a non-monotonic dependence of the activation energy on f. The comparison with the case of homogeneous nanoparticles clarifies that the effect of the heterogeneity increases on approaching the polymer glass transition.

Tunable hydrodynamics: a field-frequency phase diagram of a non-equilibrium order-to-disorder transition

We present experiments on a model system consisting of dielectric (silicone oil) drops in a "leaky dielectric" (castor oil) carrier fluid that exhibits dynamic non-equilibrium phases as a function of the amplitude and frequency of an external AC electric field. At high frequencies, the dielectric drops are pinned to a periodic lattice by dielectrophoretic forces induced by a patterned bottom electrode. Beginning with this state of imposed order, we examine the processes that take this system from order to disorder, with decreasing frequency corresponding to an increase in the range of the hydrodynamic forces. We find two kinds of disorder, shape- and translational disorder, that occur in frequency-amplitude space. We also find regimes where drop breakup is dominant, and where order/disorder of large drops can be probed without significant drop breakup. With decreasing frequency (i.e., increasing hydrodynamic coupling between drops) and on timescales from seconds to minutes, the drops exhibit motion that resembles Brownian motion of particles in a crystal, with an effective temperature that increases with the strength of the electrohydrodynamic driving force. In this limit, the system behaves like a thermal system and the lattice is seen to melt at an effective Lindemann parameter of L_eff ∼ 0.08. This non-equilibrium thermodynamics, probed on timescales from seconds to minutes, likely arises from the pseudo-random velocity fields in the carrier fluid, as evidenced by the fractional, t^3/2, super-diffusive tracer dynamics at shorter timescales.