Differential Dynamic Microscopy Research Articles

Crowding and confinement act in concert to slow DNA diffusion within cell-sized droplets

SummaryDynamics of biological macromolecules, such as DNA, in crowded and confined environments are critical to understanding cellular processes such as transcription, infection, and replication. However, the combined effects of cellular confinement and crowding on macromolecular dynamics remain poorly understood. Here, we use differential dynamic microscopy to investigate the diffusion of large DNA molecules confined in cell-sized droplets and crowded by dextran polymers. We show that confined and crowded DNA molecules exhibit universal anomalous subdiffusion with scaling that is insensitive to the degree of confinement and crowding. However, effective DNA diffusion coefficients decrease up to 2 orders of magnitude as droplet size decreases—an effect that is enhanced by increased crowding. We mathematically model the coupling of crowding and confinement by combining polymer scaling theories with confinement-induced depletion effects. The generality and tunability of our system and models render them applicable to elucidating wide-ranging crowded and confined systems.

Dynamics of domain formation in a ferromagnetic fluid

Ferrofluids are colloidal suspensions of magnetic nanoparticles. Ferromagnetic ordering – with spontaneous net magnetization in the absence of external fields – has been described for a system of permanently magnetic nanoplatelets suspended in n-butanol, concentrated enough to undergo the transition to the nematic phase. Such material shows magnetic domain structures analogous to those of solid-state ferromagnets. Through optimization of fundamental interactions, the threshold concentration for nematic ordering was reduced. The optimized material allows reproducible and controllable analysis of domain structures and their formation dynamics, with domains forming on the time scale of the order of seconds. Finally, the effect of an external applied magnetic field on the nematic director fundamental fluctuations inside a domain has been studied with differential dynamic microscopy. Interestingly, the results provide an estimation of the ferrofluid's spontaneous magnetization in the absence of external magnetic fields.

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.

Quantifying Cytoskeleton Dynamics Using Differential Dynamic Microscopy.

Cells can crawl, self-heal, and tune their stiffness due to their remarkably dynamic cytoskeleton. As such, reconstituting networks of cytoskeletal biopolymers may lead to a host of active and adaptable materials. However, engineering such materials with precisely tuned properties requires measuring how the dynamics depend on the network composition and synthesis methods. Quantifying such dynamics is challenged by variations across the time, space, and formulation space of composite networks. The protocol here describes how the Fourier analysis technique, differential dynamic microscopy (DDM), can quantify the dynamics of biopolymer networks and is particularly well suited for studies of cytoskeleton networks. DDM works on time sequences of images acquired using a range of microscopy modalities, including laser-scanning confocal, widefield fluorescence, and brightfield imaging. From such image sequences, one can extract characteristic decorrelation times of density fluctuations across a span of wave vectors. A user-friendly, open-source Python package to perform DDM analysis is also developed. With this package, one can measure the dynamics of labeled cytoskeleton components or of embedded tracer particles, as demonstrated here with data of intermediate filament (vimentin) networks and active actin-microtubule networks. Users with no prior programming or image processing experience will be able to perform DDM using this software package and associated documentation.

Particle-Based Microrheology As a Tool for Characterizing Protein-Based Materials.

Microrheology based on video microscopy of embedded tracer particles has the potential to be used for high-throughput protein-based materials characterization. This potential is due to a number of characteristics of the techniques, including the suitability for measurement of low sample volumes, noninvasive and noncontact measurements, and the ability to set up a large number of samples for facile, sequential measurement. In addition to characterization of the bulk rheological properties of proteins in solution, for example, viscosity, microrheology can provide insight into the dynamics and self-assembly of protein-based materials as well as heterogeneities in the microenvironment being probed. Specifically, passive microrheology in the form of multiple particle tracking and differential dynamic microscopy holds promise for applications in high-throughput characterization because of the lack of user interaction required while making measurements. Herein, recent developments in the use of multiple particle tracking and differential dynamic microscopy are reviewed for protein characterization and their potential to be applied in a high-throughput, automatable setting.

DNA topology dictates emergent bulk elasticity and hindered macromolecular diffusion in DNA-dextran composites

Polymer architecture plays critical roles in both bulk rheological properties and microscale macromolecular dynamics in entangled polymer solutions and composites. Ring polymers, in particular, have been the topic of much debate due to the inability of the celebrated reptation model to capture their observed dynamics. Macrorheology and differential dynamic microscopy (DDM) are powerful methods to determine entangled polymer dynamics across scales; yet, they typically require different samples under different conditions, preventing direct coupling of bulk rheological properties to the underlying macromolecular dynamics. Here, we perform macrorheology on composites of highly overlapping DNA and dextran polymers, focusing on the role of DNA topology (rings versus linear chains) as well as the relative volume fractions of DNA and dextran. On the same samples under the same conditions, we perform DDM and single-molecule tracking on embedded fluorescent-labeled DNA molecules immediately before and after bulk measurements. We show DNA-dextran composites exhibit unexpected nonmonotonic dependences of bulk viscoelasticity and molecular-level transport properties on the fraction of DNA comprising the composites, with characteristics that are strongly dependent on the DNA topology. We rationalize our results as arising from stretching and bundling of linear DNA versus compaction, swelling, and threading of rings driven by dextran-mediated depletion interactions.

Reciprocal Space Study of Brownian Yet Non-Gaussian Diffusion of Small Tracers in a Hard-Sphere Glass

The simultaneous presence of normal (Brownian) diffusion and non-Gaussian statistics of particle displacements has been identified as a recurring motif for a broad spectrum of physical and biological systems. While not yet fully understood, it is generally accepted that a key ingredient for observing this Brownian yet non-Gaussian (BNG) diffusion is that the environment hosting the particles appears stationary and homogenous on the small length and time scales, while displaying significant fluctuations on larger distances and/or longer time scales. To date, most of the experimental studies on systems displaying BNG diffusion have been performed in direct space, usually via a combination of optical microscopy and particle tracking to quantify the particle’s self-diffusion. Here, we demonstrate that a reciprocal space analysis of the density fluctuations caused by the particle motion as a function of the wave vector enables the investigation of BNG diffusion in situations where single-particle tracking is impossible. To accomplish this aim, we use confocal differential dynamic microscopy (ConDDM) to study the BNG dynamics of diluted sub-resolution tracers diffusing in a glassy matrix of larger hard spheres. We first elucidate the nontrivial connection between the tracer self-diffusion and collective relaxation of the resulting density fluctuations. We find that the experimentally determined intermediate scattering functions are in excellent agreement with the recent predictions of a “diffusing diffusivity” model of BNG diffusion, whose analytical predictions are available only in reciprocal space. Our results show that studying BNG diffusion in reciprocal space can be an invaluable strategy to access the fast, anomalous dynamics occurring at very small scales in crowded environments.

Dynamic arrest and aging of biomolecular condensates are modulated by low-complexity domains, RNA and biochemical activity

Biomolecular condensates require suitable control of material properties for their function. Here we apply Differential Dynamic Microscopy (DDM) to probe the material properties of an in vitro model of processing bodies consisting of out-of-equilibrium condensates formed by the DEAD-box ATPase Dhh1 in the presence of ATP and RNA. By applying this single-droplet technique we show that condensates within the same population exhibit a distribution of material properties, which are regulated on several levels. Removal of the low-complexity domains (LCDs) of the protein decreases the fluidity of the condensates. Structured RNA leads to a larger fraction of dynamically arrested condensates with respect to unstructured polyuridylic acid (polyU). Promotion of the enzymatic ATPase activity of Dhh1 reduces aging of the condensates and the formation of arrested structures, indicating that biochemical activity and material turnover can maintain fluid-like properties over time.

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.

Diffusive dynamics of Brownian nanoparticles in a flashing optical field

We experimentally studied the diffusive dynamics of polystyrene nanoparticles in a flashing optical field using coaxial differential dynamic microscopy. When using a chopper to generate a periodic optical field from a semiconductor laser, we observed the oscillatory motion, which reduced the effective diffusion coefficient of the nanoparticles, making it smaller than that in a continuous optical field (reaching a minimum at a fixed frequency of 2400 Hz). Moreover, the diffusion of the nanoparticles slowed as the laser power increased in the flashing optical field. Our experimental results not only facilitated our understanding of the diffusion of nanoparticles in complex optical fields but also paved the way for potential applications in optical micromanipulation and atom cooling.

Scattering fingerprints of two-state dynamics

Particle transport in complex environments such as the interior of living cells is often (transiently) non-Fickian or anomalous, that is, it deviates from the laws of Brownian motion. Such anomalies may be the result of small-scale spatio-temporal heterogeneities in, or viscoelastic properties of, the medium, molecular crowding, etc. Often the observed dynamics displays multi-state characteristics, i.e. distinct modes of transport dynamically interconverting between each other in a stochastic manner. Reliably distinguishing between single- and multi-state dynamics is challenging and requires a combination of distinct approaches. To complement the existing methods relying on the analysis of the particle’s mean squared displacement, position- or displacement-autocorrelation function, and propagators, we here focus on ‘scattering fingerprints’ of multi-state dynamics. We develop a theoretical framework for two-state scattering signatures—the intermediate scattering function and dynamic structure factor—and apply it to the analysis of simple model systems as well as particle-tracking experiments in living cells. We consider inert tracer-particle motion as well as systems with an internal structure and dynamics. Our results may generally be relevant for the interpretation of state-of-the-art differential dynamic microscopy experiments on complex particulate systems, as well as inelastic or quasielastic neutron (incl. spin-echo) and x-ray scattering probing structural and dynamical properties of macromolecules, when the underlying dynamics displays two-state transport.

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.

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.

The modern structurator: increased performance for calculating the structure function

The autocorrelation function is a statistical tool that is often combined with dynamic light scattering (DLS) techniques to investigate the dynamical behavior of the scattered light fluctuations in order to measure, for example, the diffusive behavior of transparent particles dispersed in a fluid. An alternative approach to the autocorrelation function for the analysis of DLS data has been proposed decades ago and consists of calculating the autocorrelation function starting from difference of the signal at different times by using the so-called structure function. The structure function approach has been proven to be more robust than the autocorrelation function method in terms of noise and drift rejection. Therefore, the structure function analysis has gained visibility, in particular in combination with imaging techniques such as dynamic shadowgraphy and differential dynamic microscopy. Here, we show how the calculation of the structure function over thousands of images, typical of such techniques, can be accelerated, with the aim of achieving real-time analysis. The acceleration is realized by taking advantage of the Wiener–Khinchin theorem, i.e., by calculating the difference of images through Fourier transform in time. The new algorithm was tested both on CPU and GPU hardware, showing that the acceleration is particularly large in the case of CPU.

Engineering Gelation Kinetics in Living Silk Hydrogels by Differential Dynamic Microscopy Microrheology and Machine Learning.

Microbes embedded in hydrogels comprise one form of living material. Discovering formulations that balance potentially competing for mechanical and biological properties in living hydrogels-for example, gel time of the hydrogel formulation and viability of the embedded organisms-can be challenging. In this study, a pipeline is developed to automate the characterization of the gel time of hydrogel formulations. Using this pipeline, living materials comprised of enzymatically crosslinked silk and embedded E. coli-formulated from within a 4D parameter space-are engineered to gel within a pre-selected timeframe. Gelation time is estimated using a novel adaptation of microrheology analysis using differential dynamic microscopy (DDM). In order to expedite the discovery of gelation regime boundaries, Bayesian machine learning models are deployed with optimal decision-making under uncertainty. The rate of learning is observed to vary between artificial intelligence (AI)-assisted planning and human planning, with the fastest rate occurring during AI-assisted planning following a round of human planning. For a subset of formulations gelling within a targeted timeframe of 5-15 min, fluorophore production within the embedded cells is substantially similar across treatments, evidencing that gel time can be tuned independent of other material properties-at least over a finite range-while maintaining biological activity.

Uncertainty quantification and estimation in differential dynamic microscopy.

Differential dynamic microscopy (DDM) is a form of video image analysis that combines the sensitivity of scattering and the direct visualization benefits of microscopy. DDM is broadly useful in determining dynamical properties including the intermediate scattering function for many spatiotemporally correlated systems. Despite its straightforward analysis, DDM has not been fully adopted as a routine characterization tool, largely due to computational cost and lack of algorithmic robustness. We present statistical analysis that quantifies the noise, reduces the computational order, and enhances the robustness of DDM analysis. We propagate the image noise through the Fourier analysis, which allows us to comprehensively study the bias in different estimators of model parameters, and we derive a different way to detect whether the bias is negligible. Furthermore, through use of Gaussian process regression (GPR), we find that predictive samples of the image structure function require only around 0.5%-5% of the Fourier transforms of the observed quantities. This vastly reduces computational cost, while preserving information of the quantities of interest, such as quantiles of the image scattering function, for subsequent analysis. The approach, which we call DDM with uncertainty quantification (DDM-UQ), is validated using both simulations and experiments with respect to accuracy and computational efficiency, as compared with conventional DDM and multiple particle tracking. Overall, we propose that DDM-UQ lays the foundation for important new applications of DDM, as well as to high-throughput characterization.

Differential dynamic microscopy for the characterization of polymer systems

AbstractThis review summarizes recent progress in investigating polymer systems by using Differential dynamic microscopy (DDM), a rapidly emerging approach that transforms a commercial microscope by combining real‐space information with the powerful capabilities of conventional light scattering analysis. DDM analysis of a single microscope movie gives access to the sample dynamics in a wide range of scattering wave‐vectors, enabling contemporary polymer science experiments that would be difficult or impossible with standard light scattering techniques. Examples of application include the characterization of polymer solutions and networks, of polymer based colloidal systems, of biopolymers, and of cellular motility in polymeric fluids. Further applications of DDM to a variety of polymer systems are suggested to be just behind the corner and it is thus likely that DDM will become a tool of choice of the modern experimental polymer scientists.

Probing roto-translational diffusion of small anisotropic colloidal particles with a bright-field microscope

Soft and biological materials are often composed of elementary constituents exhibiting an incessant roto-translational motion at the microscopic scale. Tracking this motion with a bright-field microscope becomes increasingly challenging when the particle size becomes smaller than the microscope resolution, a case which is frequently encountered. Here we demonstrate squared-gradient differential dynamic microscopy (SG-DDM) as a tool to successfully use bright-field microscopy to extract the roto-translational dynamics of small anisotropic colloidal particles, whose rotational motion cannot be tracked accurately in direct space. We provide analytical justification and experimental demonstration of the method by successful application to an aqueous suspension of peanut-shaped particles.Graphic abstract

Two modes of cluster dynamics govern the viscoelasticity of colloidal gels.

Colloidal gels formed by strongly attractive particles at low particle volume fractions are composed of space-spanning networks of uniformly sized clusters. We study the thermal fluctuations of the clusters using differential dynamic microscopy by decomposing them into two modes of dynamics, and link them to the macroscopic viscoelasticity via rheometry. The first mode, dominant at early times, represents the localized, elastic fluctuations of individual clusters. The second mode, pronounced at late times, reflects the collective, viscoelastic dynamics facilitated by the connectivity of the clusters. By mixing two types of particles of distinct attraction strengths in different proportions, we control the transition time at which the collective mode starts to dominate, and hence tune the frequency dependence of the linear viscoelastic moduli of the binary gels.

Scattering methods for determining structure and dynamics of polymer gels

Polymer gels are unique materials, which consist of a polymer network swollen in a solvent. The modulus and the overall state of the gel depend on thermodynamic parameters, such as strand length, structure, and chemical compatibility of the solvent. Scattering techniques have been used to study the gel structure and osmotic pressure and are discussed in this Tutorial pedagogically. These techniques are not always straightforward because of trapped inhomogeneities and complicated interactions. Nevertheless, there has been considerable progress in developing analytical tools to determine the internal structure and dynamics of polymer gels. In addition to these tools, we showcase modern spatially resolved techniques, such as Diffusing Wave Spectroscopy, and offer a perspective on similar methods such as Dynamic Small Angle Light Scattering and Differential Dynamic Microscopy, which can be used to study local and interface effects in gel systems as well as any anisotropy. These new tools can fundamentally advance our understanding of local gel dynamics, which have so far been too challenging to observe.