Dark field differential dynamic microscopy enables accurate characterization of the roto-translational dynamics of bacteria and colloidal clusters

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

Dynamics 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 Deff 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.

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DNA diffusion measured in cell-sized droplets with differential dynamic microscopy

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Combination of crowding and confinement leads to subdiffusion and slowing

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Diffusion coefficients of DNA decrease strongly with decreasing droplet size

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Polymer scaling theories and depletion effects predict observed dynamics

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.

Two-dimensional Brownian motion of anisotropic dimers

We study the two-dimensional motion of colloidal dimers by single-particle tracking and compare the experimental observations obtained by bright-field microscopy to theoretical predictions for anisotropic diffusion. The comparison is based on the mean-square displacements in the laboratory and particle frame as well as generalizations of the self-intermediate scattering functions, which provide insights into the rotational dynamics of the dimer. The diffusional anisotropy leads to a measurable translational-rotational coupling that becomes most prominent by aligning the coordinate system with the initial orientation of the particles. In particular, we find a splitting of the time-dependent diffusion coefficients parallel and perpendicular to the long axis of the dimer which decays over the orientational relaxation time. Deviations of the self-intermediate scattering functions from pure exponential relaxation are small but can be resolved experimentally. The theoretical predictions and experimental results agree quantitatively.

Multiple dynamic regimes in a coarsening foam

Intermittent dynamics driven by internal stress imbalances in disordered systems is a fascinating yet poorly understood phenomenon. Here, we study it for a coarsening foam. By exploiting differential dynamic microscopy and particle tracking we determine the dynamical characteristics of the foam at different ages in reciprocal and direct space, respectively. At all wavevectors q investigated, the intermediate scattering function exhibits a compressed exponential decay. However, the access to unprecedentedly small values of q highlights the existence of two distinct regimes for the q-dependence of the foam relaxation rate Γ(q). At high q, Γ(q) ∼ q consistent with directionally-persistent and intermittent bubble displacements. At low q, we find the surprising scaling Γ(q) ∼ q ^δ , with δ = 1.6 ± 0.2. The analysis of the bubble displacement distribution in real space reveals the existence of a displacement cut-off of the order of the bubble diameter. Introducing such cut-off length in an existing model, describing stress-driven dynamics in disordered systems, fully accounts for the observed behavior in direct and reciprocal space.