Diffusive dynamics of nanoparticles in arrays of nanoposts

Topological DNA blends exhibit resonant deformation fields and strain propagation dynamics tuned by steric constraints

Understanding how polymers deform in response to local stresses and strains, and how strains propagate from a local disturbance, are grand challenges in wide-ranging fields from materials manufacturing to cell mechanics. These dynamics are particularly complex for blends of polymers of distinct topologies, for which several different species-dependent mechanisms may contribute. Here, we use OpTiDDM (Optical Tweezers integrating Differential Dynamic Microscopy) to elucidate deformation fields and propagation dynamics of binary blends of linear, ring and supercoiled DNA of varying sizes. We reveal robust non-monotonic dependence of strain alignment and superdiffusive transport with strain rate. However, peak alignment and superdiffusivity are surprisingly decoupled, occurring at different strain rates resonant with the distinct relaxation rates of the different topologies. Despite this universal resonance, we find that strain propagation of ring-linear blends is dictated by entanglements while supercoiled-ring blends are governed by Rouse dynamics. Our results capture critical subtleties in propagation and deformation dynamics of topological blends, shedding new light on the governing physics and offering a route towards decoupled tuning of response features. We anticipate our approach to be broadly generalizable to mapping the deformation dynamics of polymer blends, with an eye towards bottom-up bespoke materials design. STATEMENT OF SIGNIFICANCE: In biology and in manufacturing, biomaterials are often subject to localized and spatially nonuniform strains and stresses. Yet, understanding the extent to which strains are absorbed, distributed, or propagated across different spatiotemporal scales remains a grand challenge. Here, we combine optical tweezers with differential dynamic microscopy to elucidate deformation fields and propagation dynamics of blends of linear, ring and supercoiled DNA, revealing robust non-monotonic trends and decoupling of strain alignment and superdiffusivity, and capturing critical subtleties in propagation and deformation dynamics. Our results, shedding important new physical insight to guide decoupled tuning of response features, may be leveraged to map the deformation dynamics of wide-ranging systems of biopolymers and other macromolecules, with an eye towards bottom-up bespoke biomaterials design.

Modeling Mass Transport Dynamics in Deformable Hydrogels during Evaporation

Hydrogels possess exceptional mechanical properties and biocompatibility, making them widely used in contemporary bioengineering. Specifically, in the development of wearable and implantable health monitoring devices as well as drug delivery systems, hydrogels are utilized to enable precise control over the transport of solutes. Nonetheless, predicting the distribution of substances within hydrogels still poses a significant challenge due to the complex interplay between the movement of water content, migration of solutes, and deformability of the hydrogel polymer network, which presents challenges to theoretical modeling. Our work introduces a numerical model that addresses the movement of water and solute within a flexible hydrogel, accounting for evaporation and/or moisture absorption at the boundary. The model solves for water saturation, solute concentration, and hydrogel deformation iteratively at each time step while computing the boundary movement velocity based on the transport process. By comparing the modeled results of geometry deformation and water and solute distributions during evaporation with our experiments, we demonstrate the accuracy and applicability of our proposed model. This capability to precisely analyze water and solute concentrations in deformable and nonuniform hydrogel environments paves the way for advancements in biosensing and drug delivery methods that rely on elastic porous materials.

Microscopic Particle Image Velocimetry Analysis of Multiphase Flow in a Porous Media Micromodel

Pore-scale oil displacement behavior was investigated in a porous media micromodel using microscopic particle image velocimetry (μPIV). Porous media micromodels consisting of an ordered square array of cylindrical pillars with 50 and 70% porosities were fabricated with photolithography. The oil displacement was performed with the injection of water at flow rates of 37.5, 75, and 150 μL/h. These flow rates correspond to Reynolds number of 1.1 × 10-2, 2.2 × 10-2, and 4.4 × 10-2, respectively in the 50% porous channel, and 1.84 × 10-3, 3.69 × 10-3, and 7.38 × 10-3, respectively in the 70% porous channel. The capillary numbers for these flow rates are 2.18 × 10-5, 4.36 × 10-5, and 8.72 × 10-5, respectively in the 50% porous channel, and 1.56 × 10-5, 3.12 × 10-5, and 6.23 × 10-5, respectively in the 70% porous channel. The micromodel is initially saturated with oil, with the invading water phase following the path of least resistance as it displaces the oil. The μPIV data were used to construct probability density functions (PDFs) which show an initial, nonzero, peak in transverse velocity as the water enters the micromodel. The PDFs broaden with time, indicating that the water is spreading, before retracting to a peak velocity of 0 mm/s, indicating that the water displacement has achieved equilibrium. We developed a model based on conservation of mass to describe the efficiency of the displacement process. All flow conditions demonstrate peak displacement efficiency when the amount of oil phase displacement is ∼9 pore volumes in 50% porous channel and ∼4 pore volumes in 70% porous channel.

Experimentally Probing the Effect of Confinement Geometry on Lipid Diffusion

The lateral mobility of molecules within the cell membrane is ultimately governed by the local environment of the membrane. Confined regions induced by membrane structures, such as protein aggregates or the actin meshwork, occur over a wide range of length scales and can impede or steer the diffusion of membrane components. However, a detailed picture of the origins and nature of these confinement effects remains elusive. Here, we prepare model lipid systems on substrates patterned with confined domains of varying geometries constructed with different materials to explore the influences of physical boundary conditions and specific molecular interactions on diffusion. We demonstrate a platform that is capable of significantly altering and steering the long-range diffusion of lipids by using simple oxide deposition approaches, enabling us to systematically explore how confinement size and shape impact diffusion over multiple length scales. While we find that a "boundary condition" description of the system captures underlying trends in some cases, we are also able to directly compare our systems to analytical models, revealing the unexpected breakdown of several approximate solutions. Our results highlight the importance of considering the length scale dependence when discussing properties such as diffusion.

Anomalous lateral diffusion of lipids during the fluid/gel phase transition of a lipid membrane

A lipid membrane undergoes a phase transition from fluid to gel phase upon changing external thermodynamic conditions, such as decreasing temperature and increasing pressure. Extremophilic organisms face the challenge of preventing this deleterious phase transition. The main focus of their adaptive strategy is to facilitate effective temperature sensing through sensor proteins, relying on the drastic changes in packing density and membrane fluidity during the phase transition. Although the changes in packing density parameters due to the fluid/gel phase transition are studied in detail, the impact on membrane fluidity is less explored in the literature. Understanding the lateral diffusive dynamics of lipids in response to temperature, particularly during the fluid/gel phase transition, is albeit crucial. Here we have simulated the phase transition of a single component lipid membrane composed of dipalmitoylphosphatidylcholine (DPPC) lipids using a coarse-grained (CG) model and studied the changes of the structural and dynamical properties. It is observed that near the phase transition point, both fluid and gel phase domains coexist together. The dynamics remains highly non-Gaussian for a long time even when the mean square displacement reaches the Fickian regime at a much earlier time. This Fickian yet non-Gaussian diffusion (FnGD) is a characteristic of a highly heterogeneous system, previously observed for the lateral diffusion of lipids in raft mimetic membranes having liquid-ordered and liquid-disordered phases co-existing together. We have analyzed the molecular trajectories and calculated the jump-diffusion of the lipids, stemming from sudden jump translations, using a translational jump-diffusion (TJD) approach. An overwhelming contribution of the jump-diffusion of the lipids is observed suggesting anomalous diffusion of lipids during fluid/gel phase transition of the membrane. These results are important in unravelling the intricate nature of lipid diffusion during the phase transition of the membrane and open up a new possibility of investigating the most significant change of membrane properties during phase transition, which can be effectively sensed by proteins.

Fickian yet non-Gaussian diffusion of a quasi-2D colloidal system in an optical speckle field: experiment and simulations

We investigate a quasi-2D suspension of Brownian particles in an optical speckle field produced by holographic manipulation of a laser wavefront. This system was developed to study, in a systematic and controllable way, a distinctive instance of diffusion, called Fickian yet Non Gaussian diffusion (FnGD), observed, during the last decade, for colloidal particles in a variety of complex and biological fluids. Our setup generates an optical speckle field that behaves like a disordered set of optical traps. First, we describe the experimental setup and the dynamics of the particles, focusing on mean square displacements, displacement distributions and kurtosis. Then, we present Brownian Dynamics simulations of point-like particles in a complex energy landscape, mimicking that generated by the optical speckle field. We show that our simulations can capture the salient features of the experimental results, including the emergence of FnGD, also covering times longer than the ones so far achieved in experiments. Some deviations are observed at long time only, with the Gaussian restoring being slower in simulations than in experiments. Overall, the introduced numerical model might be exploited to guide the design of upcoming experiments targeted, for example, to fully monitor the recovery of Gaussianity.

Universal Evolution of Fickian Non-Gaussian Diffusion in Two- and Three-Dimensional Glass-Forming Liquids

Recent works show that glass-forming liquids display Fickian non-Gaussian Diffusion, with non-Gaussian displacement distributions persisting even at very long times, when linearity in the mean square displacement (Fickianity) has already been attained. Such non-Gaussian deviations temporarily exhibit distinctive exponential tails, with a decay length λ growing in time as a power-law. We herein carefully examine data from four different glass-forming systems with isotropic interactions, both in two and three dimensions, namely, three numerical models of molecular liquids and one experimentally investigated colloidal suspension. Drawing on the identification of a proper time range for reliable exponential fits, we find that a scaling law λ(t)∝tα, with α≃1/3, holds for all considered systems, independently from dimensionality. We further show that, for each system, data at different temperatures/concentration can be collapsed onto a master-curve, identifying a characteristic time for the disappearance of exponential tails and the recovery of Gaussianity. We find that such characteristic time is always related through a power-law to the onset time of Fickianity. The present findings suggest that FnGD in glass-formers may be characterized by a "universal" evolution of the distribution tails, independent from system dimensionality, at least for liquids with isotropic potential.

Diffusion of gold nanoparticles in porous silica monoliths determined by dynamic light scattering

HYPOTHESIS

The applicability of the dynamic light scattering method for the determination of particle diffusivity under confinement without applying refractive index matching was not adequately explored so far. The confinement effect on particle diffusion in a porous material which is relevant for particle chromatography has also not yet been fully characterized.

EXPERIMENTS

Dynamic light scattering experiments were performed for unimodal dispersions of 11-mercaptoundecanoic acid-capped gold nanoparticles. Diffusion coefficients of gold nanoparticles in porous silica monoliths were determined without limiting refractive index matching fluids. Comparative experiments were also performed with the same nanoparticles and porous silica monolith but applying refractive index matching.

FINDINGS

Two distinct diffusivities could be determined inside the porous silica monolith, both smaller than that in free media, showing a slowing-down of the diffusion processes of nanoparticles under confinement. While the larger diffusivity can be related to the slightly slowed-down diffusion of particles in the bulk of the pores and in the necks connecting individual pores, the smaller diffusivity might be related to the diffusion of particles near the pore walls. It shows that the dynamic light scattering method with a heterodyne detection scheme can be used as a reliable and competitive tool for determining particle diffusion under confinement.

Motor-driven advection competes with crowding to drive spatiotemporally heterogeneous transport in cytoskeleton composites

The cytoskeleton-a composite network of biopolymers, molecular motors, and associated binding proteins-is a paradigmatic example of active matter. Particle transport through the cytoskeleton can range from anomalous and heterogeneous subdiffusion to superdiffusion and advection. Yet, recapitulating and understanding these properties-ubiquitous to the cytoskeleton and other out-of-equilibrium soft matter systems-remains challenging. Here, we combine light sheet microscopy with differential dynamic microscopy and single-particle tracking to elucidate anomalous and advective transport in actomyosin-microtubule composites. We show that particles exhibit multi-mode transport that transitions from pronounced subdiffusion to superdiffusion at tunable crossover timescales. Surprisingly, while higher actomyosin content increases the range of timescales over which transport is superdiffusive, it also markedly increases the degree of subdiffusion at short timescales and generally slows transport. Corresponding displacement distributions display unique combinations of non-Gaussianity, asymmetry, and non-zero modes, indicative of directed advection coupled with caged diffusion and hopping. At larger spatiotemporal scales, particles in active composites exhibit superdiffusive dynamics with scaling exponents that are robust to changing actomyosin fractions, in contrast to normal, yet faster, diffusion in networks without actomyosin. Our specific results shed important new light on the interplay between non-equilibrium processes, crowding and heterogeneity in active cytoskeletal systems. More generally, our approach is broadly applicable to active matter systems to elucidate transport and dynamics across scales.

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

Optical-Tweezers-integrating-Differential-Dynamic-Microscopy maps the spatiotemporal propagation of nonlinear strains in polymer blends and composites

How local stresses propagate through polymeric fluids, and, more generally, how macromolecular dynamics give rise to viscoelasticity are open questions vital to wide-ranging scientific and industrial fields. Here, to unambiguously connect polymer dynamics to force response, and map the deformation fields that arise in macromolecular materials, we present Optical-Tweezers-integrating-Differential -Dynamic-Microscopy (OpTiDMM) that simultaneously imposes local strains, measures resistive forces, and analyzes the motion of the surrounding polymers. Our measurements with blends of ring and linear polymers (DNA) and their composites with stiff polymers (microtubules) uncover an unexpected resonant response, in which strain alignment, superdiffusivity, and elasticity are maximized when the strain rate is comparable to the entanglement rate. Microtubules suppress this resonance, while substantially increasing elastic storage, due to varying degrees to which the polymers buildup, stretch and flow along the strain path, and configurationally relax induced stress. More broadly, the rich multi-scale coupling of mechanics and dynamics afforded by OpTiDDM, empowers its interdisciplinary use to elucidate non-trivial phenomena that sculpt stress propagation dynamics-critical to commercial applications and cell mechanics alike.

Structural relaxation dynamics of colloidal nanotrimers

By Molecular Dynamics simulation, we investigate the dynamics of isotropic fluids of colloidal nanotrimers whose interactions are described by varying the strength of attractive and repulsive terms of the Mie potential. To provide a consistent comparison between the systems described by different force fields, we determine the phase diagram and critical points of each system, characterize the morphology of high-density liquid phases at the same reduced temperature and density, and finally investigate their long-time relaxation dynamics. In particular, we detect an especially complex dynamics that reveals the existence of slow and fast nanotrimers and the resulting occurrence of non-Gaussianity, which develops at intermediate timescales. Deviations from Gaussianity are temporary and vanish within the timescales of the system's density fluctuations decay, when a Fickian-like diffusion regime is eventually observed.

Fickian Non-Gaussian Diffusion in Glass-Forming Liquids

Fickian yet non-Gaussian diffusion (FnGD), a most intriguing open issue in soft matter, is generically associated with some dynamical and/or structural heterogeneity of the environment. Here we investigate the features of FnGD in glass-forming liquids, the epitome of dynamical heterogeneity, drawing on experiments on hard-sphere colloidal suspensions and simulations of a simple model of molecular liquid. We demonstrate that FnGD strengthens on approaching the glass transition, by identifying distinct timescales for Fickianity, τ_{F}, and for restoring of Gaussianity, τ_{G}>τ_{F}, as well as their associated length scales, ξ_{F} and ξ_{G}. We find τ_{G}∝τ_{F}^{γ} with γ≃1.8 for both systems. In the deep FnGD regime, the displacement distributions display exponential tails. We show that, in simulations, the time-dependent decay lengths l(t) at different temperatures all collapse onto a power-law master curve [l(t)/(ξ_{G})]∝(t/τ_{G})^{α}, with α=0.33. A similar collapse, if less sharp, is also found in experiments, seemingly with the same exponent α. We further discuss the connections of the timescales and length scales characterizing FnGD with structural relaxation and dynamic heterogeneity.

A model-system of Fickian yet non-Gaussian diffusion: light patterns in place of complex matter

Fickian yet non-Gaussian Diffusion (FnGD), widely observed for colloidal particles in a variety of complex and biological fluids, emerges as a most intriguing open issue in Soft Matter. To fully monitor FnGD and advance its understanding, recording many trajectories over a large time range is crucial, which makes experiments challenging. Here we exploit a recently introduced experimental model of finely tunable FnGD: a quasi-2d system of Brownian beads in water moving in a heterogeneous energy landscape generated by a static and spatially random optical force field (speckle pattern). By performing experiments at different optical power, we succeed in monitoring the evolution as well as the precursors of FnGD. Fickian scaling of the mean square displacement is always attained after a subdiffusive regime while the displacement distributions keep on being non-Gaussian, which allows for measuring a characteristic length- and time-scale for the onset of FnGD, ξ_f and t_f. We find that ξ_f stays constant, whereas t_f grows as the inverse of the long-time diffusion coefficient t_f ∝ D^-1 for increasing the optical power. Deviations from the standard Gaussian shape of the displacement distribution are neatly characterized on a broad range of times, focusing on the excess probability at small displacements and on the decay-length of the distinctive exponential tails. Such deviations are fully built in the subdiffusive regime and, at the FnGD onset, grow with the optical power. As time goes on, the small-displacement probability narrows and the exponential tails progressively break up, with a tendency to recover the Gaussian behaviour. Overall, both subdiffusion and FnGD become more marked and persistent on increasing the optical power, suggesting a strict relation between these two regimes. As clearly demonstrated by our results, the adopted model-system represents a privileged stage for in-depth study of FnGD and opens the way to unveil the nature of this phenomenon through finely tuned and well-controlled experiments.

Nanoparticle dispersion in porous media: Effects of array geometry and flow orientation

We investigate the effects of array geometry and flow orientation on transport of finite-sized particles in ordered arrays using Stokesian dynamics simulations. We find that quiescent diffusion is independent of array geometry over the range of volume fraction of the nanoposts examined. Longitudinal dispersion under flow depends on the direction of incident flow relative to the array lattice vectors. Taylor-Aris behavior is recovered for flow along the lattice directions, whereas a nonmonotonic dependence of the dispersion coefficient on the Péclet number is obtained for flow orientations slightly perturbed from certain lattice vectors, owing to a competition between directional locking and spatial velocity variations.

The Curvature Effect on the Diffusion of Single Brownian Squares on a Cylindrical Surface in the Presence of Depletion Attractions

The diffusion of single micron-sized Brownian square platelets on cylindrical surfaces with different radii of curvature in the presence of depletion attractions was studied experimentally by video microscopy. The translational motion of a square is found to be diffusive along the axial direction of the cylinder but sub-diffusive along the circumferential direction due to the confinement induced by gravity, while its rotational motion displays a sub-diffusive behavior due to the confinement induced by orientation-dependent depletion attractions. Such a confinement effect decreases as the radius of curvature increases and can be tuned both through surface curvatures and/or depletion attractions. Our work provides a new way to control the translational and rotational dynamics of anisotropic particles through curved surfaces in the presence of depletion attractions.

Subtle changes in crosslinking drive diverse anomalous transport characteristics in actin-microtubule networks

Anomalous diffusion in crowded and complex environments is widely studied due to its importance in intracellular transport, fluid rheology and materials engineering. Specifically, diffusion through the cytoskeleton, a network comprised of semiflexible actin filaments and rigid microtubules that interact both sterically and via crosslinking, plays a principal role in viral infection, vesicle transport and targeted drug delivery. Here, we elucidate the impact of crosslinking on particle diffusion in composites of actin and microtubules with actin-actin, microtubule-microtubule and actin-microtubule crosslinking. We analyze a suite of transport metrics by coupling single-particle tracking and differential dynamic microscopy. Using these complementary techniques, we find that particles display non-Gaussian and non-ergodic subdiffusion that is markedly enhanced by cytoskeletal crosslinking, which we attribute to suppressed microtubule mobility. However, the extent to which transport deviates from normal Brownian diffusion depends strongly on the crosslinking motif - with actin-microtubule crosslinking inducing the most pronounced anomalous characteristics. Our results reveal that subtle changes to actin-microtubule interactions can have complex impacts on particle diffusion in cytoskeleton composites, and suggest that a combination of reduced filament mobility and more variance in actin mobilities leads to more strongly anomalous particle transport.

Rapid Fickian Yet Non-Gaussian Diffusion after Subdiffusion

The recently discovered Fickian yet non-Gaussian diffusion (FnGD) is here finely tuned and investigated over a wide range of probabilities and timescales using a quasi-2D suspension of colloidal beads under the action of a static and spatially random optical force field. This experimental model allows one to demonstrate that a "rapid" FnGD regime with a diffusivity close to that of free suspension can originate from earlier subdiffusion. We show that these two regimes are strictly tangled: as subdiffusion deepens upon increasing the optical force, deviations from Gaussianity in the FnGD regime become larger and more persistent in time. In addition, the distinctive exponential tails of FnGD are quickly built up in the subdiffusive regime. Our results shed new light on previous experimental observations and suggest that FnGD may generally be a memory effect of earlier subdiffusive processes.

Diffusion of colloidal particles in model porous media

Using video microscopy and simulations, we study the long-time diffusion of colloidal tracers in a wide range of model porous media composed of frozen colloidal matrices with different structures. We found that the diffusion coefficient of a tracer can be quantitatively determined by the structures of porous media. In particular, a universal scaling relation exists between the dimensionless diffusion coefficient of the tracer and the structural entropy of the system. This universal scaling relation is an extension of the scaling law previously discovered for the diffusion of colloidal particles in fluctuating media.

Diffusion of Anisotropic Colloids in Periodic Arrays of Obstacles

Colloidal suspensions in confined geometries exhibit rich diffusion dynamics governed by particle shapes and particle-confinement interactions. Here, we propose a colloidal system, consisting of ellipsoids in periodic array of obstacles, to investigate the confined diffusion of anisotropic colloids. From the obstacle density-dependent diffusion, we discover a decoupling of translational and rotational diffusion in which only rotational motion is localized while translational motion remains diffusive. Moreover, by evaluating the probability distributions of displacements, we found Brownian but non-Gaussian diffusion behaviors with increasing the obstacle densities, which originates from the shape anisotropy of the colloid and the multiplicity of the local configurations of the ellipsoids with respect to the obstacle. Our results suggest that the shape anisotropy and spatial confinements play a vital role in the diffusion dynamics. It is important for understanding the transportations of anisotropic objects in complex environments.

Anomalous and heterogeneous DNA transport in biomimetic cytoskeleton networks

The cytoskeleton, a complex network of protein filaments and crosslinking proteins, dictates diverse cellular processes ranging from division to cargo transport. Yet, the role the cytoskeleton plays in the intracellular transport of DNA and other macromolecules remains poorly understood. Here, using single-molecule conformational tracking, we measure the transport and conformational dynamics of linear and relaxed circular (ring) DNA in composite networks of actin and microtubules with variable types of crosslinking. While both linear and ring DNA undergo anomalous, non-Gaussian, and non-ergodic subdiffusion, the detailed dynamics are controlled by both DNA topology (linear vs. ring) and crosslinking motif. Ring DNA swells, exhibiting heterogeneous subdiffusion controlled via threading by cytoskeleton filaments, while linear DNA compacts, exhibiting transport via caging and hopping. Importantly, while the crosslinking motif has little effect on ring DNA, linear DNA in networks with actin-microtubule crosslinking is significantly less ergodic and shows more heterogeneous transport than with actin-actin or microtubule-microtubule crosslinking.

Diffusion of Nanoparticles with Activated Hopping in Crowded Polymer Solutions

A long-distance hop of diffusive nanoparticles (NPs) in crowded environments was commonly considered unlikely, and its characteristics remain unclear. In this work, we experimentally identify the occurrence of the intermittent hops of large NPs in crowded entangled poly(ethylene oxide) (PEO) solutions, which are attributed to thermally induced activated hopping. We show that the diffusion of NPs in crowded solutions is considered as a superposition of the activated hopping and the reptation of the polymer solution. Such activated hopping becomes significant when either the PEO molecular weight is large enough or the NP size is relatively small. We reveal that the time-dependent non-Gaussianity of the NP diffusion is determined by the competition of the short-time relaxation of a polymer entanglement strand, the activated hopping, and the long-time reptation. We propose an exponential scaling law τ_hop/τ_e ∼ exp(d/d_t) to characterize the hopping time scale, suggesting a linear dependence of the activated hopping energy barrier on the dimensionless NP size. The activated hopping motion can only be observed between the onset time scale of the short-time relaxation of local entanglement strands and the termination time scale of the long-time relaxation. Our findings on activated hopping provide new insights into long-distance transportation of NPs in crowded biological environments, which is essential to the delivery and targeting of nanomedicines.

Particle diffusion in extracellular hydrogels

Hyaluronic acid is an abundant polyelectrolyte in the human body that forms extracellular hydrogels in connective tissues. It is essential for regulating tissue biomechanics and cell-cell communication, yet hyaluronan overexpression is associated with pathological situations such as cancer and multiple sclerosis. Due to its enormous molecular weight (in the range of millions of Daltons), accumulation of hyaluronan hinders transport of macromolecules including nutrients and growth factors through tissues and also hampers drug delivery. However, the exact contribution of hyaluronan to tissue penetrability is poorly understood due to the complex structure and molecular composition of tissues. Here we reconstitute biomimetic hyaluronan gels and systematically investigate the effects of gel composition and crosslinking on the diffusion of microscopic tracer particles. We combine ensemble-averaged measurements via differential dynamic microscopy with single-particle tracking. We show that the particle diffusivity depends on the particle size relative to the network pore size and also on the stress relaxation dynamics of the network. We furthermore show that addition of collagen, the other major biopolymer in tissues, causes the emergence of caged particle dynamics. Our findings are useful for understanding macromolecular transport in tissues and for designing biomimetic extracellular matrix hydrogels for drug delivery and tissue regeneration.

Filament Rigidity Vies with Mesh Size in Determining Anomalous Diffusion in Cytoskeleton

The diffusion of microscopic particles through the cell, important to processes such as viral infection, gene delivery, and vesicle transport, is largely controlled by the complex cytoskeletal network, comprised of semiflexible actin filaments and rigid microtubules, that pervades the cytoplasm. By varying the relative concentrations of actin and microtubules, the cytoskeleton can display a host of different structural and dynamic properties that, in turn, impact the diffusion of particles through the composite network. Here, we couple single-particle tracking with differential dynamic microscopy to characterize the transport of microsphere tracers diffusing through composite in vitro networks with varying ratios of actin and microtubules. We analyze multiple complementary metrics for anomalous transport to show that particles exhibit anomalous subdiffusion in all networks, which our data suggest arises from caging by networks. Further, subdiffusive characteristics are markedly more pronounced in actin-rich networks, which exhibit similarly more prominent viscoelastic properties compared to microtubule-rich composites. While the smaller mesh size of actin-rich composites compared to microtubule-rich composites plays an important role in these results, the rigidity of the filaments comprising the network also influences the anomalous characteristics that we observe. Our results suggest that as microtubules in our composites are replaced with actin filaments, the decreasing filament rigidity competes with increasing network connectivity to drive anomalous transport.

Fickian yet non-Gaussian diffusion in two-dimensional Yukawa liquids

We investigate Fickian diffusion in two-dimensional (2D) Yukawa liquids using molecular dynamics simulations. We compute the self-van Hove correlation function G_{s}(r,t) and the self-intermediate scattering function F_{s}(k,t), and we compare these functions with those obtained from mean-squared displacement (MSD) using the Gaussian approximation. According to this approximation, a linear MSD with time implies a Gaussian behavior for G_{s}(r,t) and F_{s}(k,t) at all times. Surprisingly, we find that these functions deviate from Gaussian at intermediate timescales, indicating the failure of the Gaussian approximation. Furthermore, we quantify these deviations by the non-Gaussian parameter, and we find that the deviations increase when the temperature of the liquid decreases. The origin of the non-Gaussian behavior may be the heterogeneous dynamics of dust particles observed in 2D Yukawa liquids.

Coaxial differential dynamic microscopy for measurement of Brownian motion in weak optical field

Weak optical fields cause less damage to active cells and are easier to realize than traditional and tightly focused optical fields. While these fields are promising for biomedical science and particle manipulation applications, they lack a method for precise particle diffusion measurement because the weak fields cause the small changes in particle motion caused by weak fields. In this paper, we present a coaxial differential dynamic microscopy (CDDM) technique that uses a differential dynamic microscopy system, combined with an adjustable optical field. We use this technique to study Brownian motion of colloidal particles in weak optical fields. CDDM can quantitatively measure both the intensity and the pattern of the weak optical field and the diffusion coefficient of the particles. While the light paths of both the weak optical field and the illumination are coaxially incident on the sample cell, they remain independent. The optical field can be designed to have any pattern and adjusted to any intensity, while the measurements' sample illumination requirements are also satisfied. To verify the accuracy of the technique, we measured particle diffusion in weak Gaussian optical fields of different strengths. The diffusion coefficient was found to decrease with increasing field strength. These experimental results agree well with those results predicted using the Fokker-Planck equation and Euler algorithm simulations. This technique is expected to provide an efficient tool for research into particle manipulation by using weak optical fields, particularly for delicate systems, such as colloidal particles and biological cells.

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.

Nanoscale Rheology and Anisotropic Diffusion Using Single Gold Nanorod Probes

The complex rotational and translational Brownian motion of anisotropic particles depends on their shape and the viscoelasticity of their surroundings. Because of their strong optical scattering and chemical versatility, gold nanorods would seem to provide the ultimate probes of rheology at the nanoscale, but the suitably accurate orientational tracking required to compute rheology has not been demonstrated. Here we image single gold nanorods with a laser-illuminated dark-field microscope and use optical polarization to determine their three-dimensional orientation to better than one degree. We convert the rotational diffusion of single nanorods in viscoelastic polyethylene glycol solutions to rheology and obtain excellent agreement with bulk measurements. Extensions of earlier models of anisotropic translational diffusion to three dimensions and viscoelastic fluids give excellent agreement with the observed motion of single nanorods. We find that nanorod tracking provides a uniquely capable approach to microrheology and provides a powerful tool for probing nanoscale dynamics and structure in a range of soft materials.

Non-Gaussianity, population heterogeneity, and transient superdiffusion in the spreading dynamics of amoeboid cells

What is the underlying diffusion process governing the spreading dynamics and search strategies employed by amoeboid cells?

Mapping the Functional Tortuosity and Spatiotemporal Heterogeneity of Porous Polymer Membranes with Super-Resolution Nanoparticle Tracking

As particles flow through porous media, they follow complex pathways and experience heterogeneous environments that are challenging to characterize. Tortuosity is often used as a parameter to characterize the complexity of pathways in porous materials and is useful in understanding hindered mass transport in industrial filtration and mass separation processes. However, conventional calculations of tortuosity provide only average values under static conditions; they are insensitive to the intrinsic heterogeneity of porous media and do not account for potential effects of operating conditions. Here, we employ a high-throughput nanoparticle tracking method which enables the observation of actual particle trajectories in polymer membranes under relevant operating conditions. Our results indicate that tortuosity is not simply a structural material property but is instead a functional property that depends on flow rate and particle size. We also resolved the spatiotemporal heterogeneity of flowing particles in these porous media. The distributions of tortuosity and of local residence/retention times were surprisingly broad, exhibiting heavy tails representing a population of highly tortuous trajectories and local regions with anomalously long residence times. Interestingly, local tortuosity and residence times were directly correlated, suggesting the presence of highly confining regions that cause more meandering trajectories and longer retention times. The comprehensive information about tortuosity and spatiotemporal heterogeneity provided by these methods will advance the understanding of complex mass transport and assist rational design and synthesis of porous materials.

Vincristine liposomes with smaller particle size have stronger diffusion ability in tumor and improve tumor accumulation of vincristine significantly

The passive targeting is the premise of active targeting that could make nanocarrier detained in tumor tissue. The particle size is the most important factor that influences the diffusion and distribution of nanoparticle both in vivo and in vitro. In order to investigate the relationship between particle size and diffusion ability, two kinds of liposome loaded with Vincristine (VCR-Lip) were prepared. The diffusion behavior of VCR-Lip with different particle size and free VCR was compared through diffusion stability study. The diffusion ability from 12-well culture plate to Millipore transwell of each formulation reflected on HepG-2 cytotoxicity results. Different cell placement methods and drug adding positions were used to study the VCR-Lip diffusion behaviors, which influenced the apoptosis of HepG-2 cell. The different cell uptake of Nile red–Lip and free Nile red was compared when changed the adding way of fluorescent fluorescein. To study the penetration ability in HepG-2 tumor spheroids, we constructed 30 nm and 100 nm Cy5.5-Lip to compare with free Cy5.5. Then the anti-tumor effect, tissue distribution of free VCR injection, 30 nm and 100 nm VCR-Lip were further investigated on the HepG-2 tumor bearing nude mice. The results of these study showed that the diffusion ability of free drug and fluorescent fluorescein was remarkable stronger than which encapsulated in liposomes. Moreover, diffusion ability of smaller liposome was stronger than larger one. In this way, 30 nm liposome had not only faster and stronger tumor distribution than 100 nm liposome, but also higher tumor drug accumulation than free drug as well. Our study provided a new thinking to improve the targeting efficiency of nano drug delivery system, no matter passive or active targeting.

Test of the diffusing-diffusivity mechanism using near-wall colloidal dynamics

The mechanism of diffusing diffusivity predicts that, in environments where the diffusivity changes gradually, the displacement distribution becomes non-Gaussian, even though the mean-square displacement grows linearly with time. Here, we report single-particle tracking measurements of the diffusion of colloidal spheres near a planar substrate. Because the local effective diffusivity is known, we have been able to carry out a direct test of this mechanism for diffusion in inhomogeneous media.

Interfacial and Confined Colloidal Rod Diffusion

Optical microscopy is used to measure translational and rotational diffusion of colloidal rods near a single wall, confined between parallel walls, and within quasi-2D porous media as a function of rod aspect ratio and aqueous solution ionic strength. Translational and rotational diffusivities are obtained as rod particles experience positions closer to boundaries and for larger aspect ratios. Models based on position dependent hydrodynamic interactions quantitatively capture diffusivities in all geometries and indicate particle-wall separations in agreement with independent estimates based on electrostatic interactions. Short-time translational diffusion in quasi-2D porous media is insensitive to porous media area fraction, which appears to arise from a balance of hydrodynamic hindrance and enhanced translation due to parallel alignment along surfaces. Findings in this work provide a basis to interpret and predict interfacial and confined colloidal rod transport relevant to biological, environmental, and synthetic material systems.

Differential dynamic microscopy of bidisperse colloidal suspensions

Research tasks in microgravity include monitoring the dynamics of constituents of varying size and mobility in processes such as aggregation, phase separation, or self-assembly. We use differential dynamic microscopy, a method readily implemented with equipment available on the International Space Station, to simultaneously resolve the dynamics of particles of radius 50 nm and 1 μm in bidisperse aqueous suspensions. Whereas traditional dynamic light scattering fails to detect a signal from the larger particles at low concentrations, differential dynamic microscopy exhibits enhanced sensitivity in these conditions by accessing smaller wavevectors where scattering from the large particles is stronger. Interference patterns due to scattering from the large particles induce non-monotonic decay of the amplitude of the dynamic correlation function with the wavevector. We show that the position of the resulting minimum contains information on the vertical position of the particles. Together with the simple instrumental requirements, the enhanced sensitivity of differential dynamic microscopy makes it an appealing alternative to dynamic light scattering to characterize samples with complex dynamics.

Particle dispersion in porous media: Differentiating effects of geometry and fluid rheology

We investigate the effects of geometric order and fluid rheology on the dispersion of micron-sized particles in two-dimensional microfluidic porous media. Particles suspended in a mixture of glycerol and water or in solutions of partially hydrolyzed polyacrylamide (HPAM) polymers were imaged as they flowed through arrays of microscale posts. From the trajectories of the particles, we calculated the velocity distributions and thereafter obtained the longitudinal and transverse dispersion coefficients. Particles flowed in the shear-thinning HPAM solution through periodic arrays of microposts were more likely to switch between streamlines, due to elastic instabilities. As a result, the distributions of particle velocity were broader in HPAM solutions than in glycerol-water mixtures for ordered geometries. In a disordered array of microposts, however, there was little difference between the velocity distributions obtained in glycerol-water and in HPAM solutions. Correspondingly, particles flowed through ordered post arrays in HPAM solutions exhibited enhanced transverse dispersion. This result suggests that periodic geometric order amplifies the effects of the elasticity-induced velocity fluctuations, whereas geometric disorder of barriers effectively averages out the fluctuations.

Confinement-driven organization of a histone-complexed DNA molecule in a dense array of nanoposts

The first step in the controlled storage of lengthy DNA molecules is to keep DNA molecules separated while integrated in micrometer-sized space. Herein, we present hybrid Monte Carlo simulations of a histone-complexed DNA (hcDNA) molecule confined in a dense array of nanoposts. Depending on the nanopost dimension, a single, 8.7 kilobase pair hcDNA molecule was either localized and elongated in a single inter-post space surrounded by four nanoposts or spread over several inter-post spaces through passages between two neighboring nanoposts. The conformational change of a hcDNA molecule is interpreted in terms of competitive effects of confinements in the inter-post and passage spaces. We propose that, by elaborately designing nanopost arrays, the competitive confinement effects can be adjusted such that each hcDNA molecule is localized in a single inter-post space, and thereby multiple hcDNA molecules can be physically separated from each other while stored together in the nanopost array.

Single Particle Tracking: From Theory to Biophysical Applications

After three decades of developments, single particle tracking (SPT) has become a powerful tool to interrogate dynamics in a range of materials including live cells and novel catalytic supports because of its ability to reveal dynamics in the structure-function relationships underlying the heterogeneous nature of such systems. In this review, we summarize the algorithms behind, and practical applications of, SPT. We first cover the theoretical background including particle identification, localization, and trajectory reconstruction. General instrumentation and recent developments to achieve two- and three-dimensional subdiffraction localization and SPT are discussed. We then highlight some applications of SPT to study various biological and synthetic materials systems. Finally, we provide our perspective regarding several directions for future advancements in the theory and application of SPT.

Crowding-facilitated macromolecular transport in attractive micropost arrays

Our study of DNA dynamics in weakly attractive nanofabricated post arrays revealed crowding enhances polymer transport, contrary to hindered transport in repulsive medium. The coupling of DNA diffusion and adsorption to the microposts results in more frequent cross-post hopping and increased long-term diffusivity with increased crowding density. We performed Langevin dynamics simulations and found maximum long-term diffusivity in post arrays with gap sizes comparable to the polymer radius of gyration. We found that macromolecular transport in weakly attractive post arrays is faster than in non-attractive dense medium. Furthermore, we employed hidden Markov analysis to determine the transition of macromolecular adsorption-desorption on posts and hopping between posts. The apparent free energy barriers are comparable to theoretical estimates determined from polymer conformational fluctuations.

Diffusive dynamics of polymer chains in an array of nanoposts

The diffusion of the head, side, and middle segments in confined polymer chains displays different dynamics in different directions.

Nanoparticle diffusion in crowded and confined media

We identify distinct mechanisms controlling slowing of nanoparticle diffusion through complex media featuring both rigid geometrical confinement and soft mobile crowders. Towards this end, we use confocal microscopy and single particle tracking to probe the diffusion of 400 nm nanoparticles suspended in Newtonian water, in a Newtonian glycerol/water mixture, or in a non-Newtonian polymer solution through a model porous medium, a packed bed of microscale glass beads. The mobility of nanoparticles, as quantified by the long-time diffusion coefficient extracted from the particle mean-squared displacement, slows as the average pore size of the packed bed media decreases for both Newtonian and non-Newtonian solutions. The distribution of particle displacements is non-Gaussian, consistent with the spatial heterogeneity of the geometrical confinement imposed by the packed bed. The slowing of nanoparticle mobility in all solutions follows the predictions of models that describe hydrodynamic interactions with the packed bed. In non-Newtonian solutions, depletion interactions due to the polymers near the glass beads result in temporary adsorption of particles onto the bead surface, as indicated by a stretched-exponential distribution of residence times. Our results therefore suggest that the confined diffusive dynamics of nanoparticles in polymer solutions is controlled by two competing mechanisms: hydrodynamic interactions between particles and spatial obstacles, which dictate the long-time slowing of diffusion, and depletion interactions between particles and confining walls due to the macromolecules, which control transient adsorption and hence alter the statistics of the short-time motion.

Light-sheet microscopy with digital Fourier analysis measures transport properties over large field-of-view

Using light-sheet microscopy combined with digital Fourier methods we probe the dynamics of colloidal samples and DNA molecules. This combination, referred to as selective-plane illumination differential dynamic microscopy (SPIDDM), has the benefit of optical sectioning to study, with minimal photobleaching, thick samples allowing us to measure the diffusivity of colloidal particles at high volume fractions. Further, SPIDDM exploits the inherent spatially-varying thickness of Gaussian light-sheets. Where the excitation sheet is most focused, we capture high spatial frequency dynamics as the signal-to-background is high. In thicker regions, we capture the slower dynamics as diffusion out of the sheet takes longer.

Subsurface to substrate: dual-scale micro/nanofluidic networks for investigating transport anomalies in tight porous media

Micro/nanofluidic experiments in synthetic representations of tight porous media, often referred to as "reservoir-on-a-chip" devices, are an emerging approach to researching anomalous fluid transport trends in energy-bearing and fluid-sequestering geologic porous media. We detail, for the first time, the construction of dual-scale micro/nanofluidic devices that are relatively large-scale, two-dimensional network representations of granular and fractured nanoporous media. The fabrication scheme used in the development of the networks on quartz substrates (master patterns) is facile and replicable: transmission electron microscopy (TEM) grids with lacey carbon support film were used as shadow masks in thermal evaporation/deposition and reactive ion etch (RIE) was used for hardmask pattern transfer. The reported nanoscale network geometries are heterogeneous and composed of hydraulically resistive paths (throats) meeting at junctures (pores) to mimic the low topological connectivity of nanoporous sedimentary rocks such as shale. The geometry also includes homogenous microscale grid patterns that border the nanoscale networks and represent microfracture pathways. Master patterns were successfully replicated with a sequence of polydimethylsiloxane (PDMS) and Norland Optical Adhesive (NOA) 63 polymers. The functionality of the fabricated quartz and polymer nanofluidic devices was validated with aqueous imbibition experiments and differential interference contrast microscopy. These dual-scale fluidic devices are promising predictive tools for hypothesis testing and calibration against bulk fluid measurements in tight geologic, biologic, and synthetic porous material of similar dual-scale pore structure. Applications to shale/mudrock transport studies in particular are focused on herein.

Polymer Surface Transport Is a Combination of in-Plane Diffusion and Desorption-Mediated Flights

Previous studies of polymer motion at solid/liquid interfaces described the transport in the context of a continuous time random walk (CTRW) process, in which diffusion switches between desorption-mediated "flights" (i.e., hopping) and surface-adsorbed waiting-time intervals. However, it has been unclear whether the waiting times represented periods of complete immobility or times during which molecules engaged in a different (e.g., slower or confined) mode of interfacial transport. Here we designed high-throughput, single-molecule tracking measurements to address this question. Specifically, we studied polymer dynamics on either chemically homogeneous or nanopatterned surfaces (hexagonal diblock copolymer films) with chemically distinct domains, where polymers were essentially excluded from the low-affinity domains, eliminating the possibility of significant continuous diffusion in the absence of desorption-mediated flights. Indeed, the step-size distributions on homogeneous surfaces exhibited an additional diffusive mode that was missing on the chemically heterogeneous nanopatterned surfaces, confirming the presence of a slow continuous mode due to 2D in-plane diffusion. Kinetic Monte Carlo simulations were performed to test this model and, with the theoretical in-plane diffusion coefficient of D_2D = 0.20 μm²/s, we found a good agreement between simulations and experimental data on both chemically homogeneous and nanopatterned surfaces.

Optical tracking of nanoscale particles in microscale environments

The trajectories of nanoscale particles through microscale environments record useful information about both the particles and the environments. Optical microscopes provide efficient access to this information through measurements of light in the far field from nanoparticles. Such measurements necessarily involve trade-offs in tracking capabilities. This article presents a measurement framework, based on information theory, that facilitates a more systematic understanding of such trade-offs to rationally design tracking systems for diverse applications. This framework includes the degrees of freedom of optical microscopes, which determine the limitations of tracking measurements in theory. In the laboratory, tracking systems are assemblies of sources and sensors, optics and stages, and nanoparticle emitters. The combined characteristics of such systems determine the limitations of tracking measurements in practice. This article reviews this tracking hardware with a focus on the essential functions of nanoparticles as optical emitters and microenvironmental probes. Within these theoretical and practical limitations, experimentalists have implemented a variety of tracking systems with different capabilities. This article reviews a selection of apparatuses and techniques for tracking multiple and single particles by tuning illumination and detection, and by using feedback and confinement to improve the measurements. Prior information is also useful in many tracking systems and measurements, which apply across a broad spectrum of science and technology. In the context of the framework and review of apparatuses and techniques, this article reviews a selection of applications, with particle diffusion serving as a prelude to tracking measurements in biological, fluid, and material systems, fabrication and assembly processes, and engineered devices. In so doing, this review identifies trends and gaps in particle tracking that might influence future research.