Diffusion Of Tracer Particles Research Articles

Impact of ageing on structure of random sequential adsorption packings of discorectangles

The ageing processes in the systems of elongated particles (discorectangles) adsorbed on a plane was studied numerically. An off-lattice model with continuous positional and orientational degrees of freedom was tested. The initial jammed state was produced using the random sequential adsorption (RSA) model. The transition from the jammed to equilibrium states were performed via translational and rotational Brownian motions. An aspect ratio of the particles (length-to-width ratio) was varied within the range ε=1−12 . At ɛ < 10 the relaxation into the isotropic state was always observed. In the intermediate range, 10⩽ε⩽11 , the relaxation transition into the states with ordered domains was observed. Particularly, for ɛ = 10 this transition was related with significant finite size scaling effects. For particles with ɛ = 12 formation of the large scale quasi-nematic domains and unlimited domain growth was observed. The impact of the relaxation on the domain structure, porosity, percolation connectivity and tracer particle diffusion in such barrier systems was also discussed.

Behind sporadic ALS: A biophysical characterization of motor neurons in health and disease.

Amyotrophic lateral sclerosis (ALS) is characterized by death of motor neurons due to accumulation of aggregates and perturbation of intracellular transport. The underlying causes of these changes remain yet mysterious. Although a fraction of cases are caused by inherited mutations, the majority are sporadic, and the risk increases with age. The cell interior is extremely crowded with organelles and macromolecular complexes. This intracellular molecular crowding crucially impacts molecular assembly and transport. We hypothesized that age-associated changes could perturb macromolecular crowding and participate in the pathogenesis of ALS. We generated and leveraged genetically encoded multimeric nanoparticles (GEMs) to quantify macromolecular crowding in human iPSC-derived motor neurons, for the first time. The diffusivity of tracer particles like GEMs is generally decreased by molecular crowding and increased by active cellular processes. GEMs’ diffusivity was different depending on the subcellular localization. We observed that GEMs’ diffusivity is sensitive to the compressive state of the cell overall, while is oriented and regulated by ATP-dependent processes only in the neurites (axons and dendrites). Mechanical and osmotic pressures can increase in the aged brain. Motor neurons from ALS patients did not show modified basal molecular crowding, but might be more sensitive to mechanical perturbations. We are now studying how molecular crowding perturbations impact aggregation and transport of TDP-43, a protein found in ALS aggregates, in human motor neurons. We are performing the first high-throughput characterization of the biophysical properties of motor neurons to decipher the relationship between intracellular biophysical changes and initiation of protein aggregation in ALS.

Equivalence of Fluctuation-Dissipation and Edwards' Temperature in Cyclically Sheared Granular Systems.

Using particle trajectory data obtained from x-ray tomography, we determine two kinds of effective temperatures in a cyclically sheared granular system. The first one is obtained from the fluctuation-dissipation theorem which relates the diffusion and mobility of lighter tracer particles immersed in the system. The second is the Edwards compactivity defined via the packing volume fluctuations. We find robust agreement between these two temperatures, independent of the type of the tracers, cyclic shear amplitudes, and particle surface roughness, giving therefore the first experimental evidence that the concept of effective temperature is valid in driven frictional granular systems.

The structure of cellulose nanofibril networks at low concentrations and their stabilizing action on colloidal particles

The structure and dynamics of networks formed by rod-shaped particles can be indirectly investigated by measuring the diffusion of spherical tracer particles. This method was used to characterize cellulose nanofibril (CNF) networks in both dispersed and arrested states, the results of which were compared with coarse-grained Brownian dynamics simulations. At a CNF concentration of 0.2 wt% a transition was observed where, below this concentration tracer diffusion is governed by the increasing macroscopic viscosity of the dispersion. Above 0.2 wt%, the diffusion of small particles (20–40 nm) remains viscosity controlled, while particles (100–500 nm) become trapped in the CNF network. Sedimentation of silica microparticles (1–5 μm) in CNF dispersions was also determined, showing that sedimentation of larger particles is significantly affected by the presence of CNF. At concentrations of 0.2 wt%, the sedimentation velocity of 5 μm particles was reduced by 99 % compared to pure water.

Microrheology of Mucin-Albumin Assembly Using Diffusing Wave Spectroscopy.

Mucus plays an important role in the protection of the epithelial cells from various pathogens and low pH environments besides helping in the absorption of nutrients. Alteration of the rheology of the mucus layer leads to various disease conditions such as cystic fibrosis, Crohn's disease, and gastric ulcers, among others. Importantly, mucus consists of various mucins along with proteins such as immunoglobulin, lysozyme, and albumin. In the present study, we explore the effect of pH on the interactions between bovine serum albumin (BSA) and porcine gastric mucins using diffusing wave spectroscopy (DWS). The study unveils that BSA actively binds with mucin to form mucin-BSA complexes, which is largely driven by electrostatic interactions. Interestingly, such physical interactions significantly alter the microrheology of these biomaterials, which is indicated by a reduction in the diffusivity of tracer particles in DWS. An array of DWS experiments suggests that the interaction between mucin and BSA is the highest at pH 7.4 and the least at pH 3. Further analyses using atomic force microscopy showed the formation of a compact cross-linked colloidal network of mucin-BSA complexes at pH 7.4, which is the main reason for the reduction in the diffusivity of the tracer particles in DWS. Furthermore, the circular dichroism analysis revealed that the secondary structures of mucin-BSA complexes are markedly different from those of only mucin at pH 7.4. Importantly, such a difference has not been observed at pH 3, which confirms that largely electrostatic interactions drive the formation of mucin-BSA complexes at neutral pH. In such a scenario, the presence of Ca2+ ions is also found to facilitate bridging between BSA molecules, which is also reflected in the microrheology of the suspension of BSA-mucin complexes.

Hydrodynamics induce superdiffusive jumps of passive tracers along critical paths of random networks and colloidal gels.

We present a numerical study on the effect of hydrodynamic interactions (HI) on the diffusion of inert point tracer particles in several fixed random structures. As expected, the diffusion is hampered by the extra hydrodynamic friction introduced by the obstacle network. However, a non-trivial effect due to HI appears in the analysis of the van-Hove displacement probability close to the percolation threshold, where tracers diffuse through critical fractal paths. We show that the tracer dynamics can be split up into short and long jumps, the latter being ruled by either exponential or Gaussian van Hove distribution tails. While at short time HI slow down the tracer diffusion, at long times, hydrodynamic interactions with the obstacles increase the probability of longer jumps, which circumvent the traps of the labyrinth more easily. Notably, the relation between the anomalous diffusion exponent and the fractal dimension of the critical (intricate) paths is greater than one, which implies that the long-time (long-jump) diffusion is mildly superdiffuse. A possible reason for such a hastening of the diffusion along the network corridors is the hydrodynamically induced mobility anisotropy, which favours displacements parallel to the walls, an effect which has already been experimentally observed in collagen gels.

Measurements and characterization of the dynamics of tracer particles in an actin network.

The underlying physics governing the diffusion of a tracer particle in a viscoelastic material is a topic of some dispute. The long-term memory in the mechanical response of such materials should induce diffusive motion with a memory kernel, such as fractional Brownian motion (fBM). This is the reason that microrheology is able to provide the shear modulus of polymer networks. Surprisingly, the diffusion of a tracer particle in a network of a purified protein, actin, was found to conform to the continuous time random walk type (CTRW). We set out to resolve this discrepancy by studying the tracer particle diffusion using two different tracer particle sizes, in actin networks of different mesh sizes. We find that the ratio of tracer particle size to the characteristic length scale of a bio-polymer network plays a crucial role in determining the type of diffusion it performs. We find that the diffusion of the tracer particles has features of fBm when the particle is large compared to the mesh size, of normal diffusion when the particle is much smaller than the mesh size, and of the CTRW in between these two limits. Based on our findings, we propose and verify numerically a new model for the motion of the tracer in all regimes. Our model suggests that diffusion in actin networks consists of fBm of the tracer particle coupled with caging events with power-law distributed escape times.

Simulation study of passive rod diffusion in active bath: Nonmonotonic length dependence and abnormal translation-rotation coupling

Diffusion of tracer particles in active bath has attracted extensive attention in recent years. So far, most studies have considered isotropic spherical tracer particles, while the diffusion of anisotropic particles has rarely been involved. Here we investigate the diffusion dynamics of a rigid rod tracer in a bath of active particles by using Langevin dynamics simulations in a two-dimensional space. Particular attention is paid to how the translation (rotation) diffusion coefficient DT (DR) change with the length of rod L and active strength Fa. In all cases, we find that rod exhibits superdiffusion behavior in a short time scale and returns to normal diffusion in the long time limit. Both DT and DR increase with Fa, but interestingly, a nonmonotonic dependence of DT (DR) on the rod length has been observed. We have also studied the translation-rotation coupling of rod, and interestingly, a negative translation-rotation coupling is observed, indicating that rod diffuses more slowly in the parallel direction compared to that in the perpendicular direction, a counterintuitive phenomenon that would not exist in an equilibrium counterpart system. Moreover, this anomalous (diffusion) behavior is reentrant with the increase of Fa, suggesting two competitive roles played by the active feature of bath particles.

High-resolution, depth-resolved vascular leakage measurements using contrast-enhanced, correlation-gated optical coherence tomography in mice.

Vascular leakage plays a key role in vision-threatening retinal diseases such as diabetic retinopathy and age-related macular degeneration. Fluorescence angiography is the current gold standard for identification of leaky vasculature in vivo, however it lacks depth resolution, providing only 2D images that complicate precise identification and localization of pathological vessels. Optical coherence tomography (OCT) has been widely adopted for clinical ophthalmology due to its high, micron-scale resolution and rapid volumetric scanning capabilities. Nevertheless, OCT cannot currently identify leaky blood vessels. To address this need, we have developed a new method called exogenous contrast-enhanced leakage OCT (ExCEL-OCT) which identifies the diffusion of tracer particles around leaky vasculature following injection of a contrast agent. We apply this method to a mouse model of retinal neovascularization and demonstrate high-resolution 3D vascular leakage measurements in vivo for the first time.

Swimming Suppresses Correlations in Dilute Suspensions of Pusher Microorganisms

Active matter exhibits various forms of non-equilibrium states in the absence of external forcing, including macroscopic steady-state currents. Such states are often too complex to be modelled from first principles and our understanding of their physics relies heavily on minimal models. These have mostly been studied in the case of "dry" active matter, where particle dynamics are dominated by friction with their surroundings. Significantly less is known about systems with long-range hydrodynamic interactions that belong to "wet" active matter. Dilute suspensions of motile bacteria, modelled as self-propelled dipolar particles interacting solely through long-ranged hydrodynamic fields, are arguably the most studied example from this class of active systems. Their phenomenology is well-established: at sufficiently high density of bacteria, there appear large-scale vortices and jets comprising many individual organisms, forming a chaotic state commonly known as bacterial turbulence. As revealed by computer simulations, below the onset of collective motion, the suspension exhibits very strong correlations between individual microswimmers stemming from the long-ranged nature of dipolar fields. Here we demonstrate that this phenomenology is captured by the minimal model of microswimmers. We develop a kinetic theory that goes beyond the commonly used mean-field assumption, and explicitly takes into account such correlations. Notably, these can be computed exactly within our theory. We calculate the fluid velocity variance, spatial and temporal correlation functions, the fluid velocity spectrum, and the enhanced diffusivity of tracer particles. We find that correlations are suppressed by particle self-propulsion, although the mean-field behaviour is not restored even in the limit of very fast swimming.

Elucidating the Origin of Heterogeneous Anomalous Diffusion in the Cytoplasm of Mammalian Cells.

Diffusion of tracer particles in the cytoplasm of mammalian cells is often anomalous with a marked heterogeneity even within individual particle trajectories. Despite considerable efforts, the mechanisms behind these observations have remained largely elusive. To tackle this problem, we performed extensive single-particle tracking experiments on quantum dots in the cytoplasm of living mammalian cells at varying conditions. Analyses of the trajectories reveal a strong, microtubule-dependent subdiffusion with antipersistent increments and a substantial heterogeneity. Furthermore, particles stochastically switch between different mobility states, most likely due to transient associations with the cytoskeleton-shaken endoplasmic reticulum network. Comparison to simulations highlight that all experimental observations can be fully described by an intermittent fractional Brownian motion, alternating between two states of different mobility.

Anomalous diffusion and nonergodicity for heterogeneous diffusion processes with fractional Gaussian noise.

Heterogeneous diffusion processes (HDPs) feature a space-dependent diffusivity of the form D(x)=D_{0}|x|^{α}. Such processes yield anomalous diffusion and weak ergodicity breaking, the asymptotic disparity between ensemble and time averaged observables, such as the mean-squared displacement. Fractional Brownian motion (FBM) with its long-range correlated yet Gaussian increments gives rise to anomalous and ergodic diffusion. Here, we study a combined model of HDPs and FBM to describe the particle dynamics in complex systems with position-dependent diffusivity driven by fractional Gaussian noise. This type of motion is, inter alia, relevant for tracer-particle diffusion in biological cells or heterogeneous complex fluids. We show that the long-time scaling behavior predicted theoretically and by simulations for the ensemble- and time-averaged mean-squared displacements couple the scaling exponents α of HDPs and the Hurst exponent H of FBM in a characteristic way. Our analysis of the simulated data in terms of the rescaled variable y∼|x|^{1/(2/(2-α))}/t^{H} coupling particle position x and time t yields a simple, Gaussian probability density function (PDF), P_{HDP-FBM}(y)=e^{-y^{2}}/sqrt[π]. Its universal shape agrees well with theoretical predictions for both uni- and bimodal PDF distributions.

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.

Theory of tracer diffusion in concentrated hard-sphere suspensions

A phenomenological theory of diffusion and cross-diffusion of tracer particles in concentrated hard-sphere suspensions is developed. Expressions for the diffusion coefficients as functions of the host particle volume fraction are obtained up to the close-packing limit. In concentrated systems the tracer diffusivity decreases because of the reduced pore space available for diffusion. The tracer diffusivity can be modelled by a Stokes–Einstein equation with an effective viscosity that depends on the pore size. Tracer diffusion and segregation during sedimentation cease at a critical trapping volume fraction corresponding to a tracer glass transition. The tracer cross-diffusion coefficient, however, increases near the glass transition and diverges in the close-packed limit.

Absolute diffusion measurements of active enzyme solutions by NMR.

The diffusion of enzymes is of fundamental importance for many biochemical processes. Enhanced or directed enzyme diffusion can alter the accessibility of substrates and the organization of enzymes within cells. Several studies based on fluorescence correlation spectroscopy report enhanced diffusion of enzymes upon interaction with their substrate or inhibitor. In this context, major importance is given to the enzyme fructose-bisphosphate aldolase, for which enhanced diffusion has been reported even though the catalysed reaction is endothermic. Additionally, enhanced diffusion of tracer particles surrounding the active aldolase enzymes has been reported. These studies suggest that active enzymes can act as chemical motors that self-propel and give rise to enhanced diffusion. However, fluorescence studies of enzymes can, despite several advantages, suffer from artefacts. Here, we show that the absolute diffusion coefficients of active enzyme solutions can be determined with Pulsed Field Gradient Nuclear Magnetic Resonance (PFG-NMR). The advantage of PFG-NMR is that the motion of the molecule of interest is directly observed in its native state without the need for any labelling. Furthermore, PFG-NMR is model-free and thus yields absolute diffusion constants. Our PFG-NMR experiments of solutions containing active fructose-bisphosphate aldolase from rabbit muscle do not show any diffusion enhancement for the active enzymes, nor the surrounding molecules. Additionally, we do not observe any diffusion enhancement of aldolase in the presence of its inhibitor pyrophosphate.

Structural changes in nanoparticle-hydrogel composites at very low filler concentrations.

We study the enhancement of the stiffness of two families of hydrogels (polyacrylamide, PAAm, and polydimethylacrylamide, PDMA) due to the additions of very small amounts of silica nanofillers. It is well established that high concentrations of silica nanoparticles enhance the toughness of both hydrogel types, but significantly more for the PDMA based gels that adsorb readily to silica surfaces. In order to decouple the structural changes in the gels that stem either from polymerization kinetics or from the interactions between nanofillers and polymers, we use a photoinitiator for the polymerization of the composite gels that promotes the structural homogeneity of the hydrogels. We characterize both the mechanical and structural properties of the composite hydrogels as a function of nanofiller concentration, by calculating the single particle diffusion of inert polystyrene tracer particles of three different sizes. In agreement with previous experiments, we find that silica nanoparticles increase the stiffness of PAAm gels more than expected for passive fillers. Surprisingly, we find that a small addition of silica nanoparticles during gel polymerization to PDMA based hydrogels softens them. We attribute this effect to an increase of the average mesh size of the gel, allowing particles of 0.49 μm in diameter to diffuse normally through the gel, but restricting the motion of larger particles. A further increase in silica nanoparticle concentration results in the expected stiffening of the gel. PDMA based composites with a large mean pore size, as reported here, may find applications in particle separation and gentle fixation of microorganisms and cells.

Anomalous Diffusion of Sand Tracer Particles Under Waves

A model is presented for the horizontal and vertical diffusion of sand tracer particles by waves and is verified using a reanalysis of the experiments of Miller and Komar (1979, https://doi.org/10.1086/628455). In the model, sand particles take random jumps at a rate associated with the wave period but also can bury one another resulting in intermittent long rest times between jumps. The particle jump length between burials is modeled by considering a vortex entrainment and advection mechanism, resulting in a probability distribution as a function of wave orbital excursion amplitude and particle settling velocity. The model is formalized using the theory of continuous time random walks to obtain closed‐form expressions for the horizontal particle spreading rate, and plume shape, without tunable parameters. Importantly, the model predicts subdiffusive particle spreading, a previously unconsidered phenomenon that is apparent in the experimental data. The plume horizontal extent versus time is also well predicted compared to experimental data.

Dispersion in two-dimensional periodic channels with discontinuous profiles.

The effective diffusivity of Brownian tracer particles confined in periodic micro-channels is smaller than the microscopic diffusivity due to entropic trapping. Here, we study diffusion in two-dimensional periodic channels whose cross section presents singular points, such as abrupt changes of radius or the presence of thin walls, with openings, delimiting periodic compartments composing the channel. Dispersion in such systems is analyzed using the Fick-Jacobs (FJ) approximation. This approximation assumes a much faster equilibration in the lateral than in the axial direction, along which the dispersion is measured. If the characteristic width a of the channel is much smaller than the period L of the channel, i.e., ε = a/L is small, this assumption is clearly valid for Brownian particles. For discontinuous channels, the FJ approximation is only valid at the lowest order in ε and provides a rough, though on occasions rather accurate, estimate of the effective diffusivity. Here we provide formulas for the effective diffusivity in discontinuous channels that are asymptotically exact at the next-to-leading order in ε. Each discontinuity leads to a reduction of the effective diffusivity. We show that our theory is consistent with the picture of effective trapping rates associated with each discontinuity, for which our theory provides explicit and asymptotically exact formulas. Our analytical predictions are confirmed by numerical analysis. Our results provide a precise quantification of the kinetic entropic barriers associated with profile singularities.

Probe manipulators for Wendelstein 7-X and their interaction with the magnetic topology

Probe manipulators are a versatile addition to typical plasma edge diagnostics. Equipped with material samples they allow for detailed investigation of plasma–wall interaction processes, such as material erosion, deposition or impurity transport pathways. When combined with electrical probes, a study of scrape-off layer and plasma edge density, temperature and flow profiles as well as magnetic topologies is possible. A mid-plane manipulator is already in operation on Wendelstein 7-X. A system in the divertor region is currently under development. In the present paper we discuss the critical issue of heat and power loads, power redistribution and experimental access to the complex magnetic topology of Wendelstein 7-X. All the aforementioned aspects are of relevance for the design and operation of a probe manipulator in a device like Wendelstein 7-X. A focus is put on the topological region that is accessible for the different coil current configurations at Wendelstein 7-X and the power load on the manipulator with respect to the resulting different magnetic configurations. Qualitative analysis of power loads on plasma-facing components is performed using a numerical tracer particle diffusion tool provided via the Wendelstein 7-X Webservices.

Relative distance between tracers as a measure of diffusivity within moving aggregates

Tracking of particles, be it a passive tracer or an actively moving bacterium in the growing bacterial colony, is a powerful technique to probe the physical properties of the environment of the particles. One of the most common measures of particle motion driven by fluctuations and random forces is its diffusivity, which is routinely obtained by measuring the mean squared displacement of the particles. However, often the tracer particles may be moving in a domain or an aggregate which itself experiences some regular or random motion and thus masks the diffusivity of tracers. Here we provide a method for assessing the diffusivity of tracer particles within mobile aggregates by measuring the so-called mean squared relative distance (MSRD) between two tracers. We provide analytical expressions for both the ensemble and time averaged MSRD allowing for direct identification of diffusivities from experimental data.