Statistical and sampling issues when using multiple particle tracking

Comparative analysis of fluctuations in viscoelastic stress: A comparison of the temporary network and dumbbell models

Traditionally, stress fluctuations in flowing and deformed materials are overlooked, with an obvious focus on average stresses in a continuum mechanical approximation. However, these fluctuations, often dismissed as "noise," hold the potential to provide direct insights into the material structure and its structure-stress coupling, uncovering detailed aspects of fluid transport and relaxation behaviors. Despite advancements in experimental techniques allowing for the visualization of these fluctuations, their significance remains largely untapped as modeling efforts continue to target Newtonian fluids within the confines of Gaussian noise assumptions. In the present work, a comparative analysis of stress fluctuations in two distinct microstructural models is carried out: the temporary network model and the hydrodynamic dumbbell model. Despite both models conforming to the upper convected Maxwell model at a macroscopic level, the temporary network model predicts non-Gaussian fluctuations. We find that stress fluctuations within the temporary network model exhibit more pronounced abruptness at the local scale, with only an enlargement of the control volume leading to a gradual Gaussian-like noise, diminishing the differences between the two models. These findings underscore the heightened sensitivity of fluctuating rheology to microstructural details and the microstructure-flow coupling, beyond what is captured by macroscopically averaged stresses.

Extreme heterogeneity in the microrheology of lamellar surfactant gels analyzed with neural networks

The heterogeneity of the viscoelasticity of a lamellar gel network based on cetyl-trimethylammonium chloride and cetostearyl alcohol was studied using particle-tracking microrheology. A recurrent neural network (RNN) architecture was used for estimating the Hurst exponent, H, on small sections of tracks of probe spheres moving with fractional Brownian motion. Thus, dynamic segmentation of tracks via neural networks was used in microrheology and it is significantly more accurate than using mean square displacements (MSDs). An ensemble of 414 particles produces a MSD that is subdiffusive in time, t, with a power law of the form t^{0.74±0.02}, indicating power law viscoelasticity. RNN analysis of the probability distributions of H, combined with detailed analysis of the time-averaged MSDs of individual tracks, revealed diverse diffusion processes belied by the simple scaling of the ensemble MSD, such as caging phenomena, which give rise to the complex viscoelasticity of lamellar gels.

Microrheological characterisation of Cyanoflan in human blood plasma

Naturally occurring polysaccharidic biopolymers released by marine cyanobacteria are of great interest for numerous biomedical applications, such as wound healing and drug delivery. Such polymers generally exhibit high molecular weight and an entangled structure that impact the rheology of biological fluids. However, biocompatibility tests focus not so much on rheological properties as on immune response. In the present study, the rheological behaviour of native blood plasma as a function of the concentration of a cyanobacterium biopolymer is investigated via multiple particle tracking microrheology, which measures the Brownian motion of probes embedded in a sample, and cryogenic scanning electron microscope microstructural characterisation. We use Cyanoflan as the biopolymer of choice, and profit from our knowledge of its chemical structure and its exciting potential for biotechnological applications. A sol-gel transition is identified using time-concentration superposition and the power-law behaviour of the incipient network's viscoelastic response is observed in a variety of microrheological data. Our results point to rheology-based principles for blood compatibility tests by facilitating the assignment of quantitative values to specific properties, as opposed to more heuristic approaches.

Physiological Concentrations of Calcium Interact with Alginate and Extracellular DNA in the Matrices of Pseudomonas aeruginosa Biofilms to Impede Phagocytosis by Neutrophils

Biofilms are communities of interacting microbes embedded in a matrix of polymer, protein, and other materials. Biofilms develop distinct mechanical characteristics that depend on their predominant matrix components. These matrix components may be produced by microbes themselves or, for infections in vivo, incorporated from the host environment. Pseudomonas aeruginosa (P. aeruginosa) is a human pathogen that forms robust biofilms that extensively tolerate antibiotics and effectively evade clearance by the immune system. Two of the important bacterial-produced polymers in the matrices of P. aeruginosa biofilms are alginate and extracellular DNA (eDNA), both of which are anionic and therefore have the potential to interact electrostatically with cations. Many physiological sites of infection contain significant concentrations of the calcium ion (Ca2+). In this study, we investigate the structural and mechanical impacts of Ca2+ supplementation in alginate-dominated biofilms grown in vitro, and we evaluate the impact of targeted enzyme treatments on clearance by immune cells. We use multiple-particle tracking microrheology to evaluate the changes in biofilm viscoelasticity caused by treatment with alginate lyase or DNase I. For biofilms grown without Ca2+, we correlate a decrease in relative elasticity with increased phagocytic success. However, we find that growth with Ca2+ supplementation disrupts this correlation except in the case where both enzymes are applied. This suggests that the calcium cation may be impacting the microstructure of the biofilm in nontrivial ways. Indeed, confocal laser scanning fluorescence microscopy and scanning electron microscopy reveal unique Ca2+-dependent eDNA and alginate microstructures. Our results suggest that the presence of Ca2+ drives the formation of structurally and compositionally discrete microdomains within the biofilm through electrostatic interactions with the anionic matrix components eDNA and alginate. Further, we observe that these structures serve a protective function as the dissolution of both components is required to render biofilm bacteria vulnerable to phagocytosis by neutrophils.

Physiological concentrations of calcium interact with alginate and extracellular DNA in the matrices of Pseudomonas aeruginosa biofilms to impede phagocytosis by neutrophils

Biofilms are communities of interacting microbes embedded in a matrix of polymer, protein, and other materials. Biofilms develop distinct mechanical characteristics that depend on their predominant matrix components. These matrix components may be produced by microbes themselves or, for infections in vivo, incorporated from the host environment. Pseudomonas aeruginosa is a human pathogen that forms robust biofilms that extensively tolerate antibiotics and effectively evade clearance by the immune system. Two of the important bacterial-produced polymers in the matrices of P. aeruginosa biofilms are alginate and extracellular DNA (eDNA), both of which are anionic and therefore have the potential to interact electrostatically with cations. Many physiological sites of infection contain significant concentrations of the calcium ion (Ca2+). In this study we investigate the structural and mechanical impacts of Ca2+ supplementation in alginate-dominated biofilms grown in vitro and we evaluate the impact of targeted enzyme treatments on clearance by immune cells. We use multiple particle tracking microrheology to evaluate the changes in biofilm viscoelasticity caused by treatment with alginate lyase and/or DNAse I. For biofilms grown without Ca2+, we correlate a decrease in relative elasticity with increased phagocytic success. However, we find that growth with Ca2+ supplementation disrupts this correlation except in the case where both enzymes are applied. This suggests that the calcium cation may be impacting the microstructure of the biofilm in non-trivial ways. Indeed, confocal laser scanning fluorescence microscopy and scanning electron microscopy reveal unique Ca2+-dependent eDNA and alginate microstructures. Our results suggest that the presence of Ca2+ drives the formation of structurally and compositionally discrete microdomains within the biofilm through electrostatic interactions with the anionic matrix components eDNA and alginate. Further, we observe that these structures serve a protective function as the dissolution of both components is required to render biofilm bacteria vulnerable to phagocytosis by neutrophils.

Molecular Diffusion in Nanoreactors' Pore Channel System: Measurement Techniques, Structural Regulation, and Catalytic Effects

Nanoreactors, as a new class of materials with highly enriched and ordered pore channel structures, can achieve special catalytic effects by precisely identifying and controlling the molecular diffusion behavior within the ordered pore channel system. Nanoreactors-driven molecular diffusion within the ordered pore channels can be highly dependent on the local microenvironment in the nanoreactors' pore channel system. Although the diffusion process of molecules within the ordered pore channels of nanoreactors is crucial for the regulation of catalytic behaviors, it has not yet been as clearly elucidated as it deserves to be in this study. In this review, fundamental theory and measurement techniques for molecular diffusion in the pore channel system of nanoreactors are presented, structural regulation strategies of pore channel parameters for controlling molecular diffusion are discussed, and the effects of molecular diffusion in the pore channel system on catalytic reactivity and selectivity are further analyzed. This article attempts to further develop the underlying theory of molecular diffusion within the theoretical framework of nanoreactor-driven catalysis, and the proposed perspectives may contribute to the rational design of advanced catalytic materials and the precise control of complex catalytic kinetics.

Uncovering diffusive states of the yeast membrane protein, Pma1, and how labeling method can change diffusive behavior

We present and analyze video-microscopy-based single-particle-tracking measurements of the budding yeast (Saccharomyces cerevisiae) membrane protein, Pma1, fluorescently labeled either by direct fusion to the switchable fluorescent protein, mEos3.2, or by a novel, light-touch, labeling scheme, in which a 5 amino acid tag is directly fused to the C-terminus of Pma1, which then binds mEos3.2. The track diffusivity distributions of these two populations of single-particle tracks differ significantly, demonstrating that labeling method can be an important determinant of diffusive behavior. We also applied perturbation expectation maximization (pEMv2) (Koo and Mochrie in Phys Rev E 94(5):052412, 2016), which sorts trajectories into the statistically optimum number of diffusive states. For both TRAP-labeled Pma1 and Pma1-mEos3.2, pEMv2 sorts the tracks into two diffusive states: an essentially immobile state and a more mobile state. However, the mobile fraction of Pma1-mEos3.2 tracks is much smaller ([Formula: see text]) than the mobile fraction of TRAP-labeled Pma1 tracks ([Formula: see text]). In addition, the diffusivity of Pma1-mEos3.2's mobile state is several times smaller than the diffusivity of TRAP-labeled Pma1's mobile state. Thus, the two different labeling methods give rise to very different overall diffusive behaviors. To critically assess pEMv2's performance, we compare the diffusivity and covariance distributions of the experimental pEMv2-sorted populations to corresponding theoretical distributions, assuming that Pma1 displacements realize a Gaussian random process. The experiment-theory comparisons for both the TRAP-labeled Pma1 and Pma1-mEos3.2 reveal good agreement, bolstering the pEMv2 approach.

Insights and Heuristics for Predicting Diffusion Rates of Chemical Warfare Agents in Zirconium Metal-Organic Frameworks

Designing nanoporous catalysts to destroy chemical warfare agents (CWAs) and environmental contaminants requires consideration of both intrinsic catalytic activity and the mass transfer of molecules in and out of the pores. Polar adsorbates such as CWAs experience a heterogeneous environment in many metal-organic frameworks (MOFs) due to the arrangement of the metal nodes and organic linkers of the MOF. However, quantitative relationships between the pore architecture and the resulting diffusion properties of polar molecules have not been established. We used molecular dynamics simulations to calculate the diffusion coefficients of the CWA simulant dimethyl methyl phosphonate (DMMP) in a diverse set of 776 MOFs with Zr₆ nodes. We developed a 4-parameter machine learning model to predict DMMP diffusivities in Zr₆ MOFs and found the model to be transferable to the CWA sarin. We then developed a simplified heuristic based on the machine learning model that the node-node distance and accessible surface area should be maximized to find MOFs with rapid CWA diffusion.

A particulate blood analogue based on artificial viscoelastic blood plasma and RBC-like microparticles at a concentration matching the human haematocrit

There has been enormous interest in the production of fluids with rheological properties similar to those of real blood over the last few years. Application fields range from biomicrofluidics (microscale) to forensic science (macroscale). The inclusion of flexible microparticles in blood analogue fluids has been demonstrated to be essential in order to reproduce the behaviour of blood flow in these fields. Here, we describe a protocol to produce a whole human blood analogue composed of a proposed plasma analogue and flexible spherical microparticles that mimic the key structural attributes of RBCs (size and mechanical properties), at a concentration matching the human haematocrit (∼42% by volume). Polydimethylsiloxane (PDMS) flexible microparticles were used to mimic RBCs, whose capability to deform is tunable by means of the mixing ratio of the PDMS precursor. Their flow through glass micronozzles allowed us to find the appropriate mixing ratio of PDMS to have approximately the same Young's modulus (E) as that exhibited by real RBCs. Shear and extensional rheology and microrheology techniques were used to match the properties exhibited by human plasma and whole blood at body temperature (37 °C). Finally, we study the flow of our proposed fluid through a microfluidic channel, showing the in vitro reproduction of the multiphase flow effects taking place in the human microcirculatory system, such as the cell-free layer (CFL) and the Fåhræus-Lindqvist effect. A macroscale application in the field of forensic science is also presented, concerning the impact of our blood analogue droplets on a solid surface for bloodstain pattern analysis.

Brownian motion on an out-of-thermal-equilibrium surface

The motion of colloidal species on an out-of-thermal equilibrium surface is studied experimentally by optical microscopy. Water droplets of size in the micrometer range, spontaneously formed at a spherical-like interface between water and oil, are the colloidal species. The interface appears as a convex meniscus when putting water on oil with an added nonionic surfactant. Since the water density is greater than that of oil, the interface is produced into the oil. The spontaneously formed water droplets move attached to the interface while still growing from submicrometer sizes to a few micrometers. Although the dynamic nature of the process, with both the interface and the particles still changing, produces heterogeneities in the system, anomalous diffusion was not observed. The motion of the droplets has a well-identified Brownian component with a Gaussian distribution of steps due to the thermal agitation of the media surrounding the droplets and a drift component due to the effect of gravity.

Microrheology of Pseudomonas aeruginosa biofilms grown in wound beds

A new technique was used to measure the viscoelasticity of in vivo Pseudomonas aeruginosa biofilms. This was done through ex vivo microrheology measurements of in vivo biofilms excised from mouse wound beds. To our knowledge, this is the first time that the mechanics of in vivo biofilms have been measured. In vivo results are then compared to typical in vitro measurements. Biofilms grown in vivo are more relatively elastic than those grown in a wound-like medium in vitro but exhibited similar compliance. Using various genetically mutated P. aeruginosa strains, it is observed that the contributions of the exopolysaccharides Pel, Psl, and alginate to biofilm viscoelasticity were different for the biofilms grown in vitro and in vivo. In vitro experiments with collagen containing medium suggest this likely arises from the incorporation of host material, most notably collagen, into the matrix of the biofilm when it is grown in vivo. Taken together with earlier studies that examined the in vitro effects of collagen on mechanical properties, we conclude that collagen may, in some cases, be the dominant contributor to biofilm viscoelasticity in vivo.

Nanoconfinement and mass transport in metal-organic frameworks

The ubiquity of metal-organic frameworks in recent scientific literature underscores their highly versatile nature. MOFs have been developed for use in a wide array of applications, including: sensors, catalysis, separations, drug delivery, and electrochemical processes. Often overlooked in the discussion of MOF-based materials is the mass transport of guest molecules within the pores and channels. Given the wide distribution of pore sizes, linker functionalization, and crystal sizes, molecular diffusion within MOFs can be highly dependent on the MOF-guest system. In this review, we discuss the major factors that govern the mass transport of molecules through MOFs at both the intracrystalline and intercrystalline scale; provide an overview of the experimental and computational methods used to measure guest diffusivity within MOFs; and highlight the relevance of mass transfer in the applications of MOFs in electrochemical systems, separations, and heterogeneous catalysis.

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.

Effect of collagen and EPS components on the viscoelasticity of Pseudomonas aeruginosa biofilms

Pseudomonas aeruginosa is an opportunistic pathogen that causes thousands of deaths every year in part due to its ability to form biofilms composed of bacteria embedded in a matrix of self-secreted extracellular polysaccharides (EPS), e-DNA, and proteins. In chronic wounds, biofilms are exposed to the host extracellular matrix, of which collagen is a major component. How bacterial EPS interacts with host collagen and whether this interaction affects biofilm viscoelasticity is not well understood. Since physical disruption of biofilms is often used in their removal, knowledge of collagen's effects on biofilm viscoelasticity may enable new treatment strategies that are better tuned to biofilms growing in host environments. In this work, biofilms are grown in the presence of different concentrations of collagen that mimic in vivo conditions. In order to explore collagen's interaction with EPS, nine strains of P. aeruginosa with different patterns of EPS production were used to grow biofilms. Particle tracking microrheology was used to characterize the mechanical development of biofilms over two days. Collagen is found to decrease biofilm compliance and increase relative elasticity regardless of the EPS present in the system. However, this effect is minimized when biofilms overproduce EPS. Collagen appears to become a de facto component of the EPS, through binding to bacteria or physical entanglement.

Topology-Dependent Alkane Diffusion in Zirconium Metal-Organic Frameworks

Metal-organic frameworks (MOFs) can be designed for chemical applications by modulating the size and shape of intracrystalline pores through selection of their nodes and linkers. Zirconium nodes with variable connectivity to organic linkers allow for a broad range of topological nets that have diverse pore structures even for a consistent set of linkers. Identifying an optimal pore structure for a given application, however, is complicated by the large material space of possible MOFs. In this work, molecular dynamics simulations were used to determine how a MOF's topology affects the diffusion of propane and isobutane over the full range of loadings and to understand how MOFs can be tuned to reduce transport limitations for applications in separations and catalysis. High-throughput simulation techniques were employed to efficiently calculate loading-dependent diffusivities in 38 MOFs. The results show that topologies with higher node connectivity have reduced alkane diffusivities compared to topologies with lower node connectivity. Molecular siting techniques were used to elucidate how the pore structures in different topologies affect adsorbate diffusivities.

3D rotational motion of an endocytic vesicle on a complex microtubule network in a living cell

The transport dynamics of endocytic vesicles in a living cell contains essential biomedical information. Although the movement mechanism of a vesicle by motor proteins has been revealed, understanding the precise movement of vesicles on the cytoskeleton in a living cell has been considered challenging, due to the complex 3D network of cytoskeletons. Here, we specify the shape of the 3D interaction between the vesicle and microtubule, based on the theoretically estimated location of the microtubule and the vesicle trajectory data acquired at high spatial and temporal precision. We detected that vesicles showed more frequent direction changes with either in very acute or in obtuse angles than right angles, on similar time scales in a microtubule network. Interestingly, when a vesicle interacted with a relatively longer (> 400 nm) microtubule filament, rotational movement along the axis of the microtubule was frequently observed. Our results are expected to give in-depth insight into understanding the actual 3D interactions between the intracellular molecule and complex cytoskeletal network.

Predicting in situ nanoparticle behavior using multiple particle tracking and artificial neural networks

Predictive models of nanoparticle transport can drive design of nanotherapeutic platforms to overcome biological barriers and achieve localized delivery. In this paper, we demonstrate the ability of artificial neural networks to predict both nanoparticle properties, such as size and protein adsorption, and aspects of the brain microenvironment, such as cell internalization, viscosity, and brain region by using large (>100 000) trajectory datasets collected via multiple particle tracking in in vitro gel models of the brain and cultured organotypic brain slices. Our neural network achieved a 0.75 recall score when predicting gel viscosity based on trajectory datasets, compared to 0.49 using an obstruction scaling model. When predicting in situ nanoparticle size based on trajectory datasets, neural networks achieved a 0.90 recall score compared to 0.83 using an optimized Stokes-Einstein predictor. To distinguish between nanoparticles of different sizes in more complex nanoparticle mixtures, our neural network achieved up to a recall score of 0.85. Even in cases of more nuanced output variables where mathematical models are not available, such as protein adhesion, neural networks retained the ability to distinguish between particle populations (recall score of 0.89). These findings demonstrate how trajectory datasets in combination with machine learning techniques can be used to characterize the particle-microenvironment interaction space.

Improving Diameter Accuracy for Dynamic Imaging Microscopy for Different Particle Types

Dynamic imaging analysis instruments are used for sizing particles of different types that might appear in a biopharmaceutical. These instruments are calibrated using polystyrene latex microspheres in water, which is a significantly different system than the typical particles imaged in a formulation. We show how the instruments, when reporting an equivalent diameter, set a threshold for image processing and then apply a built-in correction to account for fuzzy boundary effects. We investigate the degree to which the threshold value and built-in correction influences the size, and ultimately particle size distribution, that the instrument reports on other particle types. Size corrections for a dynamic imaging system in a typical optical configuration were determined by comparison of equivalent image diameters with diameters from Brownian motion tracking of particles. A variety of particles were characterized: aggregates made from a monoclonal antibody available as reference material RM 8671 from the National Institute of Standards and Technology, bovine serum albumin aggregates, silicone oil droplets, polystyrene microspheres, and ethylene tetrafluoroethylene particles, a protein aggregate simulant (National Institute of Standards and Technology reference material RM 8634). The results show that the protein aggregates and ethylene tetrafluoroethylene are very similar to one another but quite different from the polystyrene calibration spheres. This points the way to developing new correction factors and calibration procedures based on particle type.

Characterization of the Kinetics and Mechanism of Degradation of Human Mesenchymal Stem Cell-Laden Poly(ethylene glycol) Hydrogels

Human mesenchymal stem cells (hMSCs) are motile cells that migrate from their native niche to wounded sites where they regulate inflammation during healing. New materials are being developed as hMSC delivery platforms to enhance wound healing. To act as an effective wound healing material, the hydrogel must degrade at the same rate as tissue regeneration, while maintaining a high cell viability. This work determines the kinetics and mechanism of cell-mediated degradation in hMSC-laden poly(ethylene glycol) (PEG) hydrogels. We use a well-established hydrogel scaffold that is composed of a backbone of four-arm star PEG functionalized with norbornene that is cross-linked with a matrix metalloproteinase (MMP) degradable peptide. This peptide sequence is cleaved by cell-secreted MMPs, which allow hMSCs to actively degrade the hydrogel during motility. Three mechanisms of degradation are characterized: hydrolytic, noncellular enzymatic and cell-mediated degradation. We use bulk rheology to characterize hydrogel material properties and quantify degradation throughout the entire reaction. Hydrolysis and noncellular enzymatic degradation are first characterized in hydrogels without hMSCs, and follow first-order and Michaelis-Menten kinetics, respectively. A high cell viability is measured in hMSC-laden hydrogels, even after shearing on the rheometer. After confirming hMSC viability, bulk rheology characterizes cell-mediated degradation. When comparing cell-mediated degradation to noncellular degradation mechanisms, cell-mediated degradation is dominated by enzymatic degradation. This indicates hydrogels with hMSCs are degraded primarily due to cell-secreted MMPs and very little network structure is lost due to hydrolysis. Modeling cell-mediated degradation provides an estimate of the initial concentration of MMPs secreted by hMSCs. By changing the concentration of hMSCs, we determine the initial MMP concentration increases with increasing hMSC concentration. This work characterizes the rate and mechanism of scaffold degradation, giving new insight into the design of these materials as implantable scaffolds.

Measurement of Average Aggregate Density by Sedimentation and Brownian Motion Analysis

The spatially averaged density of protein aggregates is an important parameter that can be used to relate size distributions measured by orthogonal methods, to characterize protein particles, and perhaps to estimate the amount of protein in aggregate form in a sample. We obtained a series of images of protein aggregates exhibiting Brownian diffusion while settling under the influence of gravity in a sealed capillary. The aggregates were formed by stir-stressing a monoclonal antibody (NISTmAb). Image processing yielded particle tracks, which were then examined to determine settling velocity and hydrodynamic diameter down to 1 μm based on mean square displacement analysis. Measurements on polystyrene calibration microspheres ranging in size from 1 to 5 μm showed that the mean square displacement diameter had improved accuracy over the diameter derived from imaged particle area, suggesting a future method for correcting size distributions based on imaging. Stokes' law was used to estimate the density of each particle. It was found that the aggregates were highly porous with density decreasing from 1.080 to 1.028 g/cm³ as the size increased from 1.37 to 4.9 μm.

Molecular Simulation Insights on Xe/Kr Separation in a Set of Nanoporous Crystalline Membranes

Separation of xenon and krypton is highly relevant to several applications such as spent nuclear fuel processing. Molecular simulation has been extensively used to understand the Kr/Xe separation performance of nanoporous materials for adsorption-based technologies but less frequently for membrane-based technologies. Motivated by recent experimental reports on krypton-selective membranes, herein, we present grand canonical Monte Carlo and biased molecular dynamics simulations (using adaptive biasing force) to elucidate the nature of adsorption- and diffusion-based Kr/Xe separation mechanisms in a set of nanoporous materials: SAPO-34, ZIF-8, UiO-66, and IRMOF-1. Xenon is found to preferentially adsorb on all materials, but diffusion selectivity for krypton is found to dominate the overall membrane separation selectivity. To increase adsorption selectivity for krypton, large pore cages are found to be desirable. To increase diffusion selectivity for krypton, stiff pore windows with a diameter smaller than xenon (but larger than krypton) are found to be desirable. No perfect molecular sieving was found, but the relatively rigid SAPO-34 was more effective at excluding xenon than the more flexible ZIF-8. Indeed, during xenon "window crossing," the SAPO-34 window opened to only 3.8 Å, while the ZIF-8 window opened to 4.1 Å, resulting in a lower free energy "diffusion" barrier for xenon in ZIF-8. Therefore, an ideal membrane material for Kr/Xe separation should be rigid and have large pore cages and small pore windows. Temperature was found to have opposite effects on adsorption and diffusion selectivity, but because of the dominance of diffusion selectivity, our simulations indicate that it is preferable to operate membranes for Kr/Xe separation at lower temperatures than at higher ones.

Multiple particle tracking study of thermally-gelling nanoemulsions

We perform multiple particle tracking (MPT) on a thermally-gelling oil-in-water nanoemulsion system. Carboxylated and plain polystyrene probes are used to investigate the role of colloidal probe size and surface chemistry on MPT in the nanoemulsion system. As temperature increases, hydrophobic groups of PEG-based gelators (PEGDA) partition into the oil/water interface and bridge droplets. This intercolloidal attraction generates a wide variety of microstructures consisting of droplet-rich and droplet-poor phases. By tailoring the MPT colloidal probe surface chemistry, we can control the residence of probes in each domain, thus allowing us to independently probe each phase. Our results show stark differences in probe dynamics in each domain. For certain conditions, the mean squared displacement (MSD) can differ by over four orders of magnitude for the same probe size but different surface chemistry. Carboxylated probe surface chemistries result in "slippery" probes while plain polystyrene probes appear to tether to the nanoemulsion gel network. We also observe probe hopping between pores in the gel for carboxylated probes. Our approach demonstrates that probes with different surface chemistries are useful in probing the local regions of a colloidal gel and allows the measurement of local properties within structurally heterogeneous hydrogels.

Decorrelation correction for nanoparticle tracking analysis of dilute polydisperse suspensions in bulk flow

Nanoparticle tracking analysis, a multiprobe single particle tracking technique, is a widely used method to quickly determine the concentration and size distribution of colloidal particle suspensions. Many popular tools remove non-Brownian components of particle motion by subtracting the ensemble-average displacement at each time step, which is termed dedrifting. Though critical for accurate size measurements, dedrifting is shown here to introduce significant biasing error and can fundamentally limit the dynamic range of particle size that can be measured for dilute heterogeneous suspensions such as biological extracellular vesicles. We report a more accurate estimate of particle mean-square displacement, which we call decorrelation analysis, that accounts for correlations between individual and ensemble particle motion, which are spuriously introduced by dedrifting. Particle tracking simulation and experimental results show that this approach more accurately determines particle diameters for low-concentration polydisperse suspensions when compared with standard dedrifting techniques.

Real-Space, in Situ Maps of Hydrogel Pores

We characterize the porosity of hydrogels by imaging the displacement trajectories of embedded tracer particles. This offers the possibility of characterizing the size and projected shape of individual pores as well as direct, real-space maps of heterogeneous porosity and its distribution. The scheme shows that when fluorescent spherical particles treated to avoid specific adsorption are loaded into the gel, their displacement trajectories from Brownian motion report on the size and projected shape in which the pore resides, convoluted by the particle size. Of special interest is how pores and their distribution respond to stimuli. These ideas are validated in agarose gels loaded with latex particles stabilized by adsorbed bovine serum albumin. Gels heated from room temperature produced an increasingly more monodisperse pore size distribution because increasing temperature preferentially enlarges smaller pores, but this was irreversible upon cooling, and shearing agarose gels beyond the yield point destroyed larger pores preferably. The method is considered to be generalizable beyond the agarose system presented here as proof of concept.

Systems-level approach to uncovering diffusive states and their transitions from single-particle trajectories

The stochastic motions of a diffusing particle contain information concerning the particle's interactions with binding partners and with its local environment. However, an accurate determination of the underlying diffusive properties, beyond normal diffusion, has remained challenging when analyzing particle trajectories on an individual basis. Here, we introduce the maximum-likelihood estimator (MLE) for confined diffusion and fractional Brownian motion. We demonstrate that this MLE yields improved estimation over traditional mean-square displacement analyses. We also introduce a model selection scheme (that we call mleBIC) that classifies individual trajectories to a given diffusion mode. We demonstrate the statistical limitations of classification via mleBIC using simulated data. To overcome these limitations, we introduce a version of perturbation expectation-maximization (pEMv2), which simultaneously analyzes a collection of particle trajectories to uncover the system of interactions that give rise to unique normal and/or non-normal diffusive states within the population. We test and evaluate the performance of pEMv2 on various sets of simulated particle trajectories, which transition among several modes of normal and non-normal diffusion, highlighting the key considerations for employing this analysis methodology.

Minimizing biases associated with tracking analysis of submicron particles in heterogeneous biological fluids

Tracking the dynamic motion of individual nanoparticles or viruses offers quantitative insights into their real-time behavior and fate in different biological environments. Indeed, particle tracking is a powerful tool that has facilitated the development of drug carriers with enhanced penetration of mucus, brain tissues and other extracellular matrices. Nevertheless, heterogeneity is a hallmark of nanoparticle diffusion in such complex environments: identical particles can exhibit strongly hindered or unobstructed diffusion within microns of each other. The common practice in 2D particle tracking, namely analyzing all trackable particle traces with equal weighting, naturally biases towards rapidly diffusing sub-populations at shorter time scales. This in turn results in misrepresentation of particle behavior and a systematic underestimate of the time necessary for a population of nanoparticles to diffuse specific distances. We show here via both computational simulation and experimental data that this bias can be rigorously corrected by weighing the contribution by each particle trace on a 'frame-by-frame' basis. We believe this methodology presents an important step towards objective and accurate assessment of the heterogeneous transport behavior of submicron drug carriers and pathogens in biological environments.

Heterogeneous Diffusion of Alkanes in the Hierarchical Metal-Organic Framework NU-1000

The metal-organic framework (MOF) NU-1000 is a hierarchical material that comprises both micropores and mesopores in its crystalline structure. Because the pore structure is perfectly defined, NU-1000 is an interesting material for improving our understanding of diffusion in hierarchically structured materials. Here, we present molecular dynamics simulations aimed at probing the transport properties of n-alkanes in NU-1000 and introduce methods from the microrheology literature for analyzing the mean-squared displacements and their spatial heterogeneity. Adsorption occurs initially in the smaller channels, and diffusion at low loading is limited by interaction between adsorbate and framework atoms. The larger channels provide a region of low density where molecules are able to diffuse at higher rates predominantly along the channel axes. The disparate size of the channels gives rise to heterogeneity in the diffusivity of the guest molecules, whereas the asymmetry of the channels leads to anisotropic diffusion. Together, the channels form a network of "highways" and "side streets" that provide enhanced diffusion in one dimension.

Material properties of biofilms-a review of methods for understanding permeability and mechanics

Microorganisms can form biofilms, which are multicellular communities surrounded by a hydrated extracellular matrix of polymers. Central properties of the biofilm are governed by this extracellular matrix, which provides mechanical stability to the 3D biofilm structure, regulates the ability of the biofilm to adhere to surfaces, and determines the ability of the biofilm to adsorb gases, solutes, and foreign cells. Despite their critical relevance for understanding and eliminating of biofilms, the materials properties of the extracellular matrix are understudied. Here, we offer the reader a guide to current technologies that can be utilized to specifically assess the permeability and mechanical properties of the biofilm matrix and its interacting components. In particular, we highlight technological advances in instrumentation and interactions between multiple disciplines that have broadened the spectrum of methods available to conduct these studies. We review pioneering work that furthers our understanding of the material properties of biofilms.

Micro-heterogeneity metrics for diffusion in soft matter

Passive particle tracking of diffusive paths in soft matter, coupled with analysis of the path data, is firmly established as a fundamental methodology for characterization of both diffusive transport properties (the focus here) and linear viscoelasticity. For either focus, particle time series are typically analyzed by ensemble averaging over paths, a perfectly natural protocol for homogeneous materials or for applications where mean properties are sufficient. Many biological materials, however, are heterogeneous over length scales above the probe diameter, and the implications of heterogeneity for biologically relevant transport properties (e.g. diffusive passage times through a complex fluid layer) motivate this paper. Our goals are three-fold: first, to detect heterogeneity as reflected by the ensemble path data; second, to further decompose the ensemble of particle paths into statistically distinct clusters; and third, to fit the path data in each cluster to a model for the underlying stochastic process. After reviewing current best practices for detection and assessment of heterogeneity in diffusive processes, we introduce our strategy toward the first two goals with methods from the statistics and machine learning literature that have not found application thus far to passive particle tracking data. We apply an analysis based solely on the path data that detects heterogeneity and yields a decomposition of particle paths into statistically distinct clusters. After these two goals are achieved, one can then pursue model-fitting. We illustrate these heterogeneity metrics on diverse datasets: for numerically generated and experimental particle paths, with tunable and unknown heterogeneity, on numerical models for simple diffusion and anomalous sub-diffusion, and experimentally on sucrose, hyaluronic acid, agarose, and human lung culture mucus solutions.

A microrheological study of hydrogel kinetics and micro-heterogeneity

The real-time dynamic heterogeneity of the gelation process of the amino acid derivative Fmoc-tyrosine (Fmoc-Y) is studied using particle tracking microrheology. To trigger gelation, glucono-δ-lactone (GdL) is added, which gradually lowers the p H over several hours. The onset of self-assembly in the system is signified by a sharp drop in the mean-squared displacement of embedded particles, a phenomenon that is found to correlate with the p H of the system reaching the pK(a) of Fmoc-Y. The gel point is identified and found to be dependent on the GdL concentration. Analysis of embedded probe particle dynamics allows the heterogeneity of the sample to be quantified, using three metrics: the heterogeneity ratio (HR), the non-Gaussian parameter of the van Hove correlation function (N and the bin distribution of the mean-squared displacement (MSD) of single particles (f(z)). Results from the three techniques are found to be approximately comparable, with increases in heterogeneity observed in all samples for incubation times t(w) = 0-3 hours. The final heterogeneity in all samples is found to be remarkably low compared to other systems previously reported in the literature.

On the correction of errors in some multiple particle tracking experiments

A common source of error in particle tracking experiments is identified, and a theoretical model for the magnitude of the error is offered. In many cases, the error is small, but in systems where only a few particles are being tracked, the measured mean squared displacement can be up to 50% smaller than the actual value. The theoretical model predictions are confirmed using numerical simulations and experimental observations of polystyrene microspheres in water.

Decoupling directed and passive motion in dynamic systems: particle tracking microrheology of sputum

Probing the physical properties of heterogeneous materials is essential to understand the structure, function and dynamics of complex fluids including cells, mucus, and polymer solutions. Particle tracking microrheology is a useful method to passively probe viscoelastic properties on micron length scales by tracking the thermal motion of beads embedded in the sample. However, errors associated with active motion have limited the implementation to dynamic systems. We present a simple method to decouple active and Brownian motion, enabling particle tracking to be applied to fluctuating heterogeneous systems. We use the movement perpendicular to the major axis of motion in time to calculate rheological properties. Through simulated data we demonstrate that this method removes directed motion and performs equally well when there is no directed motion, with an average percent error of <1%. We use this method to measure glycerol-water mixtures to show the capability to measure a range of materials. Finally, we use this technique to characterize the compliance of human sputum. We also investigate the effect of a liquefaction agent used to prepare sputum for diagnostic purposes. Our results suggest that the addition of high concentration sodium hydroxide increases sample heterogeneity by increasing the maximum observed creep compliance.

Python algorithms in particle tracking microrheology

BACKGROUND

Particle tracking passive microrheology relates recorded trajectories of microbeads, embedded in soft samples, to the local mechanical properties of the sample. The method requires intensive numerical data processing and tools allowing control of the calculation errors.

RESULTS

We report the development of a software package collecting functions and scripts written in Python for automated and manual data processing, to extract viscoelastic information about the sample using recorded particle trajectories. The resulting program package analyzes the fundamental diffusion characteristics of particle trajectories and calculates the frequency dependent complex shear modulus using methods published in the literature. In order to increase conversion accuracy, segmentwise, double step, range-adaptive fitting and dynamic sampling algorithms are introduced to interpolate the data in a splinelike manner.

CONCLUSIONS

The presented set of algorithms allows for flexible data processing for particle tracking microrheology. The package presents improved algorithms for mean square displacement estimation, controlling effects of frame loss during recording, and a novel numerical conversion method using segmentwise interpolation, decreasing the conversion error from about 100% to the order of 1%.

Microrheological consequences of attractive colloid-colloid potentials in a two-dimensional Brownian fluid

By using microrheological methods commonly employed in videomicroscopy experiments, we study the rheology of a two-dimensional computational fluid formed by Brownian disks with the aim of exploring the influence of some effective colloid-colloid attractive interactions. The model of fluid is developed by Brownian dynamics simulations without hydrodynamical interactions, and it is characterized by calculating its equation of state from the pair distribution function. Micromechanical properties, relative and intrinsic viscosity and freezing are discussed. Then, we include attractive forces such a Asakura-Oosawa depletion force or an empiric expression proposed by Grier and Hal (GH) for an anomalous electrostatic potential observed in confined and charged colloids. By using both potentials, viscosity is clearly increased, but when the GH potential is included, viscoelastic gel state is reached for intermediate values of surface concentration. Finally, we analyse the influence of the attractive potentials in the breaking-up by thermal fluctuations of linear chains formed by 2D particles, finding that the GH potential reduces the characteristical time at which the disks can be considered as disaggregated. In this work, we employ an experimental-like methodology for the study of a Brownian hard-disk fluid, providing a very useful link with experimental procedures.

Insights into cell membrane microdomain organization from live cell single particle tracking of the IgE high affinity receptor FcϵRI of mast cells

Current models propose that the plasma membrane of animal cells is composed of heterogeneous and dynamic microdomains known variously as cytoskeletal corrals, lipid rafts and protein islands. Much of the experimental evidence for these membrane compartments is indirect. Recently, live cell single particle tracking studies using quantum dot-labeled IgE bound to its high affinity receptor FcϵRI, provided direct evidence for the confinement of receptors within micrometer-scale cytoskeletal corrals. In this study, we show that an innovative time-series analysis of single particle tracking data for the high affinity IgE receptor, FcϵRI, on mast cells provides substantial quantitative information about the submicrometer organization of the membrane. The analysis focuses on the probability distribution function of the lengths of the jumps in the positions of the quantum dots labeling individual IgE FcϵRI complexes between frames in movies of their motion. Our results demonstrate the presence, within the micrometer-scale cytoskeletal corrals, of smaller subdomains that provide an additional level of receptor confinement. There is no characteristic size for these subdomains; their size varies smoothly from a few tens of nanometers to a over a hundred nanometers. In QD-IGE labeled unstimulated cells, jumps of less than 70 nm predominate over longer jumps. Addition of multivalent antigen to crosslink the QD-IgE-FcϵRI complexes causes a rapid slowing of receptor motion followed by a long tail of mostly jumps less than 70 nm. The reduced receptor mobility likely reflects both the membrane heterogeneity revealed by the confined motion of the monomeric receptor complexes and the antigen-induced cross linking of these complexes into dimers and higher oligomers. In both cases, the probability distribution of the jump lengths is well fit, from 10 nm to over 100 nm, by a novel power law. The fit for short jumps suggests that the motion of the quantum dots can be modeled as diffusion in a fractal space of dimension less than two.

Optimal diffusion coefficient estimation in single-particle tracking

Single-particle tracking is increasingly used to extract quantitative parameters on single molecules and their environment, while advances in spatial and temporal resolution of tracking techniques inspire new questions and avenues of investigation. Correspondingly, sophisticated analytical methods are constantly developed to obtain more refined information from measured trajectories. Here we point out some fundamental limitations of these approaches due to the finite length of trajectories, the presence of localization error, and motion blur, focusing on the simplest motion regime of free diffusion in an isotropic medium (Brownian motion). We show that two recently proposed algorithms approach the theoretical limit of diffusion coefficient uncertainty. We discuss the practical performance of the algorithms as well as some important implications of these results for single-particle tracking.

Time-averaged quadratic functionals of a Gaussian process

The characterization of a stochastic process from its single random realization is a challenging problem for most single-particle tracking techniques which survey an individual trajectory of a tracer in a complex or viscoelastic medium. We consider two quadratic functionals of the trajectory: the time-averaged mean-square displacement (MSD) and the time-averaged squared root mean-square displacement (SRMS). For a large class of stochastic processes governed by the generalized Langevin equation with arbitrary frictional memory kernel and harmonic potential, the exact formulas for the mean and covariance of these functionals are derived. The formula for the mean value can be directly used for fitting experimental data, e.g., in optical tweezers microrheology. The formula for the variance (and covariance) allows one to estimate the intrinsic fluctuations of measured (or simulated) time-averaged MSD or SRMS for choosing the experimental setup appropriately. We show that the time-averaged SRMS has smaller fluctuations than the time-averaged MSD, in spite of much broader applications of the latter one. The theoretical results are successfully confirmed by Monte Carlo simulations of the Langevin dynamics. We conclude that the use of the time-averaged SRMS would result in a more accurate statistical analysis of individual trajectories and more reliable interpretation of experimental data.

Mean square displacement analysis of single-particle trajectories with localization error: Brownian motion in an isotropic medium

We examine the capability of mean square displacement (MSD) analysis to extract reliable values of the diffusion coefficient D of a single particle undergoing Brownian motion in an isotropic medium in the presence of localization uncertainty. The theoretical results, supported by simulations, show that a simple unweighted least-squares fit of the MSD curve can provide the best estimate of D provided an optimal number of MSD points are used for the fit. We discuss the practical implications of these results for data analysis in single-particle tracking experiments.

Multiple particle tracking investigations of acid milk gels using tracer particles with designed surface chemistries and comparison with diffusing wave spectroscopy studies

Multiple particle tracking (MPT) has been used in an attempt to probe the heterogeneity of acid milk gels, made with and without added pectin, by following the distribution of the displacements of added tracer beads during and after gelation using the Van Hove distribution. Furthermore, the surface chemistry of the latex probe particles was modified in an attempt to control their location in the system and probe the microrheological properties of the protein network and aqueous-phase voids independently. In addition, the mean square displacement (MSD) of the casein micelles/casein aggregates themselves, obtained by diffusing wave spectroscopy (DWS), has been compared to the ensemble-averaged MSD calculated from the data obtained by tracking the movement of the added tracers, with and without a kappa-casein coating. For the kappa-casein-coated tracer particles, upon acidification and subsequent gel formation, the MSDs obtained by MPT superimpose remarkably well with the MSDs obtained by DWS, despite the fact that one is obtained by tracking the movement of the particle network elements themselves and the other is obtained from directly tracking added tracers. This result has important implications: (i) it demonstrates that, although the DWS measurement is intrinsically ensemble-averaged, it really gives insight into the dynamics of the colloidal gel network; (ii) it confirms that the kappa-casein-coated probes used in this MPT experiment are well incorporated into the gel network; and hence (iii) that at least in gelled systems kappa-casein-coated latex probes are interesting probes that reveal the dynamics of the casein network.

Passive microrheology of solvent-induced fibrillar protein networks

Particle tracking microrheology (PTM) has been used to study the sol-gel transition in solvent-induced fibrillar beta-lactoglobulin gels at room temperature and pH 7. The passive nature of microrheology allowed measurements to be made around and below the critical gelation concentration. The method of superposition introduced by Larsen and Furst (Larsen, T. H.; Furst, E. M. Phys. Rev. Lett. 2008, 100, 146001) was applied to the one-particle mean square displacement (MSD), yielding a critical relaxation exponent of n = 0.58 at concentrations close to the measured critical concentration of 4% (w/v). At a higher concentration of 12% (w/v), n was observed to decrease. The pregel and gel master curves were used to find the viscoelastic moduli over 8 decades of frequency. Combined with the measured shift factors, this allowed cure curves at 1 Hz to be constructed for direct comparison with results from bulk rheology. Time-independent modulus superposition was found for all concentrations. Good agreement for concentration scaling was found between the traditional methods for characterizing gels and the recently described microrheological determination of the gel time and critical behavior.

Mapping of spatiotemporal heterogeneous particle dynamics in living cells

Colloidal particles embedded in the cytoplasm of living mammalian cells have been found to display remarkable heterogeneity in their amplitude of motion. However, consensus on the significance and origin of this phenomenon is still lacking. We conducted experiments on Hmec-1 cells loaded with about 100 particles to reveal the intracellular particle dynamics as a function of both location and time. Central quantity in our analysis is the amplitude (A) of the individual mean-squared displacement (iMSD), averaged over a short time. Histograms of A were measured, (1) over all particles present at the same time and (2) for individual particles as a function of time. Both distributions showed significant broadening compared to particles in Newtonian liquid, indicating that the particle dynamics varies with both location and time. However, no systematic dependence of A on intracellular location was found. Both the (strong) spatial and (weak) temporal variations were further analyzed by correlation functions of A . Spatial cross correlations were rather weak down to interparticle distances of 1 microm , suggesting that the precise intracellular probe distribution is not crucial for observing a dynamic behavior that is representative for the whole cell. Temporal correlations of A decayed at approximately 10 s , possibly suggesting an intracellular reorganization at this time scale. These findings imply (1) that both individual particle dynamics and the ensemble averaged behavior in a given cell can be measured if there are enough particles per cell and (2) that the amplitude and power-law exponent of iMSDs can be used to reveal local dynamics. We illustrate this by showing how superdiffusive and subdiffusive behaviors may be hidden under an apparently diffusive global dynamics.