Static and dynamic errors in particle tracking microrheology

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.

Quantifying the dynamic transition of hydrogenated castor oil gels measured via multiple particle tracking microrheology

Rheological modifiers are essential ingredients in commercial materials that exploit facile and repeatable phase transitions. Although rheological modifiers are used to change flow behavior or quiescent stability, the complex properties of particulate gels during dilution is not well studied. We characterize a dynamically evolving colloidal gel, hydrogenated castor oil (HCO), a naturally sourced material, used in consumer products. This HCO scaffold consists of fibrous colloids, a surfactant (linear alkylbenzene sulfonate) and water. The gel undergoes critical transitions, degradation and formation, in response to an osmotic pressure gradient. Multiple particle tracking microrheology (MPT) measures the evolving material properties. In MPT, fluorescent probe particles are embedded into the sample and Brownian motion is measured. MPT data are analyzed using time-cure superposition, identifying critical transition times and critical relaxation exponents for degradation and formation where tc,deg = 102.5 min, ndeg = 0.77 ± 0.09, tc,for = 31.9 min, and nfor = 0.94 ± 0.11, respectively. During degradation and formation HCO gels evolve heterogeneously, this heterogeneity is characterized spatially and temporally. Heterogeneity of the gel is quantified by comparing variances of single particle van Hove correlation functions using an F-test with a 95% confidence interval. HCO transitions have rheological heterogeneous microenvironments that are homogeneously distributed throughout the field of view. Although HCO gels do evolve heterogeneously, this work determines that these heterogeneities do not significantly change traditional MPT measurements but the analysis techniques developed provide additional information on the unique heterogeneous scaffold microenvironments. This creates a toolbox that can be widely applied to other scaffolds during dynamic transitions.

Local collective motion analysis for multi-probe dynamic imaging and microrheology

Dynamical artifacts, such as mechanical drift, advection, and hydrodynamic flow, can adversely affect multi-probe dynamic imaging and passive particle-tracking microrheology experiments. Alternatively, active driving by molecular motors can cause interesting non-Brownian motion of probes in local regions. Existing drift-correction techniques, which require large ensembles of probes or fast temporal sampling, are inadequate for handling complex spatio-temporal drifts and non-Brownian motion of localized domains containing relatively few probes. Here, we report an analytical method based on local collective motion (LCM) analysis of as few as two probes for detecting the presence of non-Brownian motion and for accurately eliminating it to reveal the underlying Brownian motion. By calculating an ensemble-average, time-dependent, LCM mean square displacement (MSD) of two or more localized probes and comparing this MSD to constituent single-probe MSDs, we can identify temporal regimes during which either thermal or athermal motion dominates. Single-probe motion, when referenced relative to the moving frame attached to the multi-probe LCM trajectory, provides a true Brownian MSD after scaling by an appropriate correction factor that depends on the number of probes used in LCM analysis. We show that LCM analysis can be used to correct many different dynamical artifacts, including spatially varying drifts, gradient flows, cell motion, time-dependent drift, and temporally varying oscillatory advection, thereby offering a significant improvement over existing approaches.

Optimizing experimental parameters for tracking of diffusing particles

We describe how a single-particle tracking experiment should be designed in order for its recorded trajectories to contain the most information about a tracked particle's diffusion coefficient. The precision of estimators for the diffusion coefficient is affected by motion blur, limited photon statistics, and the length of recorded time series. We demonstrate for a particle undergoing free diffusion that precision is negligibly affected by motion blur in typical experiments, while optimizing photon counts and the number of recorded frames is the key to precision. Building on these results, we describe for a wide range of experimental scenarios how to choose experimental parameters in order to optimize the precision. Generally, one should choose quantity over quality: experiments should be designed to maximize the number of frames recorded in a time series, even if this means lower information content in individual frames.

Control of Transmembrane Protein Diffusion within the Postsynaptic Density Assessed by Simultaneous Single-Molecule Tracking and Localization Microscopy

Postsynaptic transmembrane proteins are critical elements of synapses, mediating trans-cellular contact, sensitivity to neurotransmitters and other signaling molecules, and flux of Ca and other ions. Positioning and mobility of each member of this large class of proteins is critical to their individual function at the synapse. One critical example is that the position of glutamate receptors within the postsynaptic density (PSD) strongly modulates their function by aligning or misaligning them with sites of presynaptic vesicle fusion. In addition, the regulated ability of receptors to move in or out of the synapse is critical for activity-dependent plasticity. However, factors that control receptor mobility within the boundaries of the synapse are not well understood. Notably, PSD scaffold molecules accumulate in domains much smaller than the synapse. Within these nanodomains, the density of proteins is considerably higher than that of the synapse as a whole, so high that steric hindrance is expected to reduce receptor mobility substantially. However, while numerical modeling has demonstrated several features of how the varying protein density across the face of a single PSD may modulate receptor motion, there is little experimental information about the extent of this influence. To address this critical aspect of synaptic organizational dynamics, we performed single-molecule tracking of transmembrane proteins using universal point accumulation-for-imaging-in-nanoscale-topography (uPAINT) over PSDs whose internal structure was simultaneously resolved using photoactivated localization microscopy (PALM). The results provide important experimental confirmation that PSD scaffold protein density strongly influences the mobility of transmembrane proteins. A protein with a cytosolic domain that does not bind PSD-95 was still slowed in regions of high PSD-95 density, suggesting that crowding by scaffold molecules and perhaps other proteins is sufficient to stabilize receptors even in the absence of binding. Because numerous proteins thought to be involved in establishing PSD structure are linked to disorders including autism and depression, this motivates further exploration of how PSD nanostructure is created. The combined application PALM and uPAINT should be invaluable for distinguishing the interactions of mobile proteins with their nano-environment both in synapses and other cellular compartments.

Measuring rotational diffusion of colloidal spheres with confocal microscopy

We report an experimental method to measure the translational and rotational dynamics of colloidal spheres in three dimensions with confocal microscopy and show that the experimental values reasonably agree with the theoretical values. This method can be extended to study rotational dynamics in concentrated colloidal systems and complex bio-systems.

Single-Molecule Tracking and Its Application in Biomolecular Binding Detection

In the past two decades significant advances have been made in single-molecule detection, which enables the direct observation of single biomolecules at work in real time and under physiological conditions. In particular, the development of single-molecule tracking (SMT) microscopy allows us to monitor the motion paths of individual biomolecules in living systems, unveiling the localization dynamics and transport modalities of the biomolecules that support the development of life. Beyond the capabilities of traditional camera-based tracking techniques, state-of-the-art SMT microscopies developed in recent years can record fluorescence lifetime while tracking a single molecule in the 3D space. This multiparameter detection capability can open the door to a wide range of investigations at the cellular or tissue level, including identification of molecular interaction hotspots and characterization of association/dissociation kinetics between molecules. In this review, we discuss various SMT techniques developed to date, with an emphasis on our recent development of the next generation 3D tracking system that not only achieves ultrahigh spatiotemporal resolution but also provides sufficient working depth suitable for live animal imaging. We also discuss the challenges that current SMT techniques are facing and the potential strategies to tackle those challenges.

Parallel temperature-dependent microrheological measurements in a microfluidic chip

Microfluidic stickers are used as a sample environment to measure the microrheology of monoclonal antibody (mAb) protein solutions. A Peltier-based microscope stage is implemented and validated, and is capable of controlling the sample temperature over the range 0.9-40 °C. The design accounts for heat transfer to and from the objective, controls the sample environment humidity to mitigate condensation, and provides adequate damping to reduce vibration from the cooling system. A concentrated sucrose solution is used as a standard sample to provide an in situ temperature measurement by the Stokes-Einstein-Sutherland relation. By combining microfluidic stickers and microrheology, 72 temperature-concentration viscosity measurements of mAb solutions can be made in 1 day, a significant increase in throughput over conventional rheometry.

Advances in the microrheology of complex fluids

New developments in the microrheology of complex fluids are considered. Firstly the requirements for a simple modern particle tracking microrheology experiment are introduced, the error analysis methods associated with it and the mathematical techniques required to calculate the linear viscoelasticity. Progress in microrheology instrumentation is then described with respect to detectors, light sources, colloidal probes, magnetic tweezers, optical tweezers, diffusing wave spectroscopy, optical coherence tomography, fluorescence correlation spectroscopy, elastic- and quasi-elastic scattering techniques, 3D tracking, single molecule methods, modern microscopy methods and microfluidics. New theoretical techniques are also reviewed such as Bayesian analysis, oversampling, inversion techniques, alternative statistical tools for tracks (angular correlations, first passage probabilities, the kurtosis, motor protein step segmentation etc), issues in micro/macro rheological agreement and two particle methodologies. Applications where microrheology has begun to make some impact are also considered including semi-flexible polymers, gels, microorganism biofilms, intracellular methods, high frequency viscoelasticity, comb polymers, active motile fluids, blood clots, colloids, granular materials, polymers, liquid crystals and foods. Two large emergent areas of microrheology, non-linear microrheology and surface microrheology are also discussed.

Controlled levels of canonical Wnt signaling are required for neural crest migration

Canonical Wnt signaling plays a dominant role in the development of the neural crest (NC), a highly migratory cell population that generates a vast array of cell types. Canonical Wnt signaling is required for NC induction as well as differentiation, however its role in NC migration remains largely unknown. Analyzing nuclear localization of β-catenin as readout for canonical Wnt activity, we detect nuclear β-catenin in premigratory but not migratory Xenopus NC cells suggesting that canonical Wnt activity has to decrease to basal levels to enable NC migration. To define a possible function of canonical Wnt signaling in Xenopus NC migration, canonical Wnt signaling was modulated at different time points after NC induction. This was accomplished using either chemical modulators affecting β-catenin stability or inducible glucocorticoid fusion constructs of Lef/Tcf transcription factors. In vivo analysis of NC migration by whole mount in situ hybridization demonstrates that ectopic activation of canonical Wnt signaling inhibits cranial NC migration. Further, NC transplantation experiments confirm that this effect is tissue-autonomous. In addition, live-cell imaging in combination with biophysical data analysis of explanted NC cells confirms the in vivo findings and demonstrates that modulation of canonical Wnt signaling affects the ability of NC cells to perform single cell migration. Thus, our data support the hypothesis that canonical Wnt signaling needs to be tightly controlled to enable migration of NC cells.

Fluctuation Analysis of Centrosomes Reveals a Cortical Function of Kinesin-1

The actin and microtubule networks form the dynamic cytoskeleton. Network dynamics is driven by molecular motors applying force onto the networks and the interactions between the networks. Here we assay the dynamics of centrosomes in the scale of seconds as a proxy for the movement of microtubule asters. With this assay we want to detect the role of specific motors and of network interaction. During interphase of syncytial embryos of Drosophila, cortical actin and the microtubule network depend on each other. Centrosomes induce cortical actin to form caps, whereas F-actin anchors microtubules to the cortex. In addition, lateral interactions between microtubule asters are assumed to be important for regular spatial organization of the syncytial embryo. The functional interaction between the microtubule asters and cortical actin has been largely analyzed in a static manner, so far. We recorded the movement of centrosomes at 1 Hz and analyzed their fluctuations for two processes—pair separation and individual movement. We found that F-actin is required for directional movements during initial centrosome pair separation, because separation proceeds in a diffusive manner in latrunculin-injected embryos. For assaying individual movement, we established a fluctuation parameter as the deviation from temporally and spatially slowly varying drift movements. By analysis of mutant and drug-injected embryos, we found that the fluctuations were suppressed by both cortical actin and microtubules. Surprisingly, the microtubule motor Kinesin-1 also suppressed fluctuations to a similar degree as F-actin. Kinesin-1 may mediate linkage of the microtubule (+)-ends to the actin cortex. Consistent with this model is our finding that Kinesin-1-GFP accumulates at the cortical actin caps.

Motion blur filtering: A statistical approach for extracting confinement forces and diffusivity from a single blurred trajectory

Single particle tracking (SPT) can aid in understanding a variety of complex spatiotemporal processes. However, quantifying diffusivity and confinement forces from individual live cell trajectories is complicated by inter- and intratrajectory kinetic heterogeneity, thermal fluctuations, and (experimentally resolvable) statistical temporal dependence inherent to the underlying molecule's time correlated confined dynamics experienced in the cell. The problem is further complicated by experimental artifacts such as localization uncertainty and motion blur. The latter is caused by the tagged molecule emitting photons at different spatial positions during the exposure time of a single frame. The aforementioned experimental artifacts induce spurious time correlations in measured SPT time series that obscure the information of interest (e.g., confinement forces and diffusivity). We develop a maximum likelihood estimation (MLE) technique that decouples the above noise sources and systematically treats temporal correlation via time series methods. This ultimately permits a reliable algorithm for extracting diffusivity and effective forces in confined or unconfined environments. We illustrate how our approach avoids complications inherent to mean square displacement or autocorrelation techniques. Our algorithm modifies the established Kalman filter (which does not handle motion blur artifacts) to provide a likelihood based time series estimation procedure. The result extends A. J. Berglund's motion blur model [Phys. Rev. E 82, 011917 (2010)PLEEE81539-375510.1103/PhysRevE.82.011917] to handle confined dynamics. The approach can also systematically utilize (possibly time dependent) localization uncertainty estimates afforded by image analysis if available. This technique, which explicitly treats confinement and motion blur within a time domain MLE framework, uses an exact likelihood (time domain methods facilitate analyzing nonstationary signals). Our estimator is demonstrated to be consistent over a wide range of exposure times (5 to 100 ms), diffusion coefficients (1×10^{-3} to 1μm^{2}/s), and confinement widths (100 nm to 2μm). We demonstrate that neglecting motion blur or confinement can substantially bias estimation of kinetic parameters of interest to researchers. The technique also permits one to check statistical model assumptions against measured individual trajectories without "ground truth." The ability to reliably and consistently extract motion parameters in trajectories exhibiting confined and/or non-stationary dynamics, without exposure time artifacts corrupting estimates, is expected to aid in directly comparing trajectories obtained from different experiments or imaging modalities. A Python implementation is provided (open-source code will be maintained on GitHub; see also the Supplemental Material with this paper).

Estimation of the diffusion constant from intermittent trajectories with variable position uncertainties

The movement of a particle described by Brownian motion is quantified by a single parameter, D, the diffusion constant. The estimation of D from a discrete sequence of noisy observations is a fundamental problem in biological single-particle tracking experiments since it can provide information on the environment and/or the state of the particle itself via the hydrodynamic radius. Here, we present a method to estimate D that takes into account several effects that occur in practice, important for the correct estimation of D, and that have hitherto not been combined together for an estimation of D. These effects are motion blur from the finite integration time of the camera, intermittent trajectories, and time-dependent localization uncertainty. Our estimation procedure, a maximum-likelihood estimation with an information-based confidence interval, follows directly from the likelihood expression for a discretely observed Brownian trajectory that explicitly includes these effects. We begin with the formulation of the likelihood expression and then present three methods to find the exact solution. Each method has its own advantages in either computational robustness, theoretical insight, or the estimation of hidden variables. The Fisher information for this likelihood distribution is calculated and analyzed to show that localization uncertainties impose a lower bound on the estimation of D. Confidence intervals are established and then used to evaluate our estimator on simulated data with experimentally relevant camera effects to demonstrate the benefit of incorporating variable localization errors.

Charge renormalization in nominally apolar colloidal dispersions

We present high-resolution measurements of the pair interactions between dielectric spheres dispersed in a fluid medium with a low dielectric constant. Despite the absence of charge control agents or added organic salts, these measurements reveal strong and long-ranged repulsions consistent with substantial charges on the particles whose interactions are screened by trace concentrations of mobile ions in solution. The dependence of the estimated charge on the particles' radii is consistent with charge renormalization theory and, thus, offers insights into the charging mechanism in this interesting class of model systems. The measurement technique, based on optical-tweezer manipulation and artifact-free particle tracking, makes use of optimal statistical methods to reduce measurement errors to the femtonewton frontier while covering an extremely wide range of interaction energies.

Dark-field differential dynamic microscopy

Differential dynamic microscopy (DDM) is an emerging technique to measure the ensemble dynamics of colloidal and complex fluid motion using optical microscopy in systems that would otherwise be difficult to measure using other methods. To date, DDM has successfully been applied to linear space invariant imaging modes including bright-field, fluorescence, confocal, polarised, and phase-contrast microscopy to study diverse dynamic phenomena. In this work, we show for the first time how DDM analysis can be extended to dark-field imaging, i.e. a linear space variant (LSV) imaging mode. Specifically, we present a particle-based framework for describing dynamic image correlations in DDM, and use it to derive a correction to the image structure function obtained by DDM that accounts for scatterers with non-homogeneous intensity distributions as they move within the imaging plane. To validate the analysis, we study the Brownian motion of gold nanoparticles, whose plasmonic structure allows for nanometer-scale particles to be imaged under dark-field illumination, in Newtonian liquids. We find that diffusion coefficients of the nanoparticles can be reliably measured by dark-field DDM, even under optically dense concentrations where analysis via multiple-particle tracking microrheology fails. These results demonstrate the potential for DDM analysis to be applied to linear space variant forms of microscopy, providing access to experimental systems unavailable to other imaging modes.

Bacterial Chromosome Dynamics by Locus Tracking in Fluorescence Microscopy

Bacterial chromosomes have been shown in the last two decades to have remarkable spatial organization at various scales, and also well-defined movements during the cell cycle, for example, to reliably segregate daughter chromosomes. More recently, various labs have begun investigating the short-time dynamics (displacements during time intervals of 0.1-100 s), which one hopes to link to structure, in analogy to "microrheology" approaches applied successfully to study mechanical response of complex fluids. These studies of chromosome fluctuation dynamics have revealed differences of fluctuation amplitude across the chromosome, and different characters of motion depending on the time window of interest. The highly nontrivial motion at the shortest experimentally accessible times is still not fully understood in terms of physical models of DNA and cytosol. We describe how to carry out tracking experiments of single locus and how to analyze locus motility. We point out the importance of considering in the analysis the number of GFP molecules per fluorescent locus.

In situ multi-modal monitoring of solvent vapor swelling in polymer thin films

Polymer processing techniques involving solvent vapor swelling are typically challenging to control and thus reproduce. Moreover, traditional descriptions of solvent swollen films lack microscopic detail. We describe the design and use of an apparatus that facilitates macroscopic and microscopic characterization of samples undergoing solvent vapor swelling in a controlled environment. The experimental design incorporates three critical characteristics: (1) a mass-flow controlled solvent vapor delivery system allows for precise control of the amount of solvent vapor delivered to the sample, (2) a sample prepared on a quartz crystal microbalance allows for real-time assessment of the extent of sample swelling, (3) a second sample prepared and assessed in parallel on a coverslip allows real-time fluorescence microscopy during swelling. We demonstrate that this apparatus allows for single-particle tracking, which in turn facilitates in situ monitoring of local environments within the solvent-swollen film.

Studying the Dynamics of Chromatin-Binding Proteins in Mammalian Cells Using Single-Molecule Localisation Microscopy

Single-molecule localisation microscopy (SMLM) allows the super-resolved imaging of proteins within mammalian nuclei at spatial resolutions comparable to that of a nucleosome itself (~20 nm). The technique is therefore well suited to the study of chromatin structure. Fixed-cell SMLM has already allowed temporal 'snapshots' of how proteins are arranged on chromatin within mammalian nuclei. In this chapter, we focus on how recent developments, for example in selective plane illumination and protein labelling, have led to a range of live-cell SMLM studies. We describe how to carry out single-particle tracking (SPT) of single proteins and, by analysing their diffusion parameters, how to determine whether proteins interact with chromatin, diffuse freely or do both. We can study the numbers of proteins that interact with chromatin and also determine their residence time on chromatin. We can determine whether these proteins form functional clusters within the nucleus as well as whether they form specific nuclear structures.

2D dynamical arrest transition in a mixed nanoparticle-phospholipid layer studied in real and momentum spaces

We investigate the interfacial dynamics of a 2D self-organized mixed layer made of silica nanoparticles interacting with phospholipid (DPPC) monolayers at the air/water interface. This system has biological relevance, allowing investigation of toxicological effects of nanoparticles on model membranes and lung surfactants. It might also provide bio-inspired technological solutions, exploiting the self-organization of DPPC to produce a non-trivial 2D structuration of nanoparticles. The characterization of interfacial dynamics yields information on the effects of NPs on the mechanical properties, important to improve performances of systems such as colloidosomes, foams, creams. For this, we combine micro-tracking in real-space with measurement in momentum-space via x-ray photon-correlation spectroscopy and Digital Fourier Microscopy. Using these complementary techniques, we extend the spatial range of investigation beyond the limits of each one. We find a dynamical transition from Brownian diffusion to an arrested state driven by compression, characterized by intermittent rearrangements, compatible with a repulsive glass phase. The rearrangement and relaxation of the monolayer structure results dramatically hindered by the presence of NPs, which is relevant to explain some the mechanical features observed for the dynamic surface pressure response of these systems and which can be relevant for the respiratory physiology and for future drug-delivery composite systems.

Extracting Diffusive States of Rho GTPase in Live Cells: Towards In Vivo Biochemistry

Resolving distinct biochemical interaction states when analyzing the trajectories of diffusing proteins in live cells on an individual basis remains challenging because of the limited statistics provided by the relatively short trajectories available experimentally. Here, we introduce a novel, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and demonstrate that pEM is capable of uncovering the proper number of underlying diffusive states with an accurate characterization of their diffusion properties. We then apply pEM to experimental protein trajectories of Rho GTPases, an integral regulator of cytoskeletal dynamics and cellular homeostasis, in vivo via single particle tracking photo-activated localization microcopy. Remarkably, pEM uncovers 6 distinct diffusive states conserved across various Rho GTPase family members. The variability across family members in the propensities for each diffusive state reveals non-redundant roles in the activation states of RhoA and RhoC. In a resting cell, our results support a model where RhoA is constantly cycling between activation states, with an imbalance of rates favoring an inactive state. RhoC, on the other hand, remains predominantly inactive.

Single particle tracking is a powerful tool that captures the diffusive dynamics of proteins as they undergo various interactions in living cells. Uncovering different biochemical interactions by analyzing the diffusive behaviors of individual protein trajectories, however, is challenging due to the limited statistics provided by short trajectories and experimental noise sources which are intimately coupled into each protein’s localization. Here, we introduce a novel, unsupervised, machine-learning based classification methodology, which we call perturbation expectation-maximization (pEM), that simultaneously analyzes a population of protein trajectories to uncover the system of diffusive behaviors which collectively result from distinct biochemical interactions. We validate the performance of pEM in silico and in vivo on the biological system of Rho GTPase, a signal transduction protein responsible for regulating cytoskeletal dynamics. We envision that the presented methodology will be applicable to a wide range of single protein tracking data where different biochemical interactions result in distinct diffusive behaviors. More generally, this study brings us an important step closer to the possibility of monitoring the endogenous biochemistry of diffusing proteins within live cells with single molecule resolution.

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.

Improving z-tracking accuracy in the two-photon single-particle tracking microscope

Here, we present a method that can improve the z-tracking accuracy of the recently invented TSUNAMI (Tracking of Single particles Using Nonlinear And Multiplexed Illumination) microscope. This method utilizes a maximum likelihood estimator (MLE) to determine the particle's 3D position that maximizes the likelihood of the observed time-correlated photon count distribution. Our Monte Carlo simulations show that the MLE-based tracking scheme can improve the z-tracking accuracy of TSUNAMI microscope by 1.7 fold. In addition, MLE is also found to reduce the temporal correlation of the z-tracking error. Taking advantage of the smaller and less temporally correlated z-tracking error, we have precisely recovered the hybridization-melting kinetics of a DNA model system from thousands of short single-particle trajectories in silico. Our method can be generally applied to other 3D single-particle tracking techniques.

Particle tracking in drug and gene delivery research: State-of-the-art applications and methods

Particle tracking is a powerful microscopy technique to quantify the motion of individual particles at high spatial and temporal resolution in complex fluids and biological specimens. Particle tracking's applications and impact in drug and gene delivery research have greatly increased during the last decade. Thanks to advances in hardware and software, this technique is now more accessible than ever, and can be reliably automated to enable rapid processing of large data sets, thereby further enhancing the role that particle tracking will play in drug and gene delivery studies in the future. We begin this review by discussing particle tracking-based advances in characterizing extracellular and cellular barriers to therapeutic nanoparticles and in characterizing nanoparticle size and stability. To facilitate wider adoption of the technique, we then present a user-friendly review of state-of-the-art automated particle tracking algorithms and methods of analysis. We conclude by reviewing technological developments for next-generation particle tracking methods, and we survey future research directions in drug and gene delivery where particle tracking may be useful.

Synthesis of Nonspherical Microcapsules through Controlled Polyelectrolyte Coating of Hydrogel Templates

We report a simple approach to fabricate custom-shape microcapsules using hydrogel templates synthesized by stop flow lithography. Cargo-containing microcapsules were made by coating hydrogel particles with a single layer of poly-l-lysine followed by a one-step core degradation and capsule cross-linking procedure. We determined appropriate coating conditions by investigating the effect of pH, ionic strength, and prepolymer composition on the diffusion of polyelectrolytes into the oppositely charged hydrogel template. We also characterized the degradation of the templating core by tracking the diffusivity of nanoparticles embedded within the hydrogel. Unlike any other technique, this approach allows for easy fabrication of microcapsules with internal features (e.g., toroids) and selective surface modification of Janus particles using any polyelectrolyte. These soft, flexible capsules may be useful for therapeutic applications as well as fundamental studies of membrane mechanics.

Confinement Induced Plastic Crystal-to-Crystal Transitions in Rodlike Particles with Long-Ranged Repulsion

Colloidal particles in geometrical confinement display a complex variety of packing structures different from their three-dimensional (3D) bulk counterpart. Here, we confined charged rodlike colloids with long-ranged repulsions to a thin wedge-shaped cell and show, by quantitative 3D confocal microscopy, that not only their positional but also their orientational order depends sensitively upon the slit width. Synchronized with transitions in lattice symmetry and number of layers confinement induces plastic crystal-to-crystal transitions. A model analysis suggests that this complex sequence of more or less rotationally ordered states originates from the subtle competition between the electrostatic repulsion of a rod with the wall and with its neighbors.

Films of bacteria at interfaces: three stages of behaviour

We report an investigation of the formation of films by bacteria at an oil-water interface using a combination of particle tracking and pendant drop elastometry. The films display a remarkably varied series of dynamical and mechanical properties as they evolve over the course of minutes to hours following the creation of an initially pristine interface. At the earliest stage of formation, which we interrogate using dispersions of colloidal probes, the interface is populated with motile bacteria. Interactions with the bacteria dominate the colloidal motion, and the interface displays canonical features of active matter in a quasi-two-dimensional context. This active stage gives way to a viscoelastic transition, presumably driven by the accumulation at the interface of polysaccharides and surfactants produced by the bacteria, which instill the interface with the hallmarks of soft glassy rheology that we characterize with microrheology. Eventually, the viscoelastic film becomes fully elastic with the capability to support wrinkling upon compression, and we investigate this final stage with the pendant drop measurements. We characterize quantitatively the dynamic and mechanical properties of the films during each of these three stages - active, viscoelastic, and elastic - and comment on their possible significance for the interfacial bacterial colony. This work also brings to the forefront the important role that interfacial mechanics may play in bacterial suspensions with free surfaces.

Nondecaying Hydrodynamic Interactions along Narrow Channels

Particle-particle interactions are of paramount importance in every multibody system as they determine the collective behavior and coupling strength. Many well-known interactions such as electrostatic, van der Waals, or screened Coulomb interactions, decay exponentially or with negative powers of the particle spacing r. Similarly, hydrodynamic interactions between particles undergoing Brownian motion decay as 1/r in bulk, and are assumed to decay in small channels. Such interactions are ubiquitous in biological and technological systems. Here we confine two particles undergoing Brownian motion in narrow, microfluidic channels and study their coupling through hydrodynamic interactions. Our experiments show that the hydrodynamic particle-particle interactions are distance independent in these channels. This finding is of fundamental importance for the interpretation of experiments where dense mixtures of particles or molecules diffuse through finite length, water-filled channels or pore networks.

Measuring dynamic cell-material interactions and remodeling during 3D human mesenchymal stem cell migration in hydrogels

Biomaterials that mimic aspects of the extracellular matrix by presenting a 3D microenvironment that cells can locally degrade and remodel are finding increased applications as wound-healing matrices, tissue engineering scaffolds, and even substrates for stem cell expansion. In vivo, cells do not simply reside in a static microenvironment, but instead, they dynamically reengineer their surroundings. For example, cells secrete proteases that degrade extracellular components, attach to the matrix through adhesive sites, and can exert traction forces on the local matrix, causing its spatial reorganization. Although biomaterials scaffolds provide initially well-defined microenvironments for 3D culture of cells, less is known about the changes that occur over time, especially local matrix remodeling that can play an integral role in directing cell behavior. Here, we use microrheology as a quantitative tool to characterize dynamic cellular remodeling of peptide-functionalized poly(ethylene glycol) (PEG) hydrogels that degrade in response to cell-secreted matrix metalloproteinases (MMPs). This technique allows measurement of spatial changes in material properties during migration of encapsulated cells and has a sensitivity that identifies regions where cells simply adhere to the matrix, as well as the extent of local cell remodeling of the material through MMP-mediated degradation. Collectively, these microrheological measurements provide insight into microscopic, cellular manipulation of the pericellular region that gives rise to macroscopic tracks created in scaffolds by migrating cells. This quantitative and predictable information should benefit the design of improved biomaterial scaffolds for medically relevant applications.

Superdiffusion dominates intracellular particle motion in the supercrowded cytoplasm of pathogenic Acanthamoeba castellanii

Acanthamoebae are free-living protists and human pathogens, whose cellular functions and pathogenicity strongly depend on the transport of intracellular vesicles and granules through the cytosol. Using high-speed live cell imaging in combination with single-particle tracking analysis, we show here that the motion of endogenous intracellular particles in the size range from a few hundred nanometers to several micrometers in Acanthamoeba castellanii is strongly superdiffusive and influenced by cell locomotion, cytoskeletal elements, and myosin II. We demonstrate that cell locomotion significantly contributes to intracellular particle motion, but is clearly not the only origin of superdiffusivity. By analyzing the contribution of microtubules, actin, and myosin II motors we show that myosin II is a major driving force of intracellular motion in A. castellanii. The cytoplasm of A. castellanii is supercrowded with intracellular vesicles and granules, such that significant intracellular motion can only be achieved by actively driven motion, while purely thermally driven diffusion is negligible.

Precise Three-Dimensional Scan-Free Multiple-Particle Tracking over Large Axial Ranges with Tetrapod Point Spread Functions

We employ a novel framework for information-optimal microscopy to design a family of point spread functions (PSFs), the Tetrapod PSFs, which enable high-precision localization of nanoscale emitters in three dimensions over customizable axial (z) ranges of up to 20 μm with a high numerical aperture objective lens. To illustrate, we perform flow profiling in a microfluidic channel and show scan-free tracking of single quantum-dot-labeled phospholipid molecules on the surface of living, thick mammalian cells.

Measuring advection and diffusion of colloids in shear flow

An analysis of the dynamics of colloids in shear flow can be challenging because of the superposition of diffusion and advection. We present a method that separates the two motions, starting from the time-dependent particle coordinates. The restriction of the tracking to flow lanes and the subtraction of estimated advective displacements are combined in an iterative scheme that eventually makes the spatial segmentation redundant. Tracking errors due to the neglect of lateral diffusion are avoided, while drifts parallel and perpendicular to the flow are eliminated. After explaining the principles of our method, we validate it against both computer simulations and experiments. A critical overall test is provided by the mean square displacement function at high Peclet numbers (up to 50). We demonstrate via simulations how the measurement accuracy depends on diffusion coefficients and flow rates, expressed in units of camera pixels and frames. Also, sample-specific issues are addressed: inaccuracies in the velocity profile for dilute suspensions (volume fraction ≤0.03) and tracking errors for concentrated ones (VF ≥ 0.3). An analysis of experiments with colloidal spheres flowing through microchannels corroborates these findings and indicates perspectives for studies on transport, mixing, or rheology in microfluidic environments.

Chromosomal locus tracking with proper accounting of static and dynamic errors

The mean-squared displacement (MSD) and velocity autocorrelation (VAC) of tracked single particles or molecules are ubiquitous metrics for extracting parameters that describe the object's motion, but they are both corrupted by experimental errors that hinder the quantitative extraction of underlying parameters. For the simple case of pure Brownian motion, the effects of localization error due to photon statistics ("static error") and motion blur due to finite exposure time ("dynamic error") on the MSD and VAC are already routinely treated. However, particles moving through complex environments such as cells, nuclei, or polymers often exhibit anomalous diffusion, for which the effects of these errors are less often sufficiently treated. We present data from tracked chromosomal loci in yeast that demonstrate the necessity of properly accounting for both static and dynamic error in the context of an anomalous diffusion that is consistent with a fractional Brownian motion (FBM). We compare these data to analytical forms of the expected values of the MSD and VAC for a general FBM in the presence of these errors.

Active cell mechanics: Measurement and theory

Living cells are active mechanical systems that are able to generate forces. Their structure and shape are primarily determined by biopolymer filaments and molecular motors that form the cytoskeleton. Active force generation requires constant consumption of energy to maintain the nonequilibrium activity to drive organization and transport processes necessary for their function. To understand this activity it is necessary to develop new approaches to probe the underlying physical processes. Active cell mechanics incorporates active molecular-scale force generation into the traditional framework of mechanics of materials. This review highlights recent experimental and theoretical developments towards understanding active cell mechanics. We focus primarily on intracellular mechanical measurements and theoretical advances utilizing the Langevin framework. These developing approaches allow a quantitative understanding of nonequilibrium mechanical activity in living cells. This article is part of a Special Issue entitled: Mechanobiology.

Determination of the positions and orientations of concentrated rod-like colloids from 3D microscopy data

Confocal microscopy in combination with real-space particle tracking has proven to be a powerful tool in scientific fields such as soft matter physics, materials science and cell biology. However, 3D tracking of anisotropic particles in concentrated phases remains not as optimized compared to algorithms for spherical particles. To address this problem, we developed a new particle-fitting algorithm that can extract the positions and orientations of fluorescent rod-like particles from three dimensional confocal microscopy data stacks. The algorithm is tailored to work even when the fluorescent signals of the particles overlap considerably and a threshold method and subsequent clusters analysis alone do not suffice. We demonstrate that our algorithm correctly identifies all five coordinates of uniaxial particles in both a concentrated disordered phase and a liquid-crystalline smectic-B phase. Apart from confocal microscopy images, we also demonstrate that the algorithm can be used to identify nanorods in 3D electron tomography reconstructions. Lastly, we determined the accuracy of the algorithm using both simulated and experimental confocal microscopy data-stacks of diffusing silica rods in a dilute suspension. This novel particle-fitting algorithm allows for the study of structure and dynamics in both dilute and dense liquid-crystalline phases (such as nematic, smectic and crystalline phases) as well as the study of the glass transition of rod-like particles in three dimensions on the single particle level.

Highly PEGylated DNA Nanoparticles Provide Uniform and Widespread Gene Transfer in the Brain

Gene delivery to the central nervous system (CNS) has potential as a means for treating numerous debilitating neurological diseases. Nonviral gene vector platforms are tailorable and can overcome key limitations intrinsic to virus-mediated delivery; however, lack of clinical efficacy with nonviral systems to date may be attributed to limited gene vector dispersion and transfection in vivo. It is shown that the brain extracellular matrix (ECM) strongly limits penetration of polymer-based gene vector nanoparticles (NP) through the brain parenchyma, even when they are very small (<60 nm) and coated with a polyethylene glycol (PEG) corona of typical density. Following convection enhanced delivery (CED), conventional gene vectors are confined to the injection site, presumably by adhesive interactions with the brain ECM and do not provide gene expression beyond the point of administration. In contrast, it is found that incorporating highly PEGylated polymers allows the production of compacted (≈43 nm) and colloidally stable DNA NP that avoid adhesive trapping within the brain parenchyma. When administered by CED into the rat striatum, highly PEGylated DNA NP distribute throughout and provide broad transgene expression without vector-induced toxicity. The use of these brain-penetrating gene vectors, in conjunction with CED, offers an avenue to improve gene therapy for CNS diseases.

The mechanical properties of early Drosophila embryos measured by high-speed video microrheology

In early development, Drosophila melanogaster embryos form a syncytium, i.e., multiplying nuclei are not yet separated by cell membranes, but are interconnected by cytoskeletal polymer networks consisting of actin and microtubules. Between division cycles 9 and 13, nuclei and cytoskeleton form a two-dimensional cortical layer. To probe the mechanical properties and dynamics of this self-organizing pre-tissue, we measured shear moduli in the embryo by high-speed video microrheology. We recorded position fluctuations of injected micron-sized fluorescent beads with kHz sampling frequencies and characterized the viscoelasticity of the embryo in different locations. Thermal fluctuations dominated over nonequilibrium activity for frequencies between 0.3 and 1000 Hz. Between the nuclear layer and the yolk, the cytoplasm was homogeneous and viscously dominated, with a viscosity three orders of magnitude higher than that of water. Within the nuclear layer we found an increase of the elastic and viscous moduli consistent with an increased microtubule density. Drug-interference experiments showed that microtubules contribute to the measured viscoelasticity inside the embryo whereas actin only plays a minor role in the regions outside of the actin caps that are closely associated with the nuclei. Measurements at different stages of the nuclear division cycle showed little variation.

Imaging and quantification of trans-membrane protein diffusion in living bacteria

The cytoplasmic membrane forms the barrier between any cell's interior and the outside world. It contains many proteins that enable essential processes such as the transmission of signals, the uptake of nutrients, and cell division. In the case of prokaryotes, which do not contain intracellular membranes, the cytoplasmic membrane also contains proteins for respiration and protein folding. Mutual interactions and specific localization of these proteins depend on two-dimensional diffusion driven by thermal fluctuations. The experimental investigation of membrane-protein diffusion in bacteria is challenging due to their small size, only a few times larger than the resolution of an optical microscope. Here, we review fluorescence microscopy-based methods to study diffusion of membrane proteins in living bacteria. The main focus is on data-analysis tools to extract diffusion coefficients from single-particle tracking data obtained by single-molecule fluorescence microscopy. We introduce a novel approach, IPODD (inverse projection of displacement distributions), to obtain diffusion coefficients from the usually obtained 2-D projected diffusion trajectories of the highly 3-D curved bacterial membrane. This method provides, in contrast to traditional mean-squared-displacement methods, correct diffusion coefficients and allows unravelling of heterogeneously diffusing populations.

A high throughput array microscope for the mechanical characterization of biomaterials

In the last decade, the emergence of high throughput screening has enabled the development of novel drug therapies and elucidated many complex cellular processes. Concurrently, the mechanobiology community has developed tools and methods to show that the dysregulation of biophysical properties and the biochemical mechanisms controlling those properties contribute significantly to many human diseases. Despite these advances, a complete understanding of the connection between biomechanics and disease will require advances in instrumentation that enable parallelized, high throughput assays capable of probing complex signaling pathways, studying biology in physiologically relevant conditions, and capturing specimen and mechanical heterogeneity. Traditional biophysical instruments are unable to meet this need. To address the challenge of large-scale, parallelized biophysical measurements, we have developed an automated array high-throughput microscope system that utilizes passive microbead diffusion to characterize mechanical properties of biomaterials. The instrument is capable of acquiring data on twelve-channels simultaneously, where each channel in the system can independently drive two-channel fluorescence imaging at up to 50 frames per second. We employ this system to measure the concentration-dependent apparent viscosity of hyaluronan, an essential polymer found in connective tissue and whose expression has been implicated in cancer progression.

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.

Turning up the heat on wormlike micelles with a hydrotopic salt in microfluidics

In equilibrium, wormlike micelles can transition from entangled to branched structures with increasing surfactant concentrations and ionic strength. Under flow conditions, structural transition of micellar solutions can follow very different trajectories. In this study we consider the flow of a semi-dilute wormlike micellar solution through an array of microposts, with focus on its rheological and microstructural evolutions. Specifically, the micellar solution (precursor) contains cationic surfactant cetyltrimethylammonium bromide (CTAB) and hydrotropic organic salt 3-hydroxynaphthalene-2-carboxylate (SHNC). We report the formation of a flow induced structured phase (FISP), with entangled, branched, and multi-connected micellar bundles, evidenced by electron microscopy and small-angle neutron scattering (SANS). By integrating gold-etched microheaters with the micropost design in a microfluidic device, we investigate the localized temperature effect on both the precursor and FISP, with complementary investigations from SANS. We observe that the FISP does not completely disintegrate at high temperatures, whereas, the precursor exhibits shortening of wormlike micelles as temperature increases. We also correlate the microstructure of both FISP and precursor with two point passive microrheology and bulk rheology characterizations.

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.

Correlations of three-dimensional motion of chromosomal loci in yeast revealed by the double-helix point spread function microscope

Single-particle tracking has been applied to study chromatin motion in live cells, revealing a wealth of dynamical behavior of the genomic material once believed to be relatively static throughout most of the cell cycle. Here we used the dual-color three-dimensional (3D) double-helix point spread function microscope to study the correlations of movement between two fluorescently labeled gene loci on either the same or different budding yeast chromosomes. We performed fast (10 Hz) 3D tracking of the two copies of the GAL locus in diploid cells in both activating and repressive conditions. As controls, we tracked pairs of loci along the same chromosome at various separations, as well as transcriptionally orthogonal genes on different chromosomes. We found that under repressive conditions, the GAL loci exhibited significantly higher velocity cross-correlations than they did under activating conditions. This relative increase has potentially important biological implications, as it might suggest coupling via shared silencing factors or association with decoupled machinery upon activation. We also found that on the time scale studied (∼0.1-30 s), the loci moved with significantly higher subdiffusive mean square displacement exponents than previously reported, which has implications for the application of polymer theory to chromatin motion in eukaryotes.

Synthesis of colloidal microgels using oxygen-controlled flow lithography

We report a synthesis approach based on stop-flow lithography (SFL) for fabricating colloidal microparticles with any arbitrary 2D-extruded shape. By modulating the degree of oxygen inhibition during synthesis, we achieved previously unattainable particle sizes. Brownian diffusion of colloidal discs in bulk suggests the out-of-plane dimension can be as small as 0.8 μm, which agrees with confocal microscopy measurements. We measured the hindered diffusion of microdiscs near a solid surface and compared our results to theoretical predictions. These colloidal particles can also flow through physiological microvascular networks formed by endothelial cells undergoing vasculogensis under minimal hydrostatic pressure (∼5 mm H2O). This versatile platform creates future opportunities for on-chip parametric studies of particle geometry effects on particle passage properties, distribution and cellular interactions.

Micro and macrorheology at fluid-fluid interfaces

Interfacial transport phenomena play an important role in the dynamics of liquid interfaces found in emulsions, foams, and membranes. Both macroscopic and microscopic measurements of interfacial transport and rheology can be made, the former typically relying on the use of at least millimeter-scale probes, and the latter exploiting the motion of micrometer-scale probes. Recent publications have shown multiple orders of magnitude differences between experimentally observed diffusivities in passive microrheology, and the diffusivities expected based on macroscopic measurements of the surface rheology. In the present work, interfacial rheological measurements were made with both microrheological and macrorheological methods and the results are compared for different monolayers at an air-water interface. We have identified multiple aspects of particle-tracking microrheology that can contribute to orders-of-magnitude disagreement with macrorheological methods. In particular, unintentional tracking of particles not residing at the interface, the presence of large-scale interfacial heterogeneities, and underestimating static noise can all decrease estimates of surface viscosity from particle-tracking microrheology by orders of magnitude. After taking care to address these artifacts, we show that viscosities obtained from both methods agree well for poly(tert-butyl methacrylate) (PtBMA), and for dipalmitoylphosphatidylcholine (DPPC), but disagree by orders of magnitude for hexadecanol. In poly(tert-butyl acrylate) (PtBA), large-scale heterogeneities prevented us from obtaining representative surface viscosities. By making surface viscosity measurements in an interfacial stress rheometer (ISR) with needles of different aspect ratio, we show that compressibility or Marangoni stress related effects may be contributing to the orders of magnitude disagreement in micro and macrorheological measurements observed in the hexadecanol system.

Linear and nonlinear microrheology of lysozyme layers forming at the air-water interface

We report experiments studying the mechanical evolution of layers of the protein lysozyme adsorbing at the air-water interface using passive and active microrheology techniques to investigate the linear and nonlinear rheological response, respectively. Following formation of a new interface, the linear shear rheology, which we interrogate through the Brownian motion of spherical colloids at the interface, becomes viscoelastic with a complex modulus that has approximately power-law frequency dependence. The power-law exponent characterizing this frequency dependence decreases steadily with increasing layer age. Meanwhile, the nonlinear microrheology, probed via the rotational motion of magnetic nanowires at the interface, reveals a layer response characteristic of a shear-thinning power-law fluid with a flow index that decreases with age. We discuss two possible frameworks for understanding this mechanical evolution: gelation and the formation of a soft glass phase.

Elasticity of microscale volumes of viscoelastic soft matter by cavitation rheometry

Measurement of the elastic modulus of soft, viscoelastic liquids with cavitation rheometry is demonstrated for specimens as small as 1 μl by application of elasticity theory and experiments on semi-dilute polymer solutions. Cavitation rheometry is the extraction of the elastic modulus of a material, E, by measuring the pressure necessary to create a cavity within it [J. A. Zimberlin, N. Sanabria-DeLong, G. N. Tew, and A. J. Crosby, Soft Matter 3, 763-767 (2007)]. This paper extends cavitation rheometry in three ways. First, we show that viscoelastic samples can be approximated with the neo-Hookean model provided that the time scale of the cavity formation is measured. Second, we extend the cavitation rheometry method to accommodate cases in which the sample size is no longer large relative to the cavity dimension. Finally, we implement cavitation rheometry to show that the theory accurately measures the elastic modulus of viscoelastic samples with volumes ranging from 4 ml to as low as 1 μl.