Advances in the microrheology of complex fluids

Broken detailed balance and non-equilibrium dynamics in living systems: a review

Living systems operate far from thermodynamic equilibrium. Enzymatic activity can induce broken detailed balance at the molecular scale. This molecular scale breaking of detailed balance is crucial to achieve biological functions such as high-fidelity transcription and translation, sensing, adaptation, biochemical patterning, and force generation. While biological systems such as motor enzymes violate detailed balance at the molecular scale, it remains unclear how non-equilibrium dynamics manifests at the mesoscale in systems that are driven through the collective activity of many motors. Indeed, in several cellular systems the presence of non-equilibrium dynamics is not always evident at large scales. For example, in the cytoskeleton or in chromosomes one can observe stationary stochastic processes that appear at first glance thermally driven. This raises the question how non-equilibrium fluctuations can be discerned from thermal noise. We discuss approaches that have recently been developed to address this question, including methods based on measuring the extent to which the system violates the fluctuation-dissipation theorem. We also review applications of this approach to reconstituted cytoskeletal networks, the cytoplasm of living cells, and cell membranes. Furthermore, we discuss a more recent approach to detect actively driven dynamics, which is based on inferring broken detailed balance. This constitutes a non-invasive method that uses time-lapse microscopy data, and can be applied to a broad range of systems in cells and tissue. We discuss the ideas underlying this method and its application to several examples including flagella, primary cilia, and cytoskeletal networks. Finally, we briefly discuss recent developments in stochastic thermodynamics and non-equilibrium statistical mechanics, which offer new perspectives to understand the physics of living systems.

Colloidal probe dynamics in gelatin solution during the sol-gel transition

The dynamics of the colloidal probes in a gelatin solution during the time-dependent sol-gel transition was investigated by multi-particle tracking. The relationship between the relaxation of the medium at the critical gel point and the mean square displacement of the probes was elucidated. Based on this understanding, the critical gel point of gelatin and the corresponding critical exponent n were unambiguously determined by the loss angle criterion and the time-cure superposition. The shift factors of the latter are further used to estimate the time/length-scale evolution of the gelatin during the sol-gel transition. The growth of the medium length scale crossed with the two measuring length scales successively at the pre-gel regime. Coinciding with the length-scale crossovers, the probability density function (PDF) of the probe displacements displayed two transient peaks of non-Gaussianity. In the post-gel regime, the third peak of Gaussianity suggested inhomogeneity in the gel network. The non-Gaussianity results from the bifurcation of diffusivity. The present work showed that the non-Gaussian dynamics of the probes are not the direct equivalence of that of the medium, but an effect of length-scale coupling.

Coping with the climate: cuticular hydrocarbon acclimation of ants under constant and fluctuating conditions

Terrestrial arthropods achieve waterproofing by a layer of cuticular hydrocarbons (CHCs). At the same time, CHCs also serve as communication signals. To maintain waterproofing under different climate conditions, insects adjust the chemical composition of their CHC layer, but this may affect the communication via CHCs. The detailed acclimatory changes of CHCs and how these influence their physical properties are still unknown. Here, we studied acclimation in two closely related ant species with distinct CHC profiles, Myrmica rubra and Myrmica ruginodis, in response to constant or fluctuating temperature and humidity regimes. We measured how acclimation affected CHC composition and viscosity, and the ants' drought survival. In both species, CHC composition showed strong, predictable responses to temperature regimes. Warm-acclimated individuals had higher proportions of linear alkanes, and less methyl-branched or unsaturated CHCs. These changes coincided with higher solid content and viscosity of CHCs in warm-acclimated ants. Temperature fluctuation caused effects similar to those observed under constant-cool conditions in Mrubra, but led to entirely different profiles in Mruginodis, suggesting that fluctuating and constant conditions pose very different challenges. Acclimation to dry conditions led to higher absolute amounts of CHCs, which increased the ants' drought survival, whereas temperature acclimation did not. Hence, the temperature-induced CHC changes cannot be explained by the need for waterproofing alone. Although these changes could be non-adaptive, we propose that they serve to maintain a constant CHC viscosity, which may be essential for communication and other functions.

Rheological characterization of dynamic remodeling of the pericellular region by human mesenchymal stem cell-secreted enzymes in well-defined synthetic hydrogel scaffolds

Human mesenchymal stem cells (hMSCs) dynamically remodel their microenvironment during basic processes, such as migration and differentiation. Migration requires extracellular matrix invasion, necessitating dynamic cell-material interactions. Understanding these interactions is critical to advancing materials designs that harness and manipulate these processes for applications including wound healing and tissue regeneration. In this work, we encapsulate hMSCs in a cell-degradable poly(ethylene glycol)-peptide hydrogel to determine how cell-secreted enzymes, specifically matrix metalloproteinases (MMPs) and tissue inhibitors of metalloproteinases (TIMPs), create unique pericellular microenvironments. Using multiple particle tracking microrheology (MPT), we characterize spatio-temporal rheological properties in the pericellular region during cell-mediated remodeling. In MPT, the thermal motion of probes embedded in the network is measured. A newly designed sample chamber that limits probe drift during degradation and minimizes high value antibody volumes required for cell treatments enables MPT characterization. Previous MPT measurements around hMSCs show that directly around the cell the scaffold remains intact with the cross-link density decreasing as distance from the cell increases. This degradation profile suggests that hMSCs are simultaneously secreting TIMPs, which are inactivating MMPs through MMP-TIMP complexes. By neutralizing TIMPs using antibodies, we characterize the changes in matrix degradation. TIMP inhibited hMSCs create a reaction-diffusion type degradation profile where MMPs are actively degrading the matrix immediately after secretion. In this profile, the cross-link density increases with increasing distance from the cell. This change in material properties also increases the speed of migration. This simple treatment could increase delivery of hMSCs to injuries to aid wound healing and tissue regeneration.

Mucin gel assembly is controlled by a collective action of non-mucin proteins, disulfide bridges, Ca2+-mediated links, and hydrogen bonding

Mucus is characterized by multiple levels of assembly at different length scales which result in a unique set of rheological (flow) and mechanical properties. These physical properties determine its biological function as a highly selective barrier for transport of water and nutrients, while blocking penetration of pathogens and foreign particles. Altered integrity of the mucus layer in the small intestine has been associated with a number of gastrointestinal tract pathologies such as Crohn’s disease and cystic fibrosis. In this work, we uncover an intricate hierarchy of intestinal mucin (Muc2) assembly and show how complex rheological properties emerge from synergistic interactions between mucin glycoproteins, non-mucin proteins, and Ca²⁺. Using a novel method of mucus purification, we demonstrate the mechanism of assembly of Muc2 oligomers into viscoelastic microscale domains formed via hydrogen bonding and Ca²⁺-mediated links, which require the joint presence of Ca²⁺ ions and non-mucin proteins. These microscale domains aggregate to form a heterogeneous yield stress gel-like fluid, the macroscopic rheological properties of which are virtually identical to that of native intestinal mucus. Through proteomic analysis, we short-list potential protein candidates implicated in mucin assembly, thus paving the way for identifying the molecules responsible for the physiologically critical biophysical properties of mucus.

Structural, microrheological and kinetic properties of a ternary silica-Pluronic F127-starch thermosensitive system

HYPOTHESIS

The sol-gel transition in aqueous suspensions consisting of silica particles and thermosensitive polymer is controlled by inter-particle forces and solution properties of the polymer. Addition of a second non-thermosensitive polymer may affect the transition. The purpose of this work was to characterize the kinetics of the sol-gel transition and to understand the effects of a second non-thermosensitive polymer on the microstructure, using a combination of classical rheology and microrheology.

EXPERIMENTS

Classical rotational rheology as well as two microrheology methods, Multiple Particle Tracking (MPT) and Diffusing Wave Spectroscopy (DWS), were used to investigate the sol-gel transition of a ternary silica-Pluronic F127-starch thermosensitive system.

FINDINGS

Classical rheometry and DWS indicated sol-gel transition temperature ∼25 °C at 1 wt% Pluronic, independently of the concentration of the other components. DWS showed a fast gelation process, less than two minutes for all samples, beside a second slow kinetic process. In the gel state, MPT indicated micro-structural and micro-viscoelastic differences compared to rotational rheology. This was explained by formation of an elastic matrix of silica and polymers in combination with assembly of silica particles in large macroporous agglomerates. Presence of starch led to breakdown of the macroporous network, leaving the homogeneous elastic network left.

Multifrequency AFM reveals lipid membrane mechanical properties and the effect of cholesterol in modulating viscoelasticity

The physical properties of lipid bilayers comprising the cell membrane occupy the current spotlight of membrane biology. Their traditional representation as a passive 2D fluid has gradually been abandoned in favor of a more complex picture: an anisotropic time-dependent viscoelastic biphasic material, capable of transmitting or attenuating mechanical forces that regulate biological processes. In establishing new models, quantitative experiments are necessary when attempting to develop suitable techniques for dynamic measurements. Here, we map both the elastic and viscous properties of the model system 1,2-dipalmitoyl-sn-glycero-3-phosphocholine (DPPC) lipid bilayers using multifrequency atomic force microscopy (AFM), namely amplitude modulation-frequency modulation (AM-FM) AFM imaging in an aqueous environment. Furthermore, we investigate the effect of cholesterol (Chol) on the DPPC bilayer in concentrations from 0 to 60%. The AM-AFM quantitative maps demonstrate that at low Chol concentrations, the lipid bilayer displays a distinct phase separation and is elastic, whereas at higher Chol concentration, the bilayer appears homogenous and exhibits both elastic and viscous properties. At low-Chol contents, the Estorage modulus (elastic) dominates. As the Chol insertions increases, higher energy is dissipated; and although the bilayer stiffens (increase in Estorage), the viscous component dominates (Eloss). Our results provide evidence that the lipid bilayer exhibits both elastic and viscous properties that are modulated by the presence of Chol, which may affect the propagation (elastic) or attenuation (viscous) of mechanical signals across the cell membrane.

Sensing Magnetic Fields with Magnetosensitive Ion Channels

[-15]Magnetic nanoparticles are met across many biological species ranging from magnetosensitive bacteria, fishes, bees, bats, rats, birds, to humans. They can be both of biogenetic origin and due to environmental contamination, being either in paramagnetic or ferromagnetic state. The energy of such naturally occurring single-domain magnetic nanoparticles can reach up to 10-20 room k B T in the magnetic field of the Earth, which naturally led to supposition that they can serve as sensory elements in various animals. This work explores within a stochastic modeling framework a fascinating hypothesis of magnetosensitive ion channels with magnetic nanoparticles serving as sensory elements, especially, how realistic it is given a highly dissipative viscoelastic interior of living cells and typical sizes of nanoparticles possibly involved.

An efficient algorithm for extracting the magnitude of the measurement error for fractional dynamics

Modern live-imaging fluorescent microscopy techniques following the stochastic motion of labeled tracer particles, i.e. single particle tracking (SPT) experiments, have uncovered significant deviations from the laws of Brownian motion in a variety of biological systems. Accurately characterizing the anomalous diffusion for SPT experiments has become a central issue in biophysics. However, measurement errors raise difficulty in the analysis of single trajectories. In this paper, we introduce a novel surface calibration method based on a fractionally integrated moving average (FIMA) process as an effective tool for extracting both the magnitude of the measurement error and the anomalous exponent for autocorrelated processes of various origins. This method is developed using a toy model - fractional Brownian motion disturbed by independent Gaussian white noise - and is illustrated on both simulated and experimental biological data. We also compare this new method with the mean-squared displacement (MSD) technique, extended to capture the measurement noise in the toy model, which shows inferior results. The introduced procedure is expected to allow for more accurate analysis of fractional anomalous diffusion trajectories with measurement errors across different experimental fields and without the need for any calibration measurements.

Technological strategies to estimate and control diffusive passage times through the mucus barrier in mucosal drug delivery

In mucosal drug delivery, two design goals are desirable: 1) insure drug passage through the mucosal barrier to the epithelium prior to drug removal from the respective organ via mucus clearance; and 2) design carrier particles to achieve a prescribed arrival time and drug uptake schedule at the epithelium. Both goals are achievable if one can control "one-sided" diffusive passage times of drug carrier particles: from deposition at the mucus interface, through the mucosal barrier, to the epithelium. The passage time distribution must be, with high confidence, shorter than the timescales of mucus clearance to maximize drug uptake. For 100nm and smaller drug-loaded nanoparticulates, as well as pure drug powders or drug solutions, diffusion is normal (i.e., Brownian) and rapid, easily passing through the mucosal barrier prior to clearance. Major challenges in quantitative control over mucosal drug delivery lie with larger drug-loaded nanoparticulates that are comparable to or larger than the pores within the mucus gel network, for which diffusion is not simple Brownian motion and typically much less rapid; in these scenarios, a timescale competition ensues between particle passage through the mucus barrier and mucus clearance from the organ. In the lung, as a primary example, coordinated cilia and air drag continuously transport mucus toward the trachea, where mucus and trapped cargo are swallowed into the digestive tract. Mucus clearance times in lung airways range from minutes to hours or significantly longer depending on deposition in the upper, middle, lower airways and on lung health, giving a wide time window for drug-loaded particle design to achieve controlled delivery to the epithelium. We review the physical and chemical factors (of both particles and mucus) that dictate particle diffusion in mucus, and the technological strategies (theoretical and experimental) required to achieve the design goals. First we describe an idealized scenario - a homogeneous viscous fluid of uniform depth with a particle undergoing passive normal diffusion - where the theory of Brownian motion affords the ability to rigorously specify particle size distributions to meet a prescribed, one-sided, diffusive passage time distribution. Furthermore, we describe how the theory of Brownian motion provides the scaling of one-sided diffusive passage times with respect to mucus viscosity and layer depth, and under reasonable caveats, one can also prescribe passage time scaling due to heterogeneity in viscosity and layer depth. Small-molecule drugs and muco-inert, drug-loaded carrier particles 100nm and smaller fall into this class of rigorously controllable passage times for drug delivery. Second we describe the prevalent scenarios in which drug-loaded carrier particles in mucus violate simple Brownian motion, instead exhibiting anomalous sub-diffusion, for which all theoretical control over diffusive passage times is lost, and experiments are prohibitive if not impossible to measure one-sided passage times. We then discuss strategies to overcome these roadblocks, requiring new particle-tracking experiments and emerging advances in theory and computation of anomalous, sub-diffusive processes that are necessary to predict and control one-sided particle passage times from deposition at the mucosal interface to epithelial uptake. We highlight progress to date, remaining hurdles, and prospects for achieving the two design goals for 200nm and larger, drug-loaded, non-dissolving, nanoparticulates.

Isomeric control of the mechanical properties of supramolecular filament hydrogels

Supramolecular filament hydrogels are an emerging class of biomaterials that hold great promise for regenerative medicine, tissue engineering, and drug delivery. The use of isomeric hydrocarbons in the peptide design enables fine-tuning of the mechanical properties of their supramolecular filament hydrogels without altering their network structures.

Translational and rotational dynamics of an ultra-thin nanorod probe particle in linear polymer melts

Translational and rotational dynamics of a single rigid ultra-thin nanorod probe particle in linear polymer melts are investigated using coarse-grained molecular dynamics (CG-MD) simulations.

Aging in mortal superdiffusive Lévy walkers

A growing body of literature examines the effects of superdiffusive subballistic movement premeasurement (aging or time lag) on observations arising from single-particle tracking. A neglected aspect is the finite lifetime of these Lévy walkers, be they proteins, cells, or larger structures. We examine the effects of aging on the motility of mortal walkers, and discuss the means by which permanent stopping of walkers may be categorized as arising from "natural" death or experimental artifacts such as low photostability or radiation damage. This is done by comparison of the walkers' mean squared displacement (MSD) with the front velocity of propagation of a group of walkers, which is found to be invariant under time lags. For any running time distribution of a mortal random walker, the MSD is tempered by the stopping rate θ. This provides a physical interpretation for truncated heavy-tailed diffusion processes and serves as a tool by which to better classify the underlying running time distributions of random walkers. Tempering of aged MSDs raises the issue of misinterpreting superdiffusive motion which appears Brownian or subdiffusive over certain time scales.

On the relationship between the plateau modulus and the threshold frequency in peptide gels

Relations between static and dynamic viscoelastic responses in gels can be very elucidating and may provide useful tools to study the behavior of bio-materials such as protein hydrogels. An important example comes from the viscoelasticity of semisolid gel-like materials, which is characterized by two regimes: a low-frequency regime, where the storage modulus G'(ω) displays a constant value G_eq, and a high-frequency power-law stiffening regime, where G'(ω) ∼ ωⁿ. Recently, by considering Monte Carlo simulations to study the formation of peptides networks, we found an intriguing and somewhat related power-law relationship between the plateau modulus and the threshold frequency, i.e., G_eq∼(ω^*)^Δ with Δ = 2/3. Here we present a simple theoretical approach to describe that relationship and test its validity by using experimental data from a β-lactoglobulin gel. We show that our approach can be used even in the coarsening regime where the fractal model fails. Remarkably, the very same exponent Δ is found to describe the experimental data.

Effects of finite and discrete sampling and blur on microrheology experiments

The frequency-dependent viscous and elastic properties of fluids can be determined from measurements of the thermal fluctuations of a micron-sized particle trapped by optical tweezers. Finite bandwidth and other instrument limitations lead to systematic errors in measurement of the fluctuations. In this work, we numerically represented power spectra of bead position measurements as if collected by two different measurement devices: a quadrant photodiode, which measures the deflection of the trapping laser; and a high-speed camera, which images the trapped bead directly. We explored the effects of aliasing, camera blur, sampling frequency, and measurement time. By comparing the power spectrum, complex response function, and the complex shear modulus with the ideal values, we found that the viscous and elastic properties inferred from the data are affected by the instrument limitations of each device. We discuss how these systematic effects might affect experimental results from microrheology measurements and suggest approaches to reduce discrepancies.

Evolution of heterogeneity accompanying sol-gel transitions in a supramolecular hydrogel

When a peptide amphiphile is dispersed in water, it self-assembles into a fibrous network, leading to a supramolecular hydrogel. When the gel is physically disrupted by shaking, it transforms into a sol state. After aging at room temperature for a while, it spontaneously returns to the gel state, called sol-gel transition. However, repeating the sol-gel transition often causes a change in the rheological properties of the gel. To gain a better understanding of the sol-gel transition and its reversibility, we herein examined the thermal motion of probe particles at different locations in a supramolecular hydrogel. The sol obtained by shaking the gel was heterogeneous in terms of the rheological properties and the extent decreased with increasing aging time. This time course of heterogeneity, or homogeneity, which corresponded to the sol-to-gel transition, was observed for the 1st cycle. However, this was not the case for the 2nd and 3rd cycles; the heterogeneity was preserved even after aging. Fourier-transform infrared spectroscopy, small-angle X-ray scattering, and atomic force and confocal laser scanning microscopies revealed that, although the molecular aggregation states of amphiphiles both in the gel and sol remained unchanged with the cycles, the fibril density diversified to high and low density regions even after aging. The tracking of particles with different sizes indicated that the partial mesh size in the high density region and the characteristic length scale of the density fluctuation were smaller than 50 nm and 6 μm, respectively.

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.

Oscillating Ferrofluid Droplet Microrheology of Liquid-Immersed Sessile Droplets

The damped oscillations of liquid-immersed ferrofluid sessile droplets were studied with high-speed imaging experiments and analytical modeling to develop a novel microrheology technique. Droplet oscillations were induced with an external magnetic field, thereby avoiding transients in the resulting vibrational response of the droplet. By following the droplet relaxation with a high-speed camera, the frequency and relaxation time of the damped harmonic oscillations were measured. We extend upon existing analytical theories to describe our liquid-immersed sessile droplet system, and directly quantify the droplet relaxation with the viscosity of the internal and external fluid as well as the interfacial tension between these. The easily controllable magnetic droplets make our oscillating ferrofluid droplet technique a potential candidate for high-throughput microrheology and tensiometry in the future.

Motion of a nano-spheroid in a cylindrical vessel flow: Brownian and hydrodynamic interactions

We study the motion of a buoyant or a nearly neutrally buoyant nano-sized spheroid in a fluid filled tube without or with an imposed pressure gradient (weak Poiseuille flow). The fluctuating hydrodynamics approach and the deterministic method are both employed. We ensure that the fluctuation-dissipation relation and the principle of thermal equipartition of energy are both satisfied. The major focus is on the effect of the confining boundary. Results for the velocity and the angular velocity autocorrelations (VACF and AVACF), the diffusivities and the drag and the lift forces as functions of the shape, the aspect ratio, the inclination angle and the proximity to the wall are presented. For the parameters considered, the boundary modifies the VACF and AVACF such that three distinct regimes are discernible - an initial exponential decay followed by an algebraic decay culminating in a second exponential decay. The first is due to the thermal noise, the algebraic regime is due both to the thermal noise and the hydrodynamic correlations, while the second exponential decay shows the effect of momentum reflection from the confining wall. Our predictions display excellent comparison with published results for the algebraic regime (the only regime for which earlier results exist). We also discuss the role of the off-diagonal elements of the mobility and the diffusivity tensors that enable the quantifications of the degree of lift and margination of the nanocarrier. Our study covers a range of parameters that are of wide applicability in nanotechnology, microrheology and in targeted drug delivery.

The particle in the spider's web: transport through biological hydrogels

Biological hydrogels such as mucus, extracellular matrix, biofilms, and the nuclear pore have diverse functions and compositions, but all act as selectively permeable barriers to the diffusion of particles. Each barrier has a crosslinked polymeric mesh that blocks penetration of large particles such as pathogens, nanotherapeutics, or macromolecules. These polymeric meshes also employ interactive filtering, in which affinity between solutes and the gel matrix controls permeability. Interactive filtering affects the transport of particles of all sizes including peptides, antibiotics, and nanoparticles and in many cases this filtering can be described in terms of the effects of charge and hydrophobicity. The concepts described in this review can guide strategies to exploit or overcome gel barriers, particularly for applications in diagnostics, pharmacology, biomaterials, and drug delivery.

Tweezing of Magnetic and Non-Magnetic Objects with Magnetic Fields

Although strong magnetic fields cannot be conveniently "focused" like light, modern microfabrication techniques enable preparation of microstructures with which the field gradients - and resulting magnetic forces - can be localized to very small dimensions. This ability provides the foundation for magnetic tweezers which in their classical variant can address magnetic targets. More recently, the so-called negative magnetophoretic tweezers have also been developed which enable trapping and manipulations of completely nonmagnetic particles provided that they are suspended in a high-magnetic-susceptibility liquid. These two modes of magnetic tweezing are complimentary techniques tailorable for different types of applications. This Progress Report provides the theoretical basis for both modalities and illustrates their specific uses ranging from the manipulation of colloids in 2D and 3D, to trapping of living cells, control of cell function, experiments with single molecules, and more.

Forces and torques on rigid inclusions in an elastic environment: Resulting matrix-mediated interactions, displacements, and rotations

Embedding rigid inclusions into elastic matrix materials is a procedure of high practical relevance, for instance, for the fabrication of elastic composite materials. We theoretically analyze the following situation. Rigid spherical inclusions are enclosed by a homogeneous elastic medium under stick boundary conditions. Forces and torques are directly imposed from outside onto the inclusions or are externally induced between them. The inclusions respond to these forces and torques by translations and rotations against the surrounding elastic matrix. This leads to elastic matrix deformations, and in turn results in mutual long-ranged matrix-mediated interactions between the inclusions. Adapting a well-known approach from low-Reynolds-number hydrodynamics, we explicitly calculate the displacements and rotations of the inclusions from the externally imposed or induced forces and torques. Analytical expressions are presented as a function of the inclusion configuration in terms of displaceability and rotateability matrices. The role of the elastic environment is implicitly included in these relations. That is, the resulting expressions allow a calculation of the induced displacements and rotations directly from the inclusion configuration, without having to explicitly determine the deformations of the elastic environment. In contrast to the hydrodynamic case, compressibility of the surrounding medium is readily taken into account. We present the complete derivation based on the underlying equations of linear elasticity theory. In the future, the method will, for example, be helpful to characterize the behavior of externally tunable elastic composite materials, to accelerate numerical approaches, as well as to improve the quantitative interpretation of microrheological results.

Elastic turbulence in entangled semi-dilute DNA solutions measured with optical coherence tomography velocimetry

The flow instabilities of solutions of high molecular weight DNA in the entangled semi-dilute concentration regime were investigated using optical coherence tomography velocimetry, a technique that provides high spatial (probe volumes of 3.4 pL) and temporal resolution (sub μs) information on the flow behaviour of complex fluids in a rheometer. The velocity profiles of the opaque DNA solutions (high and low salt) were measured as a function of the distance across the gap of a parallel plate rheometer, and their evolution over time was measured. At lower DNA concentrations and low shear rates, the velocity fluctuations were well described by Gaussian functions and the velocity gradient was uniform across the rheometer gap, which is expected for Newtonian flows. As the DNA concentration and shear rate were increased there was a stable wall slip regime followed by an evolving wall slip regime, which is finally followed by the onset of elastic turbulence. Strain localization (shear banding) is observed on the boundaries of the flows at intermediate shear rates, but decreases in the high shear elastic turbulence regime, where bulk strain localization occurs. A dynamic phase diagram for non-linear flow was created to describe the different behaviours.

Refining particle positions using circular symmetry

Particle and object tracking is gaining attention in industrial applications and is commonly applied in: colloidal, biophysical, ecological, and micro-fluidic research. Reliable tracking information is heavily dependent on the system under study and algorithms that correctly determine particle position between images. However, in a real environmental context with the presence of noise including particular or dissolved matter in water, and low and fluctuating light conditions, many algorithms fail to obtain reliable information. We propose a new algorithm, the Circular Symmetry algorithm (C-Sym), for detecting the position of a circular particle with high accuracy and precision in noisy conditions. The algorithm takes advantage of the spatial symmetry of the particle allowing for subpixel accuracy. We compare the proposed algorithm with four different methods using both synthetic and experimental datasets. The results show that C-Sym is the most accurate and precise algorithm when tracking micro-particles in all tested conditions and it has the potential for use in applications including tracking biota in their environment.

Both genome and cytosol dynamics change in E. coli challenged with sublethal rifampicin

While the action of many antimicrobial drugs is well understood at the molecular level, a systems-level physiological response to antibiotics remains largely unexplored. This work considers fluctuation dynamics of both the chromosome and cytosol in Escherichia coli, and their response to sublethal treatments of a clinically important antibiotic, rifampicin. We precisely quantify the changes in dynamics of chromosomal loci and cytosolic aggregates (a rheovirus nonstructural protein known as μNS-GFP), measuring short time-scale displacements across several hours of drug exposure. To achieve this we develop an empirical method correcting for photo-bleaching and loci size effects. This procedure allows us to characterize the dynamic response to rifampicin in different growth conditions, including a customised microfluidic device. We find that sub-lethal doses of rifampicin cause a small but consistent increase in motility of both the chromosomal loci and cytosolic aggregates. Chromosomal and cytosolic responses are consistent with each other and between different growth conditions.

Application of Microrheology in Food Science

Microrheology provides a technique to probe the local viscoelastic properties and dynamics of soft materials at the microscopic level by observing the motion of tracer particles embedded within them. It is divided into passive and active microrheology according to the force exerted on the embedded particles. Particles are driven by thermal fluctuations in passive microrheology, and the linear viscoelasticity of samples can be obtained on the basis of the generalized Stokes-Einstein equation. In active microrheology, tracer particles are controlled by external forces, and measurements can be extended to the nonlinear regime. Microrheology techniques have many advantages such as the need for only small sample amounts and a wider measurable frequency range. In particular, microrheology is able to examine the spatial heterogeneity of samples at the microlevel, which is not possible using traditional rheology. Therefore, microrheology has considerable potential for studying the local mechanical properties and dynamics of soft matter, particularly complex fluids, including solutions, dispersions, and other colloidal systems. Food products such as emulsions, foams, or gels are complex fluids with multiple ingredients and phases. Their macroscopic properties, such as stability and texture, are closely related to the structure and mechanical properties at the microlevel. In this article, the basic principles and methods of microrheology are reviewed, and the latest developments and achievements of microrheology in the field of food science are presented.

Time-Dependent Fluctuations and Superdiffusivity in the Driven Lattice Lorentz Gas

We consider a tracer particle on a lattice in the presence of immobile obstacles. Starting from equilibrium, a force pulling on the particle is switched on, driving the system to a new stationary state. We solve for the complete transient dynamics of the fluctuations of the tracer position along the direction of the force. The analytic result, exact in first order of the obstacle density and for arbitrarily strong driving, is compared to stochastic simulations. Upon strong driving, the fluctuations grow superdiffusively for intermediate times; however, they always become diffusive in the stationary state. The diffusion constant is nonanalytic for small driving and is enhanced by orders of magnitude by increasing the force.

Forces on Rigid Inclusions in Elastic Media and Resulting Matrix-Mediated Interactions

To describe many-particle systems suspended in incompressible low-Reynolds-number fluids, effective hydrodynamic interactions can be introduced. Here, we consider particles embedded in elastic media. The effective elastic interactions between spherical particles are calculated analytically, inspired by the approach in the fluid case. Our experiments on interacting magnetic particles confirm the theory. In view of the huge success of the method in hydrodynamics, we similarly expect many future applications in the elastic case, e.g., for elastic composite materials.

Passive microrheology in the effective time domain: analyzing time dependent colloidal dispersions

We studied the aging dynamics of an aqueous suspension of LAPONITE®, a model time dependent soft glassy material, using a passive microrheology technique. This system is known to undergo physical aging during which its microstructure evolves progressively to explore lower free energy states. Optical microscopy is used to monitor the motion of micron-sized tracer probes embedded in a sample kept between two glass plates. The mean square displacements (MSD) obtained from the motion of the tracer particles show a systematic change from a purely diffusive behavior at short aging times to a subdiffusive behavior as the material ages. Interestingly, the MSDs at all the aging times as well as different LAPONITE® concentrations superpose remarkably to show a time-aging time master curve when the system is transformed from the real time domain to the effective time domain, which is obtained by rescaling the material clock to account for the age dependent relaxation time. The transformation of the master curve from the effective time domain to the real time domain leads to the prediction of the MSD in real time over a span of 5 decades when the measured data at individual aging times are only over 2 decades. Since the MSD obtained from microrheology is proportional to the creep compliance of a material, by using the Boltzmann superposition principle along with the convolution relation in the effective time domain, we predict the stress relaxation behavior of the system in real time. This work shows that the effective time approach applied to microrheology facilitates the prediction of long time creep and relaxation dynamics of a time dependent soft material by carrying out short time experiments at different aging times.

Nanoscale Motion of Soft Nanoparticles in Unentangled and Entangled Polymer Matrices

We have studied the motion of polyhedral oligomeric silsesquioxane (POSS) nanoparticles modified with poly(ethylene glycol) (PEG) arms immersed in PEG matrices of different molecular weight. Employing neutron spin echo spectroscopy in combination with pulsed field gradient (PFG) NMR we found the following. (i) For entangled matrices the center of mass mean square displacement (MSD) of the PEG-POSS particles is subdiffusive following a t^{0.56} power law. (ii) The diffusion coefficient as well as the crossover to Fickian diffusion is independent of the matrix molecular weight and takes place as soon as the center of mass has moved a distance corresponding to the particle radius-this holds also for unentangled hosts. (iii) For the entangled matrices Rubinstein's scaling theory is validated; however, the numbers indicate that beyond Rouse friction the entanglement constraints appear to strongly increase the effective friction even on the nanoparticle length scale imposing a caveat on the interpretation of microrheological experiments. (iv) The oligomer decorated PEG-POSS particles exhibit the dynamics of a Gaussian star with an internal viscosity that rises with an increase of the host molecular weight.

Phase correlation imaging of unlabeled cell dynamics

We present phase correlation imaging (PCI) as a novel approach to study cell dynamics in a spatially-resolved manner. PCI relies on quantitative phase imaging time-lapse data and, as such, functions in label-free mode, without the limitations associated with exogenous markers. The correlation time map outputted in PCI informs on the dynamics of the intracellular mass transport. Specifically, we show that PCI can extract quantitatively the diffusion coefficient map associated with live cells, as well as standard Brownian particles. Due to its high sensitivity to mass transport, PCI can be applied to studying the integrity of actin polymerization dynamics. Our results indicate that the cyto-D treatment blocking the actin polymerization has a dominant effect at the large spatial scales, in the region surrounding the cell. We found that PCI can distinguish between senescent and quiescent cells, which is extremely difficult without using specific markers currently. We anticipate that PCI will be used alongside established, fluorescence-based techniques to enable valuable new studies of cell function.

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.

111 years of Brownian motion

We consider the Brownian motion of a particle and present a tutorial review over the last 111 years since Einstein's paper in 1905. We describe Einstein's model, Langevin's model and the hydrodynamic models, with increasing sophistication on the hydrodynamic interactions between the particle and the fluid. In recent years, the effects of interfaces on the nearby Brownian motion have been the focus of several investigations. We summarize various results and discuss some of the controversies associated with new findings about the changes in Brownian motion induced by the interface.

Concentration-dependent changes in apparent diffusion coefficients as indicator for colloidal stability of protein solutions

The colloidal stability of a protein solution during downstream processing, formulation, and storage is a key issue for the biopharmaceutical production process. Thus, knowledge about colloidal solution characteristics, such as the tendency to form aggregates or high viscosity, at various processing conditions is of interest. This work correlates changes in the apparent diffusion coefficient as a parameter of protein interactions with observed protein aggregation and dynamic viscosity of the respective protein samples. For this purpose, the diffusion coefficient, the protein phase behavior, and the dynamic viscosity in various systems containing the model proteins α-lactalbumin, lysozyme, and glucose oxidase were studied. Each of these experiments revealed a wide range of variations in protein interactions depending on protein type, protein concentration, pH, and the NaCl concentration. All these variations showed to be mirrored by changes in the apparent diffusion coefficient in the respective samples. Whereas stable samples with relatively low viscosity showed an almost linear dependence, the deviation from the concentration-dependent linearity indicated both an increase in the sample viscosity and probability of protein aggregation. This deviation of the apparent diffusion coefficient from concentration-dependent linearity was independent of protein type and solution properties for this study. Thus, this single parameter shows the potential to act as a prognostic tool for colloidal stability of protein solutions.

Microfluidic viscometers for shear rheology of complex fluids and biofluids

The rich diversity of man-made complex fluids and naturally occurring biofluids is opening up new opportunities for investigating their flow behavior and characterizing their rheological properties. Steady shear viscosity is undoubtedly the most widely characterized material property of these fluids. Although widely adopted, macroscale rheometers are limited by sample volumes, access to high shear rates, hydrodynamic instabilities, and interfacial artifacts. Currently, microfluidic devices are capable of handling low sample volumes, providing precision control of flow and channel geometry, enabling a high degree of multiplexing and automation, and integrating flow visualization and optical techniques. These intrinsic advantages of microfluidics have made it especially suitable for the steady shear rheology of complex fluids. In this paper, we review the use of microfluidics for conducting shear viscometry of complex fluids and biofluids with a focus on viscosity curves as a function of shear rate. We discuss the physical principles underlying different microfluidic viscometers, their unique features and limits of operation. This compilation of technological options will potentially serve in promoting the benefits of microfluidic viscometry along with evincing further interest and research in this area. We intend that this review will aid researchers handling and studying complex fluids in selecting and adopting microfluidic viscometers based on their needs. We conclude with challenges and future directions in microfluidic rheometry of complex fluids and biofluids.

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.

Simultaneous characterization of rotational and translational diffusion of optically anisotropic particles by optical microscopy

We probe the roto-translational Brownian motion of optically anisotropic particles suspended in water with a simple and straightforward optical microscopy experiment that does not require positional or rotational particle tracking. We acquire a movie of the suspension placed between two polarizing elements and we extract the translational diffusion coefficient D T and the rotational diffusion coefficient D R from the analysis of the temporal correlation properties of the spatial Fourier modes of the intensity fluctuations in the movie. Our method is successfully tested with a dilute suspension of birefringent spherical colloidal particles obtained by polymerizing an emulsion of droplets of liquid crystal in a nematic phase, whose roto-translational dynamics is found to be well described by theory. The simplicity of our approach makes our method a viable alternative to particle tracking and depolarized dynamic light scattering.