Advances in the microrheology of complex fluids

Viscoelastic Properties of ECM-Rich Embryonic Microenvironments

The material properties of tissues and their mechanical state is an important factor in development, disease, regenerative medicine and tissue engineering. Here we describe a microrheological measurement technique utilizing aggregates of microinjected ferromagnetic nickel particles to probe the viscoelastic properties of embryonic tissues. Quail embryos were cultured in a plastic incubator chamber located at the center of two pairs of crossed electromagnets. We found a pronounced viscoelastic behavior within the ECM-rich region separating the mesoderm and endoderm in Hamburger Hamilton stage 10 quail embryos, consistent with a Zener (standard generalized solid) model. The viscoelastic response is about 45% of the total response, with a characteristic relaxation time of 1.3 s.

Scale-dependent particle diffusivity and apparent viscosity in polymer solutions as probed by dynamic magnetic nanorheology

In several upcoming rheological approaches, including methods of micro- and nanorheology, the measurement geometry is of critical impact on the interpretation of the results. The relative size of the probe objects employed (as compared to the intrinsic length scales of the sample to be investigated) becomes of crucial importance, and there is increasing interest to investigate the dynamic processes and mobility in nanostructured materials. A combination of different rheological approaches based on the rotation of magnetically blocked nanoprobes is used to systematically investigate the size-dependent diffusion behavior in aqueous poly(ethylene glycol) (PEG) solutions with special attention paid to the relation of probe size to characteristic length scales within the polymer solutions. We employ two types of probe particles: nickel rods of hydrodynamic length L_h between 200 nm and 650 nm, and cobalt ferrite spheres with diameter d_h between 13 nm and 23 nm, and examine the influence of particle size and shape on the nanorheological information obtained in model polymer solutions based on two related, dynamic-magnetic approaches. The results confirm that as long as the investigated solutions are not entangled, and the particles are much larger than the macromolecular correlation length, a good accordance between macroscopic and nanoscopic results, whereas a strong size-dependent response is observed in cases where the particles are of similar size or smaller than the radius of gyration R_g or the correlation length ξ of the polymer solution.

Diffusive transport of nanoscale objects through cell membranes: a computational perspective

Diffusion is an essential and fundamental means of transport of substances on cell membranes, and the dynamics of biomembranes plays a crucial role in the regulation of numerous cellular processes. The understanding of the complex mechanisms and the nature of particle diffusion have a bearing on establishing guidelines for the design of efficient transport materials and unique therapeutic approaches. Herein, this review article highlights the most recent advances in investigating diffusion dynamics of nanoscale objects on biological membranes, focusing on the approaches of tailored computer simulations and theoretical analysis. Due to the presence of the complicated and heterogeneous environment on native cell membranes, the diffusive transport behaviors of nanoparticles exhibit unique and variable characteristics. The general aspects and basic theories of normal diffusion and anomalous diffusion have been introduced. In addition, the influence of a series of external and internal factors on the diffusion behaviors is discussed, including particle size, membrane curvature, particle-membrane interactions or particle-inclusion, and the crowding degree of membranes. Finally, we seek to identify open problems in the existing experimental, simulation, and theoretical research studies, and to propose challenges for future development.

Surface Response of a Polymer Network: Semi-infinite Network

We study theoretically the surface response of a semi-infinite viscoelastic polymer network using the two-fluid model. We focus on the overdamped limit and on the effect of the network's intrinsic length scales. We calculate the decay rate of slow surface fluctuations, and the surface displacement in response to a localized force. Deviations from the large-scale continuum response are found at length scales much larger than the network's mesh size. We discuss implications for surface scattering and microrheology. We provide closed-form expressions that can be used for surface microrheology: the extraction of viscoelastic moduli and intrinsic length scales from the motions of tracer particles lying on the surface without doping the bulk material.

Integrated Optofluidic Chip for Oscillatory Microrheology

We propose and demonstrate an on-chip optofluidic device allowing active oscillatory microrheological measurements with sub-μL sample volume, low cost and high flexibility. Thanks to the use of this optofluidic microrheometer it is possible to measure the viscoelastic properties of complex fluids in the frequency range 0.01-10 Hz at different temperatures. The system is based on the optical forces exerted on a microbead by two counterpropagating infrared laser beams. The core elements of the optical part, integrated waveguides and an optical modulator, are fabricated by fs-laser writing on a glass substrate. The system performance is validated by measuring viscoelastic solutions of aqueous worm-like micelles composed by Cetylpyridinium Chloride (CPyCl) and Sodium Salicylate (NaSal).

Deciphering anomalous heterogeneous intracellular transport with neural networks

Intracellular transport is predominantly heterogeneous in both time and space, exhibiting varying non-Brownian behavior. Characterization of this movement through averaging methods over an ensemble of trajectories or over the course of a single trajectory often fails to capture this heterogeneity. Here, we developed a deep learning feedforward neural network trained on fractional Brownian motion, providing a novel, accurate and efficient method for resolving heterogeneous behavior of intracellular transport in space and time. The neural network requires significantly fewer data points compared to established methods. This enables robust estimation of Hurst exponents for very short time series data, making possible direct, dynamic segmentation and analysis of experimental tracks of rapidly moving cellular structures such as endosomes and lysosomes. By using this analysis, fractional Brownian motion with a stochastic Hurst exponent was used to interpret, for the first time, anomalous intracellular dynamics, revealing unexpected differences in behavior between closely related endocytic organelles.

Size effects on rotational particle diffusion in complex fluids as probed by Magnetic Particle Nanorheology

Rheological approaches based on micro- or nanoscopic probe objects are of interest due to the low volume requirement, the option of spatially resolved probing, and the minimal-invasive nature often connected to such probes. For the study of microstructured systems or biological environments, such methods show potential for investigating the local, size-dependent diffusivity and particle-matrix interactions. For the latter, the relative length scale of the used probes compared to the size of the structural units of the matrix becomes relevant. In this study, a rotational-dynamic approach based on Magnetic Particle Nanorheology (MPN) is used to extract size- and frequency-dependent nanorheological properties by using an otherwise well-established polymer model system. We use magnetically blocked CoFe2O4 nanoparticles as tracers and systematically vary their hydrodynamic size by coating them with a silica shell. On the polymer side, we employ aqueous solutions of poly(ethylene glycol) (PEG) by varying molar mass M and volume fraction φ. The complex Brownian relaxation behavior of the tracer particles in solutions of systematically varied composition is investigated by means of AC susceptometry (ACS), and the results provide access to frequency dependent rheological properties. The size-dependent particle diffusivity is evaluated based on theoretical descriptions and macroscopic measurements. The results allow the classification of the investigated compositions into three regimes, taking into account the probe particle size and the length scales of the polymer solution. While a fuzzy cross-over is indicated between the well-known macroscopic behavior and structurally dominated spectra, where the hydrodynamic radius is equal to the radius of gyration of the polymer (rh ∼ Rg), the frequency-related scaling behavior is dominated by the correlation length ξ respectively by the tube diameter a in entangled solutions for rh < Rg.

Determination of rheology and surface tension of airway surface liquid: a review of clinical relevance and measurement techniques

By airway surface liquid, we mean a thin fluid continuum consisting of the airway lining layer and the alveolar lining layer, which not only serves as a protective barrier against foreign particles but also contributes to maintaining normal respiratory mechanics. In recent years, measurements of the rheological properties of airway surface liquid have attracted considerable clinical attention due to new advances in microrheology instruments and methods. This article reviews the clinical relevance of measurements of airway surface liquid viscoelasticity and surface tension from four main aspects: maintaining the stability of the airways and alveoli, preventing ventilator-induced lung injury, optimizing surfactant replacement therapy for respiratory syndrome distress, and characterizing the barrier properties of airway mucus to improve drug and gene delivery. Primary measuring techniques and methods suitable for determining the viscoelasticity and surface tension of airway surface liquid are then introduced with respect to principles, advantages and limitations. Cone and plate viscometers and particle tracking microrheometers are the most commonly used instruments for measuring the bulk viscosity and microviscosity of airway surface liquid, respectively, and pendant drop methods are particularly suitable for the measurement of airway surface liquid surface tension in vitro. Currently, in vivo and in situ measurements of the viscoelasticity and surface tension of the airway surface liquid in humans still presents many challenges.

Endotracheal tube mucus as a source of airway mucus for rheological study

Muco-obstructive lung diseases (MOLDs), like cystic fibrosis and chronic obstructive pulmonary disease, affect a spectrum of subjects globally. In MOLDs, the airway mucus becomes hyperconcentrated, increasing osmotic and viscoelastic moduli and impairing mucus clearance. MOLD research requires relevant sources of healthy airway mucus for experimental manipulation and analysis. Mucus collected from endotracheal tubes (ETT) may represent such a source with benefits, e.g., in vivo production, over canonical sample types such as sputum or human bronchial epithelial (HBE) mucus. Ionic and biochemical compositions of ETT mucus from healthy human subjects were characterized and a stock of pooled ETT samples generated. Pooled ETT mucus exhibited concentration-dependent rheologic properties that agreed across spatial scales with reported individual ETT samples and HBE mucus. We suggest that the practical benefits compared with other sample types make ETT mucus potentially useful for MOLD research.

Spectroscopic photonic force optical coherence elastography

We demonstrate spectroscopic photonic force optical coherence elastography (PF-OCE). Oscillations of microparticles embedded in viscoelastic hydrogels were induced by harmonically modulated optical radiation pressure and measured by phase-sensitive spectral-domain optical coherence tomography. PF-OCE can detect microparticle displacements with pico- to nano-meter sensitivity and millimeter-scale volumetric coverage. With spectroscopic PF-OCE, we quantified viscoelasticity over a broad frequency range from 1 Hz to 7 kHz, revealing rich microstructural dynamics of polymer networks across multiple microrheological regimes. Reconstructed frequency-dependent loss moduli of polyacrylamide hydrogels were observed to follow a general power scaling law G''∼ω0.75, consistent with that of semiflexible polymer networks. Spectroscopic PF-OCE provides an all-optical approach to microrheological studies with high sensitivity and high spatiotemporal resolution, and could be especially beneficial for time-lapse and volumetric mechanical characterization of viscoelastic materials.

Microrheology of interphase chromosomes with spatial constraints: a computational study

Chromatin fibers within the interior of the nucleus of the cell make stable interactions with the nucleoskeleton, an ensemble of 'extra-chromatin' structures which help ensuring genome stability. Although the role of these interactions appears crucial to the correct behavior of the cell, their impact on chromatin structure and dynamics remains to be elucidated. In order to tackle this important issue, in this work we introduce a simple polymer model for chromatin fibers in interphase which takes into account the two generic properties of chain-versus-chain mutual uncrossability and the presence of stable binding interactions to an extra-chromatin nuclear matrix. To study how these constraints affect chromatin structure from small to large scales, we employ extensive molecular dynamics computer simulations and we monitor the motion of nanoprobes of different sizes embedded within the polymer medium. Our results demonstrate that nanoprobes show hampered motion whenever their linear size becomes larger than chromatin stiffness. This transition is also displaying features which usually belong to the realm of glassy systems, namely long-tail correlations in the distribution functions of nanoprobe spatial displacements and heterogeneous behavior accompanied by ergodicity breaking.

Errors in Energy Landscapes Measured with Particle Tracking

Tracking Brownian particles is often employed to map the energy landscape they explore. Such measurements have been exploited to study many biological processes and interactions in soft materials. Yet video tracking is irremediably contaminated by localization errors originating from two imaging artifacts: the "static" errors come from signal noise, and the "dynamic" errors arise from the motion blur due to finite frame-acquisition time. We show that these errors result in systematic and nontrivial biases in the measured energy landscapes. We derive a relationship between the true and the measured potential that elucidates, among other aberrations, the presence of false double-well minima in the apparent potentials reported in recent studies. We further assess several canonical trapping and pair-interaction potentials by using our analytically derived results and Brownian dynamics simulations. In particular, we show that the apparent spring stiffness of harmonic potentials (such as optical traps) is increased by dynamic errors but decreased by static errors. Our formula allows for the development of efficient corrections schemes, and we also present in this work a provisional method for reconstructing true potentials from the measured ones.

Endotracheal tube mucus as a source of airway mucus for rheological study

Muco-obstructive lung diseases (MOLDs), like cystic fibrosis and chronic obstructive pulmonary disease, affect a spectrum of subjects globally. In MOLDs, the airway mucus becomes hyperconcentrated, increasing osmotic and viscoelastic moduli and impairing mucus clearance. MOLD research requires relevant sources of healthy airway mucus for experimental manipulation and analysis. Mucus collected from endotracheal tubes (ETT) may represent such a source with benefits, e.g., in vivo production, over canonical sample types such as sputum or human bronchial epithelial (HBE) mucus. Ionic and biochemical compositions of ETT mucus from healthy human subjects were characterized and a stock of pooled ETT samples generated. Pooled ETT mucus exhibited concentration-dependent rheologic properties that agreed across spatial scales with reported individual ETT samples and HBE mucus. We suggest that the practical benefits compared with other sample types make ETT mucus potentially useful for MOLD research.

Measuring local properties inside a cell-mimicking structure using rotating optical tweezers

Exploring the rheological properties of intracellular materials is essential for understanding cellular and subcellular processes. Optical traps have been widely used for physical manipulation of micro and nano objects within fluids enabling studies of biological systems. However, experiments remain challenging as it is unclear how the probe particle's mobility is influenced by the nearby membranes and organelles. We use liposomes (unilamellar lipid vesicles) as a simple biomimetic model of living cells, together with a trapped particle rotated by optical tweezers to study mechanical and rheological properties inside a liposome both theoretically and experimentally. Here, we demonstrate that this system has the capacity to predict the hydrodynamic interaction between three-dimensional spatial membranes and internal probe particles within submicron distances, and it has the potential to aid in the design of high resolution optical micro/nanorheology techniques to be used inside living cells.

Stratification in the dynamics of sedimenting colloidal platelet-sphere mixtures

The dynamics of sedimentation in a binary mixture of colloidal platelets-spheres is studied theoretically using the minimal energy model. Revisiting a sedimenting mixture of platelets, we find that nematic phase behaviors are formed, coupled with certain stratification structures in the mixed sediments, which has never been discussed before. Non-equilibrium sedimentation-diffusion equations involving excluded volume interactions between the colloids have been developed to show the occurrence of the stratified structures in the mixed platelet-sphere sediments. The model shows clearly how the nematic configuration occurs corresponding to the stratifications (the peak-like concentration profiles) over time. Both initial sphere concentration and size ratio are found to have great effects on these two coupled structural configurations, which has been illustrated in two state diagrams in detail. It is found that the stratification structure of sphere-on-top corresponds to the nematic bottom phase configuration for a small size ratio; meanwhile, the platelet-on-top structure occurs corresponding to the floating nematic phase configuration for a large size ratio. Interestingly, we can specify a moderate range of size ratio in which the mixture displays only the nematic phase configuration (either the nematic bottom phase or the floating nematic phase depending on the sphere loadings), while the mixed sediments are unstratified as a bulk.

Structural Changes in Polymeric Gel Scaffolds Around the Overlap Concentration

Cross-linked polymeric gels are an important class of materials with applications that broadly range from synthetic wound healing scaffolds to materials used in enhanced oil recovery. To effectively design these materials for each unique applications a deeper understanding of the structure and rheological properties as a function of polymeric interactions is required. Increasing the concentration of polymer in each scaffold increases physical interactions between the molecules that can be reflected in the material structure. To characterize the structure and material properties, we use multiple particle tracking microrheology (MPT) to measure scaffolds during gelation. In MPT, fluorescently labeled probe particles are embedded in the material and the Brownian motion of these particles is captured using video microscopy. Particle motion is related to rheological properties using the Generalized Stokes-Einstein Relation. In this work, we characterize gelation of a photopolymerized scaffold composed of a poly(ethylene glycol) (PEG)-acrylate backbone and a PEG-dithiol cross-linker. Scaffolds with backbone concentrations below and above the overlap concentration, concentration where polymer pervaded volume begins to overlap, are characterized. Using time-cure superposition (TCS) we determine the critical relaxation exponent, n, of each scaffold. The critical relaxation exponent is a quantitative measure of the scaffold structure and is similar to a complex modulus, G^*, which is a measure of energy storage and dissipation. Our results show that below the overlap concentration the scaffold is a tightly cross-linked network, n_avg = 0.40 ± 0.03, which stores energy but can also dissipate energy. As polymeric interactions increase, we measure a step change in the critical relaxation exponent above the overlap concentration to n_avg = 0.20 ± 0.03. After the overlap concentration the scaffold has transitioned to a more tightly cross-linked network that primarily stores energy. Additionally, continuing to increase concentration results in no change in the scaffold structure. Therefore, we determined that the properties of this scaffold can be tuned above and below the overlap concentration by changing the polymer concentration but the structure will remain the same in each concentration regime. This is advantageous for a wide range of applications that require scaffolds with varying stiffness and the same scaffold architecture.

Effects of Collagenase Type II on Vitreous Humor—An In Situ Rheological Study

The purpose of this study is to quantify the impact of enzyme activity on the vitreous humor structure over time to understand the mechanical characteristics of the vitreous humor gel. Changes in the mechanical behavior of the vitreous occur due to many reasons including aging, which may lead to many vitreoretinal diseases. The degeneration process of the vitreous has been studied; however, in situ experimental procedures to validate the existing hypotheses are limited. We examined thirty-eight porcine eyes using in situ rheological creep tests to measure the mechanical properties of the vitreous humor of the eyes prior to, 1 h and 24 h after the intravitreal injection. Eyes in one group were injected with collagenase type II solution and eyes in the control group were injected with phosphate buffered saline solution (PBS) with calcium and magnesium chloride. Prior to the injection, viscosity and creep compliance intercept values between both groups were not statistically different. At 1 h and 24 h after the injection, vitreous properties in the eyes from the first group showed a statistically significant increase in the J intercept values (representing the inverse of elasticity) compared to the control group. In addition, 1 h and 24 h after the injection, vitreous viscosity was lower in the eyes from the first group than in the eyes from the control group. These findings are a foundation for future studies on the effectiveness of intravitreal drugs that modify the mechanical properties of the vitreous humor.

Microrheology and Spatial Heterogeneity of Staphylococcus aureus Biofilms Modulated by Hydrodynamic Shear and Biofilm-Degrading Enzymes

Particle tracking microrheology was used to investigate the viscoelasticity of Staphylococcus aureus biofilms grown in microfluidic cells at various flow rates and when subjected to biofilm-degrading enzymes. Biofilm viscoelasticity was found to harden as a function of shear rate but soften with increasing height away from the attachment surface in good agreement with previous bulk results. Ripley's K-function was used to quantify the spatial distribution of the bacteria within the biofilm. For all conditions, biofilms would cluster as a function of height during growth. The effects of proteinase K and DNase-1 on the viscoelasticity of biofilms were also investigated. Proteinase K caused an order of magnitude change in the compliances, softening the biofilms. However, DNase-1 was found to have no significant effects over the first 6 h of development, indicating that DNA is less important in biofilm maintenance during the initial stages of growth. Our results demonstrate that during the preliminary stages of Staphylococcus aureus biofilm development, column-like structures with a vertical gradient of viscoelasticity are established and modulated by the hydrodynamic shear caused by fluid flow in the surrounding environment. An understanding of these mechanical properties will provide more accurate insights for removal strategies of early-stage biofilms.

Non-Markovian intracellular transport with sub-diffusion and run-length dependent detachment rate

Intracellular transport of organelles is fundamental to cell function and health. The mounting evidence suggests that this transport is in fact anomalous. However, the reasons for the anomaly is still under debate. We examined experimental trajectories of organelles inside a living cell and propose a mathematical model that describes the previously reported transition from sub-diffusive to super-diffusive motion. In order to explain super-diffusive behaviour at long times, we introduce non-Markovian detachment kinetics of the cargo: the rate of detachment is inversely proportional to the time since the last attachment. Recently, we observed the non-Markovian detachment rate experimentally in eukaryotic cells. Here we further discuss different scenarios of how this effective non-Markovian detachment rate could arise. The non-Markovian model is successful in simultaneously describing the time averaged variance (the time averaged mean squared displacement corrected for directed motion), the mean first passage time of trajectories and the multiple peaks observed in the distributions of cargo velocities. We argue that non-Markovian kinetics could be biologically beneficial compared to the Markovian kinetics commonly used for modelling, by increasing the average distance the cargoes travel when a microtubule is blocked by other filaments. In turn, sub-diffusion allows cargoes to reach neighbouring filaments with higher probability, which promotes active motion along the microtubules.

Optical Tweezers Microrheology: From the Basics to Advanced Techniques and Applications

Over the past few decades, microrheology has emerged as a widely used technique to measure the mechanical properties of soft viscoelastic materials. Optical tweezers offer a powerful platform for performing microrheology measurements and can measure rheological properties at the level of single molecules out to near macroscopic scales. Unlike passive microrheology methods, which use diffusing microspheres to extract rheological properties, optical tweezers can probe the nonlinear viscoelastic response, and measure the space- and time-dependent rheological properties of heterogeneous, nonequilibrium materials. In this Viewpoint, I describe the basic principles underlying optical tweezers microrheology, the instrumentation and material requirements, and key applications to widely studied soft biological materials. I also describe several sophisticated approaches that include coupling optical tweezers to fluorescence microscopy and microfluidics. The described techniques can robustly characterize noncontinuum mechanics, nonlinear mechanical responses, strain-field heterogeneities, stress propagation, force relaxation dynamics, and time-dependent mechanics of active materials.

Perspective: Differential dynamic microscopy extracts multi-scale activity in complex fluids and biological systems

Differential dynamic microscopy (DDM) is a technique that exploits optical microscopy to obtain local, multi-scale quantitative information about dynamic samples, in most cases without user intervention. It is proving extremely useful in understanding dynamics in liquid suspensions, soft materials, cells, and tissues. In DDM, image sequences are analyzed via a combination of image differences and spatial Fourier transforms to obtain information equivalent to that obtained by means of light scattering techniques. Compared to light scattering, DDM offers obvious advantages, principally (a) simplicity of the setup; (b) possibility of removing static contributions along the optical path; (c) power of simultaneous different microscopy contrast mechanisms; and (d) flexibility of choosing an analysis region, analogous to a scattering volume. For many questions, DDM has also advantages compared to segmentation/tracking approaches and to correlation techniques like particle image velocimetry. The very straightforward DDM approach, originally demonstrated with bright field microscopy of aqueous colloids, has lately been used to probe a variety of other complex fluids and biological systems with many different imaging methods, including dark-field, differential interference contrast, wide-field, light-sheet, and confocal microscopy. The number of adopting groups is rapidly increasing and so are the applications. Here, we briefly recall the working principles of DDM, we highlight its advantages and limitations, we outline recent experimental breakthroughs, and we provide a perspective on future challenges and directions. DDM can become a standard primary tool in every laboratory equipped with a microscope, at the very least as a first bias-free automated evaluation of the dynamics in a system.

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.

Plant cell walls

Plants are able to generate large leaf surfaces that act as two-dimensional solar panels with a minimum investment in building material, thanks to a hydrostatic skeleton. This requires high intracellular pressures (up to 1 MPa), which depend on the presence of strong cell walls. The walls of growing cells (also called primary walls), are remarkably able to reconcile extreme tensile strength (up to 100 MPa) with the extensibility necessary for growth. All walled organisms are confronted with this dilemma - the need to balance strength and extensibility - and bacteria, fungi and plants have evolved independent solutions to cope. In this Primer, we discuss how plant cells have solved this problem, allowing them to support often very large increases in volume and to develop a broad variety of shapes (Figure 1A,B,D). This shape variation reflects the targeted deposition of wall material combined with local variations in cell-wall extensibility, processes that remain incompletely understood. Once the cell has reached its final size, it can lay down secondary wall layers, the composition and architecture of which are optimized to exert specific functions in different cell types (Figure 1E-G). Such functions include: providing mechanical support, for instance, for fibre cells in tree trunks or grass internodes; impermeabilising and strengthening vascular tissue to resist the negative pressure of the transpiration stream; increasing the surface area of the plasma membrane to facilitate solute exchange between cells (Figure 1C); or allowing important elastic deformation, for instance, to support the opening and closing of stomates. Specialized secondary walls, such as those constituting seed mucilage, are stored in a dehydrated form in seedcoat epidermis cells and show rapid swelling upon hydration of the seed. Other walls, in particular in reserve tissues, can accommodate large amounts of storage polysaccharides, which can be easily mobilized as a carbon source. Here we will discuss some general principles underlying wall architecture and wall growth that have emerged from recent studies, as well as future questions for investigation (Box 1).

Brownian motion near an elastic cell membrane: A theoretical study

Elastic confinements are an important component of many biological systems and dictate the transport properties of suspended particles under flow. In this paper, we review the Brownian motion of a particle moving in the vicinity of a living cell whose membrane is endowed with a resistance towards shear and bending. The analytical calculations proceed through the computation of the frequency-dependent mobility functions and the application of the fluctuation-dissipation theorem. Elastic interfaces endow the system with memory effects that lead to a long-lived anomalous subdiffusive regime of nearby particles. In the steady limit, the diffusional behavior approaches that near a no-slip hard wall. The analytical predictions are validated and supplemented with boundary-integral simulations.

Dark field differential dynamic microscopy enables accurate characterization of the roto-translational dynamics of bacteria and colloidal clusters

Micro- and nanoscale objects with anisotropic shape are key components of a variety of biological systems and inert complex materials, and represent fundamental building blocks of novel self-assembly strategies. The time scale of their thermal motion is set by their translational and rotational diffusion coefficients, whose measurement may become difficult for relatively large particles with small optical contrast. Here we show that dark field differential dynamic microscopy is the ideal tool for probing the roto-translational Brownian motion of anisotropic shaped particles. We demonstrate our approach by successful application to aqueous dispersions of non-motile bacteria and of colloidal aggregates of spherical particles.

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.

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.

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.

Dynamic Light Scattering Microrheology Reveals Multiscale Viscoelasticity of Polymer Gels and Precious Biological Materials

The development of experimental techniques capable of probing the viscoelasticity of soft materials over a broad range of time scales is essential to uncovering the physics that governs their behavior. In this work, we develop a microrheology technique that requires only 12 μL of sample and is capable of resolving dynamic behavior ranging in time scales from 10^-6 to 10 s. Our approach, based on dynamic light scattering in the single-scattering limit, enables the study of polymer gels and other soft materials over a vastly larger hierarchy of time scales than macrorheology measurements. Our technique captures the viscoelastic modulus of polymer hydrogels with a broad range of stiffnesses from 10 to 10⁴ Pa. We harness these capabilities to capture hierarchical molecular relaxations in DNA and to study the rheology of precious biological materials that are impractical for macrorheology measurements, including decellularized extracellular matrices and intestinal mucus. The use of a commercially available benchtop setup that is already available to a variety of soft matter researchers renders microrheology measurements accessible to a broader range of users than existing techniques, with the potential to reveal the physics that underlies complex polymer hydrogels and biological materials.

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.

Sheathless Microflow Cytometry Using Viscoelastic Fluids

Microflow cytometry is a powerful technique for characterization of particles suspended in a solution. In this work, we present a microflow cytometer based on viscoelastic focusing. 3D single-line focusing of microparticles was achieved in a straight capillary using viscoelastic focusing which alleviated the need for sheath flow or any other actuation mechanism. Optical detection was performed by fiber coupled light source and photodetectors. Using this system, we present the detection of microparticles suspended in three different viscoelastic solutions. The rheological properties of the solutions were measured and used to assess the focusing performance both analytically and numerically. The results were verified experimentally, and it has been shown that polyethlyene oxide (PEO) and hyaluronic acid (HA) based sheathless microflow cytometer demonstrates similar performance to state-of-the art flow cytometers. The sheathless microflow cytometer was shown to present 780 particles/s throughput and 5.8% CV for the forward scatter signal for HA-based focusing. The presented system is composed of a single capillary to accommodate the fluid and optical fibers to couple the light to the fluid of interest. Thanks to its simplicity, the system has the potential to widen the applicability of microflow cytometers.

Physicochemical and colloidal aspects of food matrix effects on gastrointestinal fate of ingested inorganic nanoparticles

Inorganic nanoparticles, such as titanium dioxide, silicon dioxide, iron oxide, zinc oxide, or silver nanoparticles, are added to some food products and food packaging materials to obtain specific functional attributes, such as lightening, powder flow, nutrition, or antimicrobial properties. These engineered nanomaterials (ENMs) all have dimensions below 100nm, but may still vary considerably in composition, morphology, charge, surface properties and aggregation state, which effects their gastrointestinal fate and potential toxicity. In addition to their intrinsic physicochemical and morphological properties, the extrinsic properties of the media they are suspended in also affects their biotransformation, gastrointestinal fate and bioactivity. For instance, inorganic nanoparticles are usually consumed as part of a food or meal that contains numerous other components, such as lipids, proteins, carbohydrates, surfactants, minerals, and water, which may alter their gastrointestinal fate. This review article provides an overview of the potential effects of food components on the behavior of ENMs in the gastrointestinal tract (GIT), and highlights some important physicochemical and colloidal mechanisms by which the food matrix may alter the properties of inorganic nanoparticles. This information is essential for developing appropriate test methods to establish the potential toxicity and biokinetics of inorganic nanoparticles in foods.

Correlations in suspensions confined between viscoelastic surfaces: Noncontact microrheology

We study theoretically the velocity cross-correlations of a viscous fluid confined in a slit between two viscoelastic media. We analyze the effect of these correlations on the motions of particles suspended in the fluid. The compliance of the confining boundaries gives rise to a long-ranged pair correlation, decaying only as 1/r with the interparticle distance r. We show how this long-ranged effect may be used to extract the viscoelastic properties of the confining media without embedding tracer particles in them. We discuss the remarkable robustness of such a potential technique with respect to details of the confinement, and its expected statistical advantages over standard two-point microrheology.

Separation of two attractive ferromagnetic ellipsoidal particles by hydrodynamic interactions under alternating magnetic field

In applications where magnetic particles are used to detect and dose targeted molecules, it is of major importance to prevent particle clustering and aggregation during the capture stage in order to maximize the capture rate. Elongated ferromagnetic particles can be more interesting than spherical ones due to their large magnetic moment, which facilitates their separation by magnets or the detection by optical measurement of their orientation relaxation time. Under alternating magnetic field, the rotational dynamics of elongated ferromagnetic particles results from the balance between magnetic torque that tends to align the particle axis with the field direction and viscous torque. As for their translational motion, it results from a competition between direct magnetic particle-particle interactions and solvent-flow-mediated hydrodynamic interactions. Due to particle anisotropy, this may lead to intricate translation-rotation couplings. Using numerical simulations and theoretical modeling of the system, we show that two ellipsoidal magnetic particles, initially in a head-to-tail attractive configuration resulting from their remnant magnetization, can repel each other due to hydrodynamic interactions when alternating field is operated. The separation takes place in a range of low frequencies f_{c1}<f<f_{c2}. The upper frequency limit f_{c2}τ_{r}≈0.04 (where τ_{r} is the rotation time scale) depends weakly on the ratio of magnetic field to particle magnetization strength, whereas f_{c1} tends to zero when this ratio increases.

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.

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.

Hydrodynamic mobility of a solid particle near a spherical elastic membrane: Axisymmetric motion

We use the image solution technique to compute the leading order frequency-dependent self-mobility function of a small solid particle moving perpendicular to the surface of a spherical capsule whose membrane possesses shearing and bending rigidities. Comparing our results with those obtained earlier for an infinitely extended planar elastic membrane, we find that membrane curvature leads to the appearance of a prominent additional peak in the mobility. This peak is attributed to the fact that the shear resistance of the curved membrane involves a contribution from surface-normal displacements, which is not the case for planar membranes. In the vanishing frequency limit, the particle self-mobility near a no-slip hard sphere is recovered only when the membrane possesses a nonvanishing resistance toward shearing. We further investigate capsule motion, finding that the pair-mobility function is solely determined by membrane shearing properties. Our analytical predictions are validated by fully resolved boundary integral simulations where a very good agreement is obtained.

Flow of DNA in micro/nanofluidics: From fundamentals to applications

Thanks to direct observation and manipulation of DNA in micro/nanofluidic devices, we are now able to elucidate the relationship between the polymer microstructure and its rheological properties, as well as to design new single-molecule platforms for biophysics and biomedicine. This allows exploration of many new mechanisms and phenomena, which were previously unachievable with conventional methods such as bulk rheometry tests. For instance, the field of polymer rheology is at a turning point to relate the complex molecular conformations to the nonlinear viscoelasticity of polymeric fluids (such as coil-stretch transition, shear thinning, and stress overshoot in startup shear). In addition, nanofluidic devices provided a starting point for manipulating single DNA molecules by applying basic principles of polymer physics, which is highly relevant to numerous processes in biosciences. In this article, we review recent progress regarding the flow and deformation of DNA in micro/nanofluidic systems from both fundamental and application perspectives. We particularly focus on advances in the understanding of polymer rheology and identify the emerging research trends and challenges, especially with respect to future applications of nanofluidics in the biomedical field.