Experimental observations of fractal landscape dynamics in a dense emulsion.

Many soft and biological materials display so-called 'soft glassy' dynamics; their constituents undergo anomalous random motions and complex cooperative rearrangements. A recent simulation model of one soft glassy material, a coarsening foam, suggested that the random motions of its bubbles are due to the system configuration moving over a fractal energy landscape in high-dimensional space. Here we show that the salient geometrical features of such high-dimensional fractal landscapes can be explored and reliably quantified, using empirical trajectory data from many degrees of freedom, in a model-free manner. For a mayonnaise-like dense emulsion, analysis of the observed trajectories of oil droplets quantitatively reproduces the high-dimensional fractal geometry of the configuration path and its associated local energy minima generated using a computational model. That geometry in turn drives the droplets' complex random motion observed in real space. Our results indicate that experimental studies can elucidate whether the similar dynamics in different soft and biological materials may also be due to fractal landscape dynamics.

Measuring Cytoskeletal Mechanical Fluctuations and Rheology with Active Micropost Arrays.

The dynamics of the cellular actomyosin cytoskeleton are crucial to many aspects of cellular function. Here, we describe techniques that employ active micropost array detectors (AMPADs) to measure cytoskeletal rheology and mechanical force fluctuations. The AMPADS are arrays of flexible poly(dimethylsiloxane) (PDMS) microposts with magnetic nanowires embedded in a subset of microposts to enable actuation of those posts via an externally applied magnetic field. Techniques are described to track the magnetic microposts' motion with nanometer precision at up to 100 video frames per second to measure the local cellular rheology at well-defined positions. Application of these high-precision tracking techniques to the full array of microposts in contact with a cell also enables mapping of the cytoskeletal mechanical fluctuation dynamics with high spatial and temporal resolution. This article describes (1) the fabrication of magnetic micropost arrays, (2) measurement protocols for both local rheology and cytoskeletal force fluctuation mapping, and (3) special-purpose software routines to reduce and analyze these data. © 2022 The Authors. Current Protocols published by Wiley Periodicals LLC. Basic Protocol 1: Fabrication of magnetic micropost arrays Basic Protocol 2: Data acquisition for cellular force fluctuations on non-magnetic micropost arrays Basic Protocol 3: Data acquisition for local cellular rheology measurements with magnetic microposts Basic Protocol 4: Data reduction: determining microposts' motion Basic Protocol 5: Data analysis: determining local rheology from magnetic microposts Basic Protocol 6: Data analysis for force fluctuation measurements Support Protocol 1: Fabrication of magnetic Ni nanowires by electrodeposition Support Protocol 2: Configuring Streampix for magnetic rheology measurements.

Pervasive cytoquakes in the actomyosin cortex across cell types and substrate stiffness.

The actomyosin cytoskeleton enables cells to resist deformation, crawl, change their shape and sense their surroundings. Despite decades of study, how its molecular constituents can assemble together to form a network with the observed mechanics of cells remains poorly understood. Recently, it has been shown that the actomyosin cortex of quiescent cells can undergo frequent, abrupt reconfigurations and displacements, called cytoquakes. Notably, such fluctuations are not predicted by current physical models of actomyosin networks, and their prevalence across cell types and mechanical environments has not previously been studied. Using micropost array detectors, we have performed high-resolution measurements of the dynamic mechanical fluctuations of cells' actomyosin cortex and stress fiber networks. This reveals cortical dynamics dominated by cytoquakes-intermittent events with a fat-tailed distribution of displacements, sometimes spanning microposts separated by 4 µm, in all cell types studied. These included 3T3 fibroblasts, where cytoquakes persisted over substrate stiffnesses spanning the tissue-relevant range of 4.3 kPa-17 kPa, and primary neonatal rat cardiac fibroblasts and myofibroblasts, human embryonic kidney cells and human bone osteosarcoma epithelial (U2OS) cells, where cytoquakes were observed on substrates in the same stiffness range. Overall, these findings suggest that the cortex self-organizes into a marginally stable mechanical state whose physics may contribute to cell mechanical properties, active behavior and mechanosensing.

Maximized Hole Trapping in a Polystyrene Transistor Dielectric from a Highly Branched Iminobis(aminoarene) Side Chain.

We synthesized highly branched and electron-donating side chain subunits and attached them to polystyrene (PS) used as a dielectric layer in a pentacene field-effect transistor. The influence of these groups on dielectric function, charge retention, and threshold voltage shifts (ΔVth) depending on their positions in dielectric multilayers was determined. We compared the observations made on an N-perphenylated iminobisaniline side chain with those from the same side chains modified with ZnO nanoparticles and with an adduct formed from tetracyanoethylene (TCNE). We also synthesized an analogue in which six methoxy groups are present instead of two amine nitrogens. At 6 mol % side chain, hopping transport was sufficient to cause shorting of the gate, while at 2 mol %, charge trapping was observable as transistor threshold voltage shifts (ΔVth). We created three types of devices: with the substituted PS layer as single-layer dielectric, on top of a cross-linked PS layer but in contact with the pentacene (bilayers), and sandwiched between two PS layers in trilayers. Especially large bias stress effects and ΔVth, larger than those in the case of the hexamethoxy and previously studied dimethoxy analogues, were observed in the second case, and the effects increased with the increasing electron-donating properties of the modified side chains. The highest ΔVth was consistent with a majority of the side chains stabilizing the trapped charge. Trilayer devices showed decreased charge storage capability compared to previous work in which we used less donating side chains but in higher concentrations. The ZnO and TCNE modifications resulted in slightly more and less negative ΔVth, respectively, when the side chain polystyrene was not in contact with the pentacene and isolated from the gate electrode. The results indicate a likely maximum combination of molecular charge stabilizing activity and side chain concentration that still allows gate dielectric function.

Extracellular Matrix Alignment Directs Provisional Matrix Assembly and Three Dimensional Fibrous Tissue Closure.

Gap closure is a dynamic process in wound healing, in which a wound contracts and a provisional matrix is laid down, to restore structural integrity to injured tissues. The efficiency of wound closure has been found to depend on the shape of a wound, and this shape dependence has been echoed in various in vitro studies. While wound shape itself appears to contribute to this effect, it remains unclear whether the alignment of the surrounding extracellular matrix (ECM) may also contribute. In this study, we investigate the role both wound curvature and ECM alignment have on gap closure in a 3D culture model of fibrous tissue. Using microfabricated flexible micropillars positioned in rectangular and octagonal arrangements, seeded 3T3 fibroblasts embedded in a collagen matrix formed microtissues with different ECM alignments. Wounding these microtissues with a microsurgical knife resulted in wounds with different shapes and curvatures that closed at different rates. Observing different regions around the wounds, we noted local wound curvature did not impact the rate of production of provisional fibronectin matrix assembled by the fibroblasts. Instead, the rate of provisional matrix assembly was lowest emerging from regions of high fibronectin alignment and highest in the areas of low matrix alignment. Our data suggest that the underlying ECM structure affects the shape of the wound as well as the ability of fibroblasts to build provisional matrix, an important step in the process of tissue closure and restoration of tissue architecture. The study highlights an important interplay between ECM alignment, wound shape, and tissue healing that has not been previously recognized and may inform approaches to engineer tissues. Impact statement Current models of tissue growth have identified a role for curvature in driving provisional matrix assembly. However, most tissue repair occurs in fibrous tissues with different levels of extracellular matrix (ECM) alignment. Here, we show how this underlying ECM alignment may affect the ability of fibroblasts to build new provisional matrix, with implications for in vivo wound healing and providing insight for engineering of new tissues.

Optogenetic current in myofibroblasts acutely alters electrophysiology and conduction of co-cultured cardiomyocytes.

Interactions between cardiac myofibroblasts and myocytes may slow conduction and generate spontaneous beating in fibrosis, increasing the chance of life-threatening arrhythmia. While co-culture studies have shown that myofibroblasts can affect cardiomyocyte electrophysiology in vitro, the extent of myofibroblast-myocyte electrical conductance in a syncytium is unknown. In this neonatal rat study, cardiac myofibroblasts were transduced with Channelrhodopsin-2, which allowed acute and selective increase of myofibroblast current, and plated on top of cardiomyocytes. Optical mapping revealed significantly decreased conduction velocity (- 27 ± 6%, p < 10-3), upstroke rate (- 13 ± 4%, p = 0.002), and action potential duration (- 14 ± 7%, p = 0.004) in co-cultures when 0.017 mW/mm2 light was applied, as well as focal spontaneous beating in 6/7 samples and a decreased cycle length (- 36 ± 18%, p = 0.002) at 0.057 mW/mm2 light. In silico modeling of the experiments reproduced the experimental findings and suggested the light levels used in experiments produced excess current similar in magnitude to endogenous myofibroblast current. Fitting the model to experimental data predicted a tissue-level electrical conductance across the 3-D interface between myofibroblasts and cardiomyocytes of ~ 5 nS/cardiomyocyte, and showed how increased myofibroblast-myocyte conductance, increased myofibroblast/myocyte capacitance ratio, and increased myofibroblast current, which occur in fibrosis, can work in tandem to produce pro-arrhythmic increases in conduction and spontaneous beating.

Driven topological transitions in active nematic films.

The topological properties of many materials are central to their behavior. In intrinsically out-of-equilibrium active materials, the dynamics of topological defects can be particularly important. In this paper, local manipulation of the order, dynamics, and topological properties of microtubule-based active nematic films is demonstrated in a joint experimental and simulation study. Hydrodynamic stresses created by magnetically actuated rotation of disk-shaped colloids in proximity to the films compete with internal stresses in the active nematic, influencing the local motion of +1/2 charge topological defects that are intrinsic to the nematic order in the spontaneously turbulent active films. Sufficiently large applied stresses drive the formation of +1 charge topological vortices through the merger of two +1/2 defects. The directed motion of the defects is accompanied by ordering of the vorticity and velocity of the active flows within the film that is qualitatively unlike the response of passive viscous films. Many features of the film's response to the stress are captured by lattice Boltzmann simulations, providing insight into the anomalous viscoelastic nature of the active nematic. The topological vortex formation is accompanied by a rheological instability in the film that leads to significant increase in the flow velocities. Comparison of the velocity profile in vicinity of the vortex with fluid-dynamics calculations provides an estimate of the film viscosity.

Induced pluripotent stem cell-derived vascular smooth muscle cells.

The reproducible generation of human-induced pluripotent stem cell (hiPSC)-derived vascular smooth muscle cells (vSMCs) in vitro has been critical to overcoming many limitations of animal and primary cell models of vascular biology and disease. Since this initial advance, research in the field has turned toward recapitulating the naturally occurring subtype specificity found in vSMCs throughout the body, and honing functional models of vascular disease. In this review, we summarize vSMC derivation approaches, including current phenotype and developmental origin-specific methods, and applications of vSMCs in functional disease models and engineered tissues. Further, we discuss the challenges of heterogeneity in hiPSC-derived tissues and propose approaches to identify and isolate vSMC subtype populations.

Force-dependent trans-endocytosis by breast cancer cells depletes costimulatory receptor CD80 and attenuates T cell activation.

In this study, we investigated the biophysical interaction between cytotoxic T-lymphocyte-associated protein 4 (CTLA-4) and CD80. CTLA-4 is a key molecule in immunosuppression, and CD80 is a costimulatory receptor promoting T cell activation. We observed that after cell-cell contact was established between breast cancer cells and antigen presenting cells (APCs), CTLA-4 expressed on the breast cancer cells bind to CD80 expressed on the APCs, and underwent trans-endocytosis to deplete CD80. Force measurement and live cell imaging revealed that upon binding to CD80, forces generated by breast cancer cells and transmitted via CTLA-4 were sufficiently strong to displace CD80 from the surface of APCs to be internalized by breast cancer cells. We further demonstrated that because of the force-dependent trans-endocytosis of CD80, the capacity of APCs to activate T cells was significantly attenuated. Furthermore, inhibiting force generation in cancer cells would increase the T cell activating capacity of APCs. Our results provide a possible mechanism behind the immunosuppression commonly seen in breast cancer patients, and may lead to a new strategy to restore anti-tumor immunity by inhibiting pathways of force-generation.

Enhancement of human iPSC-derived cardiomyocyte maturation by chemical conditioning in a 3D environment.

Recent advances in the understanding and use of pluripotent stem cells have produced major changes in approaches to the diagnosis and treatment of human disease. An obstacle to the use of human induced pluripotent stem cell-derived cardiomyocytes (hiPSC-CMs) for regenerative medicine, disease modeling and drug discovery is their immature state relative to adult myocardium. We show the effects of a combination of biochemical factors, thyroid hormone, dexamethasone, and insulin-like growth factor-1 (TDI) on the maturation of hiPSC-CMs in 3D cardiac microtissues (CMTs) that recapitulate aspects of the native myocardium. Based on a comparison of the gene expression profiles and the structural, ultrastructural, and electrophysiological properties of hiPSC-CMs in monolayers and CMTs, and measurements of the mechanical and pharmacological properties of CMTs, we find that TDI treatment in a 3D tissue context yields a higher fidelity adult cardiac phenotype, including sarcoplasmic reticulum function and contractile properties consistent with promotion of the maturation of hiPSC derived cardiomyocytes.

Dissecting fat-tailed fluctuations in the cytoskeleton with active micropost arrays.

The ability of animal cells to crawl, change their shape, and respond to applied force is due to their cytoskeleton: A dynamic, cross-linked network of actin protein filaments and myosin motors. How these building blocks assemble to give rise to cells' mechanics and behavior remains poorly understood. Using active micropost array detectors containing magnetic actuators, we have characterized the mechanics and fluctuations of cells' actomyosin cortex and stress fiber network in detail. Here, we find that both structures display remarkably consistent power law viscoelastic behavior along with highly intermittent fluctuations with fat-tailed distributions of amplitudes. Notably, this motion in the cortex is dominated by occasional large, step-like displacement events, with a spatial extent of several micrometers. Overall, our findings for the cortex appear contrary to the predictions of a recent active gel model, while suggesting that different actomyosin contractile units act in a highly collective and cooperative manner. We hypothesize that cells' actomyosin components robustly self-organize into marginally stable, plastic networks that give cells' their unique biomechanical properties.

Phase-dependent shear-induced order of nanorods in isotropic and nematic wormlike micelle solutions.

Small angle X-ray scattering with in situ shear was employed to study the assembly and ordering of dispersions of gold nanorods within wormlike micelle solutions formed by the surfactant cetylpyridinium chloride (CPyCl) and counter-ion sodium salicylate (NaSal). Above a threshold CPyCl concentration but below the isotropic-to-nematic transition of the micelles, the nanorods self-assembled under quiescent conditions into isotropically oriented domains with hexagonal order. Under steady shear at rates between 0.5 and 7.5 s-1, the nanorod assemblies acquired macroscopic orientational order in which the hexagonal planes were coincident with the flow-vorticity plane. The nanorods could be re-dispersed by strong shear but re-assembled following cessation of the shear. In the nematic phase of the micelles at higher surfactant concentration, the nanorods did not acquire hexagonal order but instead formed smectic-like layers in the gradient-vorticity plane under shear. Finally, at still higher surfactant concentration, where the micelles form a hexagonal phase, the nanorods showed no translational ordering but did acquire nematic-like order under shear due to alignment in the flow. Depletion forces mediated by the wormlike micelles are identified as the driving mechanism for this sequence of nanorod ordering behaviors, suggesting a novel mechanism for controlled, reconfigurable assembly of nanoparticles in solution.

Effects of Geometry on the Mechanics and Alignment of Three-Dimensional Engineered Microtissues.

The structure and stiffness of the extracellular matrix (ECM) in living tissues play a significant role in facilitating cellular functions and maintaining tissue homeostasis. However, the wide variation and complexity in tissue composition across different tissue types make comparative study of the impact of matrix architecture and alignment on tissue mechanics difficult. Here we present a microtissue-based system capable of controlling the degree of ECM alignment in 3D self-assembled fibroblast-populated collagen matrix, anchored around multiple elastic micropillars. The pillars provide structural constraints, control matrix alignment, enable measurement of the microtissues' contractile forces, and provide the ability to apply tensile strain using magnetic particles. Utilizing finite element models (FEMs) to parametrize results of mechanical measurements, spatial variations in the microtissues' Young's moduli across different regions were shown to be correlated with the degree of ECM fiber alignment. The aligned regions were up to six times stiffer than the unaligned regions. The results were not affected by suppression of cellular contractile forces in matured microtissues. However, comparison to a distributed fiber anisotropic model shows that variations in fiber alignment alone cannot account for the variations in the observed moduli, indicating that fiber density and tissue geometry also play important roles in the microtissues' properties. These results suggest a complex interplay between mechanical boundary constraints, ECM alignment, density, and mechanics and offer an approach combining engineered microtissues and computational modeling to elucidate these relationships.

Fabrication and Mechanical Properties Measurements of 3D Microtissues for the Study of Cell-Matrix Interactions.

Cell interactions with the extracellular matrix (ECM) are critical to cell and tissue functions involving adhesion, communication, and differentiation. Three-dimensional (3D) in vitro culture systems are an important approach to mimic in vivo cell-matrix interactions for mechanobiology studies and tissue engineering applications. This chapter describes the use of engineered microtissues as 3D constructs in combination with a magnetic tissue gauge (µTUG) system to analyze tissue mechanical properties. The µTUG system is composed of poly(dimethylsiloxane) (PDMS) microwells with vertical pillars in the wells. Self-assembled microtissues containing cells and ECM gel can form between the pillars, and generate mechanical forces that deform the pillars, which provides a readout of those forces. Herein, detailed procedures for microfabrication of the PDMS µTUG system, seeding and growth of cells with ECM gels in the microwells, and measurements of the mechanical properties of the resulting microtissues via magnetic actuation of magnetic sphere-tagged µTUGs are described.

Highly Contrasting Static Charging and Bias Stress Effects in Pentacene Transistors with Polystyrene Heterostructures Incorporating Oxidizable N,N'-Bis(4-methoxyphenyl)aniline Side Chains as Gate Dielectrics.

Charge storage and trapping properties of polymer dielectrics govern the charge densities of adjacent semiconductors and greatly influence the on-off switching voltage (threshold voltage, V t h ) of organic field-effect transistors (OFETs) when the polymers are used as gate insulators. Intentional charging of polymer dielectrics in OFETs can change V t h and affect the bias stress. We describe a chemical design and fabrication protocol to construct multilayer-stack dielectrics for pentacene-based OFETs using different polystyrene (PS)-based polymers in each layer, with oxidizable N,N-bis(4-methoxyphenyl)anilino (TPAOMe)-substituted styrene copolymers in arbitrary vertical positions in the stacks. Thermal, byproduct-free cross-linking of benzocyclobutene subunits provides integrity to the multilayer structure by preventing dissolution of the previous deposited layer. Neutron reflectivity data verified the multilayer morphology. We compared the V t h shift before and after charging the stacks by application of ±100 V across 0.5-1 µm total film thicknesses. Bias stress was the dominant effect in bilayer devices with a TPAOMe layer in contact with the pentacene, indicated by the direction of V t h shift associated with either polarity of external electric field. In structures with no TPAOMe subunit in contact with the pentacene, when charging with -100 V on top of the source and drain electrodes, electron injection from pentacene to dielectric was the major charging mechanism, again consistent with the bias stress direction. When charging with +100 V, bilayer devices without TPAOMe showed little change in V t h , suggesting there was no bias stress effect or charge injection in these devices for this charging polarity. For the bilayer devices with the TPAOMe layer in the bottom, and the trilayer devices with TPOMe in the middle, when +100 V was applied, the V t h shifts were opposite those expected from bias stress. Dipole formation or partial ionization of chargeable groups at the interface between the dielectric layers are likely polarization mechanisms in these cases. A simple analytical model levelports the plausibility of these mechanisms. This work provides examples of both stabilization and shifting of V t h , and therefore controlling charge carrier density, in semiconductors overlying the dielectric multilayers.

Colloidal transport within nematic liquid crystals with arrays of obstacles.

We have investigated the gravity-driven transport of spherical colloids suspended in the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) within microfluidic arrays of cylindrical obstacles arranged in a square lattice. Homeotropic anchoring at the surfaces of the obstacles created periodic director-field patterns that strongly influenced the motion of the colloids, whose surfaces had planar anchoring. When the gravitational force was oriented parallel to a principal axis of the lattice, the particles moved along channels between columns of obstacles and displayed pronounced modulations in their velocity. Quantitative analysis indicates that this modulation resulted from a combination of a spatially varying effective drag viscosity and elastic interactions engendered by the periodic director field. The interactions differed qualitatively from a sum of pair-wise interactions between the colloids and isolated obstacles, reflecting the distinct nematic environment created by confinement within the array. As the angle α between the gravitational force and principal axis of the lattice was varied, the velocity did not follow the force but instead locked into a discrete set of directions commensurate with the lattice. The transitions between these directions occurred at values of α that were different from those observed when the spheres were in an isotropic liquid, indicating the ability of the liquid crystal forces to tune the lateral displacement behavior in such devices.

Matrix viscoplasticity and its shielding by active mechanics in microtissue models: experiments and mathematical modeling.

The biomechanical behavior of tissues under mechanical stimulation is critically important to physiological function. We report a combined experimental and modeling study of bioengineered 3D smooth muscle microtissues that reveals a previously unappreciated interaction between active cell mechanics and the viscoplastic properties of the extracellular matrix. The microtissues' response to stretch/unstretch actuations, as probed by microcantilever force sensors, was dominated by cellular actomyosin dynamics. However, cell lysis revealed a viscoplastic response of the underlying model collagen/fibrin matrix. A model coupling Hill-type actomyosin dynamics with a plastic perfectly viscoplastic description of the matrix quantitatively accounts for the microtissue dynamics, including notably the cells' shielding of the matrix plasticity. Stretch measurements of single cells confirmed the active cell dynamics, and were well described by a single-cell version of our model. These results reveal the need for new focus on matrix plasticity and its interactions with active cell mechanics in describing tissue dynamics.

A microfabricated magnetic actuation device for mechanical conditioning of arrays of 3D microtissues.

This paper describes an approach to actuate magnetically arrays of microtissue constructs for long-term mechanical conditioning and subsequent biomechanical measurements. Each construct consists of cell/matrix material self-assembled around a pair of flexible poly(dimethylsiloxane) (PDMS) pillars. The deflection of the pillars reports the tissues' contractility. Magnetic stretching of individual microtissues via magnetic microspheres mounted on the cantilevers has been used to elucidate the tissues' elastic modulus and response to varying mechanical boundary conditions. This paper describes the fabrication of arrays of micromagnetic structures that can transduce an externally applied uniform magnetic field to actuate simultaneously multiple microtissues. These structures are fabricated on silicon-nitride coated Si wafers and contain electrodeposited Ni bars. Through-etched holes provide optical and culture media access when the devices are mounted on the PDMS microtissue scaffold devices. Both static and AC forces (up to 20 µN on each microtissue) at physiological frequencies are readily generated in external fields of 40 mT. Operation of the magnetic arrays was demonstrated via measurements of elastic modulus and dynamic stiffening in response to AC actuation of fibroblast populated collagen microtissues.

Anisotropic colloidal transport and periodic stick-slip motion in cholesteric finger textures.

We have investigated the mobility of discoidal colloidal particles sedimenting within cholesteric finger textures formed by mixtures of the nematic liquid crystal 4-cyano-4'-pentylbiphenyl (5CB) and the chiral dopant 4-(2-methylbutyl)-4'-cyanobiphenyl (CB15) with cholesteric pitch p between 24 and 114 µm. The nickel disks, with radius 17 µm and thickness 300 nm, displayed varied transport behavior that depended on the size of the pitch and the orientation of the gravitational force with respect to the cholesteric axis. In textures with small pitch (p < 40 µm), the disks moved perpendicular to the axis irrespective of the orientation of gravity as a result of an elastic retarding force that prevented motion along the axis. In textures with larger pitch, the disks similarly moved perpendicular to the axis when the angle between the force and axis was large. When the angle was small, the disks displayed stick-slip motion caused by periodic yielding of the finger texture. A model considering viscous drag on the particles and the elastic energy cost of deforming the finger texture describes the stick-slip motion accurately. The effective drag viscosities obtained from the disk motion are anomalously large compared with those of pure nematic 5CB indicating a large contribution to the dissipation from the motion of disclinations in the texture in the vicinity of the translating disks.

Proteins at air-water interfaces: a coarse-grained model.

We present a coarse-grained model to describe the adsorption and deformation of proteins at an air-water interface. The interface is introduced empirically in the form of a localized field that couples to a hydropathy scale of amino acids. We consider three kinds of proteins: protein G, egg-white lysozyme, and hydrophobin. We characterize the nature of the deformation and the orientation of the proteins induced by their proximity to and association with the interface. We also study protein diffusion in the layer formed at the interface and show that the diffusion slows with increasing concentration in a manner similar to that for a colloidal suspension approaching the glass transition.