Confocal microscopy was used to directly observe three-dimensional dynamics of particles in colloidal supercooled fluids and colloidal glasses. The fastest particles moved cooperatively; connected clusters of these mobile particles could be identified; and the cluster size distribution, structure, and dynamics were investigated. The characteristic cluster size grew markedly in the supercooled fluid as the glass transition was approached, in agreement with computer simulations; at the glass transition, however, there was a sudden drop in their size. The clusters of fast-moving particles were largest near the alpha-relaxation time scale for supercooled colloidal fluids, but were also present, albeit with a markedly different nature, at shorter beta-relaxation time scales, in both supercooled fluid and glass colloidal phases.
We demonstrate a novel method for measuring the microrheology of soft viscoelastic media, based on cross correlating the thermal motion of pairs of embedded tracer particles. The method does not depend on the exact nature of the coupling between the tracers and the medium, and yields accurate rheological data for highly inhomogeneous materials. We demonstrate the accuracy of this method with a guar solution, for which other microscopic methods fail due to the polymer's mesoscopic inhomogeneity. Measurements in an F-actin solution suggest conventional microrheology measurements may not reflect the true bulk behavior. PACS numbers: 87.19.Tt, 83.70.Hq, 83.80.Lz Many interesting and important materials such as polymers, gels, and biomaterials are viscoelastic; when responding to an external stress, they both store and dissipate energy. This behavior is quantified by the complex shear modulus, G ء ͑v͒, which provides insight into the material's microscopic dynamics. Typically, G ء ͑v͒ is measured by applying oscillatory strain to a sample and measuring the resulting stress. Recently a new method, called microrheology, has been developed which determines G ء ͑v͒ from the thermal motion of microscopic tracer particles embedded in the material [1,2]. Microrheology offers significant potential advantages: it provides a local probe of G ء ͑v͒ in miniscule sample volumes and can do so at very high frequencies. While microrheology provides an accurate measure of G ء ͑v͒ for simple systems, its validity in common complex systems is far from certain. If the tracers locally modify the structure of the medium, or sample only pores in an inhomogeneous matrix, then bulk rheological properties will not be determined. Such subtle effects currently limit many interesting applications of microrheology.In this Letter, we introduce a new formalism, which we term "two-point microrheology," based on measuring the cross-correlated thermal motion of pairs of tracer particles to determine G ء ͑v͒. This new technique overcomes the limitations of single-particle microrheology. It does not depend on the size or shape of the tracer particle; moreover it is independent of the coupling between the tracer and the medium. We demonstrate the validity of this approach with measurements on a highly inhomogeneous material, a solution of the polysaccharide guar. Two-point microrheology correctly reproduces results obtained with a mechanical rheometer, whereas single-particle microrheology gives erroneous results. We also compare ordinary and two-point microrheology of F-actin [2-4], a semiflexible biopolymer constituent of the cytoskeleton. Different results are obtained with the two techniques, suggesting that earlier interpretations of F-actin microrheology should be reexamined. Conventional microrheology [1,2] uses the equation:wherer 2 ͑s͒ is the Laplace transform of the tracers' mean squared displacement, ͗Dr 2 ͑t͒͘, as a function of Laplace frequency s, and a is their radius. Equation (1) (1) is subject to the same conditions as the...
We report the first measurements of the intrinsic strain fluctuations of living cells using a recentlydeveloped tracer correlation technique along with a theoretical framework for interpreting such data in heterogeneous media with non-thermal driving. The fluctuations' spatial and temporal correlations indicate that the cytoskeleton can be treated as a course-grained continuum with powerlaw rheology, driven by a spatially random stress tensor field. Combined with recent cell rheology results, our data imply that intracellular stress fluctuations have a nearly 1/ω 2 power spectrum, as expected for a continuum with a slowly evolving internal prestress.PACS numbers: 87.16. Ac, 87.15.Ya, 87.10.+e An accurate physical picture of the viscoelasticity and motion of the cytoskeleton is crucial for a complete understanding of processes such as intracellular transport [1], cell crawling [2], and mechano-chemical transduction [2]. Microrheology [3], based on the analysis of embedded tracer particle motion, has recently emerged as an experimental probe of cytoskeleton viscoelasticity and dynamics [4,5,6,7]. The viscoelastic properties of eucaryotic cells arise from an intricate network of protein filaments driven by specialized motor proteins and directional polymerization, that convert the chemical energy of adenosine triphosphate (ATP) to mechanical work and motion. A cell is thus a nonequilibrium soft material whose fluctuations are actively driven. Unlike the thermal fluctuations in an equilibrium material, the amplitude and spatial distribution of active fluctuations can be controlled via biochemical signaling pathways; perhaps allowing the cell to locally adjust its' mechanical properties to suit its' needs. Indeed, microscopic force generators play a central role in existing cell mechanics models such as the sol-gel [8], soft glassy rheology [4] and tensegrity [9] hypotheses.In this Letter, we extend a recently introduced method, termed two-point microrheology [10], and show that it can be used to characterize the activity of intracellular force generators by directly measuring a cell's intrinsic, random stress fluctuations. Our experimental data and theoretical framework show that a cell can be modelled as a coarse-grained viscoelastic continuum driven by a spatially random stress field having a 1/ω 2 power spectrum in our observable frequency range, 1 < ω < 60 rad/s.There are two distinct approaches to microrheology: the active approach measures the displacements of tracer particles induced by external forces and the passive approach measures fluctuations of particle positions in the absence of driving forces. The active approach provides a direct measure of the complex shear modulus µ(ω). In equilibrium systems the passive approach also measures µ(ω) because of the fluctuation-dissipation theorem (FDT) [11]. Literature results in cells using singleparticle versions of the two approaches yield shear moduli differing by orders of magnitude and exhibiting qualitatively different frequency dependencies [4,6]. These ...
We show that actin filaments, shortened to physiological lengths by gelsolin and cross-linked with recombinant human filamins (FLNs), exhibit dynamic elastic properties similar to those reported for live cells. To achieve elasticity values of comparable magnitude to those of cells, the in vitro network must be subjected to external prestress, which directly controls network elasticity. A molecular requirement for the strain-related behavior at physiological conditions is a flexible hinge found in FLNa and some FLNb molecules. Basic physical properties of the in vitro filamin-F-actin network replicate the essential mechanical properties of living cells. This physical behavior could accommodate passive deformation and internal organelle trafficking at low strains yet resist externally or internally generated high shear forces.cytoskeleton ͉ cell mechanics ͉ nonlinear rheology
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