Microheterogeneity controls the rate of gelation of actin filament networks

Morphological control of bundled actin networks subject to fixed-mass depletion

Depletion interactions are thought to significantly contribute to the organization of intracellular structures in the crowded cytosol. The strength of depletion interactions depends on physical parameters such as the depletant number density and the depletant size ratio. Cells are known to dynamically regulate these two parameters by varying the copy number of proteins of a wide distribution of sizes. However, mammalian cells are also known to keep the total protein mass density remarkably constant, to within 0.5% throughout the cell cycle. We thus ask how the strength of depletion interactions varies when the total depletant mass is held fixed, a.k.a. fixed-mass depletion. We answer this question via scaling arguments, as well as by studying depletion effects on networks of reconstituted semiflexible actin in silico and in vitro. We examine the maximum strength of the depletion interaction potential U∗ as a function of q, the size ratio between the depletant and the matter being depleted. We uncover a scaling relation U∗ ∼ qζ for two cases: fixed volume fraction φ and fixed mass density ρ. For fixed volume fraction, we report ζ < 0. For the fixed mass density case, we report ζ > 0, which suggests that the depletion interaction strength increases as the depletant size ratio is increased. To test this prediction, we prepared our filament networks at fixed mass concentrations with varying sizes of the depletant molecule poly(ethylene glycol) (PEG). We characterize the depletion interaction strength in our simulations via the mesh size. In experiments, we observe two distinct actin network morphologies, which we call weakly bundled and strongly bundled. We identify a mass concentration where different PEG depletant sizes lead to weakly bundled or strongly bundled morphologies. For these conditions, we find that the mesh size and intra-bundle spacing between filaments across the different morphologies do not show significant differences, while the dynamic light scattering relaxation time and storage modulus between the two states do show significant differences. Our results demonstrate the ability to tune actin network morphology and mechanics by controlling depletant size and give insights into depletion interaction mechanisms under the fixed-depletant-mass constraint relevant to living cells.

Characterizing rheological properties and microstructure of thioester networks during degradation

Covalent adaptable networks are designed for applications including cell and drug delivery and tissue regeneration. These applications require network degradation at physiological conditions and on a physiological timescale with microstructures that can: (1) support, protect and deliver encapsulated cells or molecules and (2) provide structure to surrounding tissue. Due to this, the evolving microstructure and rheological properties during scaffold degradation must be characterized. In this work, we characterize degradation of covalent adaptable poly(ethylene glycol) (PEG)-thioester networks with different amounts of excess thiol. Networks are formed between PEG-thiol and PEG-thioester norbornene using photopolymerization. These networks are adaptable because of a thioester exchange reaction that takes place in the presence of excess thiol. We measure degradation of PEG-thioester networks with L-cysteine using multiple particle tracking microrheology (MPT). MPT measures the Brownian motion of fluorescent probe particles embedded in a material and relates this motion to rheological properties. Using time-cure superposition (TCS), we characterize the microstructure of these networks at the gel-sol phase transition by calculating the critical relaxation exponent, n, for each network with different amounts of excess thiol. Based on the measured n values, networks formed with 0% and 50% excess thiol are tightly cross-linked and elastic in nature. While networks formed with 100% excess are similar to ideal, percolated networks, which have equal viscous and elastic components. MPT measurements during degradation of these networks also measure a non-monotonic increase in probe motility. We hypothesize that this is network rearrangement near the phase transition. We then measure macroscopic material properties including the equilibrium modulus and stress relaxation. We measure a trend in bulk network properties that agrees with the values of n. Elastic modulus and stress relaxation measurements show that networks with 50% excess thiol are more elastic compared to the other two networks. As the amount of excess thiol is increased from 0% to 50%, the networks become more elastic. Further increasing excess thiol to 100% reduces the elastically effective cross-links. We hypothesize that these properties are due to network non-idealities, resulting in networks with 50% excess thiol that are more elastic. This work characterizes dynamic rheological properties during degradation, which mimics processes that could occur during implantation. This work provides information that can be used in the future design of implantable materials enabling both the rheological properties and timescale of degradation to be specified.

Simulations of dynamically cross-linked actin networks: Morphology, rheology, and hydrodynamic interactions

Cross-linked actin networks are the primary component of the cell cytoskeleton and have been the subject of numerous experimental and modeling studies. While these studies have demonstrated that the networks are viscoelastic materials, evolving from elastic solids on short timescales to viscous fluids on long ones, questions remain about the duration of each asymptotic regime, the role of the surrounding fluid, and the behavior of the networks on intermediate timescales. Here we perform detailed simulations of passively cross-linked non-Brownian actin networks to quantify the principal timescales involved in the elastoviscous behavior, study the role of nonlocal hydrodynamic interactions, and parameterize continuum models from discrete stochastic simulations. To do this, we extend our recent computational framework for semiflexible filament suspensions, which is based on nonlocal slender body theory, to actin networks with dynamic cross linkers and finite filament lifetime. We introduce a model where the cross linkers are elastic springs with sticky ends stochastically binding to and unbinding from the elastic filaments, which randomly turn over at a characteristic rate. We show that, depending on the parameters, the network evolves to a steady state morphology that is either an isotropic actin mesh or a mesh with embedded actin bundles. For different degrees of bundling, we numerically apply small-amplitude oscillatory shear deformation to extract three timescales from networks of hundreds of filaments and cross linkers. We analyze the dependence of these timescales, which range from the order of hundredths of a second to the actin turnover time of several seconds, on the dynamic nature of the links, solvent viscosity, and filament bending stiffness. We show that the network is mostly elastic on the short time scale, with the elasticity coming mainly from the cross links, and viscous on the long time scale, with the effective viscosity originating primarily from stretching and breaking of the cross links. We show that the influence of nonlocal hydrodynamic interactions depends on the network morphology: for homogeneous meshworks, nonlocal hydrodynamics gives only a small correction to the viscous behavior, but for bundled networks it both hinders the formation of bundles and significantly lowers the resistance to shear once bundles are formed. We use our results to construct three-timescale generalized Maxwell models of the networks.

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.

Uncovering the dynamic precursors to motor-driven contraction of active gels

Cells and tissues have the remarkable ability to actively generate the forces required to change their shape. This active mechanical behavior is largely mediated by the actin cytoskeleton, a crosslinked network of actin filaments that is contracted by myosin motors. Experiments and active gel theories have established that the length scale over which gel contraction occurs is governed by a balance between molecular motor activity and crosslink density. By contrast, the dynamics that govern the contractile activity of the cytoskeleton remain poorly understood. Here we investigate the microscopic dynamics of reconstituted actin-myosin networks using simultaneous real-space video microscopy and Fourier-space dynamic light scattering. Light scattering reveals different regimes of microscopic dynamics as a function of sample age. We uncover two dynamical precursors that precede macroscopic gel contraction. One is characterized by a progressive acceleration of stress-induced rearrangements, while the other consists of sudden, heterogeneous rearrangements. Intriguingly, our findings suggest a qualitative analogy between self-driven rupture and collapse of active gels and the delayed rupture of passive gels observed in earlier studies of colloidal gels under external loads.

Active rotational and translational microrheology beyond the linear spring regime

Active particle tracking microrheometers have the potential to perform accurate broadband measurements of viscoelasticity within microscopic systems. Generally, their largest possible precision is limited by Brownian motion and low frequency changes to the system. The signal to noise ratio is usually improved by increasing the size of the driven motion compared to the Brownian as well as averaging over repeated measurements. New theory is presented here whereby error in measurements of the complex shear modulus can be significantly reduced by analyzing the motion of a spherical particle driven by nonlinear forces. In some scenarios error can be further reduced by applying a variable transformation which linearizes the equation of motion. This enables normalization that eliminates error introduced by low frequency drift in the particle's equilibrium position. Our measurements indicate that this can further resolve an additional decade of viscoelasticity at high frequencies. Using this method will easily increase the signal strength enough to significantly reduce the measurement time for the same error. Thus the method is more conducive to measuring viscoelasticity in slowly changing microscopic systems, such as a living cell.

Both monovalent cations and plectin are potent modulators of mechanical properties of keratin K8/K18 networks

Intermediate filament (IF) networks are a major contributor to cell rigidity and thus serve as vital elements to preserve the integrity of entire cell layers. Keratin K8 and K18 IFs are the basic constituents of the cytoskeleton of epithelial cells. The mechanical properties of K8/K18 networks depend on the structural arrangements of individual filaments within the network. This paper investigates the architecture of these networks in vitro under the influence of the monovalent cation potassium and that of the cytolinker protein plectin. Whereas increasing amounts of potassium ions lead to filament bundling, plectin interlinks filaments at filament intersection points but does not lead to bundle formation. The mechanics of the resulting networks are investigated by microrheology with assembled K8/K18 networks. It is shown that bundling induced by potassium ions significantly stiffens the network. Furthermore, our measurements reveal an increase in plectin-mediated keratin network rigidity as soon as an amount corresponding to more than 20% of the plectin present in cells is added to the keratin IF networks. In parallel, we investigated the influence of plectin on cell rigidity in detergent-extracted epithelial vulva carcinoma derived A431 cells in situ. These cytoskeletons, containing mostly IFs, actin filaments and associated proteins, exhibit a significantly decreased stiffness, when plectin is downregulated to ≈10% of the normal value. Therefore, we assume that plectin, via the formation of IF-IF connections and crosslinking of IFs to actin filaments, is an important contributor to cell stiffness.

Advances in the microrheology of complex fluids

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

Advances in the microrheology of complex fluids

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

A microrheological study of hydrogel kinetics and micro-heterogeneity

The real-time dynamic heterogeneity of the gelation process of the amino acid derivative Fmoc-tyrosine (Fmoc-Y) is studied using particle tracking microrheology. To trigger gelation, glucono-δ-lactone (GdL) is added, which gradually lowers the p H over several hours. The onset of self-assembly in the system is signified by a sharp drop in the mean-squared displacement of embedded particles, a phenomenon that is found to correlate with the p H of the system reaching the pK(a) of Fmoc-Y. The gel point is identified and found to be dependent on the GdL concentration. Analysis of embedded probe particle dynamics allows the heterogeneity of the sample to be quantified, using three metrics: the heterogeneity ratio (HR), the non-Gaussian parameter of the van Hove correlation function (N and the bin distribution of the mean-squared displacement (MSD) of single particles (f(z)). Results from the three techniques are found to be approximately comparable, with increases in heterogeneity observed in all samples for incubation times t(w) = 0-3 hours. The final heterogeneity in all samples is found to be remarkably low compared to other systems previously reported in the literature.

Microrheological characterization of collagen systems: from molecular solutions to fibrillar gels

Collagen is the most abundant protein in the extracellular matrix (ECM), where its structural organization conveys mechanical information to cells. Using optical-tweezers-based microrheology, we investigated mechanical properties both of collagen molecules at a range of concentrations in acidic solution where fibrils cannot form and of gels of collagen fibrils formed at neutral pH, as well as the development of microscale mechanical heterogeneity during the self-assembly process. The frequency scaling of the complex shear modulus even at frequencies of ∼10 kHz was not able to resolve the flexibility of collagen molecules in acidic solution. In these solutions, molecular interactions cause significant transient elasticity, as we observed for 5 mg/ml solutions at frequencies above ∼200 Hz. We found the viscoelasticity of solutions of collagen molecules to be spatially homogeneous, in sharp contrast to the heterogeneity of self-assembled fibrillar collagen systems, whose elasticity varied by more than an order of magnitude and in power-law behavior at different locations within the sample. By probing changes in the complex shear modulus over 100-minute timescales as collagen self-assembled into fibrils, we conclude that microscale heterogeneity appears during early phases of fibrillar growth and continues to develop further during this growth phase. Experiments in which growing fibrils dislodge microspheres from an optical trap suggest that fibril growth is a force-generating process. These data contribute to understanding how heterogeneities develop during self-assembly, which in turn can help synthesis of new materials for cellular engineering.

Differential mechanical response of mesenchymal stem cells and fibroblasts to tumor-secreted soluble factors

The progression of neoplastic malignancies is a complex process resulting not only from the accumulation of mutations within tumor cells, but also modulation of the tumor microenvironment. Recent advances have shown that the recruitment and subsequent heterotypic interactions of stromal cells--including fibroblasts and bone marrow-derived mesenchymal stem cells (MSCs)--are crucial for carcinogenesis. Though extensive work has been done analyzing the signals that recruit these cells, the governing mechanical properties have not been fully investigated. Here, we report that despite their initial similarities, MSCs respond not only faster but also more dramatically to pro-migratory tumor-secreted soluble factors. Utilizing multiple particle tracking microrheology to probe the cytoskeletal mechanical properties, we show that MSCs stiffen completely within one hour, three times faster than fibroblasts. In addition, unlike fibroblasts, MSCs exposed to tumor-secreted soluble factors display a functionally different phenotype characterized by morphological elongation, decreased actin stress fiber density, and decreased adhesion. Quantitative real-time PCR indicates these phenomena occur based on differential expression of small GTPases RhoA and Cdc42, but not Rac1. These findings demonstrate a fundamental difference in the recruitment of fibroblasts and MSCs.

Particle-tracking microrheology of living cells: principles and applications

A multitude of cellular and subcellular processes depend critically on the mechanical deformability of the cytoplasm. We have recently introduced the method of particle-tracking microrheology, which measures the viscoelastic properties of the cytoplasm locally and with high spatiotemporal resolution. Here we establish the basic principles of particle-tracking microrheology, describing the advantages of this approach over more conventional approaches to cell mechanics. We present basic concepts of molecular mechanics and polymer physics relevant to the microrheological response of cells. Particle-tracking microrheology can probe the mechanical properties of live cells in experimentally difficult, yet more physiological, environments, including cells embedded inside a 3D matrix, adherent cells subjected to shear flows, and cells inside a developing embryo. Particle-tracking microrheology can readily reveal the lost ability of diseased cells to resist shear forces.

Altering mucus rheology to "solidify" human mucus at the nanoscale

The ability of mucus to function as a protective barrier at mucosal surfaces rests on its viscous and elastic properties, which are not well understood at length scales relevant to pathogens and ultrafine environmental particles. Here we report that fresh, undiluted human cervicovaginal mucus (CVM) transitions from an impermeable elastic barrier to non-adhesive objects sized 1 microm and larger to a highly permeable viscoelastic liquid to non-adhesive objects smaller than 500 nm in diameter. Addition of a nonionic detergent, present in vaginal gels, lubricants and condoms, caused CVM to behave as an impermeable elastic barrier to 200 and 500 nm particles, suggesting that the dissociation of hydrophobically-bundled mucin fibers created a finer elastic mucin mesh. Surprisingly, the macroscopic viscoelasticity, which is critical to proper mucus function, was unchanged. These findings provide important insight into the nanoscale structural and barrier properties of mucus, and how the penetration of foreign particles across mucus might be inhibited.

Control of granule mobility and exocytosis by Ca2+ -dependent formation of F-actin in pancreatic duct epithelial cells

Elevation of intracellular Ca(2+) concentration ([Ca(2+)](i)) triggers exocytosis of secretory granules in pancreatic duct epithelia. In this study, we find that the signal also controls granule movement. Motions of fluorescently labeled granules stopped abruptly after a [Ca(2+)](i) increase, kinetically coincident with formation of filamentous actin (F-actin) in the whole cytoplasm. At high resolution, the new F-actin meshwork was so dense that cellular structures of granule size appeared physically trapped in it. Depolymerization of F-actin with latrunculin B blocked both the F-actin formation and the arrest of granules. Interestingly, when monitored with total internal reflection fluorescence microscopy, the immobilized granules still moved slowly and concertedly toward the plasma membrane. This group translocation was abolished by blockers of myosin. Exocytosis measured by microamperometry suggested that formation of a dense F-actin meshwork inhibited exocytosis at small Ca(2+) rises <1 microm. Larger [Ca(2+)](i) rises increased exocytosis because of the co-ordinate translocation of granules and fusion to the membrane. We propose that the Ca(2+)-dependent freezing of granules filters out weak inputs but allows exocytosis under stronger inputs by controlling granule movements.

The filamentous actin cross-linking/bundling activity of mammalian formins

Formins are multidomain proteins that regulate actin filament dynamics and are defined by the formin homology 2 domain. Biochemical assays suggest that mammalian formins display actin-filament nucleation, severing, and bundling activities. Whether formins can cross-link actin filaments into viscoelastic arrays and the effectiveness of formins' bundling activity compared with that of important filamentous actin (F-actin) cross-linking/bundling proteins are unknown. Here, we used rigorous in vitro rheologic assays to deconvolve the dynamic cross-linking activity from the bundling activity of formin FRL1 and the closely related mDia1 and mDia2. In addition, we compared these formins with the canonical F-actin bundling protein fascin and cross-linking/bundling proteins alpha-actinin and filamin. We found that FRL1 and mDia2, but not mDia1, can help F-actin form highly elastic networks. FRL1 and mDia2 mediate the formation of highly elastic F-actin networks as effectively and rapidly as alpha-actinin and filamin but only past a relatively high actin-to-formin molar ratio of 50:1. Past that threshold molar ratio, the mechanical properties of F-actin/formin networks are independent of formin concentration, similar to fascin. Moreover, unlike those for alpha-actinin and filamin but similar to those for fascin, F-actin/formin networks show no strain-induced hardening. mDia1 cannot bundle F-actin but can weakly cross-link filaments at high concentrations. Point mutagenesis reveals that reducing the barbed-end binding activity of FRL1 and mDia2 greatly enhances the rate of formation of F-actin gels but does not significantly affect the mechanical properties of the resulting networks at steady state. Together, these results suggest that the mechanical behaviors of FRL1 and mDia2 are fundamentally different from those of cross-linking/bundling proteins alpha-actinin and filamin but qualitatively similar to the mechanical behavior of the bundling protein fascin, albeit with a dramatically increased (>10-fold) threshold concentration for transition to bundling, which nevertheless leads to much stiffer F-actin networks than fascin.

Mapping local matrix remodeling induced by a migrating tumor cell using three-dimensional multiple-particle tracking

Mesenchymal cell migration through a three-dimensional (3D) matrix typically involves major matrix remodeling. The direction of matrix deformation occurs locally in all three dimensions, which cannot be measured by current techniques. To probe the local, 3D, real-time deformation of a collagen matrix during tumor cell migration, we developed an assay whereby matrix-embedded beads are tracked simultaneously in all three directions with high resolution. To establish a proof of principle, we investigated patterns of collagen I matrix deformation near fibrosarcoma cells in the absence and presence of inhibitors of matrix metalloproteinases and acto-myosin contractility. Our results indicate that migrating cells show patterns of local matrix deformation toward the cell that are symmetric in magnitude with respect to the axis of cell movement. In contrast, patterns of matrix release from the cell are asymmetric: the matrix is typically relaxed first at the back of the cell, allowing forward motion, and then at the cell's leading edge. Matrix deformation in regions of the matrix near the cell's leading edge is elastic and mostly reversible, but induces irreversible matrix rupture events near the trailing edge. Our results also indicate that matrix remodeling spatially correlates with protrusive activity. This correlation is mediated by myosin II and Rac1, and eliminated after inhibition of pericellular proteolysis or ROCK. We have developed an assay based on high-resolution 3D multiple-particle tracking that allows us to probe local matrix remodeling during mesenchymal cell migration through a 3D matrix and simultaneously monitor protrusion dynamics.

Microrheology of the liquid-solid transition during gelation

The viscoelastic properties of physical and chemical polymer gels are characterized through the liquid-solid transition using particle tracking microrheology. Measurements of the probe particle mean-squared displacement are shifted as the extent of gelation increases to generate master curves. From the shift factors, we determine the gel point and critical scaling exponents. Both systems exhibit a critical relaxation exponent n approximately 0.6, where G' approximately G'' approximately omega n for the incipient gel, consistent with the Rouse model of dynamic scaling in the percolation universality class.

Probing cellular mechanical responses to stimuli using ballistic intracellular nanorheology

We describe a new method to measure the local and global micromechanical properties of the cytoplasm of single living cells in their physiological milieu and subjected to external stimuli. By tracking spontaneous, Brownian movements of individual nanoparticles of diameter>or=100 nm distributed within the cell with high spatial and temporal resolutions, the local viscoelastic properties of the intracellular milieu can be measured in different locations within the cell. The amplitude and the time-dependence of the mean-squared displacement of each nanoparticle directly reflect the elasticity and the viscosity of the cytoplasm in the vicinity of the nanoparticle. In our previous versions of particle tracking, we delivered nanoparticles via microinjection, which limited the number of cells amenable to measurement, rendering our technique incompatible with high-throughput experiments. Here we introduce ballistic injection to effectively deliver a large number of nanoparticles to a large number of cells simultaneously. When coupled with multiple particle tracking, this new method-ballistic intracellular nanorheology (BIN)-makes it now possible to probe the viscoelastic properties of cells in high-throughput experiments, which require large quantities of injected cells for seeding in various conditions. For instance, BIN allows us to probe an ensemble of cells embedded deeply inside a three-dimensional extracellular matrix or as a monolayer of cells subjected to shear flows.

Electrostatically tuned rate of peptide self-assembly resolved by multiple particle tracking

Hydrogels formed from the self-assembly of oligopeptides are being extensively studied for biomedical applications. The kinetics of their gelation, as well as a quantitative description of the forces controlling the rate of assembly has not yet been addressed. We report here the use of multiple particle tracking to measure the self-assembly kinetics of the model peptide FKFEFKFE (KFE8). KFE8 forms well-defined β-sheet intermediates and is often used as a model peptide system that forms a fibrous network in aqueous solvent. We find that increasing the pH of this system from 3.5 to 4.0 decreases the time of KFE8 gelation by almost hundredfold, from hours to minutes. A remarkable self-similarity between measurements performed at different pH suggests that, although accelerated by the pH increase, gelation follows an invariable mechanism. We propose a semi-quantitative interpretation for the order of magnitudes of gelation time using a simple model for the interaction driving the self-assembly in terms of the Derjaguin-Landau-Verwey-Overbeek (DLVO) theory. Such understanding is important for the development of current and future therapeutic applications ( drug delivery).

Statistical and sampling issues when using multiple particle tracking

Video microscopy can be used to simultaneously track several microparticles embedded in a complex material. The trajectories are used to extract a sample of displacements at random locations in the material. From this sample, averaged quantities characterizing the dynamics of the probes are calculated to evaluate structural and/or mechanical properties of the assessed material. However, the sampling of measured displacements in heterogeneous systems is singular because the volume of observation with video microscopy is finite. By carefully characterizing the sampling design in the experimental output of the multiple particle tracking technique, we derive estimators for the mean and variance of the probes' dynamics that are independent of the peculiar statistical characteristics. We expose stringent tests of these estimators using simulated and experimental complex systems with a known heterogeneous structure. Up to a certain fundamental limitation, which we characterize through a material degree of sampling by the embedded probe tracking, these estimators can be applied to quantify the heterogeneity of a material, providing an original and intelligible kind of information on complex fluid properties. More generally, we show that the precise assessment of the statistics in the multiple particle tracking output sample of observations is essential in order to provide accurate unbiased measurements.

Collagen Gel Anisotropy Measured by 2-D Laser Trap Microrheometry

Collagen gels can serve as biomaterials ideal for tissue equivalents, especially if they are remodeled to have fibril anisotropy mimicking native tissue. Type I collagen gel remodeling was studied microscopically to investigate the changes caused by fibroblasts in collagen gel structures, with and without the growth factors PDGF-BB and TGF-beta1. A bidirectional laser trap microrheometry technique was developed that revealed a high degree of local heterogeneity and anisotropy in the structure of the collagen gels during active fibroblast contraction. The use of the growth factors increased not only the gel anisotropy, but the heterogeneity as well, indicating further changes in the collagen fibril orientations. This work shows the ability to influence the remodeling capabilities of fibroblasts by using growth factors in order to begin to elucidate the changes in the local mechanical environment of contracting collagen gels. We present this experimental technique as a method for probing changes in the fibroblast-driven anisotropy of collagen gels as a basis for understanding microstructural tissue organization important in the development of collagen-based tissue equivalents.

GTPase activity, structure, and mechanical properties of filaments assembled from bacterial cytoskeleton protein MreB

MreB, a major component of the recently discovered bacterial cytoskeleton, displays a structure homologous to its eukaryotic counterpart actin. Here, we study the assembly and mechanical properties of Thermotoga maritima MreB in the presence of different nucleotides in vitro. We found that GTP, not ADP or GDP, can mediate MreB assembly into filamentous structures as effectively as ATP. Upon MreB assembly, both GTP and ATP release the gamma phosphate at similar rates. Therefore, MreB is an equally effective ATPase and GTPase. Electron microscopy and quantitative rheology suggest that the morphologies and micromechanical properties of filamentous ATP-MreB and GTP-MreB are similar. In contrast, mammalian actin assembly is favored in the presence of ATP over GTP. These results indicate that, despite high structural homology of their monomers, T. maritima MreB and actin filaments display different assembly, morphology, micromechanics, and nucleotide-binding specificity. Furthermore, the biophysical properties of T. maritima MreB filaments, including high rigidity and propensity to form bundles, suggest a mechanism by which MreB helical structure may be involved in imposing a cylindrical architecture on rod-shaped bacterial cells.

Viscoelastic retraction of single living stress fibers and its impact on cell shape, cytoskeletal organization, and extracellular matrix mechanics

Cells change their form and function by assembling actin stress fibers at their base and exerting traction forces on their extracellular matrix (ECM) adhesions. Individual stress fibers are thought to be actively tensed by the action of actomyosin motors and to function as elastic cables that structurally reinforce the basal portion of the cytoskeleton; however, these principles have not been directly tested in living cells, and their significance for overall cell shape control is poorly understood. Here we combine a laser nanoscissor, traction force microscopy, and fluorescence photobleaching methods to confirm that stress fibers in living cells behave as viscoelastic cables that are tensed through the action of actomyosin motors, to quantify their retraction kinetics in situ, and to explore their contribution to overall mechanical stability of the cell and interconnected ECM. These studies reveal that viscoelastic recoil of individual stress fibers after laser severing is partially slowed by inhibition of Rho-associated kinase and virtually abolished by direct inhibition of myosin light chain kinase. Importantly, cells cultured on stiff ECM substrates can tolerate disruption of multiple stress fibers with negligible overall change in cell shape, whereas disruption of a single stress fiber in cells anchored to compliant ECM substrates compromises the entire cellular force balance, induces cytoskeletal rearrangements, and produces ECM retraction many microns away from the site of incision; this results in large-scale changes of cell shape (> 5% elongation). In addition to revealing fundamental insight into the mechanical properties and cell shape contributions of individual stress fibers and confirming that the ECM is effectively a physical extension of the cell and cytoskeleton, the technologies described here offer a novel approach to spatially map the cytoskeletal mechanics of living cells on the nanoscale.

How actin crosslinking and bundling proteins cooperate to generate an enhanced cell mechanical response

Actin-crosslinking proteins organize actin filaments into dynamic and complex subcellular scaffolds that orchestrate important mechanical functions, including cell motility and adhesion. Recent mutation studies have shown that individual crosslinking proteins often play seemingly non-essential roles, leading to the hypothesis that they have considerable redundancy in function. We report live-cell, in vitro, and theoretical studies testing the mechanical role of the two ubiquitous actin-crosslinking proteins, alpha-actinin and fascin, which co-localize to stress fibers and the basis of filopodia. Using live-cell particle tracking microrheology, we show that the addition of alpha-actinin and fascin elicits a cell mechanical response that is significantly greater than that originated by alpha-actinin or fascin alone. These live-cell measurements are supported by quantitative rheological measurements with reconstituted actin filament networks containing pure proteins that show that alpha-actinin and fascin can work in concert to generate enhanced cell stiffness. Computational simulations using finite element modeling qualitatively reproduce and explain the functional synergy of alpha-actinin and fascin. These findings highlight the cooperative activity of fascin and alpha-actinin and provide a strong rationale that an evolutionary advantage might be conferred by the cooperative action of multiple actin-crosslinking proteins with overlapping but non-identical biochemical properties. Thus the combination of structural proteins with similar function can provide the cell with unique properties that are required for biologically optimal responses.

The rapid onset of elasticity during the assembly of the bacterial cell-division protein FtsZ

FtsZ, a prokaryotic homolog of eukaryotic tubulin, is a major constituent of the bacterial Z-ring, which contracts the cell wall during cell division. Because the mechanical properties of FtsZ are unknown, its function in the maintenance and constriction of the Z-ring is not well understood. Here, quantitative rheometry shows that, at physiological concentrations, FtsZ filaments form, extremely rapidly, highly elastic networks within physiological time scales ( approximately minutes), much faster than other major dynamic cytoskeletal filaments, including microtubule, actin, and vimentin in eukaryotes. FtsZ networks display a relatively low viscosity and a high resilience against shear stresses, as well as an elasticity that depends weakly on concentration, G approximately C(0.57), a power-law dependence consistent with crosslinked flexible filaments. Calcium, whose intracellular concentration increases during bacterial division, further enhances the elasticity of FtsZ networks through filament bundling, an effect that occurs in the presence of GTP, not GDP. These studies suggest that FtsZ filaments have the toughness to provide strong mechanical support for the maintenance and circumferential constriction of the bacterial Z-ring.

Dendritic branching and homogenization of actin networks mediated by arp2/3 complex

The cytoskeleton of motile cells exploits accessory proteins to locally modulate its organization and micromechanics. Here, we demonstrate that the Arp2/3 complex plays the role, unique among other cytoskeleton proteins, of an actin network "homogenizer," promoting the extremely rapid formation of homogeneous and stiff networks. Nanotracking of microspheres imbedded in F-actin networks reveals that the Arp2/3 complex promotes the formation of networks that are remarkably more homogeneous than control networks, a distinctive feature that coordinates a dramatic burst of elasticity. These results suggest that the Arp2/3 complex possesses a unique function of stabilizing membrane protrusions through the formation of homogeneous and stiff actin cytoskeleton at the leading edge of crawling cells.

The assembly of MreB, a prokaryotic homolog of actin

MreB, a major component of the bacterial cytoskeleton, exhibits high structural homology to its eukaryotic counterpart actin. Live cell microscopy studies suggest that MreB molecules organize into large filamentous spirals that support the cell membrane and play a key shape-determining function. However, the basic properties of MreB filament assembly remain unknown. Here, we studied the assembly of Thermotoga maritima MreB triggered by ATP in vitro and compared it to the well-studied assembly of actin. These studies show that MreB filament ultrastructure and polymerization depend crucially on temperature as well as the ions present on solution. At the optimal growth temperature of T. maritima, MreB assembly proceeded much faster than that of actin, without nucleation (or nucleation is highly favorable and fast) and with little or no contribution from filament end-to-end annealing. MreB exhibited rates of ATP hydrolysis and phosphate release similar to that of F-actin, however, with a critical concentration of approximately 3 nm, which is approximately 100-fold lower than that of actin. Furthermore, MreB assembled into filamentous bundles that have the ability to spontaneously form ring-like structures without auxiliary proteins. These findings suggest that despite high structural homology, MreB and actin display significantly different assembly properties.

Crawling toward a unified model of cell mobility: spatial and temporal regulation of actin dynamics

Crawling cells of various morphologies displace themselves in their biological environments by a similar overall mechanism of protrusion through actin assembly at the front coordinated with retraction at the rear. Different cell types organize very distinct protruding structures, yet they do so through conserved biochemical mechanisms to regulate actin polymerization dynamics and vary the mechanical properties of these structures. The moving cell must spatially and temporally regulate the biochemical interactions of its protein components to exert control over higher-order dynamic structures created by these proteins and global cellular responses four or more orders of magnitude larger in scale and longer in time than the individual protein-protein interactions that comprise them. To fulfill its biological role, a cell globally responds with high sensitivity to a local perturbation or signal and coordinates its many intracellular actin-based functional structures with the physical environment it experiences to produce directed movement. This review attempts to codify some unifying principles for cell motility that span organizational scales from single protein polymer filaments to whole crawling cells.

Rho kinase regulates the intracellular micromechanical response of adherent cells to rho activation

Local sol-gel transitions of the cytoskeleton modulate cell shape changes, which are required for essential cellular functions, including motility and adhesion. In vitro studies using purified cytoskeletal proteins have suggested molecular mechanisms of regulation of cytoskeleton mechanics; however, the mechanical behavior of living cells and the signaling pathways by which it is regulated remains largely unknown. To address this issue, we used a nanoscale sensing method, intracellular microrheology, to examine the mechanical response of the cell to activation of the small GTPase Rho. We observe that the cytoplasmic stiffness and viscosity of serum-starved Swiss 3T3 cells transiently and locally enhances upon treatment with lysophosphatidic acid, and this mechanical behavior follows a trend similar to Rho activity. Furthermore, the time-dependent activation of Rho decreases the degree of microheterogeneity of the cytoplasm. Our results reveal fundamental differences between intracellular elasticity and cellular tension and suggest a critical role for Rho kinase in the regulation of intracellular mechanics.

The Bimodal Role of Filamin in Controlling the Architecture and Mechanics of F-actin Networks

Reconstituted actin filament networks have been used extensively to understand the mechanics of the actin cortex and decipher the role of actin cross-linking proteins in the maintenance and deformation of cell shape. However, studies of the mechanical role of the F-actin cross-linking protein filamin have led to seemingly contradictory conclusions, in part due to the use of ill-defined mechanical assays. Using quantitative rheological methods that avoid the pitfalls of previous studies, we systematically tested the complex mechanical response of reconstituted actin filament networks containing a wide range of filamin concentrations and compared the mechanical function of filamin with that of the cross-linking/bundling proteins alpha-actinin and fascin. At steady state and within a well defined linear regime of small non-destructive deformations, F-actin solutions behave as highly dynamic networks (actin polymers are still sufficiently mobile to relax the stress) below the cross-linking-to-bundling threshold filamin concentration, and they behave as covalently cross-linked gels above that threshold. Under large deformations, F-actin networks soften at low filamin concentrations and strain-harden at high filamin concentrations. Filamin cross-links F-actin into networks that are more resilient, stiffer, more solid-like, and less dynamic than alpha-actinin and fascin. These results resolve the controversy by showing that F-actin/filamin networks can adopt diametrically opposed rheological behaviors depending on the concentration in cross-linking proteins.

Comparative vibrational spectroscopy of intracellular tau and extracellular collagen I reveals parallels of gelation and fibrillar structure

The N-terminal tau 2-19 peptide undergoes gelation, syneresis, and aggregation over a period of years. These changes may be approximated on a shorter time scale by agitation and partial dehydration. The anomalously enhanced (229 nm) ultraviolet resonance Raman (UVRR) imide II band reveals a common structural feature for gels of nondehydrated tau 2-19 and collagen I and insoluble paired helical filaments (PHFs) and collagen I of weak hydrogen bonding at proline carbonyls. Anomalous UVRR enhancement of amide bands at 229 nm results from gel structure, as demonstrated by increased amide absorption at the red edge for tau 2-19 gel and implies the involvement of water in gel structure. In aged, dehydrated tau 2-19 gel, proline carbonyls lose their bonds to water and tyrosine becomes deprotonated, as demonstrated by UVRR spectroscopy. The Fourier transform infrared (FTIR) amide I band shows that antiparallel beta-sheet structure increases with syneresis in the tau 2-19 hydrogel. The comparison of FTIR results for PHFs with collagen I gel and polyproline demonstrates that the secondary structure of PHFs is polyproline II. One implication of this assignment is that the fibrillation of hydrophilic tau is thermodynamically driven by the entropy gained as hydrogen-bonded water is freed, as for collagen I. The FTIR results also show that peptide domains culled from a longer protein do not necessarily fold into identical secondary structures. A pathological, sequential mechanism of gelation, syneresis, and fibrillation for tau in AD is suggested and is supported by the observation of amorphous neurofibrillary tangle development and fibrillation in vivo.

Enhanced viscoelasticity of human cystic fibrotic sputum correlates with increasing microheterogeneity in particle transport

Current biochemical characterizations of cystic fibrosis (CF) sputum do not address the high degree of microheterogeneity in the rheological properties of the mucosal matrix and only provide bulk-average particle diffusion coefficients. The viscoelasticity of CF sputum greatly reduces the diffusion rates of colloidal particles, limiting the effectiveness of gene delivery to underlying lung cells. We determine diffusion coefficients of hundreds of individual amine-modified and carboxylated polystyrene particles (diameter 100-500 nm) embedded in human CF sputum with 5 nm and 33 ms of spatiotemporal resolution. High resolution multiple particle tracking is used to calculate the effective viscoelastic properties of CF sputum at the micron scale, which we relate to its macroscopic viscoelasticity. CF sputum microviscosity, as probed by 100- and 200-nm particles, is an order of magnitude lower than its macroviscosity, suggesting that nanoparticles dispersed in CF sputum are transported primarily through lower viscosity pores within a highly elastic matrix. Multiple particle tracking provides a non-destructive, highly sensitive method to quantify the high heterogeneity of the mucus pore network. The mean diffusion coefficient becomes dominated by relatively few but fast-moving particles as particle size is reduced from 500 to 100 nm. Neutrally charged particles with a diameter <200 nm undergo more rapid transport in CF sputum than charged particles. Treatment with recombinant human DNase (Pulmozyme) reduces macroviscoelastic properties of CF sputum by up to 50% and dramatically narrows the distribution of individual particle diffusion rates but surprisingly does not significantly alter the ensemble-average particle diffusion rate.

Effect of length, topology, and concentration on the microviscosity and microheterogeneity of DNA solutions

The viscoelastic behavior of chromosomal DNA, which is heterogeneously distributed within the nucleus, may influence the diffusion of nuclear organelles and proteins. To identify some of the parameters that affect DNA viscoelasticity, we use the high-throughput method of multiple-particle nanotracking to measure the microviscosity and degree of heterogeneity of solutions of chromosomal DNA, linear DNA, and circular double-stranded DNA over a wide range of concentrations and lengths. The thermally excited displacements of multiple fluorescent microspheres imbedded in DNA solutions are monitored with 5nm spatial resolution and 30Hz temporal resolution, from which mean-squared displacement (MSD) and viscosity distributions are generated. For all probed DNA solutions but the most concentrated solution of the longest molecules, the ensemble-averaged MSD increases linearly with time at all probed time scales, a signature of viscous transport. The associated mean viscosity of the DNA solutions increases slowly with concentration for circular DNA and more rapidly for linear DNA, but more slowly than predicted by theory. The heterogeneity of the DNA solutions is assessed by computing the relative contributions of the 10%, 25%, and 50% highest values of MSD and viscosity to the ensemble-averaged MSD and viscosity. For both linear DNA and circular DNA, these contributions are much larger than observed in homogeneous liquids such as glycerol. The microheterogeneity of the linear DNA solutions increases with concentration more significantly for linear DNA than circular DNA. These in vitro results suggest that the topology, local concentration, and length of DNA influence the microrheology and microheterogeneity of the DNA within the nucleus.

Functional synergy of actin filament cross-linking proteins

The organization of filamentous actin (F-actin) in resilient networks is coordinated by various F-actin cross-linking proteins. The relative tolerance of cells to null mutations of genes that code for a single actin cross-linking protein suggests that the functions of those proteins are highly redundant. This apparent functional redundancy may, however, reflect the limited resolution of available assays in assessing the mechanical role of F-actin cross-linking/bundling proteins. Using reconstituted F-actin networks and rheological methods, we demonstrate how alpha-actinin and fascin, two F-actin cross-linking/bundling proteins that co-localize along stress fibers and in lamellipodia, could synergistically enhance the resilience of F-actin networks in vitro. These two proteins can generate microfilament arrays that "yield" at a strain amplitude that is much larger than each one of the proteins separately. F-actin/alpha-actinin/fascin networks display strain-induced hardening, whereby the network "stiffens" under shear deformations, a phenomenon that is non-existent in F-actin/fascin networks and much weaker in F-actin/alpha-actinin networks. Strain-hardening is further enhanced at high rates of deformation and high concentrations of actin cross-linking proteins. A simplified model suggests that the optimum results of the competition between the increased stiffness of bundles and their decreased density of cross-links. Our studies support a re-evaluation of the notion of functional redundancy among cytoskeletal regulatory proteins.