Cellular orientational fluctuations, rotational diffusion and nematic order under periodic driving.

The ability of living cells to sense the physical properties of their microenvironment and to respond to dynamic forces acting on them plays a central role in regulating their structure, function and fate. Of particular importance is the cellular sensitivity and response to periodic driving forces in noisy environments, encountered in vital physiological conditions such as heart beating, blood vessel pulsation and breathing. Here, we first test and validate two predictions of a mean-field theory of cellular reorientation under periodic driving, which combines the minimization of cellular anisotropic elastic energy with active remodeling forces. We then extend the mean-field theory to include uncorrelated, additive nonequilibrium fluctuations, and show that the theory quantitatively agrees with the experimentally observed stationary probability distributions of the cell body orientation, under a range of biaxial periodic driving forces. The fluctuations theory allows the extraction of the dimensionless active noise amplitude of various cell types, and consequently their rotational diffusion coefficient. We then focus on intra-cellular nematic order, i.e. on orientational fluctuations of actin stress fibers around the cell body orientation, and show experimentally that intra-cellular nematic order increases with both the magnitude of the driving forces and the biaxiality strain ratio. These results are semi-quantitatively explained by applying the same cell body fluctuations theory to orientationally correlated actin stress fiber domains. Finally, an estimate of the energy scale of cellular orientational fluctuations for one cell type is shown to be about six order of magnitude larger than the thermal energy at room temperature. The implications of our findings, which make the quantitative analysis of cell mechanosensitivity more accessible, are discussed.

Tissue-Level Mechanosensitivity: Predicting and Controlling the Orientation of 3D Vascular Networks.

Understanding the mechanosensitivity of tissues is a fundamentally important problem having far-reaching implications for tissue engineering. Here we study vascular networks formed by a coculture of fibroblasts and endothelial cells embedded in three-dimensional biomaterials experiencing external, physiologically relevant forces. We show that cyclic stretching of the biomaterial orients the newly formed network perpendicular to the stretching direction, independent of the geometric aspect ratio of the biomaterial's sample. A two-dimensional theory explains this observation in terms of the network's stored elastic energy if the cell-embedded biomaterial features a vanishing effective Poisson's ratio, which we directly verify. We further show that under a static stretch, vascular networks orient parallel to the stretching direction due to force-induced anisotropy of the biomaterial polymer network. Finally, static stretching followed by cyclic stretching reveals a competition between the two mechanosensitive mechanisms. These results demonstrate tissue-level mechanosensitivity and constitute an important step toward developing enhanced tissue repair capabilities using well-oriented vascular networks.

The inner workings of stress fibers - from contractile machinery to focal adhesions and back.

Ventral stress fibers and focal adhesions are physically coupled structures that play key roles in cellular mechanics and force sensing. The tight functional interdependence between the two is manifested not only by their apparent proximity but also by the fact that ventral stress fibers and focal adhesions are simultaneously diminished upon actomyosin relaxation, and grow when subjected to external stretching. However, whereas the apparent co-regulation of the two structures is well-documented, the underlying mechanisms remains poorly understood. In this Commentary, we discuss some of the fundamental, yet still open questions regarding ventral stress fiber structure, its force-dependent assembly, as well as its capacity to generate force. We also challenge the common approach - i.e. ventral stress fibers are variants of the well-studied striated or smooth muscle machinery - by presenting and critically discussing alternative venues. By highlighting some of the less-explored aspects of the interplay between stress fibers and focal adhesions, we hope that this Commentary will encourage further investigation in this field.

Acquisition of inertia by a moving crack.

We experimentally investigate the dynamics of "simple" tensile cracks. Within an effectively infinite medium, a crack's dynamics perfectly correspond to inertialess behavior predicted by linear elastic fracture mechanics. Once a crack interacts with waves that it generated at earlier times, this description breaks down. Cracks then acquire inertia and sluggishly accelerate. Crack inertia increases with crack speed v and diverges as v approaches its limiting value. We show that these dynamics are in excellent accord with an equation of motion derived in the limit of an infinite strip [M. Marder, Phys. Rev. Lett. 66, 2484 (1991)].

Cellular contractile forces are nonmechanosensitive.

Cells' ability to apply contractile forces to their environment and to sense its mechanical properties (e.g., rigidity) are among their most fundamental features. Yet, the interrelations between contractility and mechanosensing, in particular, whether contractile force generation depends on mechanosensing, are not understood. We use theory and extensive experiments to study the time evolution of cellular contractile forces and show that they are generated by time-dependent actomyosin contractile displacements that are independent of the environment's rigidity. Consequently, contractile forces are nonmechanosensitive. We further show that the force-generating displacements are directly related to the evolution of the actomyosin network, most notably to the time-dependent concentration of F-actin. The emerging picture of force generation and mechanosensitivity offers a unified framework for understanding contractility.

Conformational states during vinculin unlocking differentially regulate focal adhesion properties.

Focal adhesions (FAs) are multi-protein complexes that connect the actin cytoskeleton to the extracellular matrix, via integrin receptors. The growth, stability and adhesive functionality of these structures are tightly regulated by mechanical stress, yet, despite the extensive characterization of the integrin adhesome, the detailed molecular mechanisms underlying FA mechanosensitivity are still unclear. Besides talin, another key candidate for regulating FA-associated mechanosensing, is vinculin, a prominent FA component, which possesses either closed ("auto-inhibited") or open ("active") conformation. A direct experimental demonstration, however, of the conformational transition between the two states is still absent. In this study, we combined multiple structural and biological approaches to probe the transition from the auto-inhibited to the active conformation, and determine its effects on FA structure and dynamics. We further show that the transition from a closed to an open conformation requires two sequential steps that can differentially regulate FA growth and stability.

Mechanical interplay between invadopodia and the nucleus in cultured cancer cells.

Invadopodia are actin-rich membrane protrusions through which cells adhere to the extracellular matrix and degrade it. In this study, we explored the mechanical interactions of invadopodia in melanoma cells, using a combination of correlative light and electron microscopy. We show here that the core actin bundle of most invadopodia interacts with integrin-containing matrix adhesions at its basal end, extends through a microtubule-rich cytoplasm, and at its apical end, interacts with the nuclear envelope and indents it. Abolishment of invadopodia by microtubules or src inhibitors leads to the disappearance of these nuclear indentations. Based on the indentation profile and the viscoelastic properties of the nucleus, the force applied by invadopodia is estimated to be in the nanoNewton range. We further show that knockdown of the LINC complex components nesprin 2 or SUN1 leads to a substantial increase in the prominence of the adhesion domains at the opposite end of the invadopodia. We discuss this unexpected, long-range mechanical interplay between the apical and basal domains of invadopodia, and its possible involvement in the penetration of invadopodia into the matrix.

Cell reorientation under cyclic stretching.

Mechanical cues from the extracellular microenvironment play a central role in regulating the structure, function and fate of living cells. Nevertheless, the precise nature of the mechanisms and processes underlying this crucial cellular mechanosensitivity remains a fundamental open problem. Here we provide a novel framework for addressing cellular sensitivity and response to external forces by experimentally and theoretically studying one of its most striking manifestations--cell reorientation to a uniform angle in response to cyclic stretching of the underlying substrate. We first show that existing approaches are incompatible with our extensive measurements of cell reorientation. We then propose a fundamentally new theory that shows that dissipative relaxation of the cell's passively-stored, two-dimensional, elastic energy to its minimum actively drives the reorientation process. Our theory is in excellent quantitative agreement with the complete temporal reorientation dynamics of individual cells measured over a wide range of experimental conditions, thus elucidating a basic aspect of mechanosensitivity.

Differential effect of actomyosin relaxation on the dynamic properties of focal adhesion proteins.

Treatment of cultured cells with inhibitors of actomyosin contractility induces rapid deterioration of stress fibers, and disassembly of the associated focal adhesions (FAs). In this study, we show that treatment with the Rho kinase inhibitor Y-27632, which blocks actomyosin contractility, induces disarray in the FA-associated actin bundles, followed by the differential dissociation of eight FA components from the adhesion sites. Live-cell microscopy indicated that the drug triggers rapid dissociation of VASP and zyxin from FAs (τ values of 7-8 min), followed by talin, paxillin and ILK (τ ~16 min), and then by FAK, vinculin and kindlin-2 (τ = 25-28 min). Examination of the molecular kinetics of the various FA constituents, using Fluorescence Recovery After Photobleaching (FRAP), in the absence of or following short-term treatment with the drug, revealed major changes in the kon and koff values of the different proteins tested, which are in close agreement with their differential dissociation rates from the adhesion sites. These findings indicate that mechanical, actomyosin-generated forces differentially regulate the molecular kinetics of individual FA-associated molecules, and thereby modulate FA composition and stability.

The near-tip fields of fast cracks.

In a stressed body, crack propagation is the main vehicle for material failure. Cracks create large stress amplification at their tips, leading to large material deformation. The material response within this highly deformed region will determine its mode of failure. Despite its great importance, we have only a limited knowledge of the structure of this region, because it is generally experimentally intractable. By using a brittle neo-Hookean material, we overcame this barrier and performed direct and precise measurements of the near-tip structure of rapid cracks. These experiments reveal a hierarchy of linear and nonlinear elastic zones through which energy is transported before being dissipated at a crack's tip. This result provides a comprehensive picture of how remotely applied forces drive material failure in the most fundamental of fracture states: straight, rapidly moving cracks.

Breakdown of linear elastic fracture mechanics near the tip of a rapid crack.

We present high resolution measurements of the displacement and strain fields near the tip of a dynamic (mode I) crack. The experiments are performed on polyacrylamide gels, brittle elastomers whose fracture dynamics mirror those of typical brittle amorphous materials. Over a wide range of propagation velocities (0.2-0.8c(s)), we compare linear elastic fracture mechanics (LEFM) to the measured near-tip fields. We find that, sufficiently near the tip, the measured stress intensity factor appears to be nonunique, the crack tip significantly deviates from its predicted parabolic form, and the strains ahead of the tip are more singular than the r(-1/2) divergence predicted by LEFM. These results show how LEFM breaks down as the crack tip is approached.

Weakly nonlinear theory of dynamic fracture.

The common approach to crack dynamics, linear elastic fracture mechanics, assumes infinitesimal strains and predicts a r(-1/2) strain divergence at a crack tip. We extend this framework by deriving a weakly nonlinear fracture mechanics theory incorporating the leading nonlinear elastic corrections that must occur at high strains. This yields strain contributions "more divergent" than r(-1/2) at a finite distance from the tip and logarithmic corrections to the parabolic crack tip opening displacement. In addition, a dynamic length scale, associated with the nonlinear elastic zone, emerges naturally. The theory provides excellent agreement with recent near-tip measurements that cannot be described in the linear elastic fracture mechanics framework.

Oscillations in rapid fracture.

Experiments of pure tensile fracture in thin brittle gels reveal a new dynamic oscillatory instability whose onset occurs at a critical velocity, VC=0.87CS, where CS is the shear wave speed. Until VC, crack dynamics are well described by linear elastic fracture mechanics (LEFM). These extreme speeds are obtained by suppression of the microbranching instability, which occurs when sample thicknesses are made comparable to the minimum microbranch width. The wavelength of these sinusoidal oscillations is independent of the sample dimensions, thereby suggesting that these macroscopic effects are due to an intrinsic microscopic scale that is unrelated to LEFM.