Ariel Livne

The Near-Tip Fields of Fast Cracks

Slightly Cracked While there are detailed theories to explain the propagation of a crack in the bulk of a material, our understanding of cracking breaks down near the tip of the crack. Experimentally, it is very hard to observe the propagation of a crack at the tip region because it tends to move very quickly. Livne et al. (p. 1359) approached this problem by working with a polyacrylamide gel in which cracks progress slowly enough to monitor them. A hierarchy of linear and nonlinear regions was observed through which energy is transported before being dissipated by the growing crack. How stresses are distributed during cracking will determine whether the resulting failure will be brittle or ductile. The linear and nonlinear elastic responses near a growing crack tip can reveal how materials fail. 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.

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.

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.

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

ABSTRACT 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. Summary: Ventral stress fibers play a key role in cellular mechanosensitivity. We discuss here fundamental questions regarding their structure, force-dependent assembly and force generation capacity.

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.

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.

The 1/r singularity in weakly nonlinear fracture mechanics

Material failure by crack propagation essentially involves a concentration of large displacement-gradients near a crack’s tip, even at scales where no irreversible deformation and energy dissipation occurs. This physical situation provides the motivation for a systematic gradient expansion of general nonlinear elastic constitutive laws that goes beyond the first order displacement-gradient expansion that is the basis for linear elastic fracture mechanics (LEFM). A weakly nonlinear fracture mechanics theory was recently developed by considering displacement-gradients up to second order. The theory predicts that, at scales within a dynamic lengthscale ‘ from a crack’s tip, significant log r displacements and 1=r displacement-gradient contributions arise. Whereas in LEFM the 1=r singularity generates an unbalanced force and must be discarded, we show that this singularity not only exists but is also necessary in the weakly nonlinear theory. The theory generates no spurious forces and is consistent with the notion of the autonomy of the near-tip nonlinear region. The J-integral in the weakly nonlinear theory is also shown to be path-independent, taking the same value as the linear elastic J-integral. Thus, the weakly nonlinear theory retains the key tenets of fracture mechanics, while providing excellent quantitative agreement with measurements near the tip of single propagating cracks. As ‘ is consistent with lengthscales that appear in crack tip instabilities, we suggest that this theory may serve as a promising starting point for resolving open questions in fracture dynamics.

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.

Fast Fracture in Slow Motion

We present recent results of fracture experiments in polyacrylamide gels. Polyacrylamide gels are soft polymer materials in which the characteristic sound speeds are on the order of a few meters/sec — thereby slowing down fracture dynamics by 3 orders of magnitude. We first demonstrate the universality of rapid fracture dynamics, comparing dynamics observed in gels with those seen in “classic” brittle materials such as glass. Among the common features are the appearance and form of branching instabilities as well as characteristic attributes of the resulting fracture surface that provide evidence for crack front inertia when translational invariance along the front is broken. We then demonstrate a number wholly new aspects of the fracture process, whose study is only made possible by utilizing the “slow motion” inherent in the fracture of these materials. These include both a new oscillatory instability at about 90% of the Rayleigh wave speed and measurements of the nonlinear zone at the tip of dynamic cracks.Copyright