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.Comment: For supplementary materials, see http://www.nature.com/ncomms/2014/140530/ncomms4938/extref/ncomms4938-s1.pd

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 $\ell$ 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 {\em 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 $\ell$ 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.Comment: 12 pages, 2 figure

The 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 non-unique, 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.Comment: 4 pages, 4 figures, first of a two-paper series (experiments); no change in content, minor textual revision

No Exit? Withdrawal Rights and the Law of Corporate Reorganizations

Bankruptcy scholarship is largely a debate about the comparative merits of a mandatory regime on one hand and bankruptcy by free design on the other. By the standard account, the current law of corporate reorganization is mandatory. Various rules that cannot be avoided ensure that investors’ actions are limited and they do not exercise their rights against specialized assets in a way that destroys the value of a business as a whole. These rules solve collective action problems and reduce the risk of bargaining failure. But there are costs to a mandatory regime. In particular, investors cannot design their rights to achieve optimal monitoring as they could in a system of bankruptcy by free design. This Article suggests that the academic debate has missed a fundamental feature of the law. Bankruptcy operates on legal entities, not on firms in the economic sense. For this reason, sophisticated investors do not face a mandatory regime at all. The ability of investors to place assets in separate entities gives them the ability to create specific withdrawal rights in the event the firm encounters financial distress. There is nothing mandatory about rules like the automatic stay when assets can be partitioned off into legal entities that are beyond the reach of the bankruptcy judge. Thus, by partitioning assets of one economic enterprise into different legal entities, investors can create a tailored bankruptcy regime. In this way, legal entities serve as building blocks that can be combined to create specific and varied but transparent investor withdrawal rights. This regime of tailored bankruptcy has been unrecognized and underappreciated and may be preferable to both mandatory and free design regimes. By allowing a limited number of investors to opt out of bankruptcy in a particular, discrete, and visible way, investors as a group may be able to both limit the risk of bargaining failure and at the same time enjoy the disciplining effect that a withdrawal right brings with it

Conformational states during vinculin unlocking differentially regulate focal adhesion properties

Abstract 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

Molecular composition of the novel central adhesions formed following Rho-kinase inhibition.

<p>(<b>A</b>) HeLa JW cells were treated with 10 µM Y-27632 for 60 min, and double-labeled for ILK, the most prominent component of these adhesions, as well as for additional FA components. The same field is shown for two labeled proteins; circles indicate the region of interest. (<b>B</b>) Relative intensity of the novel central adhesions marked by the studied proteins, following 60 min of Y-27632 treatment. The relative intensity was calculated as the percentage of fluorescence intensity measured for the corresponding protein in the untreated FAs. (<b>C</b>) Comparison of ILK and actin localization in FAs of untreated cells, and in the central adhesions of Y-27632 treated cells. Two-color TIRF microscopy of the cells prior to (left panel) and following 60 min of Y-27632 treatment (right panel) was used to assess the localization of ILK and actin. No correlation was found between the densities of these two proteins in the central adhesions (see inserts).</p