In this paper we study the topology of conformally compact Einstein 4-manifolds. When the conformal infinity has positive Yamabe invariant and the renormalized volume is also positive we show that the conformally compact Einstein 4-manifold will have at most finite fundamental group. Under the further assumption that the renormalized volume is relatively large, we conclude that the conformally compact Einstein 4-manifold is diffeomorphic to $B^4$ and its conformal infinity is diffeomorphic to $S^3$.

Integrins mediate cell adhesion to the extracellular matrix and enable the construction of complex, multicellular organisms, yet fundamental aspects of integrin-based adhesion remain poorly understood. Notably, the magnitude of the mechanical load experienced by individual integrins within living cells is unclear, due principally to limitations inherent to existing techniques. Here we use Förster resonance energy transfer-based molecular tension sensors to directly measure the distribution of loads experienced by individual integrins in living cells. We find that a large fraction of integrins bear modest loads of 1-3 pN, while subpopulations bearing higher loads are enriched within adhesions. Further, our data indicate that integrin engagement with the fibronectin synergy site, a secondary binding site specifically for α5β1 integrin, leads to increased levels of α5β1 integrin recruitment to adhesions but not to an increase in overall cellular traction generation. The presence of the synergy site does, however, increase cells resistance to detachment by externally applied loads. We suggest that a substantial population of integrins experiencing loads well below their peak capacities can provide cells and tissues with mechanical integrity in the presence of widely varying mechanical loads.

Integrins mediate cell adhesion to the extracellular matrix and enable the construction of complex, multicellular organisms, yet fundamental aspects of integrin-based adhesion remain poorly understood. Notably, the magnitude of the mechanical load experienced by individual integrins within living cells is unclear, due principally to limitations inherent to existing techniques. Here we use Förster resonance energy transfer-based molecular tension sensors to directly measure the distribution of loads experienced by individual integrins in living cells. We find that a large fraction of integrins bear modest loads of 1-3 pN, while subpopulations bearing higher loads are enriched within adhesions. Further, our data indicate that integrin engagement with the fibronectin synergy site, a secondary binding site specifically for α₅β₁ integrin, leads to increased levels of α₅β₁ integrin recruitment to adhesions but not to an increase in overall cellular traction generation. The presence of the synergy site does, however, increase cells' resistance to detachment by externally applied loads. We suggest that a substantial population of integrins experiencing loads well below their peak capacities can provide cells and tissues with mechanical integrity in the presence of widely varying mechanical loads.

Block polymer self-assembly typically translates molecular chain connectivity into mesoscale structure by exploiting incompatible blocks with large interaction parameters (χ_ij). In this article, we demonstrate that the converse approach, encoding low-χ interactions in ABC bottlebrush triblock terpolymers (χ_AC [Formula: see text] 0), promotes organization into a unique mixed-domain lamellar morphology, which we designate LAM_P Transmission electron microscopy indicates that LAM_P exhibits ACBC domain connectivity, in contrast to conventional three-domain lamellae (LAM₃) with ABCB periods. Complementary small-angle X-ray scattering experiments reveal a strongly decreasing domain spacing with increasing total molar mass. Self-consistent field theory reinforces these observations and predicts that LAM_P is thermodynamically stable below a critical χ_AC, above which LAM₃ emerges. Both experiments and theory expose close analogies to ABA' triblock copolymer phase behavior, collectively suggesting that low-χ interactions between chemically similar or distinct blocks intimately influence self-assembly. These conclusions provide fresh opportunities for block polymer design with potential consequences spanning all self-assembling soft materials.

Predictive modeling of human disease based on the microbiota holds great potential yet remains challenging. Here, 50 adults underwent controlled transitions from naturally occurring gingivitis, to healthy gingivae (baseline), and to experimental gingivitis (EG). In diseased plaque microbiota, 27 bacterial genera changed in relative abundance and functional genes including 33 flagellar biosynthesis-related groups were enriched. Plaque microbiota structure exhibited a continuous gradient along the first principal component, reflecting transition from healthy to diseased states, which correlated with Mazza Gingival Index. We identified two host types with distinct gingivitis sensitivity. Our proposed microbial indices of gingivitis classified host types with 74% reliability, and, when tested on another 41-member cohort, distinguished healthy from diseased individuals with 95% accuracy. Furthermore, the state of the microbiota in naturally occurring gingivitis predicted the microbiota state and severity of subsequent EG (but not the state of the microbiota during the healthy baseline period). Because the effect of disease is greater than interpersonal variation in plaque, in contrast to the gut, plaque microbiota may provide advantages in predictive modeling of oral diseases.

Piezo channels transduce mechanical stimuli into electrical and chemical signals to powerfully influence development, tissue homeostasis, and regeneration. Studies on Piezo1 have largely focused on transduction of "outside-in" mechanical forces, and its response to internal, cell-generated forces remains poorly understood. Here, using measurements of endogenous Piezo1 activity and traction forces in native cellular conditions, we show that cellular traction forces generate spatially-restricted Piezo1-mediated Ca²⁺ flickers in the absence of externally-applied mechanical forces. Although Piezo1 channels diffuse readily in the plasma membrane and are widely distributed across the cell, their flicker activity is enriched near force-producing adhesions. The mechanical force that activates Piezo1 arises from Myosin II phosphorylation by Myosin Light Chain Kinase. We propose that Piezo1 Ca²⁺ flickers allow spatial segregation of mechanotransduction events, and that mobility allows Piezo1 channels to explore a large number of mechanical microdomains and thus respond to a greater diversity of mechanical cues.

Metastasis requires tumor cells to navigate through a stiff stroma and squeeze through confined microenvironments. Whether tumors exploit unique biophysical properties to metastasize remains unclear. Data show that invading mammary tumor cells, when cultured in a stiffened three-dimensional extracellular matrix that recapitulates the primary tumor stroma, adopt a basal-like phenotype. Metastatic tumor cells and basal-like tumor cells exert higher integrin-mediated traction forces at the bulk and molecular levels, consistent with a motor-clutch model in which motors and clutches are both increased. Basal-like nonmalignant mammary epithelial cells also display an altered integrin adhesion molecular organization at the nanoscale and recruit a suite of paxillin-associated proteins implicated in invasion and metastasis. Phosphorylation of paxillin by Src family kinases, which regulates adhesion turnover, is similarly enhanced in the metastatic and basal-like tumor cells, fostered by a stiff matrix, and critical for tumor cell invasion in our assays. Bioinformatics reveals an unappreciated relationship between Src kinases, paxillin, and survival of breast cancer patients. Thus adoption of the basal-like adhesion phenotype may favor the recruitment of molecules that facilitate tumor metastasis to integrin-based adhesions. Analysis of the physical properties of tumor cells and integrin adhesion composition in biopsies may be predictive of patient outcome.