Striped periodic minimizers of a two-dimensional model for martensitic phase transitions

In this paper we consider a simplified two-dimensional scalar model for the formation of mesoscopic domain patterns in martensitic shape-memory alloys at the interface between a region occupied by the parent (austenite) phase and a region occupied by the product (martensite) phase, which can occur in two variants (twins). The model, first proposed by Kohn and Mueller, is defined by the following functional: $${\cal E}(u)=\beta||u(0,\cdot)||^2_{H^{1/2}([0,h])}+ \int_{0}^{L} dx \int_0^h dy \big(|u_x|^2 + \epsilon |u_{yy}| \big)$$ where $u:[0,L]\times[0,h]\to R$ is periodic in $y$ and $u_y=\pm 1$ almost everywhere. Conti proved that if $\beta\gtrsim\epsilon L/h^2$ then the minimal specific energy scales like $\sim \min\{(\epsilon\beta/L)^{1/2}, (\epsilon/L)^{2/3}\}$, as $(\epsilon/L)\to 0$. In the regime $(\epsilon\beta/L)^{1/2}\ll (\epsilon/L)^{2/3}$, we improve Conti's results, by computing exactly the minimal energy and by proving that minimizers are periodic one-dimensional sawtooth functions.Comment: 29 pages, 3 figure

Preservation of Piecewise Constancy under TV Regularization with Rectilinear Anisotropy

A recent result by Lasica, Moll and Mucha about the $\ell^1$-anisotropic Rudin-Osher-Fatemi model in $\mathbb{R}^2$ asserts that the solution is piecewise constant on a rectilinear grid, if the datum is. By means of a new proof we extend this result to $\mathbb{R}^n$. The core of our proof consists in showing that averaging operators associated to certain rectilinear grids map subgradients of the $\ell^1$-anisotropic total variation seminorm to subgradients

The Glial Regenerative Response to Central Nervous System Injury Is Enabled by Pros-Notch and Pros-NFκB Feedback

Organisms are structurally robust, as cells accommodate changes preserving structural integrity and function. The molecular mechanisms underlying structural robustness and plasticity are poorly understood, but can be investigated by probing how cells respond to injury. Injury to the CNS induces proliferation of enwrapping glia, leading to axonal re-enwrapment and partial functional recovery. This glial regenerative response is found across species, and may reflect a common underlying genetic mechanism. Here, we show that injury to the Drosophila larval CNS induces glial proliferation, and we uncover a gene network controlling this response. It consists of the mutual maintenance between the cell cycle inhibitor Prospero (Pros) and the cell cycle activators Notch and NFκB. Together they maintain glia in the brink of dividing, they enable glial proliferation following injury, and subsequently they exert negative feedback on cell division restoring cell cycle arrest. Pros also promotes glial differentiation, resolving vacuolization, enabling debris clearance and axonal enwrapment. Disruption of this gene network prevents repair and induces tumourigenesis. Using wound area measurements across genotypes and time-lapse recordings we show that when glial proliferation and glial differentiation are abolished, both the size of the glial wound and neuropile vacuolization increase. When glial proliferation and differentiation are enabled, glial wound size decreases and injury-induced apoptosis and vacuolization are prevented. The uncovered gene network promotes regeneration of the glial lesion and neuropile repair. In the unharmed animal, it is most likely a homeostatic mechanism for structural robustness. This gene network may be of relevance to mammalian glia to promote repair upon CNS injury or disease

Cysteine dependence of Lactobacillus iners is a potential therapeutic target for vaginal microbiota modulation

Vaginal microbiota composition affects many facets of reproductive health. Lactobacillus iners-dominated microbial communities are associated with poorer outcomes, including higher risk of bacterial vaginosis (BV), compared with vaginal microbiota rich in L. crispatus. Unfortunately, standard-of-care metronidazole therapy for BV typically results in dominance of L. iners, probably contributing to post-treatment relapse. Here we generate an L. iners isolate collection comprising 34 previously unreported isolates from 14 South African women with and without BV and 4 previously unreported isolates from 3 US women. We also report an associated genome catalogue comprising 1,218 vaginal Lactobacillus isolate genomes and metagenome-assembled genomes from >300 women across 4 continents. We show that, unlike L. crispatus, L. iners growth is dependent on L-cysteine in vitro and we trace this phenotype to the absence of canonical cysteine biosynthesis pathways and a restricted repertoire of cysteine-related transport mechanisms. We further show that cysteine concentrations in cervicovaginal lavage samples correlate with Lactobacillus abundance in vivo and that cystine uptake inhibitors selectively inhibit L. iners growth in vitro. Combining an inhibitor with metronidazole promotes L. crispatus dominance of defined BV-like communities in vitro by suppressing L. iners growth. Our findings enable a better understanding of L. iners biology and suggest candidate treatments to modulate the vaginal microbiota to improve reproductive health for women globally

Phase field modeling of nonlinear material behavior

Materials that undergo internal transformations are usually described in solid mechanics by multi-well energy functions that account for both elastic and transformational behavior. In order to separate the two effects, physicists use instead phase-field-type theories where conventional linear elastic strain is quadratically coupled to an additional field that describes the evolution of the reference state and solely accounts for nonlinearity. In this paper we propose a systematic method allowing one to split the non-convex energy into harmonic and nonharmonic parts and to convert a nonconvex mechanical problem into a partially linearized phase-field problem. The main ideas are illustrated using the simplest framework of the Peierls-Nabarro dislocation model.Comment: 12 pages, 4 figures. v1: as submitted. v2: as published (conclusion added, unessential part of appendix removed, minor typesetting revisions). To appear in: K. Hackl (ed.), Proceedings of the IUTAM Symposium on Variational Concepts with Applications to the Mechanics of Materials, September 22-26, 2008, Bochum. (Springer-Verlag, 2010 presumably

MTG16 regulates colonic epithelial differentiation, colitis, and tumorigenesis by repressing E protein transcription factors

Aberrant epithelial differentiation and regeneration contribute to colon pathologies, including inflammatory bowel disease (iBD) and colitis-associated cancer (CAC). Myeloid translocation gene 16 (MTG16, also known as CBFA2T3) is a transcriptional corepressor expressed in the colonic epithelium. MTG16 deficiency in mice exacerbates colitis and increases tumor burden in CAC, though the underlying mechanisms remain unclear. Here, we identified MTG16 as a central mediator of epithelial differentiation, promoting goblet and restraining enteroendocrine cell development in homeostasis and enabling regeneration following dextran sulfate sodium-induced (DSS-induced) colitis. Transcriptomic analyses implicated increased Ephrussi box-binding transcription factor (E protein) activity in MTG16-deficient colon crypts. Using a mouse model with a point mutation that attenuates MTG16:E protein interactions (Mtg16(P20ST)), we showed that MTG16 exerts control over colonic epithelial differentiation and regeneration by repressing E protein-mediated transcription. Mimicking murine colitis, MTG16 expression was increased in biopsies from patients with active IBD compared with unaffected controls. Finally, uncoupling MTG16:E protein interactions partially phenocopied the enhanced tumorigenicity of Mtg16(-/)(-) colon in the azoxymethane/DSS-induced model of CAC, indicating that MTG16 protects from tumorigenesis through additional mechanisms. Collectively, our results demonstrate that MTG16, via its repression of E protein targets. is a key regulator of cell fate decisions during colon homeostasis, colitis, and cancer.Peer reviewe

Notch and Prospero Repress Proliferation following Cyclin E Overexpression in the Drosophila Bristle Lineage

Understanding the mechanisms that coordinate cell proliferation, cell cycle arrest, and cell differentiation is essential to address the problem of how “normal” versus pathological developmental processes take place. In the bristle lineage of the adult fly, we have tested the capacity of post-mitotic cells to re-enter the cell cycle in response to the overexpression of cyclin E. We show that only terminal cells in which the identity is independent of Notch pathway undergo extra divisions after CycE overexpression. Our analysis shows that the responsiveness of cells to forced proliferation depends on both Prospero, a fate determinant, and on the level of Notch pathway activity. Our results demonstrate that the terminal quiescent state and differentiation are regulated by two parallel mechanisms acting simultaneously on fate acquisition and cell cycle progression

Identification of 14-3-3γ as a Mieap-interacting protein and its role in mitochondrial quality control

Mieap, a p53-inducible protein, controls mitochondrial integrity by inducing the accumulation of lysosomal proteins within mitochondria. This phenomenon is designated MALM, for Mieap-induced accumulation of lysosome-like organelles within mitochondria. To identify this novel Mieap-interacting protein(s), we performed a two-dimensional image-converted analysis of liquid chromatography and mass spectrometry (2DICAL) on the proteins immunoprecipitated by an anti-Mieap antibody. We indentified 14-3-3γ as one of the proteins that was included in the Mieap-binding protein complex when MALM was induced. The interaction between Mieap and 14-3-3γ was confirmed on the exogenous and endogenous proteins. Interestingly, 14-3-3γ was localized within mitochondria when MALM occurred. A 14-3-3γ deficiency did not affect the accumulation of Mieap and lysosomal proteins within mitochondria, but dramatically inhibited the elimination of oxidized mitochondrial proteins. These results suggest that 14-3-3γ plays a critical role in eliminating oxidized mitochondrial proteins during the MALM process by interacting with Mieap within mitochondria

Prox1 Regulates the Notch1-Mediated Inhibition of Neurogenesis

During development of the spinal cord, Prox1 controls the balance between proliferation and differentiation of neural progenitor cells via suppression of Notch1 gene expression