Biharmonic submanifolds with parallel mean curvature vector field in spheres

We present some results on the boundedness of the mean curvature of proper biharmonic submanifolds in spheres. A partial classification result for proper biharmonic submanifolds with parallel mean curvature vector field in spheres is obtained. Then, we completely classify the proper biharmonic submanifolds in spheres with parallel mean curvature vector field and parallel Weingarten operator associated to the mean curvature vector field.Comment: 15 pages. Minor changes made and one section adde

A partition of unity approach to fluid mechanics and fluid-structure interaction

For problems involving large deformations of thin structures, simulating fluid-structure interaction (FSI) remains challenging largely due to the need to balance computational feasibility, efficiency, and solution accuracy. Overlapping domain techniques have been introduced as a way to combine the fluid-solid mesh conformity, seen in moving-mesh methods, without the need for mesh smoothing or re-meshing, which is a core characteristic of fixed mesh approaches. In this work, we introduce a novel overlapping domain method based on a partition of unity approach. Unified function spaces are defined as a weighted sum of fields given on two overlapping meshes. The method is shown to achieve optimal convergence rates and to be stable for steady-state Stokes, Navier-Stokes, and ALE Navier-Stokes problems. Finally, we present results for FSI in the case of a 2D mock aortic valve simulation. These initial results point to the potential applicability of the method to a wide range of FSI applications, enabling boundary layer refinement and large deformations without the need for re-meshing or user-defined stabilization.Comment: 34 pages, 15 figur

Constant mean curvature and totally umbilical biharmonic surfaces in 3-dimensional geometries

We prove that a totally umbilical biharmonic surface in any $3$-dimensional Riemannian manifold has constant mean curvature. We use this to show that a totally umbilical surface in Thurston's 3-dimensional geometries is proper biharmonic if and only if it is a part of $S^2(1/\sqrt{2})$ in $S^3$. We also give complete classifications of constant mean curvature proper biharmonic surfaces in 3-dimensional geometries and in 3-dimensional Bianchi-Cartan-Vranceanu spaces, and a complete classifications of proper biharmonic Hopf cylinders in 3-dimensional Bianchi-Cartan-Vranceanu spaces.Comment: 15 page

The role of DNA damage response in amyotrophic lateral sclerosis.

Amyotrophic lateral sclerosis (ALS) is a rapidly disabling and fatal neurodegenerative disease. Due to insufficient disease-modifying treatments, there is an unmet and urgent need for elucidating disease mechanisms that occur early and represent common triggers in both familial and sporadic ALS. Emerging evidence suggests that impaired DNA damage response contributes to age-related somatic accumulation of genomic instability and can trigger or accelerate ALS pathological manifestations. In this review, we summarize and discuss recent studies indicating a direct link between DNA damage response and ALS. Further mechanistic understanding of the role genomic instability is playing in ALS disease pathophysiology will be critical for discovering new therapeutic avenues

Chromosome localization of microsatellite markers in the shrews of the Sorex araneus group

The extremely high rate of karyotypic evolution that characterizes the shrews of the Sorex araneus group makes this group an exceptionally interesting model for population genetics and evolutionary studies. Here, we attempted to map 46 microsatellite markers at the chromosome arm level using flow-sorted chromosomes from three karyotypically different taxa of the Sorex araneus group (S. granarius and the chromosome races Cordon and Novosibirsk of S. araneus). The most likely localizations were provided for 35 markers, among which 25 were each unambiguously mapped to a single locus on the corresponding chromosomes in the three taxa, covering the three sexual chromosomes (XY1Y2) and nine of the 18 autosomal arms of the S. araneus group. The results provide further evidence for a high degree of conservation in genome organization in the S. araneus group despite the presence of numerous Robertsonian rearrangements. These markers can therefore be used to compare the genetic structure among taxa of the S. araneus group at the chromosome level and to study the role of chromosomal rearrangements in the genetic diversification and speciation process of this grou

A high-throughput in vivo micronucleus assay for genome instability screening in mice.

We describe a sensitive, robust, high-throughput method for quantifying the formation of micronuclei, markers of genome instability, in mouse erythrocytes. Micronuclei are whole chromosomes or chromosome segments that have been separated from the nucleus. Other methods of detection rely on labor-intensive, microscopy-based techniques. Here we describe a 2-d, 96-well plate-based flow cytometric method of micronucleus scoring that is simple enough for a research technician experienced in flow cytometry to perform. The assay detects low levels of genome instability that cannot be readily identified by classic phenotyping, using 25 μl of blood. By using this assay, we have screened >10,000 blood samples and discovered novel genes that contribute to vertebrate genome maintenance, as well as novel disease models and mechanisms of genome instability disorders. We discuss experimental design considerations, including statistical power calculation, we provide troubleshooting tips and we discuss factors that contribute to a false-positive increase in the number of micronucleated red blood cells and to experimental variability.Acknowledgments We thank M. Hitcham and N. Harman for assistance with blood collections, W. Cheng for assistance with flow cytometry during high-throughput screening and K. Dry for comments on the manuscript. R.E.M. is supported by Cancer Research UK (CRUK; project grant C20510/A12401). D.J.A. is supported by CRUK. D.J.A. and B.L.N. are supported by the Wellcome Trust. Research in the Jackson Laboratory is funded by CRUK program grant no. C6/A11224, the European Research Council and the European Community Seventh Framework Programme grant agreement no. HEALTH-F2-2010-259893 (DDResponse). Core funding is provided by CRUK (C6946/A14492) and the Wellcome Trust (WT092096). S.P.J. receives his salary from the University of Cambridge, UK, supplemented by CRUK. G.B. is funded by CRUK program grant no. C6/A11224.This is the accepted manuscript for a paper published in Nature Protocols 10, 205–215 (2015) doi:10.1038/nprot.2015.010, Published online 31 December 201

Hsp90 and PKM2 Drive the Expression of Aromatase in Li-Fraumeni Syndrome Breast Adipose Stromal Cells

Li-Fraumeni syndrome (LFS) patients harbor germ line mutations in the TP53 gene and are at increased risk of hormone receptor-positive breast cancers. Recently, elevated levels of aromatase, the rate-limiting enzyme for estrogen biosynthesis, were found in the breast tissue of LFS patients. Although p53 down-regulates aromatase expression, the underlying mechanisms are incompletely understood. In the present study, we found that LFS stromal cells expressed higher levels of Hsp90 ATPase activity and aromatase compared with wild-type stromal cells. Inhibition of Hsp90 ATPase suppressed aromatase expression. Silencing Aha1 (activator of Hsp90 ATPase 1), a co-chaperone of Hsp90 required for its ATPase activity, led to both inhibition of Hsp90 ATPase activity and reduced aromatase expression. In comparison with wild-type stromal cells, increased levels of the Hsp90 client proteins, HIF-1α, and PKM2 were found in LFS stromal cells. A complex comprised of HIF-1α and PKM2 was recruited to the aromatase promoter II in LFS stromal cells. Silencing either HIF-1α or PKM2 suppressed aromatase expression in LFS stromal cells. CP-31398, a p53 rescue compound, suppressed levels of Aha1, Hsp90 ATPase activity, levels of PKM2 and HIF-1α, and aromatase expression in LFS stromal cells. Consistent with these in vitro findings, levels of Hsp90 ATPase activity, Aha1, HIF-1α, PKM2, and aromatase were increased in the mammary glands of p53 null versus wild-type mice. PKM2 and HIF-1α were shown to co-localize in the nucleus of stromal cells of LFS breast tissue. Taken together, our results show that the Aha1-Hsp90-PKM2/HIF-1α axis mediates the induction of aromatase in LFS