Semilinear mixed problems on Hilbert complexes and their numerical approximation

Arnold, Falk, and Winther recently showed [Bull. Amer. Math. Soc. 47 (2010), 281-354] that linear, mixed variational problems, and their numerical approximation by mixed finite element methods, can be studied using the powerful, abstract language of Hilbert complexes. In another recent article [arXiv:1005.4455], we extended the Arnold-Falk-Winther framework by analyzing variational crimes (a la Strang) on Hilbert complexes. In particular, this gave a treatment of finite element exterior calculus on manifolds, generalizing techniques from surface finite element methods and recovering earlier a priori estimates for the Laplace-Beltrami operator on 2- and 3-surfaces, due to Dziuk [Lecture Notes in Math., vol. 1357 (1988), 142-155] and later Demlow [SIAM J. Numer. Anal., 47 (2009), 805-827], as special cases. In the present article, we extend the Hilbert complex framework in a second distinct direction: to the study of semilinear mixed problems. We do this, first, by introducing an operator-theoretic reformulation of the linear mixed problem, so that the semilinear problem can be expressed as an abstract Hammerstein equation. This allows us to obtain, for semilinear problems, a priori solution estimates and error estimates that reduce to the Arnold-Falk-Winther results in the linear case. We also consider the impact of variational crimes, extending the results of our previous article to these semilinear problems. As an immediate application, this new framework allows for mixed finite element methods to be applied to semilinear problems on surfaces.Comment: 22 pages; v2: major revision, particularly sharpening of error estimates in Section

Identification of independent association signals and putative functional variants for breast cancer risk through fine-scale mapping of the 12p11 locus.

BACKGROUND: Multiple recent genome-wide association studies (GWAS) have identified a single nucleotide polymorphism (SNP), rs10771399, at 12p11 that is associated with breast cancer risk. METHOD: We performed a fine-scale mapping study of a 700 kb region including 441 genotyped and more than 1300 imputed genetic variants in 48,155 cases and 43,612 controls of European descent, 6269 cases and 6624 controls of East Asian descent and 1116 cases and 932 controls of African descent in the Breast Cancer Association Consortium (BCAC; http://bcac.ccge.medschl.cam.ac.uk/ ), and in 15,252 BRCA1 mutation carriers in the Consortium of Investigators of Modifiers of BRCA1/2 (CIMBA). Stepwise regression analyses were performed to identify independent association signals. Data from the Encyclopedia of DNA Elements project (ENCODE) and the Cancer Genome Atlas (TCGA) were used for functional annotation. RESULTS: Analysis of data from European descendants found evidence for four independent association signals at 12p11, represented by rs7297051 (odds ratio (OR) = 1.09, 95 % confidence interval (CI) = 1.06-1.12; P = 3 × 10(-9)), rs805510 (OR = 1.08, 95 % CI = 1.04-1.12, P = 2 × 10(-5)), and rs1871152 (OR = 1.04, 95 % CI = 1.02-1.06; P = 2 × 10(-4)) identified in the general populations, and rs113824616 (P = 7 × 10(-5)) identified in the meta-analysis of BCAC ER-negative cases and BRCA1 mutation carriers. SNPs rs7297051, rs805510 and rs113824616 were also associated with breast cancer risk at P < 0.05 in East Asians, but none of the associations were statistically significant in African descendants. Multiple candidate functional variants are located in putative enhancer sequences. Chromatin interaction data suggested that PTHLH was the likely target gene of these enhancers. Of the six variants with the strongest evidence of potential functionality, rs11049453 was statistically significantly associated with the expression of PTHLH and its nearby gene CCDC91 at P < 0.05. CONCLUSION: This study identified four independent association signals at 12p11 and revealed potentially functional variants, providing additional insights into the underlying biological mechanism(s) for the association observed between variants at 12p11 and breast cancer risk.UK funding includes Cancer Research UK and NIH.This is the final version of the article. It first appeared from BioMed Central via http://dx.doi.org/10.1186/s13058-016-0718-

An antisense transcript transcribed from Irs2 locus contributes to the pathogenesis of hepatic steatosis in insulin resistance.

During insulin resistance, lipid uptake by the liver is promoted by peroxisome proliferator-activated protein (PPAR) γ upregulation, leading to hepatic steatosis. Insulin, however, does not directly regulate adipogenic gene expression in liver, and the mechanisms for its upregulation in obesity remain unclear. Here, we show that the Irs2 locus, a critical regulator of insulin actions, encodes an antisense transcript, ASIrs2, whose expression increases in obesity or after refeeding in liver, reciprocal to that of Irs2. ASIrs2 regulates hepatic Pparg expression, and its suppression ameliorates steatosis in obese mice. The human ortholog AL162497.1, whose expression is correlated with that of hepatic PPARG and the severity of non-alcoholic steatohepatitis (NASH), shows genomic organization similar to that of ASIrs2. We also identified HARS2 as a potential binding protein for ASIrs2, functioning as a regulator of Pparg. Collectively, our data reveal a functional duality of the Irs2 gene locus, where reciprocal changes of Irs2 and ASIrs2 in obesity cause insulin resistance and steatosis

A microRNA screen reveals that elevated hepatic ectodysplasin A expression contributes to obesity-induced insulin resistance in skeletal muscle

Over 40% of microRNAs (miRNAs) are located in introns of protein-coding genes, and many of these intronic miRNAs are co-regulated with their host genes. In such cases of co-regulation, the products of host genes and their intronic miRNAs can cooperate to coordinately regulate biologically important pathways. Therefore, we screened intronic miRNAs dysregulated in the livers of mouse models of obesity to identify previously uncharacterized protein-coding host genes that may contribute to the pathogenesis of obesity-associated insulin resistance and type 2 diabetes mellitus. Our approach revealed that expression of both the gene encoding ectodysplasin A (Eda), the causal gene in X-linked hypohidrotic ectodermal dysplasia (XLHED), and its intronic miRNA, miR-676, was increased in the livers of obese mice. Moreover, hepatic EDA expression is increased in obese human subjects and reduced upon weight loss, and its hepatic expression correlates with systemic insulin resistance. We also found that reducing miR-676 expression in db/db mice increases the expression of proteins involved in fatty acid oxidation and reduces the expression of inflammatory signaling components in the liver. Further, we found that Eda expression in mouse liver is controlled via PPARγ and RXR-α, increases in circulation under conditions of obesity, and promotes JNK activation and inhibitory serine phosphorylation of IRS1 in skeletal muscle. In accordance with these findings, gain- and loss-of-function approaches reveal that liver-derived EDA regulates systemic glucose metabolism, suggesting that EDA is a hepatokine that can contribute to impaired skeletal muscle insulin sensitivity in obesity

Insulin signalling in tanycytes gates hypothalamic insulin uptake and regulation of AgRP neuron activity.

Insulin acts on neurons and glial cells to regulate systemic glucose metabolism and feeding. However, the mechanisms of insulin access in discrete brain regions are incompletely defined. Here we show that insulin receptors in tanycytes, but not in brain endothelial cells, are required to regulate insulin access to the hypothalamic arcuate nucleus. Mice lacking insulin receptors in tanycytes (IR∆Tan mice) exhibit systemic insulin resistance, while displaying normal food intake and energy expenditure. Tanycytic insulin receptors are also necessary for the orexigenic effects of ghrelin, but not for the anorexic effects of leptin. IR∆Tan mice exhibit increased agouti-related peptide (AgRP) neuronal activity, while displaying blunted AgRP neuronal adaptations to feeding-related stimuli. Lastly, a highly palatable food decreases tanycytic and arcuate nucleus insulin signalling to levels comparable to those seen in IR∆Tan mice. These changes are rooted in modifications of cellular stress responses and of mitochondrial protein quality control in tanycytes. Conclusively, we reveal a critical role of tanycyte insulin receptors in gating feeding-state-dependent regulation of AgRP neurons and systemic insulin sensitivity, and show that insulin resistance in tanycytes contributes to the pleiotropic manifestations of obesity-associated insulin resistance

Mitochondrial metabolism coordinates stage-specific repair processes in macrophages during wound healing.

Wound healing is a coordinated process that initially relies on pro-inflammatory macrophages, followed by a pro-resolution function of these cells. Changes in cellular metabolism likely dictate these distinct activities, but the nature of these changes has been unclear. Here, we profiled early- versus late-stage skin wound macrophages in mice at both the transcriptional and functional levels. We found that glycolytic metabolism in the early phase is not sufficient to ensure productive repair. Instead, by combining conditional disruption of the electron transport chain with deletion of tgcqmitochondrial aspartyl-tRNA synthetase, followed by single-cell sequencing analysis, we found that a subpopulation of early-stage wound macrophages are marked by mitochondrial ROS (mtROS) production and HIF1α stabilization, which ultimately drives a pro-angiogenic program essential for timely healing. In contrast, late-phase, pro-resolving wound macrophages are marked by IL-4Rα-mediated mitochondrial respiration and mitohormesis. Collectively, we identify changes in mitochondrial metabolism as a critical control mechanism for macrophage effector functions during wound healing

A guide to analysis of mouse energy metabolism.

We present a consolidated view of the complexity and challenges of designing studies for measurement of energy metabolism in mouse models, including a practical guide to the assessment of energy expenditure, energy intake and body composition and statistical analysis thereof. We hope this guide will facilitate comparisons across studies and minimize spurious interpretations of data. We recommend that division of energy expenditure data by either body weight or lean body weight and that presentation of group effects as histograms should be replaced by plotting individual data and analyzing both group and body-composition effects using analysis of covariance (ANCOVA)