Non-degeneracy of double-tower solutions for nonlinear Schr\"odinger equation and applications

This paper is concerned with the following nonlinear Schr\"odinger equation \begin{equation} \label{eq} - \Delta u + V(|y|)u=u^{p},\quad u>0 \ \ \mbox{in} \ \mathbb {R}^N, \ \ \ u \in H^1(\mathbb {R}^N), \end{equation} where $V(|y|)$ is a positive function, $1<p <\frac{N+2}{N-2}$. Based on the local Pohozaev identities and blow-up analysis, we first prove a non-degeneracy result for double-tower solutions constructed in [18] in a suitable symmetric space. As an application, we obtain the existence of new type solutions for (0.1).Comment: 34 pages, 0 figure

Double-tower Solutions for Higher Order Prescribed Curvature Problem

We consider the following higher order prescribed curvature problem on ${\mathbb{S}}^N :$ \begin{equation*} D^m \tilde u=\widetilde{K}(y) \tilde u^{m^{*}-1} \quad \mbox{on} \ {\mathbb {S}}^N, \qquad \tilde u >0 \quad \mbox{in} \ {\mathbb {S}}^N. \end{equation*} where $\widetilde{K}(y)>0$ is a radial function, $m^{*}=\frac{2N}{N-2m}$ and $D^m$ is $2m$ order differential operator given by \begin{equation*} D^m=\prod_{i=1}^m\left(-\Delta_g+\frac{1}{4}(N-2i)(N+2i-2)\right), \end{equation*} where $g=g_{{\mathbb{S}}^N}$is the Riemannian metric. We prove the existence of infinitely many double-tower type solutions, which are invariant under some non-trivial sub-groups of $O(3),$ and their energy can be made arbitrarily large.Comment: 34 pages, 0 figures. arXiv admin note: substantial text overlap with arXiv:2205.14482 by other author

Biocompatible FeOOH-Carbon quantum dots nanocomposites for gaseousNOx removal under visible light: Improved charge separation and Highselectivity

Development of biocompatible photocatalysts with improved charge separation and high selectivity is essential for effective removal of air pollutants. Iron-containing catalysts have attracted extensive attention due to their low-toxicity and high natural abundance. Here, carbon quantum dots (CQDs) modified FeOOH nanocomposites fabricated using a facile hydrothermal route showed enhanced NO removal efficiency (22%) compared to pure FeOOH. Moreover, generation of toxic NO2&nbsp;intermediates was significantly inhibited using the nanocomposites, demonstrating high selectivity for final nitrate formation. Photo-electrochemical results showed that both charge separation and transfer efficiency were significantly improved by CQDs addition, and the lifetime of photo-generated carriers was increased eventually. Density functional theory calculations further elucidated that the suppressed recombination of photo-induced electron-hole pairs was due to enhanced electron migration from the FeOOH to CQDs. A NO degradation mechanism was proposed based on detection of the reactive oxygen species using electron paramagnetic spectroscopy. In addition, the nanocomposite showed good biocompatibility and low cytotoxity, ensuring minimal environmental impact for potential application in large-scale.</span

High-level expression and purification of soluble recombinant FGF21 protein by SUMO fusion in Escherichia coli

<p>Abstract</p> <p>Background</p> <p>Fibroblast growth factor 21 (FGF21) is a promising drug candidate to combat metabolic diseases. However, high-level expression and purification of recombinant FGF21 (rFGF21) in <it>Escherichia coli (E. coli) </it>is difficult because rFGF21 forms inclusion bodies in the bacteria making it difficult to purify and obtain high concentrations of bioactive rFGF21. To overcome this problem, we fused the <it>FGF21 </it>with <it>SUMO </it>(Small ubiquitin-related modifier) by polymerase chain reaction (PCR), and expressed the fused gene in <it>E. coli </it>BL21(DE3).</p> <p>Results</p> <p>By inducing with IPTG, SUMO-FGF21 was expressed at a high level. Its concentration reached 30% of total protein, and exceeded 95% of all soluble proteins. The fused protein was purified by DEAE sepharose FF and Ni-NTA affinity chromatography. Once cleaved by the SUMO protease, the purity of rFGF21 by high performance liquid chromatography (HPLC) was shown to be higher than 96% with low endotoxin level (<1.0 EU/ml). The results of <it>in vivo </it>animal experiments showed that rFGF21 produced by using this method, could decrease the concentration of plasma glucose in diabetic rats by streptozotocin (STZ) injection.</p> <p>Conclusions</p> <p>This study demonstrated that SUMO, when fused with FGF21, was able to promote its soluble expression of the latter in <it>E. coli</it>, making it more convenient to purify rFGF21 than previously. This may be a better method to produce rFGF21 for pharmaceutical research and development.</p

A Single-Cell Atlas of Bovine Skeletal Muscle Reveals Mechanisms Regulating Intramuscular Adipogenesis and Fibrogenesis

Background Intramuscular fat (IMF) and intramuscular connective tissue (IMC) are often seen in human myopathies and are central to beef quality. The mechanisms regulating their accumulation remain poorly understood. Here, we explored the possibility of using beef cattle as a novel model for mechanistic studies of intramuscular adipogenesis and fibrogenesis. Methods Skeletal muscle single-cell RNAseq was performed on three cattle breeds, including Wagyu (high IMF), Brahman (abundant IMC but scarce IMF), and Wagyu/Brahman cross. Sophisticated bioinformatics analyses, including clustering analysis, gene set enrichment analyses, gene regulatory network construction, RNA velocity, pseudotime analysis, and cell-cell communication analysis, were performed to elucidate heterogeneities and differentiation processes of individual cell types and differences between cattle breeds. Experiments were conducted to validate the function and specificity of identified key regulatory and marker genes. Integrated analysis with multiple published human and non-human primate datasets was performed to identify common mechanisms. Results A total of 32 708 cells and 21 clusters were identified, including fibro/adipogenic progenitor (FAP) and other resident and infiltrating cell types. We identified an endomysial adipogenic FAP subpopulation enriched for COL4A1 and CFD (log2FC = 3.19 and 1.92, respectively; P \u3c 0.0001) and a perimysial fibrogenic FAP subpopulation enriched for COL1A1 and POSTN (log2FC = 1.83 and 0.87, respectively; P \u3c 0.0001), both of which were likely derived from an unspecified subpopulation. Further analysis revealed more progressed adipogenic programming of Wagyu FAPs and more advanced fibrogenic programming of Brahman FAPs. Mechanistically, NAB2 drives CFD expression, which in turn promotes adipogenesis. CFD expression in FAPs of young cattle before the onset of intramuscular adipogenesis was predictive of IMF contents in adulthood (R2 = 0.885, P \u3c 0.01). Similar adipogenic and fibrogenic FAPs were identified in humans and monkeys. In aged humans with metabolic syndrome and progressed Duchenne muscular dystrophy (DMD) patients, increased CFD expression was observed (P \u3c 0.05 and P \u3c 0.0001, respectively), which was positively correlated with adipogenic marker expression, including ADIPOQ (R2 = 0.303, P \u3c 0.01; and R2 = 0.348, P \u3c 0.01, respectively). The specificity of Postn/POSTN as a fibrogenic FAP marker was validated using a lineage-tracing mouse line. POSTN expression was elevated in Brahman FAPs (P \u3c 0.0001) and DMD patients (P \u3c 0.01) but not in aged humans. Strong interactions between vascular cells and FAPs were also identified. Conclusions Our study demonstrates the feasibility of beef cattle as a model for studying IMF and IMC. We illustrate the FAP programming during intramuscular adipogenesis and fibrogenesis and reveal the reliability of CFD as a predictor and biomarker of IMF accumulation in cattle and humans

T\u3cem\u3ecf\u3c/em\u3e21 Marks Visceral Adipose Mesenchymal Progenitors and Functions as a Rate-Limiting Factor During Visceral Adipose Tissue Development

Distinct locations of different white adipose depots suggest anatomy-specific developmental regulation, a relatively understudied concept. Here, we report a population of Tcf21 lineage cells (Tcf21 LCs) present exclusively in visceral adipose tissue (VAT) that dynamically contributes to VAT development and expansion. During development, the Tcf21 lineage gives rise to adipocytes. In adult mice, Tcf21 LCs transform into a fibrotic or quiescent state. Multiomics analyses show consistent gene expression and chromatin accessibility changes in Tcf21 LC, based on which we constructed a gene-regulatory network governing Tcf21 LC activities. Furthermore, single-cell RNA sequencing (scRNA-seq) identifies the heterogeneity of Tcf21 LCs. Loss of Tcf21 promotes the adipogenesis and developmental progress of Tcf21 LCs, leading to improved metabolic health in the context of diet-induced obesity. Mechanistic studies show that the inhibitory effect of Tcf21 on adipogenesis is at least partially mediated via Dlk1 expression accentuation

Loss of \u3ci\u3eActa2\u3c/i\u3e in Cardiac Fibroblasts Does Not Prevent the Myofibroblast Differentiation or Affect the Cardiac Repair After Myocardial Infarction

In response to myocardial infarction (MI), quiescent cardiac fibroblasts differentiate into myofibroblasts mediating tissue repair. One of the most widely accepted markers of myofibroblast differentiation is the expression of Acta2 which encodes smooth muscle alpha-actin (SMαA) that is assembled into stress fibers. However, the requirement of Acta2/SMαA in the myofibroblast differentiation of cardiac fibroblasts and its role in post-MI cardiac repair remained unknown. To answer these questions, we generated a tamoxifen-inducible cardiac fibroblast-specific Acta2 knockout mouse line. Surprisingly, mice that lacked Acta2 in cardiac fibroblasts had a normal post-MI survival rate. Moreover, Acta2 deletion did not affect the function or histology of infarcted hearts. No difference was detected in the proliferation, migration, or contractility between WT and Acta2-null cardiac myofibroblasts. Acta2-null cardiac myofibroblasts had a normal total filamentous actin level and total actin level. Acta2 deletion caused a significant compensatory increase in the transcription level of non-Acta2 actin isoforms, especially Actg2 and Acta1. Moreover, in myofibroblasts, the transcription levels of cytoplasmic actin isoforms were significantly higher than those of muscle actin isoforms. In addition, we found that myocardin-related transcription factor-A is critical for myofibroblast differentiation but is not required for the compensatory effects of non-Acta2 isoforms. In conclusion, the Acta2 deletion does not prevent the myofibroblast differentiation of cardiac fibroblasts or affect the post-MI cardiac repair, and the increased expression and stress fiber formation of non-SMαA actin isoforms and the functional redundancy between actin isoforms are able to compensate for the loss of Acta2 in cardiac myofibroblasts