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We settle the case of equality for the relative isoperimetric inequality outside any arbitrary convex set with not empty interior.

A quantitative sharp form of the classical isoperimetric inequality is proved, thus giving a positive answer to a conjecture by Hall.

Prune belly syndrome (PBS), also known as Eagle-Barret syndrome, is a rare, multi-system congenital myopathy primarily affecting males. Phenotypically, PBS cases manifest three cardinal pathological features: urinary tract dilation with poorly contractile smooth muscle, wrinkled flaccid ventral abdominal wall with skeletal muscle deficiency, and intra-abdominal undescended testes. Genetically, PBS is poorly understood. After performing whole exome sequencing in PBS patients, we identify one compound heterozygous variant in the PIEZO1 gene. PIEZO1 is a cation-selective channel activated by various mechanical forces and widely expressed throughout the lower urinary tract. Here we conduct an extensive functional analysis of the PIEZO1 PBS variants that reveal loss-of-function characteristics in the pressure-induced normalized open probability (NPo) of the channel, while no change is observed in single-channel currents. Furthermore, Yoda1, a PIEZO1 activator, can rescue the NPo defect of the PBS mutant channels. Thus, PIEZO1 mutations may be causal for PBS and the in vitro cellular pathophysiological phenotype could be rescued by the small molecule, Yoda1. Activation of PIEZO1 might provide a promising means of treating PBS and other related bladder dysfunctional states. PIEZO1 is a mechanosensitive ion channel. Here, authors identify PIEZO1 human mutations in Prune Belly Syndrome. At a single molecule level these mutations exhibit loss-of-function characteristics.

Advances in bladder cancer (BCa) treatment have been hampered by the lack of predictive biomarkers and targeted therapies. Here, we demonstrate that loss of the tumor suppressor NUMB promotes aggressive bladder tumorigenesis and worsens disease outcomes. Retrospective cohort studies show that NUMB-loss correlates with poor prognosis in post-cystectomy muscle-invasive BCa patients and increased risk of muscle invasion progression in non-muscle invasive BCa patients. In mouse models, targeted Numb ablation induces spontaneous tumorigenesis and sensitizes the urothelium to carcinogenic insults, accelerating tumor onset and progression. Integrative transcriptomic and functional analyses in mouse and human BCa models reveal that upregulation of YAP transcriptional activity via a RHOA/ROCK-dependent pathway is a hallmark of NUMB-deficient BCa. Pharmacological or genetic inhibition of this molecular pathway selectively inhibits proliferation and invasion of NUMB-deficient BCa cells in 3D-Matrigel organoids. Thus, NUMB-loss could serve as a biomarker for identifying high-risk patients who may benefit from targeted anti-RHOA/ROCK/YAP therapies. The transition from non-muscle-invasive bladder cancer (NMIBC) to muscle-invasive bladder cancer (MIBC) is associated with poorer patient prognosis. Here, the authors investigate NUMB loss as a driver of the NMIBC-to-MIBC transition and identify a RHOA/ROCK/YAP signaling pathway as a therapeutic vulnerability.

HCV replication disrupts normal endoplasmic reticulum (ER) function and activates a signaling network called the unfolded protein response (UPR). UPR is directed by three ER transmembrane proteins including ATF6, IRE1 and PERK. HCV increases TGF-β1 and oxidative stress, which play important roles in liver fibrogenesis. HCV has been shown to induce TGF-β1 through the generation of reactive oxygen species (ROS) and p38 MAPK, JNK, ERK1/2 and NFκB-dependent pathways. However, the relationship between HCV-induced ER stress and UPR activation with TGF-β1 production has not been fully characterized. In this study, we found that ROS and JNK inhibitors block HCV up-regulation of ER stress and UPR activation. ROS, JNK and IRE1 inhibitors blocked HCV-activated NFκB and TGF-β1 expression. ROS, ER stress, NFκB and TGF-β1 signaling were blocked by JNK specific siRNA. Knockdown IRE1 inhibited JFH1-activated NFκB and TGF-β1 activity. Knockdown of JNK and IRE1 blunted JFH1 HCV up-regulation of NFκB and TGF-β1 activation. We conclude that HCV activates NFκB and TGF-β1 through ROS production and induction of JNK and the IRE1 pathway. HCV infection induces ER stress and the UPR in a JNK-dependent manner. ER stress and UPR activation partially contribute to HCV-induced NF-κB activation and enhancement of TGF-β1.

We consider a variational model introduced in the physical literature to describe the epitaxial growth of an elastic film over a thick flat substrate when a lattice mismatch between the two materials is present. We study quantitative and qualitative properties of equilibrium configurations, that is, of local and global minimizers of the free-energy functional. More precisely, we determine analytically the critical threshold for the local minimality of the flat configuration and we also prove several results concerning its global minimality. The non-occurrence of singularities in non-flat global minimizers is also addressed. One of the main results of the paper is a new sufficient condition for local minimality, which provides the first extension of the classical criteria based on the positivity of the second variation to the context of functionals with bulk and surface energies.

Cianchi et al prove a sharp quantitative version of the isoperimetric inequality in the space R^sup n^ endowed with the Gaussian measure. The isoperimetric inequality in Gauss space asserts that among all subsets of R^sup n^ with prescribed Gaussian measure, half-spaces have the least Gaussian perimeter. They also provide a geometric proof of the Gaussian isoperimetric theorem.

A 59-year-old male with follicular lymphoma treated by anti-CD20-mediated B-cell depletion and ablative chemotherapy was hospitalized with a COVID-19 infection. Although the patient did not develop specific humoral immunity, he had a mild clinical course overall. The failure of all therapeutic options allowed infection to persist nearly 300 days with active accumulation of SARS-CoV-2 virus mutations. As a rescue therapy, an infusion of REGEN-COV (10933 and 10987) anti-spike monoclonal antibodies was performed 270 days from initial diagnosis. Due to partial clearance after the first dose (2.4 g), a consolidation dose (8 g) was infused six weeks later. Complete virus clearance could then be observed over the following month, after he was vaccinated with the Pfizer-BioNTech anti-COVID-19 vaccination. The successful management of this patient required prolonged enhanced quarantine, monitoring of virus mutations, pioneering clinical decisions based upon close consultation, and the coordination of multidisciplinary experts in virology, immunology, pharmacology, input from REGN, the FDA, the IRB, the health care team, the patient, and the patient’s family. Current decisions to take revolve around patient’s follicular lymphoma management, and monitoring for virus clearance persistence beyond disappearance of REGEN-COV monoclonal antibodies after anti-SARS-CoV-2 vaccination. Overall, specific guidelines for similar cases should be established.

Background. We and others have shown that primary hepatitis C (HCV) infection in men infected with human immunodeficiency virus (HIV) causes early-onset liver fibrosis; however, little is known about the long-term natural history of the liver disease in these HIV-infected men. Methods. We followed a cohort of HIV-infected men with primary HCV infection in New York City. Results. Four men who were not cured after their primary HCV infection developed decompensated cirrhosis within 17 months to 6 years after primary HCV infection. Three died within 8 years of primary HCV infection, and 1 survived after liver transplant done 2 years after primary HCV infection. Three of the 4 men had AIDS at the time of primary HCV infection, and the most rapid progression occurred in the 2 men with the lowest CD4 counts at the time of HCV infection. Liver histopathology was most consistent with HCV-induced damage even though some had exposures to other potential hepatotoxins. Conclusions. Primary HCV infection resulted in decompensated cirrhosis and death within 2–8 years in 4 HIV-infected men. The rapid onset of fibrosis due to primary HCV infection in HIV-infected men cannot therefore be considered benign. The rate of continued progression to liver failure may be proportional to the degree of underlying immunocompromise caused by HIV infection. More research is needed to better define the mechanisms behind accelerated liver damage.

The direct acting antiviral remdesivir (RDV) has shown promising results in randomized clinical trials. This study is a unique report of real clinical practice RDV administration for COVID-19 from alpha through delta variant circulation in New Orleans, Louisiana (NOLA). Patients in NOLA have among US worst pre-COVID health outcomes, and the region was an early epicenter for severe COVID. Data were directly extracted from electronic medical records through REACHnet. Of 9,106 adults with COVID, 1,928 were admitted to inpatient care within 7 days of diagnosis. The propensity score is based upon 22 selected covariates, related to both RDV assignment and outcome of interest. RDV and non-RDV patients were matched 1:1 with replacement, by location and calendar period of admission. Primary and secondary endpoints were, death from any cause and inpatient discharge, within 28 and 14 days after inpatient admission. Of 448 patients treated with RDV, 419 (94%) were successfully matched to a non-RDV patient. 145 (35%) patients received RDV for < 5 days, 235 (56%) for 5 days, and 39 (9%) for > 5 days. 96% of those on RDV received it within 2 days of admission. RDV was more frequently prescribed in patients with pneumonia (standardized difference: 0.75), respiratory failure, hypoxemia, or dependence on supplemental oxygen (0.69), and obesity (0.35) within 5 days prior to RDV initiation or corresponding day in non-RDV patients (index day). RDV patients were numerically more likely to be on steroids within 5 days prior to index day (86 vs. 82%) and within 7 days after inpatient admission (96 vs. 87%). RDV was significantly associated with lower risk of death within 14 days after admission (hazard ratio [HR]: 0.37, 95% CI: 0.19 to 0.69, = 0.002) but not within 28 days (HR: 0.62, 95% CI: 0.36 to 1.07, = 0.08). Discharge within 14 days of admission was significantly more likely for RDV patients ( < 0.001) and numerically more likely within 28 days after admission ( = 0.06). Overall, our findings support recommendation of RDV administration for COVID-19 in a highly comorbid, highly impoverished population representative of both Black and White subjects in the US Gulf South.