Degenerate stability of the Caffarelli–Kohn–Nirenberg inequality along the Felli–Schneider curve

We show that the Caffarelli–Kohn–Nirenberg (CKN) inequality holds with a remainder term that is quartic in the distance to the set of optimizers for the full parameter range of the Felli–Schneider (FS) curve. The fourth power is best possible. This is due to the presence of non-trivial zero modes of the Hessian of the deficit functional along the FS-curve. Following an iterated Bianchi–Egnell strategy, the heart of our proof is verifying a ‘secondary non-degeneracy condition’. Our result completes the stability analysis for the CKN-inequality to leading order started by Wei and Wu. Moreover, it is the first instance of degenerate stability for non-constant optimizers and for a non-compact domain

Degenerate Stability of the Caffarelli-Kohn-Nirenberg Inequality along the Felli-Schneider Curve

We show that the Caffarelli-Kohn-Nirenberg (CKN) inequality holds with a remainder term that is quartic in the distance to the set of optimizers for the full parameter range of the Felli-Schneider (FS) curve. The fourth power is best possible. This is due to the presence of non-trivial zero modes of the Hessian of the deficit functional along the FS-curve. Following an iterated Bianchi-Egnell strategy, the heart of our proof is verifying a `secondary non-degeneracy condition'. Our result completes the stability analysis for the CKN-inequality to leading order started by Wei and Wu. Moreover, it is the first instance of degenerate stability for non-constant optimizers and for a non-compact domain

Mechanisms of Hsp90 regulation

Heat shock protein 90 (Hsp90) is a molecular chaperone that is involved in the activation of disparate client proteins. This implicates Hsp90 in diverse biological processes that require a variety of co-ordinated regulatory mechanisms to control its activity. Perhaps the most important regulator is heat shock factor 1 (HSF1), which is primarily responsible for upregulating Hsp90 by binding heat shock elements (HSEs) within Hsp90 promoters. HSF1 is itself subject to a variety of regulatory processes and can directly respond to stress. HSF1 also interacts with a variety of transcriptional factors that help integrate biological signals, which in turn regulate Hsp90 appropriately. Because of the diverse clientele of Hsp90 a whole variety of co-chaperones also regulate its activity and some are directly responsible for delivery of client protein. Consequently, co-chaperones themselves, like Hsp90, are also subject to regulatory mechanisms such as post translational modification. This review, looks at the many different levels by which Hsp90 activity is ultimately regulated

Dopamine signaling in wake-promoting clock neurons is not required for the normal regulation of sleep in drosophila

Dopamine is a wake-promoting neuromodulator in mammals and fruit flies. In Drosophila melanogaster, the network of clock neurons that drives sleep/activity cycles comprises both wake-promoting and sleep-promoting cell types. The large ventrolateral neurons (l-LNvs) and small ventrolateral neurons (s-LNvs) have been identified as wake-promoting neurons within the clock neuron network. The l-LNvs are innervated by dopaminergic neurons, and earlier work proposed that dopamine signaling raises cAMP levels in the l-LNvs and thus induces excitatory electrical activity (action potential firing), which results in wakefulness and inhibits sleep. Here, we test this hypothesis by combining cAMP imaging and patch-clamp recordings in isolated brains. We find that dopamine application indeed increases cAMP levels and depolarizes the l-LNvs, but, surprisingly, it does not result in increased firing rates. Downregulation of the excitatory D1-like dopamine receptor (Dop1R1) in the l-LNvs and s-LNvs, but not of Dop1R2, abolished the depolarization of l-LNvs in response to dopamine. This indicates that dopamine signals via Dop1R1 to the l-LNvs. Downregulation of Dop1R1 or Dop1R2 in the l-LNvs and s-LNvs does not affect sleep in males. Unexpectedly, we find a moderate decrease of daytime sleep with downregulation of Dop1R1 and of nighttime sleep with downregulation of Dop1R2. Since the l-LNvs do not use Dop1R2 receptors and the s-LNvs also respond to dopamine, we conclude that the s-LNvs are responsible for the observed decrease in nighttime sleep. In summary, dopamine signaling in the wake-promoting LNvs is not required for daytime arousal, but likely promotes nighttime sleep via the s-LNvs.Fil: Fernández, Florencia. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; ArgentinaFil: Hermann Luibl, Christiane. University Of Würzburg; AlemaniaFil: Peteranderl, Alina. University Of Wuerzburg; AlemaniaFil: Reinhard, Nils. University Of Wuerzburg; AlemaniaFil: Senthilan, Pingkalai R.. University Of Wuerzburg; AlemaniaFil: Hieke, Marie. University Of Wuerzburg; AlemaniaFil: Selcho, Mareike. University Of Wuerzburg; AlemaniaFil: Yoshii, Taishi. Okayama University; JapónFil: Shafer, Orie T.. City University of New York; Estados UnidosFil: Muraro, Nara Ines. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Parque Centenario. Instituto de Investigación en Biomedicina de Buenos Aires - Instituto Partner de la Sociedad Max Planck; ArgentinaFil: Helfrich Förster, Charlotte. University Of Wuerzburg; Alemani

TNF Superfamily Member 14 Drives Post-Influenza Depletion of Alveolar Macrophages Enabling Secondary Pneumococcal Pneumonia

[EN] Secondary bacterial infection, often caused by Streptococcus pneumoniae (Spn), is one of the most frequent and severe complications of influenza A virus (IAV)-induced pneumonia. Phenotyping of the pulmonary immune cell landscape after IAV infection revealed a substantial depletion of the tissue-resident alveolar macrophage (TR-AM) population at day 7, which was associated with increased susceptibility to Spn outgrowth. To elucidate the molecular mechanisms underlying TR-AM depletion, and to define putative targets for treatment, we combined single-cell transcriptomics and cell-specific PCR profiling in an unbiased manner, using in vivo models of IAV infection and IAV/Spn co-infection. The TNF superfamily 14 (TNFSF14) ligand-receptor axis was revealed as the driving force behind post-influenza TR-AM death during the early infection phase, enabling the transition to pneumococcal pneumonia, while intrapulmonary transfer of genetically modified TR-AMs and antibody-mediated neutralization of specific pathway components alleviated disease severity. With a mainly neutrophilic expression and a high abundance in the bronchoalveolar fluid (BALF) of patients with severe virus-induced ARDS, TNFSF14 emerged as a key determinant of virus-driven lung injury. Targeting the TNFSF14-mediated intercellular communication network in the virus-infected lung can, therefore, improve host defense, minimizing the risk of subsequent bacterial pneumonia, and ameliorating disease outcomeSIThis work was supported by the German Research Foundation (Deutsche Forschungsgemeinschaft, DFG) under following projects: KFO309 project P2/P9, project number 284237345; SFB-TR84 project number 114933180; SFB1021 project number 197785619; the Cardiopulmonary Institute (CPI; DFG EXC 2026 project number 390649896), and by the State of Hesse: LOEWE grant ´diffusible signals` project number LOEWE/2/13/519/03/06.001(0002)/74, LOEWE professorship, funding line 4a, project ID III L7–519/05.00.002. We would like to thank Martin Witzenrath and Birgit Gutbier for providing us with the serotype 3 Spn bacterial strain. We would like to thank Maria Gross, Stefanie Jarmer, Larissa Hamann, Florian Lück, Julia Stark, and Josephine Guth, for excellent technical support. Experimental layout schematics and summary figure were created with BioRender.co