Second order optimality conditions and their role in PDE control

If f : Rn R is twice continuously differentiable, f’(u) = 0 and f’’(u) is positive definite, then u is a local minimizer of f. This paper surveys the extension of this well known second order suffcient optimality condition to the case f : U R, where U is an infinite-dimensional linear normed space. The reader will be guided from the case of finite-dimensions via a brief discussion of the calculus of variations and the optimal control of ordinary differential equations to the control of nonlinear partial differential equations, where U is a function space. In particular, the following questions will be addressed: Is the extension to infinite dimensions straightforward or will unexpected difficulties occur? How second order sufficient optimality conditions must be modified, if simple inequality constraints are imposed on u? Why do we need second order conditions and how can they be applied? If they are important, are we able to check if they are fulfilled order sufficient optimality condition to the case f : U R, where U is an infinite-dimensional linear normed space. The reader will be guided from the case of finite-dimensions via a brief discussion of the calculus of variations and the optimal control of ordinary differential equations to the control of nonlinear partial differential equations, where U is a function space. In particular, the following questions will be addressed: Is the extension to infinite dimensions straightforward or will unexpected difficulties occur? How second order sufficient optimality conditions must be modified, if simple inequality constraints are imposed on u? Why do we need second order conditions and how can they be applied? If they are important, are we able to check if they are fulfilled? It turns out that infinite dimensions cause new difficulties that do not occur in finite dimensions. We will be faced with the surprising fact that the space, where f’’(u) exists can be useless to ensure positive definiteness of the quadratic form v f’’(u)v2. In this context, the famous two-norm discrepancy, its consequences, and techniques for overcoming this difficulty are explained. To keep the presentation simple, the theory is developed for problems in function spaces with simple box constraints of the form a = u = ß. The theory of second order conditions in the control of partial differential equations is presented exemplarily for the nonlinear heat equation. Different types of critical cones are introduced, where the positivity of f’’(u) must be required. Their form depends on whether a so-called Tikhonov regularization term is part of the functional f or not. In this context, the paper contains also new results that lead to quadratic growth conditions in the strong sense. As a first application of second-order sufficient conditions, the stability of optimal solutions with respect to perturbations of the data of the control problem is discussed. Second, their use in analyzing the discretization of control problems by finite elements is studied. A survey on further related topics, open questions, and relevant literature concludes the paper.The first author was partially supported by the Spanish Ministerio de Economía y Competitividad under project MTM2011-22711, the second author by DFG in the framework of the Collaborative Research Center SFB 910, project B6

Water-induced modulation of Helicobacter pylori virulence properties

While the influence of water in Helicobacter pylori culturability and membrane integrity has been extensively studied, there are little data concerning the effect of this environment on virulence properties. Therefore, we studied the culturability of water-exposed H. pylori and determined whether there was any relation with the bacterium’s ability to adhere, produce functional components of pathogenicity and induce inflammation and alterations in apoptosis in an experimental model of human gastric epithelial cells. H. pylori partially retained the ability to adhere to epithelial cells even after complete loss of culturability. However, the microorganism is no longer effective in eliciting in vitro host cell inflammation and apoptosis, possibly due to the non-functionality of the cag type IV secretion system. These H. pylori-induced host cell responses, which are lost along with culturability, are known to increase epithelial cell turnover and, consequently, could have a deleterious effect on the initial H. pylori colonisation process. The fact that adhesion is maintained by H. pylori to the detriment of other factors involved in later infection stages appears to point to a modulation of the physiology of the pathogen after water exposure and might provide the microorganism with the necessary means to, at least transiently, colonise the human stomach.FCT (SFRH/BD/24579/2005) (to NMG

Aberrant phase separation and nucleolar dysfunction in rare genetic diseases

Thousands of genetic variants in protein-coding genes have been linked to disease. However, the functional impact of most variants is unknown as they occur within intrinsically disordered protein regions that have poorly defined functions1-3. Intrinsically disordered regions can mediate phase separation and the formation of biomolecular condensates, such as the nucleolus4,5. This suggests that mutations in disordered proteins may alter condensate properties and function6-8. Here we show that a subset of disease-associated variants in disordered regions alter phase separation, cause mispartitioning into the nucleolus and disrupt nucleolar function. We discover de novo frameshift variants in HMGB1 that cause brachyphalangy, polydactyly and tibial aplasia syndrome, a rare complex malformation syndrome. The frameshifts replace the intrinsically disordered acidic tail of HMGB1 with an arginine-rich basic tail. The mutant tail alters HMGB1 phase separation, enhances its partitioning into the nucleolus and causes nucleolar dysfunction. We built a catalogue of more than 200,000 variants in disordered carboxy-terminal tails and identified more than 600 frameshifts that create arginine-rich basic tails in transcription factors and other proteins. For 12 out of the 13 disease-associated variants tested, the mutation enhanced partitioning into the nucleolus, and several variants altered rRNA biogenesis. These data identify the cause of a rare complex syndrome and suggest that a large number of genetic variants may dysregulate nucleoli and other biomolecular condensates in humans.© 2023. The Author(s)

Vaccine responses in newborns.

Immunisation of the newborn represents a key global strategy in overcoming morbidity and mortality due to infection in early life. Potential limitations, however, include poor immunogenicity, safety concerns and the development of tolerogenicity or hypo-responsiveness to either the same antigen and/or concomitant antigens administered at birth or in the subsequent months. Furthermore, the neonatal immunological milieu is polarised towards Th2-type immunity with dampening of Th1-type responses and impaired humoral immunity, resulting in qualitatively and quantitatively poorer antibody responses compared to older infants. Innate immunity also shows functional deficiency in antigen-presenting cells: the expression and signalling of Toll-like receptors undergo maturational changes associated with distinct functional responses. Nevertheless, the effectiveness of BCG, hepatitis B and oral polio vaccines, the only immunisations currently in use in the neonatal period, is proof of concept that vaccines can be successfully administered to the newborn via different routes of delivery to induce a range of protective mechanisms for three different diseases. In this review paper, we discuss the rationale for and challenges to neonatal immunisation, summarising progress made in the field, including lessons learnt from newborn vaccines in the pipeline. Furthermore, we explore important maternal, infant and environmental co-factors that may impede the success of current and future neonatal immunisation strategies. A variety of approaches have been proposed to overcome the inherent regulatory constraints of the newborn innate and adaptive immune system, including alternative routes of delivery, novel vaccine configurations, improved innate receptor agonists and optimised antigen-adjuvant combinations. Crucially, a dual strategy may be employed whereby immunisation at birth is used to prime the immune system in order to improve immunogenicity to subsequent homologous or heterologous boosters in later infancy. Similarly, potent non-specific immunomodulatory effects may be elicited when challenged with unrelated antigens, with the potential to reduce the overall risk of infection and allergic disease in early life

Architecture of a nascent viral fusion pore

Enveloped viruses use specialized protein machinery to fuse the viral membrane with that of the host cell during cell invasion. In influenza virus, hundreds of copies of the haemagglutinin (HA) fusion glycoprotein project from the virus surface. Despite intensive study of HA and its fusion activity, the protein's modus operandi in manipulating viral and target membranes to catalyse their fusion is poorly understood. Here, the three-dimensional architecture of influenza virus–liposome complexes at pH 5.5 was investigated by electron cryo-tomography. Tomographic reconstructions show that early stages of membrane remodeling take place in a target membrane-centric manner, progressing from punctate dimples, to the formation of a pinched liposomal funnel that may impinge on the apparently unperturbed viral envelope. The results suggest that the M1 matrix layer serves as an endoskeleton for the virus and a foundation for HA during membrane fusion. Fluorescence spectroscopy monitoring fusion between liposomes and virions shows that leakage of liposome contents takes place more rapidly than lipid mixing at pH 5.5. The relation of ‘leaky' fusion to the observed prefusion structures is discussed

Clinical, neuroimaging, and molecular spectrum of TECPR2‐associated hereditary sensory and autonomic neuropathy with intellectual disability

Bi‐allelic TECPR2 variants have been associated with a complex syndrome with features of both a neurodevelopmental and neurodegenerative disorder. Here, we provide a comprehensive clinical description and variant interpretation framework for this genetic locus. Through international collaboration, we identified 17 individuals from 15 families with bi‐allelic TECPR2‐variants. We systemically reviewed clinical and molecular data from this cohort and 11 cases previously reported. Phenotypes were standardized using Human Phenotype Ontology terms. A cross‐sectional analysis revealed global developmental delay/intellectual disability, muscular hypotonia, ataxia, hyporeflexia, respiratory infections, and central/nocturnal hypopnea as core manifestations. A review of brain magnetic resonance imaging scans demonstrated a thin corpus callosum in 52%. We evaluated 17 distinct variants. Missense variants in TECPR2 are predominantly located in the N‐ and C‐terminal regions containing β‐propeller repeats. Despite constituting nearly half of disease‐associated TECPR2 variants, classifying missense variants as (likely) pathogenic according to ACMG criteria remains challenging. We estimate a pathogenic variant carrier frequency of 1/1221 in the general and 1/155 in the Jewish Ashkenazi populations. Based on clinical, neuroimaging, and genetic data, we provide recommendations for variant reporting, clinical assessment, and surveillance/treatment of individuals with TECPR2‐associated disorder. This sets the stage for future prospective natural history studies