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

Genomic DNA Pooling Strategy for Next-Generation Sequencing-Based Rare Variant Discovery in Abdominal Aortic Aneurysm Regions of Interest—Challenges and Limitations

The costs and efforts for sample preparation of hundreds of individuals, their genomic enrichment for regions of interest, and sufficient deep sequencing bring a significant burden to next-generation sequencing-based experiments. We investigated whether pooling of samples at the level of genomic DNA would be a more versatile strategy for lowering the costs and efforts for common disease-associated rare variant detection in candidate genes or associated loci in a substantial patient cohort. We performed a pilot experiment using five pools of 20 abdominal aortic aneurysm (AAA) patients that were enriched on separate microarrays for the reported 9p21.3 associated locus and 42 additional AAA candidate genes, and sequenced on the SOLiD platform. Here, we discuss challenges and limitations connected to this approach and show that the high number of novel variants detected per pool and allele frequency deviations to the usually highly false positive cut-off region for variant detection in non-pooled samples can be limiting factors for successful variant prioritization and confirmation. We conclude that barcode indexing of individual samples before pooling followed by a multiplexed enrichment strategy should be preferred for detection of rare genetic variants in larger sample sets rather than a genomic DNA pooling strategy

Comparison of blood and synovial fluid Th17 and novel peptidase inhibitor 16 Treg cell subsets in juvenile idiopathic arthritis

Objective. Early recognition and treatment of juvenile idiopathic arthritis (JIA) can prevent joint damage and minimize side effects of medication. The balance between proinflammatory and antiinflammatory mechanisms is known to be important in JIA, and we therefore investigated T cell subsets including Th cells, autoaggressive Th17 cells, and regulatory T cells (Treg), including a novel Treg subset in peripheral blood (PB) and synovial fluid (SF) of patients with JIA. Methods. Fifty children with JIA were enrolled in our study. Frequency, phenotype, and function of T lymphocytes in PB and SF were characterized using flow cytometry. Migration capabilities of PB and SF cells were compared. Results. Synovial T cells showed different phenotype and function compared with PB T cells, with an increased proportion of memory T cells, expression of CCR4, CCR5, CXCR3, interleukin 23R, and an increased ratio of Th17 to Treg. Although Treg were increased in SF compared with the PB, we found a significant decrease in the numbers of peptidase inhibitor 16 (PI16)+ Treg in active joints compared with peripheral blood. Coexpression of CCR4 and CCR6 was reduced on PI16+ Treg in PB and SF of patients with JIA compared with healthy children, however the ability of these cells to migrate toward their ligands was unaffected. Conclusion. This is a comprehensive characterization of novel PI16+ Treg and Th17 cells in matched blood and synovial fluid samples of patients with JIA. Despite an increased number of Treg within the inflamed joint, lower numbers of PI16+ Treg but high numbers of Th17 cells might contribute to the inability to control disease.Randall H. Grose, Deborah J. Millard, Chris Mavrangelos, Simon C. Barry, Heddy Zola, Ian C. Nicholson, Weng Tarng Cham, Christina A. Boros and Doreen Krumbiege

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

De novo missense variants in FBXO11 alter its protein expression and subcellular localization.

Recently, we and others identified de novo FBXO11 variants as causative for a variable neurodevelopmental disorder (NDD). We now assembled clinical and mutational information on 23 additional individuals. The phenotypic spectrum remains highly variable, with developmental delay and/or intellectual disability as the core feature and behavioral anomalies, hypotonia and various facial dysmorphism as frequent aspects. The mutational spectrum includes intragenic deletions, likely gene disrupting and missense variants distributed across the protein. To further characterize the functional consequences of FBXO11 missense variants, we analyzed their effects on protein expression and localization by overexpression of 17 different mutant constructs in HEK293 and HeLa cells. We found that the majority of missense variants resulted in subcellular mislocalization and/or reduced FBXO11 protein expression levels. For instance, variants located in the nuclear localization signal and the N-terminal F-Box domain lead to altered subcellular localization with exclusion from the nucleus or the formation of cytoplasmic aggregates and to reduced protein levels in western blot. In contrast, variants localized in the C-terminal Zn-finger UBR domain lead to an accumulation in the cytoplasm without alteration of protein levels. Together with the mutational data our functional results suggest that most missense variants likely lead to a loss of the original FBXO11 function and thereby highlight haploinsufficiency as the most likely disease mechanism for FBXO11-associated NDDs

De novo missense variants in FBXO11 alter its protein expression and subcellular localization.

Recently, we and others identified de novo FBXO11 variants as causative for a variable neurodevelopmental disorder (NDD). We now assembled clinical and mutational information on 23 additional individuals. The phenotypic spectrum remains highly variable, with developmental delay and/or intellectual disability as the core feature and behavioral anomalies, hypotonia and various facial dysmorphism as frequent aspects. The mutational spectrum includes intragenic deletions, likely gene disrupting and missense variants distributed across the protein. To further characterize the functional consequences of FBXO11 missense variants, we analyzed their effects on protein expression and localization by overexpression of 17 different mutant constructs in HEK293 and HeLa cells. We found that the majority of missense variants resulted in subcellular mislocalization and/or reduced FBXO11 protein expression levels. For instance, variants located in the nuclear localization signal and the N-terminal F-Box domain lead to altered subcellular localization with exclusion from the nucleus or the formation of cytoplasmic aggregates and to reduced protein levels in western blot. In contrast, variants localized in the C-terminal Zn-finger UBR domain lead to an accumulation in the cytoplasm without alteration of protein levels. Together with the mutational data our functional results suggest that most missense variants likely lead to a loss of the original FBXO11 function and thereby highlight haploinsufficiency as the most likely disease mechanism for FBXO11-associated NDDs

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