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

Association of LOXL1 common sequence variants in German and Italian patients with pseudoexfoliation syndrome and pseudoexfoliation glaucoma

purpose. Three common sequence variants in the lysyl oxidase-like 1 (LOXL1) gene were recently associated with both pseudoexfoliation (PEX) and pseudoexfoliation glaucoma (PEXG) in populations from Iceland and Sweden. In this study, the genetic association of these variants was investigated in patients with PEX or PEXG of German and Italian descent. methods. The three LOXL1 single-nucleotide polymorphisms (SNPs), one intronic (rs2165241) and two nonsynonymous coding SNPs (rs1048661: R141L and rs3825942: G153D) were genotyped in a total of 726 unrelated patients with PEX or PEXG (517 Germans and 209 Italians) and 418 healthy subjects who had normal findings in repeated ophthalmic examinations, and a genetic association study was performed. results. Strong association with the three LOXL1 common sequence variants was seen in both the PEX and PEXG patient groups independent of their geographic origin (rs2165241, combined OR = 3.42, P = 1.28 × 10−40; rs1048661, OR = 2.43, P = 2.90 × 10−19; and rs3825942, OR = 4.87, P = 8.22 × 10−23). Similarly, the common frequent haplotype (G-G) composed of the two coding SNPs (rs1048661 and rs3825942) was strongly associated in PEX and PEXG cohorts of both populations with the disease (combined OR = 3.58, P = 5.21× 10−43). conclusions. Genetic variants in LOXL1 confer risk to PEX in German and Italian populations, independent of the presence of secondary glaucoma, confirming findings in patients from Northern Europe

Exploring functional candidate genes for genetic association in German patients with pseudoexfoliation syndrome and pseudoexfoliation glaucoma

purpose. Pseudoexfoliation (PEX) syndrome is a generalized elastic microfibrillopathy characterized by fibrillar deposits in intra- and extraocular tissues. Genetic and nongenetic factors are known to be involved in its etiopathogenesis. This study was focused on six functional candidate genes involved in PEX material deposition and the analysis of their potential association with PEX syndrome and PEX glaucoma (PEXG). methods. Fifty single-nucleotide polymorphisms (SNPs) capturing >95% of overall genetic variance observed in Europeans at loci for FBN1, LTBP2, MFAP2, TGM2, TGF-b1, and CLU were genotyped in 333 unrelated PEX-affected and 342 healthy individuals of German origin, and a genetic association study was performed. To replicate the findings, two SNPs of the CLU gene were genotyped in a further 328 unrelated German patients with PEX as well as in 209 Italian patients with PEX and 190 Italian control subjects. results. Association with PEX was observed only for the SNP rs2279590 in intron 8 of the CLU gene coding for clusterin (corrected P = 0.0347, OR = 1.34) in our first German cohort. Likewise, a frequent haplotype encompassing the associated risk allele showed nominally significant association. None of remaining SNPs or SNP haplotypes were associated with PEX. The association found was confirmed in a second German cohort (P = 0.0244) but not in the Italian cohort (P = 0.7173). In addition, the association with CLU SNP rs2279590 was more significant in German patients with PEX syndrome than in those with PEXG. conclusions. Genetic variants in the gene encoding clusterin may represent a risk factor for PEX in German patients but not in Italian patients. Variants in FBN1, LTBP2, MFAP2, TGF-b1, and TGM2 do not play a major role in the etiology of PEX syndrome, at least in German patients

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

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

Inhibition of activation induced CD154 on CD4+ CD25- cells: a valid surrogate for human Treg suppressor function

Natural Regulatory T cells (Tregs) are defined by stable expression of the cell surface proteins CD4 and CD25, low surface expression of CD127 and expression of the transcription factor FOXP3. The contribution of Treg to the prevention of autoimmunity and the maintenance of immune homoestasis is the subject of ongoing interest, as alterations in Treg numbers and function are implicated in a wide range of diseases. The in vitro benchmark for determining Treg function is suppression of proliferation of unmatched effector T cells in a mixed lymphocyte reaction (MLR) over a 3–6-day time period. As an alternative to this assay, we show that a 7-h CD154 expression assay is rapid, simple and provides a reliable readout of suppressor function. Using multiple Treg-like cell types including natural (n)Treg, inducible (i)Treg and Treg cell lines, we show that suppression of CD154 expression is a surrogate for suppression of proliferation. We propose this as a suitable alternative to the MLR assay, as it is rapid and may be more amenable to high-throughput screening, analysing large cohorts of clinical samples or assaying transiently suppressive populations. Keywords: regulatory T cells; functional assays; iTreg; nTregDanika Hill, Nicola Eastaff-Leung, Suzanne Bresatz-Atkins, Noel Warner, Joyce Ruitenberg, Dorren Krumbiegel, Steve Pederson, Natasha McInnes, Cheryl Y. Brown, Timothy Sadlon and Simon C. Barr

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