Flexibility Properties in Complex Analysis and Affine Algebraic Geometry

In the last decades affine algebraic varieties and Stein manifolds with big (infinite-dimensional) automorphism groups have been intensively studied. Several notions expressing that the automorphisms group is big have been proposed. All of them imply that the manifold in question is an Oka–Forstnerič manifold. This important notion has also recently merged from the intensive studies around the homotopy principle in Complex Analysis. This homotopy principle, which goes back to the 1930s, has had an enormous impact on the development of the area of Several Complex Variables and the number of its applications is constantly growing. In this overview chapter we present three classes of properties: (1) density property, (2) flexibility, and (3) Oka–Forstnerič. For each class we give the relevant definitions, its most significant features and explain the known implications between all these properties. Many difficult mathematical problems could be solved by applying the developed theory, we indicate some of the most spectacular ones.

The syndromology of anorectal malformations revisited: from patterns of associated malformations to the recognition of syndromes

ackground: Although the frequency of associated malformation is high, the incidence of inheritable syndromes is widely underestimated in children with anorectal malformation (ARM). Data sources: OMIM database, patient records and charts of the Department of Pediatric Surgery, Johannes Gutenberg-University, Mainz, Germany. Methods: We analyzed all associations, sequences and syndromes listed in the OMIM database that can be accompanied by ARM. A large cohort of children born with ARM was then retrospectively investigated as to the type of ARM, presence of additional malformations and possible categorization as a syndrome, sequence or association. For this process a syndrome finder was developed and employed. This simplistic tool allows for a rapid first check of possible syndromes before a more complex analysis is started using the OMIM database and consulting specialists. Results: Among 317 children with ARM, associated malformations were present in 77.7% of 127 children with high ARM, in 68.7% of 32 with intermediate ARM, and in 25.3% of 158 with a low type ARM. Three or more organ systems were involved in 29.1% children with high type ARM and 25% with intermediate ARM and 8.2% with a low type ARM. An association of the vertebral anal tracheo-esophageal renal (VATER) and vertebral anal cardiac tracheo-esophageal renal limb (VACTERL) type was found in a total of 35 patients. Before analysis, 11 syndromes and 35 associations which were not clear previously in this patient cohort were described. In other 17 patients, 14 syndromes and 3 associations were identified. Conclusions: The high number of only retrospectively identified syndromes suggests that a routine search is necessary in every patient with ARM and additional malformations.

On the similarity of Sturm-Liouville operators with non-Hermitian boundary conditions to self-adjoint and normal operators

We consider one-dimensional Schrödinger-type operators in a bounded interval with non-self-adjoint Robin-type boundary conditions. It is well known that such operators are generically conjugate to normal operators via a similarity transformation. Motivated by recent interests in quasi-Hermitian Hamiltonians in quantum mechanics, we study properties of the transformations and similar operators in detail. In the case of parity and time reversal boundary conditions, we establish closed integral-type formulae for the similarity transformations, derive a non-local self-adjoint operator similar to the Schrödinger operator and also find the associated “charge conjugation” operator, which plays the role of fundamental symmetry in a Krein-space reformulation of the problem.

On the Density and the Volume Density Property

This article gives a short introduction into the notions of density property (DP) and volume density property (VDP). Moreover we develop an effective criterion of verifying whether a given X has VDP. As an application of this method we give a new proof of the basic fact that the product of two Stein manifolds with VDP admits VDP.

The macromolecular complex of ICP and falcipain-2 from Plasmodium: preparation, crystallization and preliminary X-ray diffraction analysis

The malaria parasite Plasmodium depends on the tight control of cysteine-protease activity throughout its life cycle. Recently, the characterization of a new class of potent inhibitors of cysteine proteases (ICPs) secreted by Plasmodium has been reported. Here, the recombinant production, purification and crystallization of the inhibitory C-terminal domain of ICP from P. berghei in complex with the P. falciparum haemoglobinase falcipain-2 is described. The 1:1 complex was crystallized in space group P4(3), with unit-cell parameters a = b = 71.15, c = 120.09 A. A complete diffraction data set was collected to a resolution of 2.6 A.

Ruminant rhombencephalitis-associated Listeria monocytogenes alleles linked to a multilocus variable-number tandem-repeat analysis complex

Listeria monocytogenes is among the most important food-borne pathogens and is well adapted to persist in the environment. To gain insight into the genetic relatedness and potential virulence of L. monocytogenes strains causing central nervous system (CNS) infections, we used multilocus variable-number tandem-repeat analysis (MLVA) to subtype 183 L. monocytogenes isolates, most from ruminant rhombencephalitis and some from human patients, food, and the environment. Allelic-profile-based comparisons grouped L. monocytogenes strains mainly into three clonal complexes and linked single-locus variants (SLVs). Clonal complex A essentially consisted of isolates from human and ruminant brain samples. All but one rhombencephalitis isolate from cattle were located in clonal complex A. In contrast, food and environmental isolates mainly clustered into clonal complex C, and none was classified as clonal complex A. Isolates of the two main clonal complexes (A and C) obtained by MLVA were analyzed by PCR for the presence of 11 virulence-associated genes (prfA, actA, inlA, inlB, inlC, inlD, inlE, inlF, inlG, inlJ, and inlC2H). Virulence gene analysis revealed significant differences in the actA, inlF, inlG, and inlJ allelic profiles between clinical isolates (complex A) and nonclinical isolates (complex C). The association of particular alleles of actA, inlF, and newly described alleles of inlJ with isolates from CNS infections (particularly rhombencephalitis) suggests that these virulence genes participate in neurovirulence of L. monocytogenes. The overall absence of inlG in clinical complex A and its presence in complex C isolates suggests that the InlG protein is more relevant for the survival of L. monocytogenes in the environment.

Fine-mapping and mutation analysis of TRPM1: a candidate gene for leopard complex (LP) spotting and congenital stationary night blindness in horses.

Leopard Complex spotting occurs in several breeds of horses and is caused by an incompletely dominant allele (LP). Homozygosity for LP is also associated with congenital stationary night blindness (CSNB) in Appaloosa horses. Previously, LP was mapped to a 6 cm region on ECA1 containing the candidate gene TRPM1 (Transient Receptor Potential Cation Channel, Subfamily M, Member 1) and decreased expression of this gene, measured by qRT-PCR, was identified as the likely cause of both spotting and ocular phenotypes. This study describes investigations for a mutation causing or associated with the Leopard Complex and CSNB phenotype in horses. Re-sequencing of the gene and associated splice sites within the 105 624 bp genomic region of TRPM1 led to the discovery of 18 SNPs. Most of the SNPs did not have a predictive value for the presence of LP. However, one SNP (ECA1:108,249,293 C>T) found within intron 11 had a strong (P < 0.0005), but not complete, association with LP and CSNB and thus is a good marker but unlikely to be causative. To further localize the association, 70 SNPs spanning over two Mb including the TRPM1 gene were genotyped in 192 horses from three different breeds segregating for LP. A single 173 kb haplotype associated with LP and CSNB (ECA1: 108,197,355- 108,370,150) was identified. Illumina sequencing of 300 kb surrounding this haplotype revealed 57 SNP variants. Based on their localization within expressed sequences or regions of high sequence conservation across mammals, six of these SNPs were considered to be the most likely candidate mutations. While the precise function of TRPM1 remains to be elucidated, this work solidifies its functional role in both pigmentation and night vision. Further, this work has identified several potential regulatory elements of the TRPM1 gene that should be investigated further in this and other species.

Increased spread and replication efficiency of Listeria monocytogenes in organotypic brain-slices is related to multilocus variable number of tandem repeat analysis (MLVA) complex.

BACKGROUND Listeria (L.) monocytogenes causes fatal infections in many species including ruminants and humans. In ruminants, rhombencephalitis is the most prevalent form of listeriosis. Using multilocus variable number tandem repeat analysis (MLVA) we recently showed that L. monocytogenes isolates from ruminant rhombencephalitis cases are distributed over three genetic complexes (designated A, B and C). However, the majority of rhombencephalitis strains and virtually all those isolated from cattle cluster in MLVA complex A, indicating that strains of this complex may have increased neurotropism and neurovirulence. The aim of this study was to investigate whether ruminant rhombencephalitis strains have an increased ability to propagate in the bovine hippocampal brain-slice model and can be discriminated from strains of other sources. For this study, forty-seven strains were selected and assayed on brain-slice cultures, a bovine macrophage cell line (BoMac) and a human colorectal adenocarcinoma cell line (Caco-2). They were isolated from ruminant rhombencephalitis cases (n = 21) and other sources including the environment, food, human neurolisteriosis cases and ruminant/human non-encephalitic infection cases (n = 26). RESULTS All but one L. monocytogenes strain replicated in brain slices, irrespectively of the source of the isolate or MLVA complex. The replication of strains from MLVA complex A was increased in hippocampal brain-slice cultures compared to complex C. Immunofluorescence revealed that microglia are the main target cells for L. monocytogenes and that strains from MLVA complex A caused larger infection foci than strains from MLVA complex C. Additionally, they caused larger plaques in BoMac cells, but not CaCo-2 cells. CONCLUSIONS Our brain slice model data shows that all L. monocytogenes strains should be considered potentially neurovirulent. Secondly, encephalitis strains cannot be conclusively discriminated from non-encephalitis strains with the bovine organotypic brain slice model. The data indicates that MLVA complex A strains are particularly adept at establishing encephalitis possibly by virtue of their higher resistance to antibacterial defense mechanisms in microglia cells, the main target of L. monocytogenes.

Using the contribution matrix to evaluate complex study limitations in a network meta-analysis: a case study of bipolar maintenance pharmacotherapy review.

BACKGROUND Limitations in the primary studies constitute one important factor to be considered in the grading of recommendations assessment, development, and evaluation (GRADE) system of rating quality of evidence. However, in the network meta-analysis (NMA), such evaluation poses a special challenge because each network estimate receives different amounts of contributions from various studies via direct as well as indirect routes and because some biases have directions whose repercussion in the network can be complicated. FINDINGS In this report we use the NMA of maintenance pharmacotherapy of bipolar disorder (17 interventions, 33 studies) and demonstrate how to quantitatively evaluate the impact of study limitations using netweight, a STATA command for NMA. For each network estimate, the percentage of contributions from direct comparisons at high, moderate or low risk of bias were quantified, respectively. This method has proven flexible enough to accommodate complex biases with direction, such as the one due to the enrichment design seen in some trials of bipolar maintenance pharmacotherapy. CONCLUSIONS Using netweight, therefore, we can evaluate in a transparent and quantitative manner how study limitations of individual studies in the NMA impact on the quality of evidence of each network estimate, even when such limitations have clear directions.