On separation of a degenerate differential operator in Hilbert space

A coercive estimate for a solution of a degenerate second order di fferential equation is installed, and its applications to spectral problems for the corresponding dif ferential operator is demonstrated. The suffi cient conditions for existence of the solutions of one class of the nonlinear second order diff erential equations on the real axis are obtained.

New insights into the long-term evolutionary history of the avian MHC

SummaryGene duplication and neofunctidnalization are important processes in the evolution of phenotypic complexity. They account for important evolutionary novelties that confer ecological adaptation, such as the major histocompatibility complex (MHC), a multigene family with a central role in vertebrates' adaptive immune system. Multigene families, which evolved in large part through duplication, represent promising systems to study the still strongly depbated relative roles of neutral and adaptive processes in the evolution of phenotypic complexity. Detailed knowledge on ecological function and a well-characterized evolutionary history place the mammals' MHC amongst ideal study systems. However mammalian MHCs usually encompass several million base pairs and hold a large number of functional and non-functional duplicate genes, which makes their study complex. Avian MHCs on the other hand are usually way more compact, but the reconstruction of. their evolutionary history has proven notoriously difficult. However, no focused attempt has been undertaken so far to study the avian MHC evolutionary history in a broad phylogenetic context and using adequate gene regions.In the present PhD, we were able to make important contributions to the understanding of the long-term evolution of the avian MHC class II Β (MHCI1B). First, we isolated and characterized MHCIIB genes in barn owl (Tyto alba?, Strigiformes, Tytonidae), a species from an avian lineage in which MHC has not been studied so far. Our results revealed that with only two functional MHCIIB genes the MHC organization of barn owl may be similar to the 'minimal essential' MHC of chicken (Gallus gallus), indicating that simple MHC organization may be ancestral to birds. Taking advantage of the sequence information from barn owl, we studied the evolution of MHCIIB genes in 13 additional species of 'typical' owls (Strigiformes, Strigidae). Phylogenetic analyses revealed that according to their function, in owls the peptide-binding region (PBR) encoding exon 2 and the non-PBR encoding exon 3 evolve by different patterns. Exon 2 exhibited an evolutionary history of positive selection and recombination, while exon 3 traced duplication history and revealed two paralogs evolving divergently from each other in owls, and in a shorebird, the great snipe {Gallinago media). The results from exon 3 were the first ever from birds to demonstrate gene orthology in species that diverged tens of millions of years ago, and strongly questioned whether the taxa studied before provided an adequate picture of avian MHC evolution. In a follow-up study, we aimed at explaining a striking pattern revealed by phylogenetic trees analyzing the owl sequences along with MHCIIB sequences from other birds: One owl paralog (termed DAB1) grouped with sequences of passerines and falcons, while the other (DAB2) grouped with wildfowl, penguins and birds of prey. This could be explained by either a duplication event preceding the evolution of these bird orders, or by convergent evolution of similar sequences in a number of orders. With extensive phylogenetic analyses we were able to show, that indeed a duplication event preceeded the major avian radiation -100 my ago, and that following this duplication, the paralogs evolved under positive selection. Furthermore, we showed that the divergently evolving amino acid residues in the MHCIIB-encoded β-chain potentially interact with the MHCI I α-chain, and that molecular coevolution of the interacting residues may have been involved in the divergent evolution of the MHCIIB paralogs.The findings of this PhD are of particular interest to the understanding of the evolutionary history of the avian MHC and, by providing essential information on long-term gene history in the avian MHC, open promising perspectives for advances in the understanding of the evolution of multigene families in general, and for avian MHC organization in particular. Amongst others I discuss the importance of including protein structure in the phylogenetic study of multigene families, and the roles of ecological versus molecular selection pressures. I conclude by providing a population genomic perspective on avian MHC, which may serve as a basis for future research to investigate the relative roles of neutral processes involving effective population size effects and of adaptation in the evolution of avian MHC diversity and organization.RésuméLa duplication de gènes et leur néo-fonctionnalisation sont des processus importants dans l'évolution de la complexité phénotypique. Ils sont impliqués dans l'apparition d'importantes nouveautés évolutives favorisant l'adaptation écologique, comme c'est le cas pour le complexe majeur d'histocompatibilité

Machine learning algorithms for spatial data. Case studies: Environmental pollution, natural hazards, renewable resources

This paper presents general problems and approaches for the spatial data analysis using machine learning algorithms. Machine learning is a very powerful approach to adaptive data analysis, modelling and visualisation. The key feature of the machine learning algorithms is that they learn from empirical data and can be used in cases when the modelled environmental phenomena are hidden, nonlinear, noisy and highly variable in space and in time. Most of the machines learning algorithms are universal and adaptive modelling tools developed to solve basic problems of learning from data: classification/pattern recognition, regression/mapping and probability density modelling. In the present report some of the widely used machine learning algorithms, namely artificial neural networks (ANN) of different architectures and Support Vector Machines (SVM), are adapted to the problems of the analysis and modelling of geo-spatial data. Machine learning algorithms have an important advantage over traditional models of spatial statistics when problems are considered in a high dimensional geo-feature spaces, when the dimension of space exceeds 5. Such features are usually generated, for example, from digital elevation models, remote sensing images, etc. An important extension of models concerns considering of real space constrains like geomorphology, networks, and other natural structures. Recent developments in semi-supervised learning can improve modelling of environmental phenomena taking into account on geo-manifolds. An important part of the study deals with the analysis of relevant variables and models' inputs. This problem is approached by using different feature selection/feature extraction nonlinear tools. To demonstrate the application of machine learning algorithms several interesting case studies are considered: digital soil mapping using SVM, automatic mapping of soil and water system pollution using ANN; natural hazards risk analysis (avalanches, landslides), assessments of renewable resources (wind fields) with SVM and ANN models, etc. The dimensionality of spaces considered varies from 2 to more than 30. Figures 1, 2, 3 demonstrate some results of the studies and their outputs. Finally, the results of environmental mapping are discussed and compared with traditional models of geostatistics.

An algebraic operator approach to the analysis of Gerber-Shiu functions

We introduce an algebraic operator framework to study discounted penalty functions in renewal risk models. For inter-arrival and claim size distributions with rational Laplace transform, the usual integral equation is transformed into a boundary value problem, which is solved by symbolic techniques. The factorization of the differential operator can be lifted to the level of boundary value problems, amounting to iteratively solving first-order problems. This leads to an explicit expression for the Gerber-Shiu function in terms of the penalty function.

Replacement of (R)-methadone by a double dose of (R,S)-methadone in addicts: interindividual variability of the (R)/(S) ratios and evidence of adaptive changes in methadone pharmacokinetics.

METHODS: Twenty-two patients receiving (R)-methadone maintenance treatment were switched to a double dose of (R,S)-methadone: blood samples were collected before and after the change, and the concentrations of the enantiomers were measured. In the second period, during racemic methadone treatment, important interindividual variability in the stereoselective disposition of the enantiomers of methadone was measured, with (R)/(S) ratios ranging from 0.63 to 2.40. This point should be taken into account particularly with respect to therapeutic drug monitoring of racemic methadone. RESULTS: A significant decrease P < 0.005 in the mean serum concentration/dose ratios of the active (R)-enantiomer before and after the change was measured (mean 3.97 and 3.33). CONCLUSION: Although of small amplitude (16%), this decrease confirms previously described adaptive changes in methadone pharmacokinetics during racemic methadone maintenance treatment and may necessitate, in some patients, a dose adjustment.

Mechanisms governing lentivirus integration site selection.

An essential step of the life cycle of retroviruses is the stable insertion of a copy of their DNA genome into the host cell genome, and lentiviruses are no exception. This integration step, catalyzed by the viral-encoded integrase, ensures long-term expression of the viral genes, thus allowing a productive viral replication and rendering retroviral vectors also attractive for the field of gene therapy. At the same time, this ability to integrate into the host genome raises safety concerns regarding the use of retroviral-based gene therapy vectors, due to the genomic locations of integration sites. The availability of the human genome sequence made possible the analysis of the integration site preferences, which revealed to be nonrandom and retrovirus-specific, i.e. all lentiviruses studied so far favor integration in active transcription units, while other retroviruses have a different integration site distribution. Several mechanisms have been proposed that may influence integration targeting, which include (i) chromatin accessibility, (ii) cell cycle effects, and (iii) tethering proteins. Recent data provide evidence that integration site selection can occur via a tethering mechanism, through the recruitment of the lentiviral integrase by the cellular LEDGF/p75 protein, both proteins being the two major players in lentiviral integration targeting.

Liver Transplantation for Neuroendocrine Tumors in Europe-Results and Trends in Patient Selection: A 213-Case European Liver Transplant Registry Study.

OBJECTIVE:: The purpose of this study was to assess outcomes and indications in a large cohort of patients who underwent liver transplantation (LT) for liver metastases (LM) from neuroendocrine tumors (NET) over a 27-year period. BACKGROUND:: LT for NET remains controversial due to the absence of clear selection criteria and the scarcity and heterogeneity of reported cases. METHODS:: This retrospective multicentric study included 213 patients who underwent LT for NET performed in 35 centers in 11 European countries between 1982 and 2009. One hundred seven patients underwent transplantation before 2000 and 106 after 2000. Mean age at the time of LT was 46 years. Half of the patients presented hormone secretion and 55% had hepatomegaly. Before LT, 83% of patients had undergone surgical treatment of the primary tumor and/or LM and 76% had received chemotherapy. The median interval between diagnosis of LM and LT was 25 months (range, 1-149 months). In addition to LT, 24 patients underwent major resection procedures and 30 patients underwent minor resection procedures. RESULTS:: Three-month postoperative mortality was 10%. At 5 years after LT, overall survival (OS) was 52% and disease-free survival was 30%. At 5 years from diagnosis of LM, OS was 73%. Multivariate analysis identified 3 predictors of poor outcome, that is, major resection in addition to LT, poor tumor differentiation, and hepatomegaly. Since 2000, 5-year OS has increased to 59% in relation with fewer patients presenting poor prognostic factors. Multivariate analysis of the 106 cases treated since 2000 identified the following predictors of poor outcome: hepatomegaly, age more than 45 years, and any amount of resection concurrent with LT. CONCLUSIONS:: LT is an effective treatment of unresectable LM from NET. Patient selection based on the aforementioned predictors can achieve a 5-year OS between 60% and 80%. However, use of overly restrictive criteria may deny LT to some patients who could benefit. Optimal timing for LT in patients with stable versus progressive disease remains unclear.

Indicators of inequality: Classification and selection of ethnic health disparity indicators

Classification and selection of ethnic disparity health indicators in New Zealand

Clonotype selection and composition of human CD8 T cells specific for persistent herpes viruses varies with differentiation but is stable over time.

Protection from reactivation of persistent herpes virus infection is mediated by Ag-specific CD8 T cell responses, which are highly regulated by still poorly understood mechanisms. In this study, we analyzed differentiation and clonotypic dynamics of EBV- and CMV-specific T cells from healthy adults. Although these T lymphocytes included all subsets, from early-differentiated (EM/CD28(pos)) to late-differentiated (EMRA/CD28(neg)) stages, they varied in the sizes/proportions of these subsets. In-depth clonal composition analyses revealed TCR repertoires, which were highly restricted for CMV- and relatively diverse for EBV-specific cells. Virtually all virus-specific clonotypes identified in the EMRA/CD28(neg) subset were also found within the pool of less differentiated "memory" cells. However, striking differences in the patterns of dominance were observed among these subsets, because some clonotypes were selected with differentiation while others were not. Late-differentiated CMV-specific clonotypes were mostly characterized by TCR with lower dependency on CD8 coreceptor interaction. Yet all clonotypes displayed similar functional avidities, suggesting a compensatory role of CD8 in the clonotypes of lower TCR avidity. Importantly, clonotype selection and composition of each virus-specific subset upon differentiation was highly preserved over time, with the presence of the same dominant clonotypes at specific differentiation stages within a period of 4 years. Remarkably, clonotypic distribution was stable not only in late-differentiated but also in less-differentiated T cell subsets. Thus, T cell clonotypes segregate with differentiation, but the clonal composition once established is kept constant for at least several years. These findings reveal novel features of the highly sophisticated control of steady state protective T cell activity in healthy adults.

The robustness of the weak selection approximation for the evolution of altruism against strong selection.

The weak selection approximation of population genetics has made possible the analysis of social evolution under a considerable variety of biological scenarios. Despite its extensive usage, the accuracy of weak selection in predicting the emergence of altruism under limited dispersal when selection intensity increases remains unclear. Here, we derive the condition for the spread of an altruistic mutant in the infinite island model of dispersal under a Moran reproductive process and arbitrary strength of selection. The simplicity of the model allows us to compare weak and strong selection regimes analytically. Our results demonstrate that the weak selection approximation is robust to moderate increases in selection intensity and therefore provides a good approximation to understand the invasion of altruism in spatially structured population. In particular, we find that the weak selection approximation is excellent even if selection is very strong, when either migration is much stronger than selection or when patches are large. Importantly, we emphasize that the weak selection approximation provides the ideal condition for the invasion of altruism, and increasing selection intensity will impede the emergence of altruism. We discuss that this should also hold for more complicated life cycles and for culturally transmitted altruism. Using the weak selection approximation is therefore unlikely to miss out on any demographic scenario that lead to the evolution of altruism under limited dispersal.

Targeted expression of human CD1d in transgenic mice reveals independent roles for thymocytes and thymic APCs in positive and negative selection of Valpha14i NKT cells.

CD1d-dependent invariant Valpha14 (Valpha14i) NKT cells are innate T lymphocytes expressing a conserved semi-invariant TCR, consisting, in mice, of the invariant Valpha14-Jalpha18 TCR alpha-chain paired mostly with Vbeta8.2 and Vbeta7. The cellular requirements for thymic positive and negative selection of Valpha14i NKT cells are only partially understood. Therefore, we generated transgenic mice expressing human CD1d (hCD1d) either on thymocytes, mainly CD4+ CD8+ double positive, or on APCs, the cells implicated in the selection of Valpha14i NKT cells. In the absence of the endogenous mouse CD1d (mCD1d), the expression of hCD1d on thymocytes, but not on APCs, was sufficient to select Valpha14i NKT cells that proved functional when activated ex vivo with the Ag alpha-galactosyl ceramide. Valpha14i NKT cells selected by hCD1d on thymocytes, however, attained lower numbers than in control mice and expressed essentially Vbeta8.2. The low number of Vbeta8.2+ Valpha14i NKT cells selected by hCD1d on thymocytes was not reversed by the concomitant expression of mCD1d, which, instead, restored the development of Vbeta7+ Valpha14i NKT cells. Vbeta8.2+, but not Vbeta7+, NKT cell development was impaired in mice expressing both hCD1d on APCs and mCD1d. Taken together, our data reveal that selective CD1d expression by thymocytes is sufficient for positive selection of functional Valpha14i NKT cells and that both thymocytes and APCs may independently mediate negative selection.

Selection of peptides and synthesis of pentameric peptabody molecules reacting specifically with ErbB-2 receptor.

The HER-2/ErbB-2 oncoprotein is overexpressed in human breast and ovarian adenocarcinomas and is clearly associated with the malignant phenotype. Although no specific ligand for this receptor has been positively identified, ErbB-2 was shown to play a central role in a network of interactions with the related ErbB-1, ErbB-3 and ErbB-4 receptors. We have selected new peptides binding to ErbB-2 extracellular domain protein (ECD) by screening 2 newly developed constrained and unconstrained random hexapeptide phage libraries. Out of 37 phage clones, which bound specifically to ErbB-2 ECD, we found 6 constrained and 10 linear different hexapeptide sequences. Among the latter, 5 consensus motifs, all with a common methionine and a positively charged residue at positions 1 and 3, respectively, were identified. Furthermore, 3 representative hexapeptides were fused to a coiled-coil pentameric recombinant protein to form the so-called peptabodies recently developed in our laboratory. The 3 peptabodies bound specifically to the ErbB-2 ECD, as determined by enzyme-linked immunosorbent assay and BIAcore analysis and to tumor cells overexpressing ErbB-2, as shown by flow cytometry. Interestingly, one of the free selected linear peptides and all 3 peptabodies inhibited the proliferation of tumor cells overexpressing ErbB-2. In conclusion, a novel type of ErbB-2-specific ligand is described that might complement presently available monoclonal antibodies.