The Gysin homomorphism for homogeneous spaces via residues

The subject of this dissertation is the Gysin homomorphism in equivariant cohomology for spaces with torus action. We consider spaces which are quotients of classical semisimple complex linear algebraic groups by a parabolic subgroup with the natural action of a maximal torus, the so-called partial flag varieties. We derive formulas for the Gysin homomorphism for the projection to a point, in the form for a certain residue operation applied to a certain complex variable map associated to the root system. The mentioned description relies on two following generalizations of theorems in symplectic geometry. We adapt to the equivariant setting (for torus actions) the Jeffrey--Kirwan nonabelian localization and a theorem relating the cohomology of symplectic reductions by a compact Lie group and by its maximal torus, following the approach by Martin. Applying the generalized theorems to certain contractible spaces acted upon by a product of unitary groups we derive the push-forward formula for partial flag varieties of types A, B, C and D.Przedmiotem niniejszej rozprawy jest homomorfizm Gysina w kohomologiach ekwiwariantnych dla przestrzeni z działaniem torusa. Rozważane są przestrzenie będące ilorazami klasycznych półprostych zespolonych liniowych grup algebraicznych przez podgrupę paraboliczną, wraz z naturalnym działaniem torusa maksymalnego, zwane inaczej przestrzeniami częściowych flag. Niniejsza rozprawa opisuje homomorfizm Gysina dla rzutowania na punkt za pomocą residuum z pewnej funkcji zespolonej wielu zmiennych, związanej z układem pierwiastków grupy. Wspomniany opis opiera się na uogólnieniach dwóch twierdzeń z geometrii symplektycznej, udowodnionych w pierwszej części rozprawy. Pierwszym z nich jest uogólnienie (w kontekście ekwiwariantnym dla działania torusa) twierdzenia Jeffrey--Kirwan o nieabelowej lokalizacji, drugim zaś twierdzenie wiążące kohomologie redukcji symplektyczniej przez zwartą grupę Liego z kohomologiami redukcji przez torus maksymalny w tej grupie, w sformułowaniu Martina. W drugiej części rozprawy uogólnione twierdzenia zostały użyte do redukcji symplektycznych pewnych przestrzeni ściągalnych z działaniem produktu grup unitarnych, w celu otrzymania wzorów opisujących homomorfizm Gysina dla przestrzeni częściowych flag typów A, B, C i D

A note on the push-forward formulas for even orthogonal Grassmannians

We revisit residue formulas for the push-forward in the cohomology of the even orthogonal Grassmannian. This space has two components, and the formula for a single component demands separate attention. We correct errors spread throughout the literature

A Comprehensive, Quantitative, and Genome-Wide Model of Translation

Translation is still poorly characterised at the level of individual proteins and its role in regulation of gene expression has been constantly underestimated. To better understand the process of protein synthesis we developed a comprehensive and quantitative model of translation, characterising protein synthesis separately for individual genes. The main advantage of the model is that basing it on only a few datasets and general assumptions allows the calculation of many important translational parameters, which are extremely difficult to measure experimentally. In the model, each gene is attributed with a set of translational parameters, namely the absolute number of transcripts, ribosome density, mean codon translation time, total transcript translation time, total time required for translation initiation and elongation, translation initiation rate, mean mRNA lifetime, and absolute number of proteins produced by gene transcripts. Most parameters were calculated based on only one experimental dataset of genome-wide ribosome profiling. The model was implemented in Saccharomyces cerevisiae, and its results were compared with available data, yielding reasonably good correlations. The calculated coefficients were used to perform a global analysis of translation in yeast, revealing some interesting aspects of the process. We have shown that two commonly used measures of translation efficiency – ribosome density and number of protein molecules produced – are affected by two distinct factors. High values of both measures are caused, i.a., by very short times of translation initiation, however, the origins of initiation time reduction are completely different in both cases. The model is universal and can be applied to any organism, if the necessary input data are available. The model allows us to better integrate transcriptomic and proteomic data. A few other possibilities of the model utilisation are discussed concerning the example of the yeast system

Tools4miRs – one place to gather all the tools for miRNA analysis

MiRNAs are short, non-coding molecules that negatively regulate gene expression and thereby play several important roles in living organisms. Dozens of computational methods for miRNA-related research have been developed, which greatly differ in various aspects. The substantial availability of difficult-to-compare approaches makes it challenging for the user to select a proper tool and prompts the need for a solution that will collect and categorize all the methods. Here, we present tools4miRs, the first platform that gathers currently more than 160 methods for broadly defined miRNA analysis. The collected tools are classified into several general and more detailed categories in which the users can additionally filter the available methods according to their specific research needs, capabilities and preferences. Tools4miRs is also a web-based target prediction meta-server that incorporates user-designated target prediction methods into the analysis of user-provided data

The High Throughput Sequence Annotation Service (HT-SAS) – the shortcut from sequence to true Medline words

<p>Abstract</p> <p>Background</p> <p>Advances in high-throughput technologies available to modern biology have created an increasing flood of experimentally determined facts. Ordering, managing and describing these raw results is the first step which allows facts to become knowledge. Currently there are limited ways to automatically annotate such data, especially utilizing information deposited in published literature.</p> <p>Results</p> <p>To aid researchers in describing results from high-throughput experiments we developed HT-SAS, a web service for automatic annotation of proteins using general English words. For each protein a poll of Medline abstracts connected to homologous proteins is gathered using the UniProt-Medline link. Overrepresented words are detected using binomial statistics approximation. We tested our automatic approach with a protein test set from SGD to determine the accuracy and usefulness of our approach. We also applied the automatic annotation service to improve annotations of proteins from <it>Plasmodium bergei </it>expressed exclusively during the blood stage.</p> <p>Conclusion</p> <p>Using HT-SAS we created new, or enriched already established annotations for over 20% of proteins from <it>Plasmodium bergei </it>expressed in the blood stage, deposited in PlasmoDB. Our tests show this approach to information extraction provides highly specific keywords, often also when the number of abstracts is limited. Our service should be useful for manual curators, as a complement to manually curated information sources and for researchers working with protein datasets, especially from poorly characterized organisms.</p