Determinantal ideals and monomial curves in the three-dimensional space

We show that the defining ideal of every monomial curve in the affine or projective three-dimensional space can be set-theoretically defined by three binomial equations, two of which set-theoretically define a determinantal ideal generated by the 2-minors of a $2\times 3$ matrix with monomial entries

Betti numbers for numerical semigroup rings

We survey results related to the magnitude of the Betti numbers of numerical semigroup rings and of their tangent cones.Comment: 22 pages; v2: updated references. To appear in Multigraded Algebra and Applications (V. Ene, E. Miller Eds.

Deterministically Computing Reduction Numbers of Polynomial Ideals

We discuss the problem of determining reduction number of a polynomial ideal I in n variables. We present two algorithms based on parametric computations. The first one determines the absolute reduction number of I and requires computation in a polynomial ring with (n-dim(I))dim(I) parameters and n-dim(I) variables. The second one computes via a Grobner system the set of all reduction numbers of the ideal I and thus in particular also its big reduction number. However,it requires computations in a ring with n.dim(I) parameters and n variables.Comment: This new version replaces the earlier version arXiv:1404.1721 and it has been accepted for publication in the proceedings of CASC 2014, Warsaw, Polna

Characterization of caspase‐2 inhibitors based on specific sites of caspase‐2‐mediated proteolysis

Since the discovery of the caspase-2 (Casp2)-mediated ∆tau314 cleavage product and its associated impact on tauopathies such as Alzheimer's disease, the design of selective Casp2 inhibitors has become a focus in medicinal chemistry research. In the search for new lead structures with respect to Casp2 selectivity and drug-likeness, we have taken an approach by looking more closely at the specific sites of Casp2-mediated proteolysis. Using seven selected protein cleavage sequences, we synthesized a peptide series of 53 novel molecules and studied them using in vitro pharmacology, molecular modeling, and crystallography. Regarding Casp2 selectivity, AcITV(Dab)D-CHO (23) and AcITV(Dap)D-CHO (26) demonstrated the best selectivity (1–6-fold), although these trends were only moderate. However, some analogous tetrapeptides, most notably AcDKVD-CHO (45), showed significantly increased Casp3 selectivities (>100-fold). Tetra- and tripeptides display decreased or no Casp2 affinity, supporting the assumption that a motif of five amino acids is required for efficient Casp2 inhibition. Overall, the results provide a reasonable basis for the development of both selective Casp2 and Casp3 inhibitors

Evolutionary history of Serpulaceae (Basidiomycota): molecular phylogeny, historical biogeography and evidence for a single transition of nutritional mode

<p>Abstract</p> <p>Background</p> <p>The fungal genus <it>Serpula </it>(Serpulaceae, Boletales) comprises several saprotrophic (brown rot) taxa, including the aggressive house-infecting dry rot fungus <it>Serpula lacrymans</it>. Recent phylogenetic analyses have indicated that the ectomycorrhiza forming genera <it>Austropaxillus </it>and <it>Gymnopaxillus </it>cluster within <it>Serpula</it>. In this study we use DNA sequence data to investigate phylogenetic relationships, historical biogeography of, and nutritional mode transitions in Serpulaceae.</p> <p>Results</p> <p>Our results corroborate that the two ectomycorrhiza-forming genera, <it>Austropaxillus </it>and <it>Gymnopaxillus</it>, form a monophyletic group nested within the saprotrophic genus <it>Serpula</it>, and that the <it>Serpula </it>species <it>S. lacrymans </it>and <it>S. himantioides </it>constitute the sister group to the <it>Austropaxillus</it>-<it>Gymnopaxillus </it>clade. We found that both vicariance (Beringian) and long distance dispersal events are needed to explain the phylogeny and current distributions of taxa within Serpulaceae. Our results also show that the transition from brown rot to mycorrhiza has happened only once in a monophyletic Serpulaceae, probably between 50 and 22 million years before present.</p> <p>Conclusions</p> <p>This study supports the growing understanding that the same geographical barriers that limit plant- and animal dispersal also limit the spread of fungi, as a combination of vicariance and long distance dispersal events are needed to explain the present patterns of distribution in Serpulaceae. Our results verify the transition from brown rot to ECM within Serpulaceae between 50 and 22 MyBP.</p

Human and mouse essentiality screens as a resource for disease gene discovery.

The identification of causal variants in sequencing studies remains a considerable challenge that can be partially addressed by new gene-specific knowledge. Here, we integrate measures of how essential a gene is to supporting life, as inferred from viability and phenotyping screens performed on knockout mice by the International Mouse Phenotyping Consortium and essentiality screens carried out on human cell lines. We propose a cross-species gene classification across the Full Spectrum of Intolerance to Loss-of-function (FUSIL) and demonstrate that genes in five mutually exclusive FUSIL categories have differing biological properties. Most notably, Mendelian disease genes, particularly those associated with developmental disorders, are highly overrepresented among genes non-essential for cell survival but required for organism development. After screening developmental disorder cases from three independent disease sequencing consortia, we identify potentially pathogenic variants in genes not previously associated with rare diseases. We therefore propose FUSIL as an efficient approach for disease gene discovery