ELAV links paused Pol II to alternative polyadenylation in the Drosophila nervious system

Alternative polyadenylation (APA) has been implicated in a variety of developmental and disease processes. A particularly dramatic form of APA occurs in the developing nervous system of flies and mammals, whereby various developmental genes undergo coordinate 3' UTR extension. In Drosophila, the RNA-binding protein ELAV inhibits RNA processing at proximal polyadenylation sites, thereby fostering the formation of exceptionally long 3' UTRs. Here, we present evidence that paused Pol II promotes recruitment of ELAV to extended genes. Replacing promoters of extended genes with heterologous promoters blocks normal 3' extension in the nervous system, while extension-associated promoters can induce 3' extension in ectopic tissues expressing ELAV. Computational analyses suggest that promoter regions of extended genes tend to contain paused Pol II and associated cis-regulatory elements such as GAGA. ChIP-seq assays identify ELAV in the promoter regions of extended genes. Our study provides evidence for a regulatory link between promoter-proximal pausing and APA

Counting smaller elements in the Tamari and m-Tamari lattices

We introduce new combinatorial objects, the interval- posets, that encode intervals of the Tamari lattice. We then find a combinatorial interpretation of the bilinear operator that appears in the functional equation of Tamari intervals described by Chapoton. Thus, we retrieve this functional equation and prove that the polynomial recursively computed from the bilinear operator on each tree T counts the number of trees smaller than T in the Tamari order. Then we show that a similar m + 1-linear operator is also used in the functionnal equation of m-Tamari intervals. We explain how the m-Tamari lattices can be interpreted in terms of m+1-ary trees or a certain class of binary trees. We then use the interval-posets to recover the functional equation of m-Tamari intervals and to prove a generalized formula that counts the number of elements smaller than or equal to a given tree in the m-Tamari lattice.Comment: 46 pages + 3 pages of code appendix, 27 figures. Long version of arXiv:1212.0751. To appear in Journal of Combinatorial Theory, Series

Geometry of quiver Grassmannians of Dynkin type with applications to cluster algebras

The paper includes a new proof of the fact that quiver Grassmannians associated with rigid representations of Dynkin quivers do not have cohomology in odd degrees. Moreover, it is shown that they do not have torsion in homology. A new proof of the Caldero-Chapoton formula is provided. As a consequence a new proof of the positivity of cluster monomials in the acyclic clusters associated with Dynkin quivers is obtained. The methods used here are based on joint works with Markus Reineke and Evgeny Feigin