Ringel duality for certain strongly quasi-hereditary algebras

We study quasi-hereditary endomorphism algebras defined over a new class of finite dimensional monomial algebras with a special ideal structure. The main result is a uniform formula describing the Ringel duals of these quasi-hereditary algebras. As special cases, we obtain a Ringel duality formula for a family of strongly quasi-hereditary algebras arising from a type A configuration of projective lines in a rational, projective surface as recently introduced by Hille and Ploog, for certain Auslander–Dlab–Ringel algebras, and for Eiriksson and Sauter’s nilpotent quiver algebras when the quiver has no sinks and no sources. We also recover Tan’s result that the Auslander algebras of self-injective Nakayama algebras are Ringel self-dual

Noncommutative Knörrer type equivalences via noncommutative resolutions of singularities

We construct Kn\"orrer type equivalences outside of the hypersurface case, namely, between singularity categories of cyclic quotient surface singularities and certain finite dimensional local algebras. This generalises Kn\"orrer's equivalence for singularities of Dynkin type A (between Krull dimensions $2$ and $0$) and yields many new equivalences between singularity categories of finite dimensional algebras. Our construction uses noncommutative resolutions of singularities, relative singularity categories, and an idea of Hille & Ploog yielding strongly quasi-hereditary algebras which we describe explicitly by building on Wemyss's work on reconstruction algebras. Moreover, K-theory gives obstructions to generalisations of our main result

Obstructions to semiorthogonal decompositions for singular threefolds I: K-theory

We investigate necessary conditions for Gorenstein projective varieties to admit semiorthogonal decompositions introduced by Kawamata, with main emphasis on threefolds with isolated compound $A_n$ singularities. We introduce obstructions coming from Algebraic $\mathrm{K}$-theory and translate them into the concept of maximal nonfactoriality. Using these obstructions we show that many classes of nodal threefolds do not admit Kawamata type semiorthogonal decompositions. These include nodal hypersurfaces and double solids, with the exception of a nodal quadric, and del Pezzo threefolds of degrees $1 \le d \le 4$ with maximal class group rank. We also investigate when does a blow up of a smooth threefold in a singular curve admit a Kawamata type semiorthogonal decomposition and we give a complete answer to this question when the curve is nodal and has only rational components

A remark on Leclerc's Frobenius categories

Leclerc recently studied certain Frobenius categories in connection with cluster algebra structures on coordinate rings of intersections of opposite Schubert cells. We show that these categories admit a description as Gorenstein projective modules over an Iwanaga-Gorenstein ring of virtual dimension at most two. This is based on a Morita type result for Frobenius categories.Comment: 5 pages, extended abstract for a talk at the Workshop Homological Bonds between Commutative Algebra and Representation Theory at CRM Barcelona, February 2015, comments welcom

Controlled Exchange of Chromosomal Arms Reveals Principles Driving Telomere Interactions in Yeast

The 32 telomeres in the budding yeast genome cluster in three to seven perinuclear foci. Although individual telomeres and telomeric foci are in constant motion, preferential juxtaposition of some telomeres has been scored. To examine the principles that guide such long-range interactions, we differentially tagged pairs of chromosome ends and developed an automated three-dimensional measuring tool that determines distances between two telomeres. In yeast, all chromosomal ends terminate in $TG _{ 1-3 }$ and middle repetitive elements, yet subgroups of telomeres also share extensive homology in subtelomeric coding domains. We find that up to 21 kb of >90% sequence identity does not promote telomere pairing in interphase cells. To test whether unique sequence elements, arm length, or chromosome territories influence juxtaposition, we reciprocally swapped terminal domains or entire chromosomal arms from one chromosome to another. We find that the distal 10 kb of Tel6R promotes interaction with Tel6L, yet only when the two telomeres are present on the same chromosome. By manipulating the length and sequence composition of the right arm of chr 5, we confirm that contact between telomeres on opposite chromatid arms of equal length is favored. These results can be explained by the polarized Rabl arrangement of yeast centromeres and telomeres, which promote to telomere pairing by allowing contact between chromosome arms of equal length in anaphase

Actin-Related Protein Arp6 Influences H2A.Z-Dependent and -Independent Gene Expression and Links Ribosomal Protein Genes to Nuclear Pores

Actin-related proteins are ubiquitous components of chromatin remodelers and are conserved from yeast to man. We have examined the role of the budding yeast actin-related protein Arp6 in gene expression, both as a component of the SWR1 complex (SWR-C) and in its absence. We mapped Arp6 binding sites along four yeast chromosomes using chromatin immunoprecipitation from wild-type and swr1 deleted (swr1Δ) cells. We find that a majority of Arp6 binding sites coincide with binding sites of Swr1, the catalytic subunit of SWR-C, and with the histone H2A variant Htz1 (H2A.Z) deposited by SWR-C. However, Arp6 binding detected at centromeres, the promoters of ribosomal protein (RP) genes, and some telomeres is independent of Swr1 and Htz1 deposition. Given that RP genes and telomeres both show association with the nuclear periphery, we monitored the ability of Arp6 to mediate the localization of chromatin to nuclear pores. Arp6 binding is sufficient to shift a randomly positioned locus to nuclear periphery, even in a swr1Δ strain. Arp6 is also necessary for the pore association of its targeted RP promoters possibly through cell cycle-dependent factors. Loss of Arp6, but not Htz1, leads to an up-regulation of these RP genes. In contrast, the pore-association of GAL1 correlates with Htz1 deposition, and loss of Arp6 reduces both GAL1 activation and peripheral localization. We conclude that Arp6 functions both together with the nucleosome remodeler Swr1 and also without it, to mediate Htz1-dependent and Htz1-independent binding of chromatin domains to nuclear pores. This association is shown to have modulating effects on gene expression

Synergistic lethality between BRCA1 and H3K9me2 loss reflects satellite derepression.

has two histone H3 Lys9 methyltransferases, MET-2 (SETDB1 homolog) and SET-25 (G9a/SUV39H1 related). In worms, we found simple repeat sequences primarily marked by H3K9me2, while transposable elements and silent tissue-specific genes bear H3K9me3. RNA sequencing (RNA-seq) in histone methyltransferase (HMT) mutants shows that MET-2-mediated H3K9me2 is necessary for satellite repeat repression, while SET-25 silences a subset of transposable elements and tissue-specific genes through H3K9me3. A genome-wide synthetic lethality screen showed that RNA processing, nuclear RNA degradation, the BRCA1/BARD1 complex, and factors mediating replication stress survival are necessary for germline viability in worms lacking MET-2 but not SET-25. Unlike mutants, -null worms accumulated satellite repeat transcripts, which form RNA:DNA hybrids on repetitive sequences, additively with the loss of BRCA1 or BARD1. BRCA1/BARD1-mediated H2A ubiquitination and MET-2 deposited H3K9me2 on satellite repeats are partially interdependent, suggesting both that the loss of silencing generates BRCA-recruiting DNA damage and that BRCA1 recruitment by damage helps silence repeats. The artificial induction of MSAT1 transcripts can itself trigger damage-induced germline lethality in a wild-type background, arguing that the synthetic sterility upon BRCA1/BARD1 and H3K9me2 loss is directly linked to the DNA damage provoked by unscheduled satellite repeat transcription

Hydride route for the palladium-catalysed cyclocarbonylation of monoterpenes

This paper focuses on the mechanism by which a monoterpene undergoes a cyclocarbonylation reaction catalysed by a palladium complex. Evidence is provided, based on intermediate species observed under pressure or with various ligands, that the catalytic cycle follows a hydride route starting from [Pd(H)(SnCl3)L-2], The [Pd(H)(SnCl3)L-2] complexes (L = PPh3 or PCy3) have been observed for the first time by multinuclear NMR spectroscopy. Cationic hydride complexes or palladium(0) precursors show either no or poor reactivity. Studies related to model platinum complex chemistry have detected an acylplatinum species. Most of the observations have been done on the cyclocarbonylation of isopulegol, di-hydromyrcenol or isolimonene into the corresponding lactones or cyclopentanones. The use of dihydromyrcene allowed us to observe the acylplatinum complex and the corresponding elusive acylpalladium species. The co-catalytic role of SnCl2 is also demonstrated

Increased mobility of double-strand breaks requires Mec1, Rad9 and the homologous recombination machinery.

Chromatin mobility is thought to facilitate homology search during homologous recombination and to shift damage either towards or away from specialized repair compartments. However, unconstrained mobility of double-strand breaks could also promote deleterious chromosomal translocations. Here we use live time-lapse fluorescence microscopy to track the mobility of damaged DNA in budding yeast. We found that a Rad52-YFP focus formed at an irreparable double-strand break moves in a larger subnuclear volume than the undamaged locus. In contrast, Rad52-YFP bound at damage arising from a protein-DNA adduct shows no increase in movement. Mutant analysis shows that enhanced double-strand-break mobility requires Rad51, the ATPase activity of Rad54, the ATR homologue Mec1 and the DNA-damage-response mediator Rad9. Consistent with a role for movement in the homology-search step of homologous recombination, we show that recombination intermediates take longer to form in cells lacking Rad9