Azumaya Objects in Triangulated Bicategories

We introduce the notion of Azumaya object in general homotopy-theoretic settings. We give a self-contained account of Azumaya objects and Brauer groups in bicategorical contexts, generalizing the Brauer group of a commutative ring. We go on to describe triangulated bicategories and prove a characterization theorem for Azumaya objects therein. This theory applies to give a homotopical Brauer group for derived categories of rings and ring spectra. We show that the homotopical Brauer group of an Eilenberg-Mac Lane spectrum is isomorphic to the homotopical Brauer group of its underlying commutative ring. We also discuss tilting theory as an application of invertibility in triangulated bicategories.Comment: 23 pages; final version; to appear in Journal of Homotopy and Related Structure

Homological Localisation of Model Categories

One of the most useful methods for studying the stable homotopy category is localising at some spectrum E. For an arbitrary stable model category we introduce a candidate for the E–localisation of this model category. We study the properties of this new construction and relate it to some well–known categories

A Frobenius variant of Seshadri constants

We define and study a version of Seshadri constant for ample line bundles in positive characteristic. We prove that lower bounds for this constant imply the global generation or very ampleness of the corresponding adjoint line bundle. As a consequence, we deduce that the criterion for global generation and very ampleness of adjoint line bundles in terms of usual Seshadri constants holds also in positive characteristic.Comment: 16 page

RationalMaps, a package for Macaulay2

This paper describes the RationalMaps package for Macaulay2. This package provides functionality for computing several aspects of rational maps such as whether a map is birational, or a closed embedding.Comment: 8 pages. The current version of the package (and other necessary files) can be accessed at https://github.com/Macaulay2/Workshop-2016-Utah/tree/master/RationalMap

The Dold-Kan Correspondence and Coalgebra Structures

By using the Dold-Kan correspondence we construct a Quillen adjunction between the model categories of non-cocommutative coassociative simplicial and differential graded coalgebras over a field. We restrict to categories of connected coalgebras and prove a Quillen equivalence between them.Comment: 24 pages. Accepted by the Journal of Homotopy and Related Structures. Online 28 November 201

Cyclic AMP induces integrin-mediated cell adhesion through Epac and Rap1 upon stimulation of the β2-adrenergic receptor

cAMP controls many cellular processes mainly through the activation of protein kinase A (PKA). However, more recently PKA-independent pathways have been established through the exchange protein directly activated by cAMP (Epac), a guanine nucleotide exchange factor for the small GTPases Rap1 and Rap2. In this report, we show that cAMP can induce integrin-mediated cell adhesion through Epac and Rap1. Indeed, when Ovcar3 cells were treated with cAMP, cells adhered more rapidly to fibronectin. This cAMP effect was insensitive to the PKA inhibitor H-89. A similar increase was observed when the cells were transfected with Epac. Both the cAMP effect and the Epac effect on cell adhesion were abolished by the expression of Rap1–GTPase-activating protein, indicating the involvement of Rap1 in the signaling pathway. Importantly, a recently characterized cAMP analogue, 8-(4-chloro-phenylthio)-2′-O-methyladenosine-3′,5′-cyclic monophosphate, which specifically activates Epac but not PKA, induced Rap-dependent cell adhesion. Finally, we demonstrate that external stimuli of cAMP signaling, i.e., isoproterenol, which activates the Gαs-coupled β2-adrenergic receptor can induce integrin-mediated cell adhesion through the Epac-Rap1 pathway. From these results we conclude that cAMP mediates receptor-induced integrin-mediated cell adhesion to fibronectin through the Epac-Rap1 signaling pathway

The Intrinsic Fundamental Group of a Linear Category

We provide an intrinsic definition of the fundamental group of a linear category over a ring as the automorphism group of the fibre functor on Galois coverings. If the universal covering exists, we prove that this group is isomorphic to the Galois group of the universal covering. The grading deduced from a Galois covering enables us to describe the canonical monomorphism from its automorphism group to the first Hochschild-Mitchell cohomology vector space.Comment: Final version, to appear in Algebras and Representation Theor

Cohesive Properties of the Caulobacter crescentus Holdfast Adhesin Are Regulated by a Novel c-di-GMP Effector Protein

When encountering surfaces, many bacteria produce adhesins to facilitate their initial attachment and to irreversibly glue themselves to the solid substrate. A central molecule regulating the processes of this motile-sessile transition is the second messenger c-di-GMP, which stimulates the production of a variety of exopolysaccharide adhesins in different bacterial model organisms. In Caulobacter crescentus, c-di-GMP regulates the synthesis of the polar holdfast adhesin during the cell cycle, yet the molecular and cellular details of this control are currently unknown. Here we identify HfsK, a member of a versatile N-acetyltransferase family, as a novel c-di-GMP effector involved in holdfast biogenesis. Cells lacking HfsK form highly malleable holdfast structures with reduced adhesive strength that cannot support surface colonization. We present indirect evidence that HfsK modifies the polysaccharide component of holdfast to buttress its cohesive properties. HfsK is a soluble protein but associates with the cell membrane during most of the cell cycle. Coincident with peak c-di-GMP levels during the C. crescentus cell cycle, HfsK relocalizes to the cytosol in a c-di-GMP-dependent manner. Our results indicate that this c-di-GMP-mediated dynamic positioning controls HfsK activity, leading to its inactivation at high c-di-GMP levels. A short C-terminal extension is essential for the membrane association, c-di-GMP binding, and activity of HfsK. We propose a model in which c-di-GMP binding leads to the dispersal and inactivation of HfsK as part of holdfast biogenesis progression.IMPORTANCE Exopolysaccharide (EPS) adhesins are important determinants of bacterial surface colonization and biofilm formation. Biofilms are a major cause of chronic infections and are responsible for biofouling on water-exposed surfaces. To tackle these problems, it is essential to dissect the processes leading to surface colonization at the molecular and cellular levels. Here we describe a novel c-di-GMP effector, HfsK, that contributes to the cohesive properties and stability of the holdfast adhesin in C. crescentus We demonstrate for the first time that c-di-GMP, in addition to its role in the regulation of the rate of EPS production, also modulates the physicochemical properties of bacterial adhesins. By demonstrating how c-di-GMP coordinates the activity and subcellular localization of HfsK, we provide a novel understanding of the cellular processes involved in adhesin biogenesis control. Homologs of HfsK are found in representatives of different bacterial phyla, suggesting that they play important roles in various EPS synthesis systems

The Protein Model Portal

Structural Genomics has been successful in determining the structures of many unique proteins in a high throughput manner. Still, the number of known protein sequences is much larger than the number of experimentally solved protein structures. Homology (or comparative) modeling methods make use of experimental protein structures to build models for evolutionary related proteins. Thereby, experimental structure determination efforts and homology modeling complement each other in the exploration of the protein structure space. One of the challenges in using model information effectively has been to access all models available for a specific protein in heterogeneous formats at different sites using various incompatible accession code systems. Often, structure models for hundreds of proteins can be derived from a given experimentally determined structure, using a variety of established methods. This has been done by all of the PSI centers, and by various independent modeling groups. The goal of the Protein Model Portal (PMP) is to provide a single portal which gives access to the various models that can be leveraged from PSI targets and other experimental protein structures. A single interface allows all existing pre-computed models across these various sites to be queried simultaneously, and provides links to interactive services for template selection, target-template alignment, model building, and quality assessment. The current release of the portal consists of 7.6 million model structures provided by different partner resources (CSMP, JCSG, MCSG, NESG, NYSGXRC, JCMM, ModBase, SWISS-MODEL Repository). The PMP is available at http://www.proteinmodelportal.org and from the PSI Structural Genomics Knowledgebase

webPIPSA: a web server for the comparison of protein interaction properties

Protein molecular interaction fields are key determinants of protein functionality. PIPSA (Protein Interaction Property Similarity Analysis) is a procedure to compare and analyze protein molecular interaction fields, such as the electrostatic potential. PIPSA may assist in protein functional assignment, classification of proteins, the comparison of binding properties and the estimation of enzyme kinetic parameters. webPIPSA is a web server that enables the use of PIPSA to compare and analyze protein electrostatic potentials. While PIPSA can be run with downloadable software (see http://projects.eml.org/mcm/software/pipsa), webPIPSA extends and simplifies a PIPSA run. This allows non-expert users to perform PIPSA for their protein datasets. With input protein coordinates, the superposition of protein structures, as well as the computation and analysis of electrostatic potentials, is automated. The results are provided as electrostatic similarity matrices from an all-pairwise comparison of the proteins which can be subjected to clustering and visualized as epograms (tree-like diagrams showing electrostatic potential differences) or heat maps. webPIPSA is freely available at: http://pipsa.eml.org