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

The Waldschmidt constant for squarefree monomial ideals

Given a squarefree monomial ideal $I \subseteq R =k[x_1,\ldots,x_n]$, we show that $\widehat\alpha(I)$, the Waldschmidt constant of $I$, can be expressed as the optimal solution to a linear program constructed from the primary decomposition of $I$. By applying results from fractional graph theory, we can then express $\widehat\alpha(I)$ in terms of the fractional chromatic number of a hypergraph also constructed from the primary decomposition of $I$. Moreover, expressing $\widehat\alpha(I)$ as the solution to a linear program enables us to prove a Chudnovsky-like lower bound on $\widehat\alpha(I)$, thus verifying a conjecture of Cooper-Embree-H\`a-Hoefel for monomial ideals in the squarefree case. As an application, we compute the Waldschmidt constant and the resurgence for some families of squarefree monomial ideals. For example, we determine both constants for unions of general linear subspaces of $\mathbb{P}^n$ with few components compared to $n$, and we find the Waldschmidt constant for the Stanley-Reisner ideal of a uniform matroid.Comment: 26 pages. This project was started at the Mathematisches Forschungsinstitut Oberwolfach (MFO) as part of the mini-workshop "Ideals of Linear Subspaces, Their Symbolic Powers and Waring Problems" held in February 2015. Comments are welcome. Revised version corrects some typos, updates the references, and clarifies some hypotheses. To appear in the Journal of Algebraic Combinatoric

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

Noncommutative Geometry in the Framework of Differential Graded Categories

In this survey article we discuss a framework of noncommutative geometry with differential graded categories as models for spaces. We outline a construction of the category of noncommutative spaces and also include a discussion on noncommutative motives. We propose a motivic measure with values in a motivic ring. This enables us to introduce certain zeta functions of noncommutative spaces.Comment: 19 pages. Minor corrections and one reference added; to appear in the proceedings volume of AGAQ Istanbul, 200

Rigidity and exotic models for v1-local G-equivariant stable homotopy theory

We prove that the v1-local G-equivariant stable homotopy category for G a finite group has a unique G-equivariant model at p=2. This means that at the prime 2 the homotopy theory of G-spectra up to fixed point equivalences on K-theory is uniquely determined by its triangulated homotopy category and basic Mackey structure. The result combines the rigidity result for K-local spectra of the second author with the equivariant rigidity result for G-spectra of the first author. Further, when the prime p is at least 5 and does not divide the order of G, we provide an algebraic exotic model as well as a G-equivariant exotic model for the v1-local G-equivariant stable homotopy category, showing that for primes p≥5 equivariant rigidity fails in general

Blocking Synthesis of the Variant Surface Glycoprotein Coat in Trypanosoma brucei Leads to an Increase in Macrophage Phagocytosis Due to Reduced Clearance of Surface Coat Antibodies

The extracellular bloodstream form parasite Trypanosoma brucei is supremely adapted to escape the host innate and adaptive immune system. Evasion is mediated through an antigenically variable Variant Surface Glycoprotein (VSG) coat, which is recycled at extraordinarily high rates. Blocking VSG synthesis triggers a precytokinesis arrest where stalled cells persist for days in vitro with superficially intact VSG coats, but are rapidly cleared within hours in mice. We therefore investigated the role of VSG synthesis in trypanosome phagocytosis by activated mouse macrophages. T. brucei normally effectively evades macrophages, and induction of VSG RNAi resulted in little change in phagocytosis of the arrested cells. Halting VSG synthesis resulted in stalled cells which swam directionally rather than tumbling, with a significant increase in swim velocity. This is possibly a consequence of increased rigidity of the cells due to a restricted surface coat in the absence of VSG synthesis. However if VSG RNAi was induced in the presence of anti-VSG221 antibodies, phagocytosis increased significantly. Blocking VSG synthesis resulted in reduced clearance of anti-VSG antibodies from the trypanosome surface, possibly as a consequence of the changed motility. This was particularly marked in cells in the G2/ M cell cycle stage, where the half-life of anti-VSG antibody increased from 39.3 ± 4.2 seconds to 99.2 ± 15.9 seconds after induction of VSG RNAi. The rates of internalisation of bulk surface VSG, or endocytic markers like transferrin, tomato lectin or dextran were not significantly affected by the VSG synthesis block. Efficient elimination of anti-VSG-antibody complexes from the trypanosome cell surface is therefore essential for trypanosome evasion of macrophages. These experiments highlight the essentiality of high rates of VSG recycling for the rapid removal of host opsonins from the parasite surface, and identify this process as a key parasite virulence factor during a chronic infection

ModelCIF: An Extension of PDBx/mmCIF Data Representation for Computed Structure Models

ModelCIF (github.com/ihmwg/ModelCIF) is a data information framework developed for and by computational structural biologists to enable delivery of Findable, Accessible, Interoperable, and Reusable (FAIR) data to users worldwide. ModelCIF describes the specific set of attributes and metadata associated with macromolecular structures modeled by solely computational methods and provides an extensible data representation for deposition, archiving, and public dissemination of predicted three-dimensional (3D) models of macromolecules. It is an extension of the Protein Data Bank Exchange / macromolecular Crystallographic Information Framework (PDBx/mmCIF), which is the global data standard for representing experimentally-determined 3D structures of macromolecules and associated metadata. The PDBx/mmCIF framework and its extensions (e.g., ModelCIF) are managed by the Worldwide Protein Data Bank partnership (wwPDB, wwpdb.org) in collaboration with relevant community stakeholders such as the wwPDB ModelCIF Working Group (wwpdb.org/task/modelcif). This semantically rich and extensible data framework for representing computed structure models (CSMs) accelerates the pace of scientific discovery. Herein, we describe the architecture, contents, and governance of ModelCIF, and tools and processes for maintaining and extending the data standard. Community tools and software libraries that support ModelCIF are also described

SnugDock: Paratope Structural Optimization during Antibody-Antigen Docking Compensates for Errors in Antibody Homology Models

High resolution structures of antibody-antigen complexes are useful for analyzing the binding interface and to make rational choices for antibody engineering. When a crystallographic structure of a complex is unavailable, the structure must be predicted using computational tools. In this work, we illustrate a novel approach, named SnugDock, to predict high-resolution antibody-antigen complex structures by simultaneously structurally optimizing the antibody-antigen rigid-body positions, the relative orientation of the antibody light and heavy chains, and the conformations of the six complementarity determining region loops. This approach is especially useful when the crystal structure of the antibody is not available, requiring allowances for inaccuracies in an antibody homology model which would otherwise frustrate rigid-backbone docking predictions. Local docking using SnugDock with the lowest-energy RosettaAntibody homology model produced more accurate predictions than standard rigid-body docking. SnugDock can be combined with ensemble docking to mimic conformer selection and induced fit resulting in increased sampling of diverse antibody conformations. The combined algorithm produced four medium (Critical Assessment of PRediction of Interactions-CAPRI rating) and seven acceptable lowest-interface-energy predictions in a test set of fifteen complexes. Structural analysis shows that diverse paratope conformations are sampled, but docked paratope backbones are not necessarily closer to the crystal structure conformations than the starting homology models. The accuracy of SnugDock predictions suggests a new genre of general docking algorithms with flexible binding interfaces targeted towards making homology models useful for further high-resolution predictions