Generalized Mayer-Vietoris sequences in algebraic K-theory

AbstractLong exact sequences of algebraic K-groups for certain kinds of multiple pullback rings are constructed, with special emphasis on Dedekind-like rings. In the case where excision holds they reduce to the usual Mayer-Vietoris sequences. These sequences are then used to obtain information about the K-groups of integral group rings of abelian groups of square-free order; about certain rings of integers in number fields; and about the coordinate ring of n lines in the plane

A Systems Biology Approach to Iron Metabolism

Iron is critical to the survival of almost all living organisms. However, inappropriately low or high levels of iron are detrimental and contribute to a wide range of diseases. Recent advances in the study of iron metabolism have revealed multiple intricate pathways that are essential to the maintenance of iron homeostasis. Further, iron regulation involves processes at several scales, ranging from the subcellular to the organismal. This complexity makes a systems biology approach crucial, with its enabling technology of computational models based on a mathematical description of regulatory systems. Systems biology may represent a new strategy for understanding imbalances in iron metabolism and their underlying cause

A mathematical model of combined CD8 T cell costimulation by 4-1BB (CD137) and OX40 (CD134) receptors.

Combined agonist stimulation of the TNFR costimulatory receptors 4-1BB (CD137) and OX40(CD134) has been shown to generate supereffector CD8 T cells that clonally expand to greater levels, survive longer, and produce a greater quantity of cytokines compared to T cells stimulated with an agonist of either costimulatory receptor individually. In order to understand the mechanisms for this effect, we have created a mathematical model for the activation of the CD8 T cell intracellular signaling network by mono- or dual-costimulation. We show that supereffector status is generated via downstream interacting pathways that are activated upon engagement of both receptors, and in silico simulations of the model are supported by published experimental results. The model can thus be used to identify critical molecular targets of T cell dual-costimulation in the context of cancer immunotherapy

A Systems Biology Approach to Understanding the Pathophysiology of High-Grade Serous Ovarian Cancer: Focus on Iron and Fatty Acid Metabolism.

Ovarian cancer (OVC) is the most lethal of the gynecological malignancies, with diagnosis often occurring during advanced stages of the disease. Moreover, a majority of cases become refractory to chemotherapeutic approaches. Therefore, it is important to improve our understanding of the molecular dependencies underlying the disease to identify novel diagnostic and precision therapeutics for OVC. Cancer cells are known to sequester iron, which can potentiate cancer progression through mechanisms that have not yet been completely elucidated. We developed an algorithm to identify novel links between iron and pathways implicated in high-grade serous ovarian cancer (HGSOC), the most common and deadliest subtype of OVC, using microarray gene expression data from both clinical sources and an experimental model. Using our approach, we identified several links between fatty acid (FA) and iron metabolism, and subsequently developed a network for iron involvement in FA metabolism in HGSOC. FA import and synthesis pathways are upregulated in HGSOC and other cancers, but a link between these processes and iron-related genes has not yet been identified. We used the network to derive hypotheses of specific mechanisms by which iron and iron-related genes impact and interact with FA metabolic pathways to promote tumorigenesis. These results suggest a novel mechanism by which iron sequestration by cancer cells can potentiate cancer progression, and may provide novel targets for use in diagnosis and/or treatment of HGSOC

An Axiomatic Setup for Algorithmic Homological Algebra and an Alternative Approach to Localization

In this paper we develop an axiomatic setup for algorithmic homological algebra of Abelian categories. This is done by exhibiting all existential quantifiers entering the definition of an Abelian category, which for the sake of computability need to be turned into constructive ones. We do this explicitly for the often-studied example Abelian category of finitely presented modules over a so-called computable ring $R$, i.e., a ring with an explicit algorithm to solve one-sided (in)homogeneous linear systems over $R$. For a finitely generated maximal ideal $\mathfrak{m}$ in a commutative ring $R$ we show how solving (in)homogeneous linear systems over $R_{\mathfrak{m}}$ can be reduced to solving associated systems over $R$. Hence, the computability of $R$ implies that of $R_{\mathfrak{m}}$. As a corollary we obtain the computability of the category of finitely presented $R_{\mathfrak{m}}$-modules as an Abelian category, without the need of a Mora-like algorithm. The reduction also yields, as a by-product, a complexity estimation for the ideal membership problem over local polynomial rings. Finally, in the case of localized polynomial rings we demonstrate the computational advantage of our homologically motivated alternative approach in comparison to an existing implementation of Mora's algorithm.Comment: Fixed a typo in the proof of Lemma 4.3 spotted by Sebastian Posu