A chain morphism for Adams operations on rational algebraic K-theory

For any regular noetherian scheme X and every k>0, we define a chain morphism between two chain complexes whose homology with rational coefficients is isomorphic to the algebraic K-groups of X tensored by the field of rational numbers. It is shown that these morphisms induce in homology the Adams operations defined by Gillet and Soule or the ones defined by Grayson.Comment: 40 page

Immunity against fungal beta 1,3 glucan carbohydrate in the gastrointestinal tract

Inflammatory Bowel Disease (IBD) is a debilitating, life- long disease that affects about 1.4 millions Americans. Little is known about the pathogenesis of IBD and an effective cure still remains to be discovered. While there are numerous T cell targeting therapies for IBD, more research is still needed. Bispecific T Cell Engagers, BiTES, is a modified protein capable of engaging two antigens simultaneously; it is capable of activating T cells by circumventing the MHC protein molecule. This provides an alternative to the current molecular therapies for IBD. In addition to monoclonal therapy research, there has been a plethora of research on immunomodulatory molecules, such as β- glucan. The benefit of β-glucan has been shown with supplements and food sources alike in animal models. In this study, we used BiTES, CMPD-1, with an anti-CD3/ Dectin-1 epitopes capable of engaging T Cells and β-glucan in beads and fungi cell wall. CMPD-1 is capable of engaging Splenic and Lamina Propia T Cells from a C57BL/6 mice. Likewise, CMPD-1 engaged T cells to hyphae of C. albicans and A. fumigatus, which have a higher concentration of β-glucan than in the candida form. The data show a delayed in hyphae growth in yeast with CMPD-1 and a decrease in yeast growth for the first four hours when compared to non- BiTES molecules. Additionally, qualitative analysis of CMPD-1 shows a decrease A. fumigatus growth after a 72-hour incubation period. Splenic T cells from mice lacking Dectin-1 and Wild-type (WT) mouse strains where incubated with BiTES compound and yeast for 23 hours followed by a PrestoBlue killing assay to assess yeast cell viability. The PrestoBlue assay showed that CMPD-1 killed more A. fumigatus in both T cell subsets; although, the difference lacked statistical significance. The applications of this molecule as a therapeutic agent for IBD are promising, although, still in its infancy. An alternative use for this molecule is to train the immune system with the BiTES molecule in conjunction with β-glucan supplements to build immunity against opportunistic pathogens such as A. fumigatus and C. albicans that often cause havoc in IBD patients as a result of the changes in microbiota, and compromised integrity of the GI tract.2017-06-16T00:00:00

Power-law Kinetics and Determinant Criteria for the Preclusion of Multistationarity in Networks of Interacting Species

We present determinant criteria for the preclusion of non-degenerate multiple steady states in networks of interacting species. A network is modeled as a system of ordinary differential equations in which the form of the species formation rate function is restricted by the reactions of the network and how the species influence each reaction. We characterize families of so-called power-law kinetics for which the associated species formation rate function is injective within each stoichiometric class and thus the network cannot exhibit multistationarity. The criterion for power-law kinetics is derived from the determinant of the Jacobian of the species formation rate function. Using this characterization we further derive similar determinant criteria applicable to general sets of kinetics. The criteria are conceptually simple, computationally tractable and easily implemented. Our approach embraces and extends previous work on multistationarity, such as work in relation to chemical reaction networks with dynamics defined by mass-action or non-catalytic kinetics, and also work based on graphical analysis of the interaction graph associated to the system. Further, we interpret the criteria in terms of circuits in the so-called DSR-graphComment: To appear in SIAM Journal on Applied Dynamical System

Node Balanced Steady States: Unifying and Generalizing Complex and Detailed Balanced Steady States

We introduce a unifying and generalizing framework for complex and detailed balanced steady states in chemical reaction network theory. To this end, we generalize the graph commonly used to represent a reaction network. Specifically, we introduce a graph, called a reaction graph, that has one edge for each reaction but potentially multiple nodes for each complex. A special class of steady states, called node balanced steady states, is naturally associated with such a reaction graph. We show that complex and detailed balanced steady states are special cases of node balanced steady states by choosing appropriate reaction graphs. Further, we show that node balanced steady states have properties analogous to complex balanced steady states, such as uniqueness and asymptotical stability in each stoichiometric compatibility class. Moreover, we associate an integer, called the deficiency, to a reaction graph that gives the number of independent relations in the reaction rate constants that need to be satisfied for a positive node balanced steady state to exist. The set of reaction graphs (modulo isomorphism) is equipped with a partial order that has the complex balanced reaction graph as minimal element. We relate this order to the deficiency and to the set of reaction rate constants for which a positive node balanced steady state exists

On the existence of Hopf bifurcations in the sequential and distributive double phosphorylation cycle

Protein phosphorylation cycles are important mechanisms of the post translational modification of a protein and as such an integral part of intracellular signaling and control. We consider the sequential phosphorylation and dephosphorylation of a protein at two binding sites. While it is known that proteins where phosphorylation is processive and dephosphorylation is distributive admit oscillations (for some value of the rate constants and total concentrations) it is not known whether or not this is the case if both phosphorylation and dephosphorylation are distributive. We study four simplified mass action models of sequential and distributive phosphorylation and show that for each of those there do not exist rate constants and total concentrations where a Hopf bifurcation occurs. To arrive at this result we use convex parameters to parameterize the steady state and Hurwitz matrices

Tikhonov-Fenichel reduction for parameterized critical manifolds with applications to chemical reaction networks

We derive a reduction formula for singularly perturbed ordinary differential equations (in the sense of Tikhonov and Fenichel) with a known parameterization of the critical manifold. No a priori assumptions concerning separation of slow and fast variables are made, or necessary.We apply the theoretical results to chemical reaction networks with mass action kinetics admitting slow and fast reactions. For some relevant classes of such systems there exist canonical parameterizations of the variety of stationary points, hence the theory is applicable in a natural manner. In particular we obtain a closed form expression for the reduced system when the fast subsystem admits complex balanced steady states