The age grading and the Chen-Ruan cup product

We prove that the obstruction bundle used to define the cup-product in Chen-Ruan cohomology is determined by the so-called `age grading' or `degree-shifting numbers'. Indeed, the obstruction bundle can be directly computed using the age grading. We obtain a Kunneth Theorem for Chen-Ruan cohomology as a direct consequence of an elementary property of the age grading, and explain how several other results - including associativity of the cup-product - can be proved in a similar way.Comment: 11 pages. Example added and minor errors correcte

String Topology for Lie Groups

In 1999 Chas and Sullivan showed that the homology of the free loop space of an oriented manifold admits the structure of a Batalin-Vilkovisky algebra. In this paper we give a direct description of this Batalin-Vilkovisky algebra in the case that the manifold is a compact Lie group G. Our answer is phrased in terms of the homology of G, the homology of the space of based loops on G, and the homology suspension. The result is applied to compute the Batalin-Vilkovisky algebra associated to the special orthogonal groups SO(n) with coefficients in the rational numbers and in the integers modulo two.Comment: 22 page

Vector Fields and Flows on Differentiable Stacks

This paper introduces the notions of vector field and flow on a general differentiable stack. Our main theorem states that the flow of a vector field on a compact proper differentiable stack exists and is unique up to a uniquely determined 2-cell. This extends the usual result on the existence and uniqueness of flows on a manifold as well as the author's existing results for orbifolds. It sets the scene for a discussion of Morse Theory on a general proper stack and also paves the way for the categorification of other key aspects of differential geometry such as the tangent bundle and the Lie algebra of vector fields.Comment: 41 page

Population stratification may bias analysis of PGC-1α as a modifier of age at Huntington disease motor onset

Huntington’s disease (HD) is an inherited neurodegenerative disorder characterized by motor, cognitive and behavioral disturbances, caused by the expansion of a CAG trinucleotide repeat in the HD gene. The CAG allele size is the major determinant of age at onset (AO) of motor symptoms, although the remaining variance in AO is highly heritable. The rs7665116 SNP in PPARGC1A, encoding the mitochondrial regulator PGC-1α, has been reported to be a significant modifier of AO in three European HD cohorts, perhaps due to affected cases from Italy. We attempted to replicate these findings in a large collection of (1,727) HD patient DNA samples of European origin. In the entire cohort, rs7665116 showed a significant effect in the dominant model (p value = 0.008) and the additive model (p value = 0.009). However, when examined by origin, cases of Southern European origin had an increased rs7665116 minor allele frequency (MAF), consistent with this being an ancestry-tagging SNP. The Southern European cases, despite similar mean CAG allele size, had a significantly older mean AO (p < 0.001), suggesting population-dependent phenotype stratification. When the generalized estimating equations models were adjusted for ancestry, the effect of the rs7665116 genotype on AO decreased dramatically. Our results do not support rs7665116 as a modifier of AO of motor symptoms, as we found evidence for a dramatic effect of phenotypic (AO) and genotypic (MAF) stratification among European cohorts that was not considered in previously reported association studies. A significantly older AO in Southern Europe may reflect population differences in genetic or environmental factors that warrant further investigation

Inherited variation in immune genes and pathways and glioblastoma risk

To determine whether inherited variations in immune function single-nucleotide polymorphisms (SNPs), genes or pathways affect glioblastoma risk, we analyzed data from recent genome-wide association studies in conjunction with predefined immune function genes and pathways. Gene and pathway analyses were conducted on two independent data sets using 6629 SNPs in 911 genes on 17 immune pathways from 525 glioblastoma cases and 602 controls from the University of California, San Francisco (UCSF) and a subset of 6029 SNPs in 893 genes from 531 cases and 1782 controls from MD Anderson (MDA). To further assess consistency of SNP-level associations, we also compared data from the UK (266 cases and 2482 controls) and the Mayo Clinic (114 cases and 111 controls). Although three correlated epidermal growth factor receptor (EGFR) SNPs were consistently associated with glioblastoma in all four data sets (Mantel–Haenzel P values = 1 × 10−5 to 4 × 10−3), independent replication is required as genome-wide significance was not attained. In gene-level analyses, eight immune function genes were significantly (minP < 0.05) associated with glioblastoma; the IL-2RA (CD25) cytokine gene had the smallest minP values in both UCSF (minP = 0.01) and MDA (minP = 0.001) data sets. The IL-2RA receptor is found on the surface of regulatory T cells potentially contributing to immunosuppression characteristic of the glioblastoma microenvironment. In pathway correlation analyses, cytokine signaling and adhesion–extravasation–migration pathways showed similar associations with glioblastoma risk in both MDA and UCSF data sets. Our findings represent the first systematic description of immune genes and pathways that characterize glioblastoma risk

A Helminth Immunomodulator Exploits Host Signaling Events to Regulate Cytokine Production in Macrophages

Parasitic worms alter their host's immune system to diminish the inflammatory responses directed against them, using very efficient immunomodulating molecules. We have previously shown that the helminth immunomodulator cystatin (AvCystatin) profoundly reduces the progression of inflammatory diseases via modulation of macrophages. Here we elucidate the signaling events in macrophages triggered by AvCystatin. Labeled AvCystatin was predominantly taken up by macrophages and subsequently induced the phosphorylation of the mitogen-activated protein kinases (MAPK) ERK1/2 and p38. IL-10 expression induced by AvCystatin in macrophages was tyrosine kinase sensitive and dependent on activation of both MAP kinases, in clear contrast to expression of IL-12/23p40. In addition, phosphorylation of the transcription factors CREB and STAT3 was induced by AvCystatin and regulated by phospho-ERK. Chemical inhibition of phosphoinositide 3-kinase (PI3K) reduced AvCystatin-induced cytokine release; however, AKT, the downstream target of PI3K, was not activated following AvCystatin exposure. To characterize signaling elements involved in alteration of the macrophage phenotype we applied mathematical modeling. Experimental testing of the in silico generated hypotheses identified dual specificity phosphatase (DUSP) 1 and 2, as regulators in AvCystatin triggered macrophages in vitro and in vivo. In particular, DUSP1 was subsequently found to be responsible for regulation of ERK- and p38-phosphorylation and controlled the IL-10 expression in macrophages by AvCystatin. Thus, we show that AvCystatin exploits activation and deactivation pathways of MAP kinases to induce regulatory macrophages. This study provides insights into molecular mechanisms of macrophage manipulation by parasites and highlights the utility of mathematical modeling for the elucidation of regulatory circuits of immune cells