Application of graph combinatorics to rational identities of type A

To a word $w$, we associate the rational function $\Psi_w = \prod (x_{w_i} - x_{w_{i+1}})^{-1}$. The main object, introduced by C. Greene to generalize identities linked to Murnaghan-Nakayama rule, is a sum of its images by certain permutations of the variables. The sets of permutations that we consider are the linear extensions of oriented graphs. We explain how to compute this rational function, using the combinatorics of the graph $G$. We also establish a link between an algebraic property of the rational function (the factorization of the numerator) and a combinatorial property of the graph (the existence of a disconnecting chain).Comment: This is the complete version of the submitted fpsac paper (2009

Linear extension sums as valuations on cones

33 pagesInternational audienceThe geometric and algebraic theory of valuations on cones is applied to understand identities involving summing certain rational functions over the set of linear extensions of a poset

Highest weight Macdonald and Jack Polynomials

Fractional quantum Hall states of particles in the lowest Landau levels are described by multivariate polynomials. The incompressible liquid states when described on a sphere are fully invariant under the rotation group. Excited quasiparticle/quasihole states are member of multiplets under the rotation group and generically there is a nontrivial highest weight member of the multiplet from which all states can be constructed. Some of the trial states proposed in the literature belong to classical families of symmetric polynomials. In this paper we study Macdonald and Jack polynomials that are highest weight states. For Macdonald polynomials it is a (q,t)-deformation of the raising angular momentum operator that defines the highest weight condition. By specialization of the parameters we obtain a classification of the highest weight Jack polynomials. Our results are valid in the case of staircase and rectangular partition indexing the polynomials.Comment: 17 pages, published versio

The Partition Function of Multicomponent Log-Gases

We give an expression for the partition function of a one-dimensional log-gas comprised of particles of (possibly) different integer charge at inverse temperature {\beta} = 1 (restricted to the line in the presence of a neutralizing field) in terms of the Berezin integral of an associated non- homogeneous alternating tensor. This is the analog of the de Bruijn integral identities [3] (for {\beta} = 1 and {\beta} = 4) ensembles extended to multicomponent ensembles.Comment: 14 page

24S‐hydroxycholesterol: cellular effects and variations in brain diseases

The adult brain exhibit a characteristic cholesterol homeostasis, with low synthesis rate and active catabolism. Brain cholesterol turnover is possible thanks to the action of the enzyme Cytochrome P450 46A1 (CYP46A1) or 24-cholesterol hydroxylase, that transforms cholesterol into 24S-hydroxycholesterol (24S-HC). But before crossing the blood-brain barrier (BBB), this oxysterol that is the most abundant in the brain can act locally, affecting the functioning of neurons, astrocytes, oligodendrocytes, and vascular cells. The first part of this review addresses different aspects of 24S-HC production and elimination from the brain. The second part concentrates in the effects of 24S-HC at the cellular level, describing how this oxysterol affects cell viability, amyloid beta production, neurotransmission, and transcriptional activity. Finally, the role of 24S-HC in Alzheimer, Huntington and Parkinson diseases, multiple sclerosis and amyotrophic lateral sclerosis, as well as the possibility of using this oxysterol as predictive and/or evolution biomarker in different brain disorders is discussed.Fil: Sodero, Alejandro Omar. Pontificia Universidad Católica Argentina "Santa María de los Buenos Aires". Instituto de Investigaciones Biomédicas. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Houssay. Instituto de Investigaciones Biomédicas; Argentin

Quantification of the 2-Deoxyribonolactone and Nucleoside 5 '-Aldehyde Products of 2-Deoxyribose Oxidation in DNA and Cells by Isotope-Dilution Gas Chromatography Mass Spectrometry: Differential Effects of gamma-Radiation and Fe2+-EDTA

The oxidation of 2-deoxyribose in DNA has emerged as a critical determinant of the cellular toxicity of oxidative damage to DNA, with oxidation of each carbon producing a unique spectrum of electrophilic products. We have developed and validated an isotope-dilution gas chromatography-coupled mass spectrometry (GC−MS) method for the rigorous quantification of two major 2-deoxyribose oxidation products: the 2-deoxyribonolactone abasic site of 1′-oxidation and the nucleoside 5′-aldehyde of 5′-oxidation chemistry. The method entails elimination of these products as 5-methylene-2(5H)-furanone (5MF) and furfural, respectively, followed by derivatization with pentafluorophenylhydrazine (PFPH), addition of isotopically labeled PFPH derivatives as internal standards, extraction of the derivatives, and quantification by GC−MS analysis. The precision and accuracy of the method were validated with oligodeoxynucleotides containing the 2-deoxyribonolactone and nucleoside 5′-aldehyde lesions. Further, the well-defined 2-deoxyribose oxidation chemistry of the enediyne antibiotics, neocarzinostatin and calicheamicin γ1I, was exploited in control studies, with neocarzinostatin producing 10 2-deoxyribonolactone and 300 nucleoside 5′-aldehyde per 106 nt per μM in accord with its established minor 1′- and major 5′-oxidation chemistry. Calicheamicin unexpectedly caused 1′-oxidation at a low level of 10 2-deoxyribonolactone per 106 nt per μM in addition to the expected predominance of 5′-oxidation at 560 nucleoside 5′-aldehyde per 106 nt per μM. The two hydroxyl radical-mediated DNA oxidants, γ-radiation and Fe2+−EDTA, produced nucleoside 5′-aldehyde at a frequency of 57 per 106 nt per Gy (G-value 74 nmol/J) and 3.5 per 106 nt per μM, respectively, which amounted to 40% and 35%, respectively, of total 2-deoxyribose oxidation as measured by a plasmid nicking assay. However, γ-radiation and Fe2+−EDTA produced different proportions of 2-deoxyribonolactone at 7% and 24% of total 2-deoxyribose oxidation, respectively, with frequencies of 10 lesions per 106 nt per Gy (G-value, 13 nmol/J) and 2.4 lesions per 106 nt per μM. Studies in TK6 human lymphoblastoid cells, in which the analytical data were corrected for losses sustained during DNA isolation, revealed background levels of 2-deoxyribonolactone and nucleoside 5′-aldehyde of 9.7 and 73 lesions per 106 nt, respectively. γ-Irradiation of the cells caused increases of 0.045 and 0.22 lesions per 106 nt per Gy, respectively, which represents a 250-fold quenching effect of the cellular environment similar to that observed in previous studies. The proportions of the various 2-deoxyribose oxidation products generated by γ-radiation are similar for purified DNA and cells. These results are consistent with solvent exposure as a major determinant of hydroxyl radical reactivity with 2-deoxyribose in DNA, but the large differences between γ-radiation and Fe2+−EDTA suggest that factors other than hydroxyl radical reactivity govern DNA oxidation chemistry.National Institute of Environmental Health Sciences (ES002109)National Center for Research Resources (U.S.) (RR023783-01)National Center for Research Resources (U.S.) (RR017905-01)National Cancer Institute (U.S.) (CA103146

Structures of (5′S)-8,5′-Cyclo-2′-deoxyguanosine Mismatched with dA or dT

pubs.acs.org/cr

AAV-CYP46A1 brain administration restores cholesterol metabolism and is neuroprotective in Huntington's disease

Conference on Changing the Face of Modern Medicine - Stem Cells and Gene Therapy, Florence, ITALY, OCT 18-21, 2016International audienceno abstrac

Impaired brain energy metabolism in the BACHD mouse model of Huntington's disease: critical role of astrocyte-neuron interactions

International audienceHuntington's disease (HD) is caused by cytosine-adenine-guanine (CAG) repeat expansions in the huntingtin (Htt) gene. Although early energy metabolic alterations in HD are likely to contribute to later neurodegenerative processes, the cellular and molecular mechanisms responsible for these metabolic alterations are not well characterized. Using the BACHD mice that express the full-length mutant huntingtin (mHtt) protein with 97 glutamine repeats, we first demonstrated localized in vivo changes in brain glucose use reminiscent of what is observed in premanifest HD carriers. Using biochemical, molecular, and functional analyses on different primary cell culture models from BACHD mice, we observed that mHtt does not directly affect metabolic activity in a cell autonomous manner. However, coculture of neurons with astrocytes from wild-type or BACHD mice identified mutant astrocytes as a source of adverse non-cell autonomous effects on neuron energy metabolism possibly by increasing oxidative stress. These results suggest that astrocyte-to-neuron signaling is involved in early energy metabolic alterations in HD