Random walks in Weyl chambers and crystals

We use Kashiwara crystal basis theory to associate a random walk W to each irreducible representation V of a simple Lie algebra. This is achieved by endowing the crystal attached to V with a (possibly non uniform) probability distribution compatible with its weight graduation. We then prove that the generalized Pitmann transform defined by Biane, Bougerol and O'Connell for similar random walks with uniform distributions yields yet a Markov chain. When the representation is minuscule, and the associated random walk has a drift in the Weyl chamber, we establish that this Markov chain has the same law as W conditionned to never exit the cone of dominant weights. At the heart of our proof is a quotient version of a renewal theorem that we state in the context of general random walks in a lattice.Comment: The second version presents minor modifications to the previous on

Conditioned one-way simple random walk and representation theory

We call one-way simple random walk a random walk in the quadrant Z_+^n whose increments belong to the canonical base. In relation with representation theory of Lie algebras and superalgebras, we describe the law of such a random walk conditioned to stay in a closed octant, a semi-open octant or other types of semi-groups. The combinatorial representation theory of these algebras allows us to describe a generalized Pitman transformation which realizes the conditioning on the set of paths of the walk. We pursue here in a direction initiated by O'Connell and his coauthors [13,14,2], and also developed in [12]. Our work relies on crystal bases theory and insertion schemes on tableaux described by Kashiwara and his coauthors in [1] and, very recently, in [5].Comment: 32 page

Harmonic functions on multiplicative graphs and inverse Pitman transform on infinite random paths

We introduce and characterize central probability distributions on Littelmann paths. Next we establish a law of large numbers and a central limit theorem for the generalized Pitmann transform. We then study harmonic functions on multiplicative graphs defined from the tensor powers of finite-dimensional Lie algebras representations. Finally, we show there exists an inverse of the generalized Pitman transform defined almost surely on the set of infinite paths remaining in the Weyl chamber and explain how it can be computed.Comment: 27 pages, minor corrections and a simpler definition of the Pitman invers

Random walks in Weyl chambers and crystals

The second version presents minor modifications to the previous one.International audienceWe use Kashiwara crystal basis theory to associate a random walk W to each irreducible representation V of a simple Lie algebra. This is achieved by endowing the crystal attached to V with a (possibly non uniform) probability distribution compatible with its weight graduation. We then prove that the generalized Pitmann transform defined by Biane, Bougerol and O'Connell for similar random walks with uniform distributions yields yet a Markov chain. When the representation is minuscule, and the associated random walk has a drift in the Weyl chamber, we establish that this Markov chain has the same law as W conditionned to never exit the cone of dominant weights. At the heart of our proof is a quotient version of a renewal theorem that we state in the context of general random walks in a lattice

Conditioned random walks from Kac-Moody root systems

30 pages, minor correctionsInternational audienceRandom paths are time continuous interpolations of random walks. By using Littelmann path model, we associate to each irreducible highest weight module of a Kac Moody algebra g a random path W. Under suitable hypotheses, we make explicit the probability of the event E: W never exits the Weyl chamber of g. We then give the law of the random walk defined by W conditioned by the event E and proves this law can be recovered by applying to W the generalized Pitmann transform introduced by Biane, Bougerol and O'Connell. This generalizes the main results of [10] and [16] to Kac Moody root systems and arbitrary highest weight modules. Moreover, we use here a completely new approach by exploiting the symmetry of our construction under the action of the Weyl group of g rather than renewal theory and Doob's theorem on Martin kernels

Adaptation of the base-paired double-helix molecular architecture to extreme pressure

The behaviour of the d(GGTATACC) oligonucleotide has been investigated by X-ray crystallography at 295 K in the range from ambient pressure to 2 GPa (∼20 000 atm). Four 3D-structures of the A-DNA form (at ambient pressure, 0.55, 1.09 and 1.39 GPa) were refined at 1.60 or 1.65 Å resolution. In addition to the diffraction pattern of the A-form, the broad meridional streaks previously explained by occluded B-DNA octamers within the channels of the crystalline A-form matrix were observed up to at least 2 GPa. This work highlights an important property of nucleic acids, their capability to withstand very high pressures, while keeping in such conditions a nearly invariant geometry of base pairs that store and carry genetic information. The double-helix base-paired architecture behaves as a molecular spring, which makes it especially adapted to very harsh conditions. These features may have contributed to the emergence of a RNA World at prebiotic stage

New Symmetrically Esterified m-Bromobenzyl Non-Aminobisphosphonates Inhibited Breast Cancer Growth and Metastases

1 - ArticleBACKGROUND: Although there was growing evidence in the potential use of Bisphosphonates (BPs) in cancer therapy, their strong osseous affinities that contrast their poor soft tissue uptake limited their use. Here, we developed a new strategy to overcome BPs hydrophilicity by masking the phosphonic acid through organic protecting groups and introducing hydrophobic functions in the side chain. METHODOLOGY/PRINCIPAL FINDINGS: We synthesized non-nitrogen BPs (non N-BPs) containing bromobenzyl group (BP7033Br) in their side chain that were symmetrically esterified with hydrophobic 4-methoxphenyl (BP7033BrALK) and assessed their effects on breast cancer estrogen-responsive cells (T47D, MCF-7) as well as on non responsive ones (SKBR3, MDA-MB-231 and its highly metastatic derived D3H2LN subclone). BP7033Br ALK was more efficient in inhibiting tumor cell proliferation, migration and survival when compared to BP7033Br. Although both compounds inhibited tumor growth without side effects, only BP7033Br ALK abrogated tumor angiogenesis and D3H2LN cells-induced metastases formation. CONCLUSION/SIGNIFICANCE: Taken together these data suggest the potential therapeutic use of this new class of esterified Bisphosphonates (BPs) in the treatment of tumor progression and metastasis without toxic adverse effects

New Synthesized Derivatives from N-Substituted-4-Oxo-[1] Benzopyrano [4,3-c] Pyrazole Influenced Proliferation, Viability, Spreading and Invasion of Human Liver Tumor Cells

Background/Aim: There is an unsatisfied clinical demand to develop new anticancer agents. The aim of the current study was to synthesize new coumarin derivatives using two different synthetic methodologies and to evaluate their anticancer activity. Materials and methods: Four coumarin derivatives were synthesized and evaluated for their anticancer activities. The structures of all compounds were confirmed by infrared (IR), UV-vis, Nuclear magnetic resonance (NMR) 13C NMR, 1H NMR, and high-resolution mass spectrometry (HRMS) analysis. All the synthesized compounds (4, 5, 8 and 9) were analyzed for their anti-proliferative (MTT and LDH assays and cell cycle studied with flow cytometry) and anti-invasive activity (spreading and invasion tests) on human hepatoma cell lines Huh-7 in vitro. Doxorubicin was used as control in order to compare their anti-tumoral effects. Results. All the synthesized compounds are potential inhibitors of proliferation, viability, spreading and invasion of human liver tumor cells with a 50% inhibitory Concentration range,  IC50=10.37 μM to 12.94 μM. Conclusion. This study could lead to the identification of a new target therapy for human Hepatocellular carcinoma (HCC) or other cancers

Synthèse de glycopeptides et recherche de nouveaux antibactériens glucidiques

Non disponible / Not availableDe nouvelles applications de carbanions alpha-phosphoryles hautement fonctionnalisés ont été développées pour la synthèse de produits d'intérêt biologique. La première partie de ce travail présente la synthèse de nouveaux glycopeptides renfermant un lien porteur carbone, insaturé ou non, à partir des dialdoses. Deux voies d'accès possibles pour greffer le motif sucre sur le peptide via « un pont énone » ont été étudiées. La première concerne l'utilisation des réactifs de Wittig-Horner peptidiques sur un aldéhyde glucidique. La deuxième consiste à préparer des acides alpha, beta-éthyléniques glucidiques à partir des mêmes dialdoses puis, à greffer le peptide sur la fonction carboxylique. Cette deuxième voie a permis de préparer une galactoenképhaline totalement déprotégée. La réactivité du motif cétone alpha, beta-éthylénique créé a fait l'objet d'une étude particulière notamment vis-à-vis des dérivés soufres. Nous avons montré que les glycopeptides éthyléniques sont de bons accepteurs de Michaël. Dans la deuxième partie, nous nous sommes intéressés à la conception d'antibactériens de nouvelle génération contre les bactéries à caractère gram-négatif. L?objectif est de synthétiser un analogue phosphore de l'acide 3-désoxy-d-manno-2-octulosonique (KDO). Différentes méthodologies originales d'introduction d'un motif alpha-cétophosphonate ont été étudiées en série glucidique. Nous avons préparé les premiers époxyphosphonates alpha-halogènes par époxydation des dérivés vinyliques aliphatiques correspondants. Nous avons greffé le motif alpha-cétophosphonate sur un mannitol active et protégé par l'intermédiaire du carbanion 1,3-dithiane-2-phosphonate de diéthyle. Après déblocage successif des différents hydroxyles du sucre, nous avons obtenu le KDO phosphore