Nilpotency of skew braces and multipermutation solutions of the Yang-Baxter equation

We study relations between different notions of nilpotency in the context of skew braces and applications to the structure of solutions to the Yang-Baxter equation. In particular, we consider annihilator nilpotent skew braces, an important class that turns out to be a brace-theoretic analog to the class of nilpotent groups. In this vein, several well-known theorems in group theory are proved in the more general setting of skew braces.Comment: 18 pages. Postprint versio

Factorizations of skew braces

We introduce strong left ideals of skew braces and prove that they produce non-trivial decomposition of set-theoretic solutions of the Yang–Baxter equation. We study factorization of skew left braces through strong left ideals and we prove analogs of Itô’s theorem in the context of skew left braces. As a corollary, we obtain applications to the retractability problem of involutive non-degenerate solutions of the Yang–Baxter equation. Finally, we classify skew braces that contain no non-trivial proper characteristic ideals.Fil: Jespers, E.. Vrije Unviversiteit Brussel; BélgicaFil: Kubat, L.. Vrije Unviversiteit Brussel; BélgicaFil: Van Antwerpen, A.. Vrije Unviversiteit Brussel; BélgicaFil: Vendramin, Claudio Leandro. Institute of Mathematical Sciences at NYU Shanghai; China. Universidad de Buenos Aires; Argentina. Consejo Nacional de Investigaciones Científicas y Técnicas; Argentin

A longitudinal analysis of the vaginal microbiota and vaginal immune mediators in women from sub-Saharan Africa

In cross-sectional studies increased vaginal bacterial diversity has been associated with vaginal inflammation which can be detrimental for health. We describe longitudinal changes at 5 visits over 8 weeks in vaginal microbiota and immune mediators in African women. Women (N = 40) with a normal Nugent score at all visits had a stable lactobacilli dominated microbiota with prevailing Lactobacillus iners. Presence of prostate-specific antigen (proxy for recent sex) and being amenorrhoeic (due to progestin-injectable use), but not recent vaginal cleansing, were significantly associated with microbiota diversity and inflammation (controlled for menstrual cycle and other confounders). Women (N = 40) with incident bacterial vaginosis (Nugent 7-10) had significantly lower concentrations of lactobacilli and higher concentrations of Gardnerella vaginalis, Atopobium vaginae, and Prevotella bivia, at the incident visit and when concentrations of proinflammatory cytokines (IL-1β, IL-12p70) were increased and IP-10 and elafin were decreased. A higher 'composite-qPCR vaginal-health-score' was directly associated with decreased concentrations of proinflammatory cytokines (IL-1α, IL-8, IL-12(p70)) and increased IP-10. This longitudinal study confirms the inflammatory nature of vaginal dysbiosis and its association with recent vaginal sex and progestin-injectable use. A potential role for proinflammatory mediators and IP-10 in combination with the vaginal-health-score as predictive biomarkers for vaginal dysbiosis merits further investigation

Factorizations of Elements in Noncommutative Rings: A Survey

We survey results on factorizations of non zero-divisors into atoms (irreducible elements) in noncommutative rings. The point of view in this survey is motivated by the commutative theory of non-unique factorizations. Topics covered include unique factorization up to order and similarity, 2-firs, and modular LCM domains, as well as UFRs and UFDs in the sense of Chatters and Jordan and generalizations thereof. We recall arithmetical invariants for the study of non-unique factorizations, and give transfer results for arithmetical invariants in matrix rings, rings of triangular matrices, and classical maximal orders as well as classical hereditary orders in central simple algebras over global fields.Comment: 50 pages, comments welcom

Mechanics of cutting manoeuvres by ostriches ('Struthio camelus')

We studied the strategies used by cursorial bipeds (ostriches) to maneuver during running. Eight ostriches were induced to run along a trackway and execute turns. Ground reaction forces and three-dimensional kinematics of the body and leg joints were simultaneously recorded, allowing calculation of joint angles and quasi-static net joint torques. Sidesteps, where the leg on the outside of the turn changes the movement direction, and crossovers using the inside leg, occurred with nearly equal frequency. Ostriches executed maneuvers using a simple control strategy that required minimal changes to leg kinematics or net torque production at individual joints. Although ostriches did use acceleration or braking forces to control body rotation, their morphology allowed for both crossovers and sidesteps to be accomplished with minimal net acceleratory/braking force production. Moreover, body roll and ab/adduction of the leg shifted the foot position away from the turn direction, reducing the acceleratory/braking forces required to prevent under-or over-rotation and aligning the leg with the ground reaction force

Cancer-related somatic mutations alter adenosine A1 receptor pharmacology: a focus on mutations in the loops and C- terminus

G protein-coupled receptors (GPCRs) are known to be involved in tumor progression and metastasis. The adenosine A1 receptor (A1 AR) has been detected to be over-expressed in various cancer cell lines. However, the role of A1 AR in tumor development is not yet well characterized. A series of A1 AR mutations were identified in the Cancer Genome Atlas from cancer patient samples. In this study, we have investigated the pharmacology of mutations located outside of the 7-transmembrane domain by using a "single-GPCR-one-G protein" yeast system. Concentration-growth curves were obtained with the full agonist CPA for 12 mutant receptors and compared to the wild-type hA1 AR. Most mutations located at the extracellular loops (EL) reduced the levels of constitutive activity of the receptor and agonist potency. For mutants at the intracellular loops (ILs) of the receptor, an increased constitutive activity was found for mutant receptor L211R5.69 , while a decreased constitutive activity and agonist response were found for mutant receptor L113F34.51 . Lastly, mutations identified on the C-terminus did not significantly influence the pharmacological function of the receptor. A selection of mutations was also investigated in a mammalian system. Overall, similar effects on receptor activation compared to the yeast system were found with mutations located at the EL, but some contradictory effects were observed for mutations located at the IL. Taken together, this study will enrich the insight of A1 AR structure and function, enlightening the consequences of these mutations in cancer. Ultimately, this may provide potential precision medicine in cancer treatment.Medicinal Chemistr

Structural Mapping of Adenosine Receptor Mutations: Ligand Binding and Signaling Mechanisms

TrendsRecent technological advances in membrane protein crystallization have resulted in a nearly exponential increase of available receptor structures. The AR family is an important example in this respect. Crystal structures of antagonist- and agonist-bound adenosine A2A receptor have recently been supplemented by a fully activated conformation in complex with a G-protein mimic, and by antagonist bound structures of the A1 receptor.SDM experiments have been essential to identify residues involved in molecular interactions between ARs and their ligands. Leveraging on recent crystal structures, this vast amount of data can now be systematically classified and interconnected with chemical and structural information of ligands and receptors.The mapping of mutational data onto crystal structures provides new understanding of molecular interactions involved in ligand recognition. Together with computational modeling, this can be used as a roadmap to create novel hypotheses and assist in the design of more systematic mutagenesis studies to answer remaining structural and functional questions.The four adenosine receptors (ARs), A1, A2A, A2B, and A3, constitute a subfamily of G protein-coupled receptors (GPCRs) with exceptional foundations for structure-based ligand design. The vast amount of mutagenesis data, accumulated in the literature since the 1990s, has been recently supplemented with structural information, currently consisting of several inactive and active structures of the A2A and inactive conformations of the A1 ARs. We provide the first integrated view of the pharmacological, biochemical, and structural data available for this receptor family, by mapping onto the relevant crystal structures all site-directed mutagenesis data, curated and deposited at the GPCR database (available through http://www.gpcrdb.org). This analysis provides novel insights into ligand binding, allosteric modulation, and signaling of the AR family.Keywords: G protein-coupled receptor, adenosine receptor, mutagenesis, chemical modulationMedicinal Chemistr

Successive statistical and structure-based modeling to identify chemically novel kinase inhibitors

Kinases are frequently studied in the context of anticancer drugs. Their involvement in cell responses, such as proliferation, differentiation, and apoptosis, makes them interesting subjects in multitarget drug design. In this study, a workflow is presented that models the bioactivity spectra for two panels of kinases: (1) inhibition of RET, BRAF, SRC, and S6K, while avoiding inhibition of MKNK1, TTK, ERK8, PDK1, and PAK3, and (2) inhibition of AURKA, PAK1, FGFR1, and LKB1, while avoiding inhibition of PAK3, TAK1, and PIK3CA. Both statistical and structure-based models were included, which were thoroughly benchmarked and optimized. A virtual screening was performed to test the workflow for one of the main targets, RET kinase. This resulted in 5 novel and chemically dissimilar RET inhibitors with remaining RET activity of 50 value of 5.1 for the most active compound. The experimental validation of inhibitors for RET strongly indicates that the multitarget workflow is able to detect novel inhibitors for kinases, and hence, this workflow can potentially be applied in polypharmacology modeling. We conclude that this approach can identify new chemical matter for existing targets. Moreover, this workflow can easily be applied to other targets as well.Toxicolog