Hopf algebra actions

Finite groups acting on rings by automorphisms, and group-graded rings are instances of Hopf algebras H acting on H-module algebras A. We study such actions. Let A^H = {a ε A¦h · A = (h) a, all h ε H}, the ring of H-invariants, and form the smash product A # H. We study the ring extensions A^H A A # H. We prove a Maschke-type theorem for A # H-modules. We form an associated Morita context [A^H, A, A, A # H] and use these to get connections between the various rings.     

Reflection of light by a slab containing electrically small dielectric spheres

Theoriginal and theenhanced Maxwell-Garnett estimates for the permittivity of a particulate medium are applied to the reflection of light by a composite dielectric slab. The reflection coefficients for incident s and p polarizations are calculated and some curves are plotted and discussed.     

Time reversal for infinite-dimensional diffusions

Summary In this paper we analize the reversibility of the diffusion property for the solution of certain infinite-dimensional systems of stochastic differential equations. Necessary and sufficient conditions ensuring this reversibility are given. The proofs use the techniques of the stochastic calculus of variations.This work was partly done when the first author was visiting the Centre de Recerca Matemàtica at Barcelona     

Validation of the thermodynamic model of inorganic arsenic in non polluted river waters of the Basque country (Spain)

The thermodynamic model of inorganic arsenic was validated by comparing the predicted As(III) concentration with the experimentally determined one in several river waters samples of the Basque Country (Spain) collected in two sampling campaigns: spring and autumn 2000. This model takes into account the acid-base equilibria of As(III) and As(V) together with the redox equilibria between the H₃AsO₃ and H₃AsO₄ species. A correct prediction of As(III) concentration requires the knowledge of the total concentration of arsenic, pH, redox potential (referred to hydrogen electrode), and ionic strength values of the solution. The estimation of the activity coefficients of the arsenic species was performed by means of the Modified Bromley’s Methodology (MBM).In order to perform the experimental As(III) determination, an analytical method was implemented by using an ion exchange separation of As(III)/As(V) on a continuous FIA-IE-HG-AAS system. The total arsenic concentration was determined together with total concentration of the main alkaline or alkaline-earth metals and anions in the natural waters. Temperature compensated measurements of the pH and redox potentials were made in-situ at the sampling sites.For both seasonal campaigns, the agreement between predicted and experimental As(III) is really high for those samples belonging to non polluted river waters.     

Application of preparative high-speed counter-current chromatography for the separation of flavonoids from the leaves of Byrsonima crassa Niedenzu (IK)

The methanolic extract of the leaves of the medicinal plant Byrsonima crassa (Malpighiaceae) contain flavonoids with antioxidant activity. They were separated in a preparative scale using high-speed counter-current chromatography. The optimum solvent system used was composed of a mixture of ethyl acetate-n-propanol-water (140:8:80 (v/v/v)) and led to a successful separation between monoglucosilated flavonoids (quercetin-3-O-alpha-L-arabinoside, quercetin-3-O-beta-D-galactoside) and the biflavonoid amentoflavone in only 3.5 h. The purities of quercetin-3-O-alpha-L-arabinoside (95 mg), quercetin-3-O-beta-D-galactoside (16 mg) and the biflavonoid amentoflavone (114 mg) were all isolated at purity over 95%. Identification was performed by 1H NMR, 13C NMR and UV analyses.     

Sequestration within biomolecular condensates inhibits Aβ-42 amyloid formation

Biomolecular condensates are emerging as an efficient strategy developed by cells to control biochemical reactions in space and time by locally modifying composition and environment. Yet, local increase in protein concentration within these compartments could promote aberrant aggregation events, including the nucleation and growth of amyloid fibrils. Understanding protein stability within the crowded and heterogeneous environment of biological condensates is therefore crucial, not only when the aggregation-prone protein is the scaffold element of the condensates but also when proteins are recruited as client molecules within the compartments. Here, we investigate the partitioning and aggregation kinetics of the amyloidogenic peptide Abeta42 (Aβ-42), the peptide strongly associated with Alzheimer''s disease, recruited into condensates based on low complexity domains (LCDs) derived from the DEAD-box proteins Laf1, Dbp1 and Ddx4, which are associated with biological membraneless organelles. We show that interactions between Aβ-42 and the scaffold proteins promote sequestration and local increase of the peptide concentration within the condensates. Yet, heterotypic interactions within the condensates inhibit the formation of amyloid fibrils. These results demonstrate that biomolecular condensates could sequester aggregation-prone proteins and prevent aberrant aggregation events, despite the local increase in their concentration. Biomolecular condensates could therefore work not only as hot-spots of protein aggregation but also as protective reservoirs, since the heterogenous composition of the condensates could prevent the formation of ordered fibrillar aggregates.

Biomolecular condensates sequester an aggregation-prone peptide and prevent its aggregation, showing that heterotypic interactions within the condensates can prevent the formation of amyloid fibrils, despite the local increase in concentration.