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.     

Boundedness and Dissipativity of Truncated Rotations on Uniform Planar Lattices

The finiteness of computer arithmetic can lead to some dramatic differences between the behaviour of a continuous dynamical system and a computer simulation. A thorough rigorous theoretical analysis of what may or what does happen is usually extremely difficult and to date little has been done even in relatively simple contexts. The comparative behaviour of a rotation mapping in the plane and on a uniform lattice in the plane is one such example. Simulations show that the rounding operator applied to a planar rotation mapping more or less preserves the qualitative behaviour of the original mapping, whereas the application of the truncation operator to a planar rotation can lead to quite different dynamical features. In this paper a theoretical justification of the properties of the planar rotation mappings under truncation to a, uniform integer lattice is provided, in particular properties of boundedness and dissipativity are investigated.     

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.     

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.