On the colored Jones polynomial and the Kashaev invariant

We express the colored Jones polynomial as the inverse of the quantum determinant of a matrix with entries in the q-Weyl algebra of q-operators, evaluated at the trivial function (plus simple substitutions). The Kashaev invariant is proved to be equal to another special evaluation of the determinant. We also discuss the similarity between our determinant formula of the Kashaev invariant and the determinant formula of the hyperbolic volume of knot complements, hoping it will lead to a proof of the volume conjecture. __________ Translated from Fundamentalnaya i Prikladnaya Matematika, Vol. 11, No. 5, pp. 57–78, 2005.     

Supramolecular Regulation of Polydopamine Formation by Amyloid Fibers

Polydopamine (PD) and melanin species are chemically complex systems, the formation and properties of which are incompletely understood. Inspired by the role of functional amyloids in melanin biosynthesis, this paper examines the influences of the supramolecular structure of amyloids on oxidative polymerization of dopamine. Kinetic analyses on the formation of PD species in the presence of hen egg white lysozyme (HEWL) fibers or soluble HEWL revealed that both forms gave rise to the total quantity of PD species, but the rate of their formation could be accelerated only by the amyloid form. PD species formed with HEWL fibers showed a morphology of bundled fibers, whereas those with soluble HEWL had a mesh-like structure. Amyloid fibers of recombinant Pmel17 had properties similar to those of HEWL fibers in modulating PD formation. The results presented here suggest how nature designs functionality with an amyloid structure and can help understand and engineer chemistries of other functional amyloids.     

Magic-angle-spinning-induced local ordering in polymer electrolytes and its effects on solid-state diffusion and relaxation NMR measurements

Magic-angle-spinning (MAS) enhances sensitivity and resolution in solid-state nuclear magnetic resonance (NMR) measurements. MAS is obtained by aerodynamic levitation and drive of a rotor, which results in large centrifugal forces that may affect the physical state of soft materials, such as polymers, and subsequent solid-state NMR measurements. Here, we investigate the effects of MAS on the solid-state NMR measurements of a polymer electrolyte for lithium-ion battery applications, poly(ethylene oxide) (PEO) doped with the lithium salt LiTFSI. We show that MAS induces local chain ordering, which manifests itself as characteristic lineshapes with doublet-like splittings in subsequent solid-state ¹ H, ⁷ Li, and ¹⁹ F static NMR spectra characterizing the PEO chains and solvated ions. MAS results in distributions of stresses and hence local chain orientations within the rotor, yielding distributions in the local magnetic susceptibility tensor that give rise to the observed NMR anisotropy and lineshapes. The effects of MAS were investigated on solid-state ⁷ Li and ¹⁹ F pulsed-field-gradient (PFG) diffusion and ⁷Li longitudinal relaxation NMR measurements. Activation energies for ion diffusion were affected modestly by MAS. ⁷Li longitudinal relaxation rates, which are sensitive to lithium-ion dynamics in the nanosecond regime, were essentially unchanged by MAS. We recommend that NMR researchers studying soft polymeric materials use only the spin rates necessary to achieve the desired enhancements in sensitivity and resolution, as well as acquire static NMR spectra after MAS experiments to reveal any signs of stress-induced local ordering.     

Spotlight on Photoinduced Aryl Migration Reactions

Rearrangement reactions are certainly one of the most useful approaches towards complex structures in organic chemistry. With efficient conditions, it is indeed possible to convert simple substrates into highly functionalized products. Moreover, combining this approach with an attractive initiation process, such as visible-light catalysis, makes these reactions particularly powerful. Recently, tremendous improvements have been made, owing to a better understanding of photoredox mechanisms. In this review, recent progress on visible-light aryl migration reactions is discussed, focusing especially on Smiles rearrangement and related reactions.     

Determination of the 15N chemical shift anisotropy in natural abundance samples by proton-detected 3D solid-state NMR under ultrafast MAS of 70 kHz

Chemical shift anisotropy (CSA) is a sensitive probe of electronic environment at a nucleus, and thus, it offers deeper insights into detailed structural and dynamic properties of different systems, for example, chemical, biological, and materials. Over the years, massive efforts have been made to develop recoupling methods that reintroduce CSA interaction under magic angle spinning (MAS) conditions. Most of them require slow or moderate MAS (≤20 kHz) and isotopically enriched samples. On the other hand, to the best of the authors' knowledge, no ¹³C or ¹⁵N CSA recoupling schemes at ultrafast MAS (≥60 kHz) suitable for cost-effective natural abundant samples have been developed. We present here a proton-detected 3D ¹⁵N CS/¹⁵N CSA/¹H CS correlation experiment which employs ¹H indirect detection for sensitivity enhancement and a γ-encoded -symmetry-based CSA recoupling scheme. In particular, two different symmetries, that is, R8³₇ and R10⁴₉, are first tested, in a 2D ¹⁵N CSA/¹H CS version, on [U-¹⁵N]-L-histidine·HCl·H₂O as a model sample under 70 kHz MAS. Then the 3D experiment is applied on glycyl-L-alanine at natural abundance, resulting in site-resolved ¹⁵N CSA lineshapes from which CSA parameters are retrieved by SIMPSON numerical fittings. We demonstrate that this 3D R-symmetry-based pulse sequence is highly robust with respect to wide-range offset mismatches and weakly dependent to rf inhomogeneity within mis-sets of ±10% from the theoretical value.     

Discovery of small molecular inhibitors for interleukin-33/ST2 protein–protein interaction: a virtual screening,molecular dynamics simulations and binding free energy calculations

The interleukin-1 receptor like ST2 has emerged as a potential drug discovery target since it was identified as the receptor of the novel cytokine IL-33, which is involved in many inflammatory and autoimmune diseases. For the treatment of such IL-33-related disorders, efforts have been made to discover molecules that can inhibit the protein–protein interactions (PPIs) between IL-33 and ST2, but to date no drug has been approved. Although several anti-ST2 antibodies have entered clinical trials, the exploration of small molecular inhibitors is highly sought-after because of its advantages in terms of oral bioavailability and manufacturing cost. The aim of this study was to discover ST2 receptor inhibitors based on its PPIs with IL-33 in crystal structure (PDB ID: 4KC3) using virtual screening tools with pharmacophore modeling and molecular docking. From an enormous chemical space ZINC, a potential series of compounds has been discovered with stronger binding affinities than the control compound from a previous study. Among them, four compounds strongly interacted with the key residues of the receptor and had a binding free energy?<????20 kcal/mol. By intensive calculations using data from molecular dynamics simulations, ZINC59514725 was identified as the most potential candidate for ST2 receptor inhibitor in this study.

Graphical abstract

     

Metric regularity of composition set-valued mappings: Metric setting and coderivative conditions

The paper concerns a new method to obtain a proof of the openness at linear rate/metric regularity of composite set-valued maps on metric spaces by the unification and refinement of several methods developed somehow separately in several works of the authors. In fact, this work is a synthesis and a precise specialization to a general situation of some techniques explored in the last years in the literature. In turn, these techniques are based on several important concepts (like error bounds, lower semicontinuous envelope of a set-valued map, local composition stability of multifunctions) and allow us to obtain two new proofs of a recent result having deep roots in the topic of regularity of mappings. Moreover, we make clear the idea that it is possible to use (co)derivative conditions as tools of proof for openness results in very general situations.     

New class of chiral ligands derived from isosorbide: first application in asymmetric transfer hydrogenation

A new class of β-amino alcohol and diamine ligands was prepared from isosorbide as a chiral renewable resource. The original wedge-shaped structure of isosorbide offers an interesting chiral pocket to promote the metal-catalyzed enantioselective reduction of ketones by transfer hydrogenation.