A Self-Assembled Cage with Endohedral Acid Groups both Catalyzes Substitution Reactions and Controls Their Molecularity

A self-assembled Fe₄L₆ cage complex internally decorated with acid functions is capable of accelerating the thioetherification of activated alcohols, ethers and amines by up to 1000-fold. No product inhibition is seen, and effective supramolecular catalysis can occur with as little as 5 % cage. The substrates are bound in the host with up to micromolar affinities, whereas the products show binding that is an order of magnitude weaker. Most importantly, the cage host alters the molecularity of the reaction: whereas the reaction catalyzed by simple acids is a unimolecular, S_N1-type substitution process, the rate of the host-mediated process is dependent on the concentration of nucleophile. The molecularity of the cage-catalyzed reaction is substrate-dependent, and can be up to bimolecular. In addition, the catalysis can be prevented by a large excess of nucleophile, where substrate inhibition dominates, and the use of tritylated anilines as substrates causes a negative feedback loop, whereby the liberated product destroys the catalyst and stops the reaction.     

Invariant discrete flows

In this paper, we investigate the evolution of joint invariants under invariant geometric flows using the theory of equivariant moving frames and the induced invariant discrete variational complex. For certain arc length preserving planar curve flows invariant under the special Euclidean group , the special linear group , and the semidirect group , we find that the induced evolution of the discrete curvature satisfies the differential‐difference mKdV, KdV, and Burgers' equations, respectively. These three equations are completely integrable, and we show that a recursion operator can be constructed by precomposing the characteristic operator of the curvature by a certain invariant difference operator. Finally, we derive the constraint for the integrability of the discrete curvature evolution to lift to the evolution of the discrete curve itself.     

The Plasticity of the Carbohydrate Recognition Domain Dictates the Exquisite Mechanism of Binding of Human Macrophage Galactose-Type Lectin

The human macrophage galactose-type lectin (MGL), expressed on macrophages and dendritic cells (DCs), modulates distinct immune cell responses by recognizing N-acetylgalactosamine (GalNAc) containing structures present on pathogens, self-glycoproteins, and tumor cells. Herein, NMR spectroscopy and molecular dynamics (MD) simulations were used to investigate the structural preferences of MGL against different GalNAc-containing structures derived from the blood group A antigen, the Forssman antigen, and the GM2 glycolipid. NMR spectroscopic analysis of the MGL carbohydrate recognition domain (MGL-CRD, C181-H316) in the absence and presence of methyl α-GalNAc (α-MeGalNAc), a simple monosaccharide, shows that the MGL-CRD is highly dynamic and its structure is strongly altered upon ligand binding. This plasticity of the MGL-CRD structure explains the ability of MGL to accommodate different GalNAc-containing molecules. However, key differences are observed in the recognition process depending on whether the GalNAc is part of the blood group A antigen, the Forssman antigen, or GM2-derived structures. These results are in accordance with molecular dynamics simulations that suggest the existence of a distinct MGL binding mechanism depending on the context of GalNAc moiety presentation. These results afford new perspectives for the rational design of GalNAc modifications that fine tune MGL immune responses in distinct biological contexts, especially in malignancy.     

Design and Synthesis of Aromatic Polyesters Bearing Pendant Clickable Maleimide Groups

A bisphenol bearing pendant maleimide group, namely, N‐maleimidoethyl‐3, 3‐bis(4‐hydroxyphenyl)‐1‐isobenzopyrrolidone (PPH‐MA) was synthesized starting from phenolphthalein. Aromatic (co)polyesters bearing pendant maleimide groups were synthesized from PPH‐MA and aromatic diacid chlorides, namely, isophthaloyl chloride (IPC), terephthaloyl chloride (TPC), and 50:50 mol % mixture of IPC and TPC by low temperature solution polycondensation technique. Copolyesters were also synthesized by polycondensation of different molar proportions of PPH‐MA and bisphenol A with IPC. Inherent viscosities and number‐average molecular weights of aromatic (co)polyesters were in the range of 0.52–0.97 dL/g and 20,200–32,800 g/mol, respectively indicating formation of medium to reasonably high‐molecular‐weight polymers. ¹³C NMR spectral analysis of copolyesters revealed the formation of random copolymers. The 10% weight loss temperature of (co)polyesters was found in the range 470–484 °C, indicating their good thermal stability. A selected aromatic polyester bearing pendant maleimide groups was chemically modified via thiol‐maleimide Michael addition reaction with two representative thiol compounds, namely, 4‐chlorothiophenol and 1‐adamantanethiol to yield post‐modified polymers in a quantitative manner. Additionally, it was demonstrated that polyester containing pendant maleimide groups could be used to form insoluble crosslinked gel in the presence of a multifunctional thiol crosslinker. © 2018 Wiley Periodicals, Inc. J. Polym. Sci., Part A: Polym. Chem. 2019 , 57, 630–640     

Sparse Multicategory Generalized Distance Weighted Discrimination in Ultra-High Dimensions

Distance weighted discrimination (DWD) is an appealing classification method that is capable of overcoming data piling problems in high-dimensional settings. Especially when various sparsity structures are assumed in these settings, variable selection in multicategory classification poses great challenges. In this paper, we propose a multicategory generalized DWD (MgDWD) method that maintains intrinsic variable group structures during selection using a sparse group lasso penalty. Theoretically, we derive minimizer uniqueness for the penalized MgDWD loss function and consistency properties for the proposed classifier. We further develop an efficient algorithm based on the proximal operator to solve the optimization problem. The performance of MgDWD is evaluated using finite sample simulations and miRNA data from an HIV study.     

有限群共轭类长度的一点注记

假设G=AB是子群A和B的互相置换积。通过A?B中元素的共轭类长度给出了群G的结构，推广了一些最近的结论。