The algebra of generating functions for multiple divisor sums and applications to multiple zeta values

We study the algebra \({{\mathrm{{\mathcal {MD}}}}}\) of generating functions for multiple divisor sums and its connections to multiple zeta values. The generating functions for multiple divisor sums are formal power series in q with coefficients in \({\mathbb {Q}}\) arising from the calculation of the Fourier expansion of multiple Eisenstein series. We show that the algebra \({{\mathrm{{\mathcal {MD}}}}}\) is a filtered algebra equipped with a derivation and use this derivation to prove linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). The (quasi-)modular forms for the full modular group \({{\mathrm{SL}}}_2({\mathbb {Z}})\) constitute a subalgebra of \({{\mathrm{{\mathcal {MD}}}}}\), and this also yields linear relations in \({{\mathrm{{\mathcal {MD}}}}}\). Generating functions of multiple divisor sums can be seen as a q-analogue of multiple zeta values. Studying a certain map from this algebra into the real numbers we will derive a new explanation for relations between multiple zeta values, including those of length 2, coming from modular forms.     

Multicanonical chain-growth algorithm

We present a temperature-independent Monte Carlo method for the determination of the density of states of lattice proteins that combines the fast ground-state search strategy of the new pruned-enriched Rosenbluth chain-growth method and multicanonical reweighting for sampling the complete energy space. Since the density of states contains all energetic information of a statistical system, we can directly calculate the mean energy, specific heat, Helmholtz free energy, and entropy for all temperatures. We apply this method to lattice proteins consisting of hydrophobic and polar monomers, and for the examples of sequences considered, we identify the transitions between native, globule, and random coil states. Since no special properties of heteropolymers are involved in this algorithm, the method applies to polymer models as well.     

Phenolic compounds,essential oil composition,and antioxidant activity of Angelica purpurascens (Avé-Lall.) Gill

In this study, methanol extracts (MEs) and essential oil (EO) of Angelica purpurascens (Avé-Lall.) Gill obtained from different parts (root, stem, leaf, and seed) were evaluated in terms of antioxidant activity, total phenolics, compositions of phenolic compound, and essential oil with the methods of 2,2-azino-bis(3ethylbenzo-thiazoline-6-sulfonic acid (ABTS•⁺), 2,2-diphenyl-1-picrylhydrazil (DPPH•) radical scavenging activities, and ferric reducing/antioxidant power (FRAP), the Folin–Ciocalteu, liquid chromatography−tandem mass spectrometry (LC−MS/MS), and gas chromatography-mass spectrometry (GC−MS), respectively. The root extract of A. purpurascens exhibited the highest ABTS•⁺, DPPH•, and FRAP activities (IC₅₀: 0.05 ± 0.0001 mg/mL, IC₅₀: 0.06 ± 0.002 mg/mL, 821.04 ± 15.96 µM TEAC (Trolox equivalent antioxidant capacity), respectively). Moreover, EO of A. purpurascens root displayed DPPH• scavenging activity (IC₅₀: 2.95 ± 0.084 mg/mL). The root extract had the highest total phenolic content (438.75 ± 16.39 GAE (gallic acid equivalent), µg/mL)). Twenty compounds were identified by LC−MS/MS. The most abundant phenolics were ferulic acid (244.39 ± 15.64 μg/g extract), benzoic acid (138.18 ± 8.84 μg/g extract), oleuropein (78.04 ± 4.99 μg/g extract), and rutin (31.21 ± 2.00 μg/g extract) in seed, stem, root, and leaf extracts, respectively. According to the GC−MS analysis, the major components were determined as α-bisabolol (22.93%), cubebol (14.39%), α-pinene (11.63%), and α-limonene (9.41%) among 29 compounds. Consequently, the MEs and EO of A. purpurascens can be used as a natural antioxidant source.     

Exact sequence analysis for three-dimensional hydrophobic-polar lattice proteins

We have exactly enumerated all sequences and conformations of hydrophobic-polar (HP) proteins with chains of up to 19 monomers on the simple cubic lattice. For two variants of the HP model, where only two types of monomers are distinguished, we determined and statistically analyzed designing sequences, i.e., sequences that have a nondegenerate ground state. Furthermore we were interested in characteristic thermodynamic properties of HP proteins with designing sequences. In order to be able to perform these exact studies, we applied an efficient enumeration method based on contact sets.     

Total synthesis and conformational analysis of the antifungal agent (-)-PF1163B

[reaction: see text]. (-)-PF1163B, a new macrocyclic antifungal antibiotic isolated from Streptomyces sp., has been prepared in eight steps from (S)-citronellene. The key step is a ring-closing metathesis reaction of an ester and amide derivative obtained from a substituted N-methyl-l-tyrosine.     

Spectroscopic studies of substrate interactions with clavaminate synthase 2, a multifunctional alpha-KG-dependent non-heme iron enzyme: correlation with mechanisms and reactivities

Using a single ferrous active site, clavaminate synthase 2 (CS2) activates O(2) and catalyzes the hydroxylation of deoxyguanidinoproclavaminic acid (DGPC), the oxidative ring closure of proclavaminic acid (PC), and the desaturation of dihydroclavaminic acid (and a substrate analogue, deoxyproclavaminic acid (DPC)), each coupled to the oxidative decarboxylation of cosubstrate, alpha-ketoglutarate (alpha-KG). CS2 can also catalyze an uncoupled decarboxylation of alpha-KG both in the absence and in the presence of substrate, which results in enzyme deactivation. Resting CS2/Fe(II) has a six-coordinate Fe(II) site, and alpha-KG binds to the iron in a bidentate mode. The active site becomes five-coordinate only when both substrate and alpha-KG are bound, the latter still in a bidentate mode. Absorption, CD, MCD, and VTVH MCD studies of the interaction of CS2 with DGPC, PC, and DPC provide significant molecular level insight into the structure/function correlations of this multifunctional enzyme. There are varying amounts of six-coordinate ferrous species in the substrate complexes, which correlate to the uncoupled reaction. Five-coordinate ferrous species with similar geometric and electronic structures are present for all three substrate/alpha-KG complexes. Coordinative unsaturation of the Fe(II) in the presence of both cosubstrate and substrate appears to be critical for the coupling of the oxidative decarboxylation of alpha-KG to the different substrate oxidation reactions. In addition to the substrate orientation relative to the open coordination position on the iron site, it is hypothesized that the enzyme can affect the nature of the reactivity by further regulating the binding energy of the water to the ferrous species in the enzyme/succinate/product complex.     

Optical Diagnosis for Thyroid and Parathyroid Tissues—A Review

Abstract

This article presents an overview of optical methodologies to aid the diagnosis and differentiation of thyroid and parathyroid tissues. In particular, we review the several techniques and associated methodologies that allow in vivo and ex vivo optical characterization of thyroid and parathyroid tissues. Emphasis is placed on the research potential of these techniques and whether intrinsic characteristics can provide useful contrast for the diagnosis of human thyroid and parathyroid malignant lesions.