Asymptotic expansions in the singular value decomposition for cross covariance and correlation under nonnormality

Asymptotic cumulants of the distributions of the sample singular vectors and values of cross covariance and correlation matrices are obtained under nonnormality. The asymptotic cumulants are used to have the approximations of the distributions of the estimators by the Edgeworth expansions up to order O(1/n) and Hall’s method with variable transformation. The cases of Studentized estimators are also considered. As an application of the method, the distributions of the parameter estimators in the model of inter-battery factor analysis are expanded. Interpreting the singular vectors and values in the context of the factor model with distributional conditions, the asymptotic robustness of some lower-order normal-theory cumulants of the distributions of the sample singular vectors and values under nonnormality is shown.     

Semisynthesis of isetexane diterpenoid analogues and their cytotoxic activity

Isetexane diterpene analogues were semisynthesized from demethylsalvicanol isolated from Perovskia abrotanoides (Labiatae). The structure and cytotoxic activity relationships (SAR) of the natural parent diterpene, demethylsalvicanol, and its semisynthetic analogues were studied by using P388 murine leukemia cells.     

Design and synthesis of skeletal analogues of gambierol: attenuation of amyloid-β and tau pathology with voltage-gated potassium channel and N-methyl-D-aspartate receptor implications

Gambierol is a potent neurotoxin that belongs to the family of marine polycyclic ether natural products and primarily targets voltage-gated potassium channels (K(v) channels) in excitable membranes. Previous work in the chemistry of marine polycyclic ethers has suggested the critical importance of the full length of polycyclic ether skeleton for potent biological activity. Although we have previously investigated structure-activity relationships (SARs) of the peripheral functionalities of gambierol, it remained unclear whether the whole polycyclic ether skeleton is needed for its cellular activity. In this work, we designed and synthesized two truncated skeletal analogues of gambierol comprising the EFGH- and BCDEFGH-rings of the parent compound, both of which surprisingly showed similar potency to gambierol on voltage-gated potassium channels (K(v)) inhibition. Moreover, we examined the effect of these compounds in an in vitro model of Alzheimer's disease (AD) obtained from triple transgenic (3xTg-AD) mice, which expresses amyloid beta (Aβ) accumulation and tau hyperphosphorylation. In vitro preincubation of the cells with the compounds resulted in significant inhibition of K(+) currents, a reduction in the extra- and intracellular levels of Aβ, and a decrease in the levels of hyperphosphorylated tau. In addition, pretreatment with these compounds reduced the steady-state level of the N-methyl-D-aspartate (NMDA) receptor subunit 2A without affecting the 2B subunit. The involvement of glutamate receptors was further suggested by the blockage of the effect of gambierol on tau hyperphosphorylation by glutamate receptor antagonists. The present study constitutes the first discovery of skeletally simplified, designed polycyclic ethers with potent cellular activity and demonstrates the utility of gambierol and its synthetic analogues as chemical probes for understanding the function of K(v) channels as well as the molecular mechanism of Aβ metabolism modulated by NMDA receptors.     

Isolation,Structure Determination,and Synthesis of Allo‐RA‐V and Neo‐RA‐V,RA‐Series Bicyclic Peptides from Rubia cordifolia L.

Two bicyclic hexapeptides, allo‐RA‐V ( 4 ) and neo‐RA‐V ( 5 ), and one cyclic hexapeptide, O‐seco‐RA‐V ( 6 ), were isolated from the roots of Rubia cordifolia L. Their gross structures were elucidated on the basis of spectroscopic analysis and X‐ray crystallography of compound 5 . The absolute stereochemistry of compounds 4 and 5 were established by their total syntheses, and the absolute stereochemistry of compound 6 by chemical correlation with deoxybouvardin ( 3 ). Comparison of the 3D structures of highly active RA‐VII ( 1 ) with less‐active compounds 4 and 5 suggests that the orientation of the Tyr‐5 and/or Tyr‐6 phenyl rings plays a significant role in their biological activity. The isolation of peptides 4 – 6 , along with compound 3 , and the comparison of their structures seem to indicate that peptide 6 may be the common precursor to bicyclic peptides 3 – 5 in the plant.     

Synthesis of phosphate-type fluorocarbon-hydrocarbon hybrid surfactants and their adsorption onto calcium hydroxyapatite

Five novel phosphate-type hybrid surfactants, C_mF_2m+1C₆H₄CH[OPO₂(OC₆H₅)Na]C_nH_2n+1 (FmPHnPPhNa: m = 4, 6, 8; n = 3, 5; C₆H₄ = p-phenylene, C₆H₅ = phenyl), have been synthesized. When compared with sulfate-type hybrid surfactants, C_mF_2m+1C₆H₄CH(OSO₃Na)C_nH_2n+1 (C₆H₄ = p-phenylene), the new hybrid surfactants are found to have comparable abilities to lower surface tension of water. The critical micelle concentrations of FmPHnPPhNa follow Klevens rule and their occupied areas per molecule increase with increasing m and n. Calcium hydroxyapatite (CaHAp) pellets modified with FmPH3PPhNa gives high hydrophobic and lipophobic surfaces. The hybrid surfactants are expected as new dental reagents for oral hygiene.     

Total Synthesis and Stereochemical Revision of Iriomoteolide‐2a

Total syntheses of the proposed and correct structures of iriomoteolide‐2a, a cytotoxic marine macrolide natural product with an unusual 23‐membered macrolactone skeleton, have been accomplished for the first time. The synthesis of the correct structure involves an asymmetric epoxidation/diepoxide cyclization cascade for the construction of the bis(tetrahydrofuran) moiety, a Suzuki–Miyaura coupling for the fragment assembly, and a ring‐closing metathesis for the closure of the macrocyclic backbone. In addition, the original stereochemical assignment of iriomoteolide‐2a was revised.     

Self-similarity and scaling of wave function for binary quasiperiodic chains associated with quadratic irrationals

By establishing the correspondence between the substitution rule (aa ⁿb; ba) and the transformation on the value of =tan by1/(n+) in the cut-and-project (CP) method, it is proved that the necessary and sufficient conditions for a binary quasiperiodic (QP) sequence made by the CP method to be self-similar is that is a quadratic irrational (QI) number. And, vice versa, the necessary condition for a binary self-similar sequence generated by the substitution rule to be obtainable by the CP method is that the corresponding substitution rule can be rewritten as a simple composition of transformations with the type (aa ⁿb; ba). To illustrate some physical properties of the self-similar QP chains associated with QI numbers, we analyze the scaling behaviour of the wave function atE=0 for an off-diagnonal tight-binding model. It is shown that the wave function atE=0 grows at most by a power-law for the QP lattices, characterized by a special class of QI numbers. For the QP chains associated with general QI numbers, with the same logic, the typical scaling behaviour of the wave function is conjectured to be the same.     

Inter- and intramolecular N-terminal methyl–side chain interactions in N-acetyl-L-glutamic acid oligomeric benzyl ester solutions. 1H NMR study

Oligomeric N-acetyl-L-glutamic acid benzyl esters with exact residue number (2, 3 or 4) have been synthesized by a stepwise procedure. The aggregational behavior of these oligomeric molecules in dioxane and benzene has been investigated by use of ¹H NMR. In particular, the concentration dependence of the ¹H signals for the N-terminal CH₃ protons has provided evidence that an intermolecular CH₃···? interaction plays a critical role in the formation of aggregates and that an intramolecular CH₃···? interaction occurs in the monomolecular state.     

Mechanism of dissociative excitation of BrCN in electron cyclotron resonance plasma flow of He

The dissociative excitation reaction of BrCN induced by the products of the electron cyclotron resonance (ECR) plasma flow of He was studied based on the electrostatic-probe measurements and on the optical emission spectra of the B²Σ⁺ − X²Σ⁺ transition of CN radicals. The partial pressures of He and BrCN were 3 and 1 mTorr, respectively, and the partial pressure of H₂O, P_H2O, was in the range of 0.0–0.6 mTorr. The electron density, n_e, showed a negative dependence on P_H2O as (2.63 ± 0.13) × 10¹² − (0.23 ± 0.10) × 10¹² m⁻³, and the electron temperature, T_e, a positive dependence, (2.38 ± 0.36) − (4.51 ± 0.15) eV. The CN(B²Σ⁺ − X²Σ⁺) emission intensity showed a negative dependence on P_H2O. Based on a kinetic analysis of these P_H2O dependencies, the decomposition of BrCN does not proceed via electron impact; instead, decomposition proceeds via the processes involving He⁺ and/or He metastable atoms.     

Synthesis and hydrolysis of a cis-chlorohydrin derived from a benzo[a]pyrene 7,8-diol 9,10-epoxide

(+/-)-7beta,8alpha-Dihydroxy-9beta,10beta-epoxy-7,8,9,10-tetrahydrobenzo[a]pyrene (DE-1) undergoes reaction with anhydrous HCl in dioxane to yield predominantly ( approximately 94%) a single chlorohydrin. This chlorohydrin was assigned structure 9, in which the chloro goup at C-10 is located cis to the C-9 hydroxyl group, on the basis of its (1)H NMR spectrum. This result is in contrast to the reaction of a diastereomeric benzo[a]pyrene 7,8-diol 9,10-epoxide (DE-2) with HCl, which yields only trans-chlorohydrin 8. The hydrolysis of cis-chlorohydrin 9 in 10:90 dioxane-water solutions yields the same ratio of tetrols ( approximately 89% cis/11% trans) as that formed by acid-catalyzed hydrolysis of DE-1. This result again contrasts with the hydrolysis of trans-chlorohydrin 8, which undergoes hydrolysis to give tetrols in a ratio different from that from acid-catalyzed hydrolysis of DE-2. A marked common ion rate depression in the hydrolysis of cis-chlorohydrin 9 is observed, which shows that hydrolysis proceeds via an intermediate carbocation that has a sufficient lifetime to be trapped by external chloride ion. The observation that DE-1 reacts with HCl to give mainly the cis-chlorohydrin is rationalized by quantum chemical calculations that suggest that the cis-chlorohydrin is more stable than the epimeric trans-chlorohydrin.