Statevector reduction in discrete time: A random walk in Hilbert space

A simple model is presented in which the statevector evolves every seconds in one of two ways, according to a particular probability rule. It is shown that this random walk in Hilbert space results in reduction of the statevector. It is also shown how the continuous spontaneous localization (CSL) theory of statevector reduction is achieved as a limiting case of this model, exactly as Brownian motion is a limiting case of ordinary random walk. Finally, a slightly different but completely equivalent form of the CSL equations suggested by the simple model given here is discussed.     

Concise synthesis of pyrrolophenanthridine alkaloids using a Pd-mediated biaryl coupling reaction with regioselective C-H activation via the intramolecular coordination of the amine to Pd

The concise synthesis of Amaryllidaceae alkaloids, such as anhydrolycorinone, anhydrolycorin-7-one, assoanine, and oxoassoanine, which have a pyrrolophenanthridine skeleton, was achieved in moderate yield using the Pd-mediated biaryl coupling reaction of 1-(2-halobenzyl)-2,3-dihydroindole, which applied the regioselective C-H activation method with intramolecular coordination of the benzylamino group to Pd.     

Comparative studies on the analysis of glycosylation heterogeneity of sialic acid-containing glycoproteins using capillary electrophoresis

Frontal affinity chromatography is a method for quantitative analysis of biomolecular interactions. We reinforced it by incorporating various merits of a contemporary liquid chromatography system. As a model study, the interaction between an immobilized Caenorhabditis elegans galectin (LEC-6) and fluorescently labeled oligosaccharides (pyridylaminated sugars) was analyzed. LEC-6 was coupled to N-hydroxysuccinimide-activated Sepharose 4 Fast Flow (100 μm diameter), and packed into a miniature column (e.g., 10×4.0 mm, 0.126 ml). Twelve pyridylaminated oligosaccharides were applied to the column through a 2-ml sample loop, and their elution patterns were monitored by fluorescence. The volume of the elution front (V) determined graphically for each sample was compared with that obtained in the presence of an excess amount of hapten saccharide, lactose (V₀); and the dissociation constant, K_d, was calculated according to the literature [K. Kasai, Y. Oda, M. Nishikawa, S. Ishii, J. Chromatogr. 376 (1986) 33]. This system also proved to be useful for an inverse confirmation; that is, application of galectins to an immobilized glycan column (in the present case, asialofetuin was immobilized on Sepharose 4 Fast Flow), and the elution profiles were monitored by fluorescence based on tryptophan. The relative affinity of various galectins for asialofetuin could be easily compared in terms of the extent of retardation. The newly constructed system proved to be extremely versatile. It enabled rapid (analysis time 12 min/cycle) and sensitive (20 nM for pyridylaminated derivatives, and 1 μg/ml for protein) analyses of lectin–carbohydrate interactions. It should become a powerful tool for elucidation of biomolecular interactions, in particular for functional analysis of a large number of proteins that should be the essential issues of post-genome projects.     

Asymptotic expansions of the distributions of some test statistics

Summary A modified Wald statistic for testing simple hypothesis against fixed as well as local alternatives is proposed. The asymptotic expansions of the distributions of the proposed statistic as well as the Wald and Rao statistics under both the null and alternative hypotheses are obtained. The powers of these statistics are compared and its is shown that for special structures of parameters some statistics have same power in the sence of order . The results obtained are applied for testing the hypothesis about the covariance matrix of the multivariate normal distribution and it is shown that none of the tests based on the above statistics is uniformly superior. Research supported by the National Science Foundation Grant MCS 830149.     

Synthesis and structure of 16 pi octaalkyltetraphenylporphyrins

The oxidized octaethyltetraphenylporphyrin (1, OETPP) and the corresponding newly prepared octaisobutyltetraphenylporphyrin (3, OisoBuTPP) could be isolated from the reaction of OETPPLi2 (or OisoBuTPPLi2) with SOCl2. The X-ray analysis and the characteristic UV-vis spectra of 1 and 3 revealed that these are the first examples of 16 pi nonaromatic porphyrins.     

Meso-tetrakis[o-(N-methyl)pyridinium]porphyrin ensembles with axially coordinated cyclodextrin-penetrating phenethylimidazole: reversible dioxygen-binding in aqueous DMF solution

alpha-Cyclodextrin (alpha CD)-penetrating 2-methyl-1-phenethylimidazole coordinates to the zinc(II) and iron(II) complexes of meso-tetrakis[o-(N-methyl)pyridinium] porphyrinate, giving non-covalently linked alpha CD-porphyrin ensembles; the iron(II) complex can reversibly bind and release dioxygen in aqueous DMF solution.     

Synthesis and characterization of 6-O-acyl-2-O-alpha-D-glucopyranosyl-L-ascorbic acids with a branched-acyl chain

We previously reported the chemical synthesis of a series of novel monoacylated vitamin C derivatives, 6-O-acyl-2-O-alpha-D-glucopyranosyl-L-ascorbic acids (6-Acyl-AA-2G) possessing a straight-acyl chain of varying length from C(4) to C(18), as effective skin antioxidants. In this paper, we describe branched type of 6-Acyl-AA-2G derivatives (6-bAcyl-AA-2G) synthesized by use of a 2-branched-chain fatty acid anhydride as an acyl donor. The stability of 6-bAcyl-AA-2G in neutral solution was much higher than that of 6-Acyl-AA-2G, while they were susceptible to enzymatic hydrolysis for exerting vitamin C effect. These branched derivatives as well as 6-Acyl-AA-2G increased the radical scavenging activity against 1, 1-diphenyl-2-picrylhydrazyl and the lipophilicity in octanol/water-partitioning systems with increasing length of their acyl group. In addition, the 6-bAcyl-AA-2G derivative with an acyl chain of C(12), 6-bDode-AA-2G had the excellent solubility to various solvents, suggesting easy handling in cosmetic use. These characteristics of 6-bAcyl-AA-2G may be available for skin care application as an effective antioxidant.     

19F NMR characterization of the thermodynamics and dynamics of the acid-alkaline transition in a reconstituted sperm whale metmyoglobin

A 19F NMR study on the acid-alkaline transition in sperm whale myoglobin reconstituted with a perfluoromethyl heme, 13,17-bis(2-carboxylatoethyl)-3,8-diethyl-2,12,18-trimethyl-7-trifluoromethylporphyrinatoiron(III), demonstrated that the thermodynamics of the transition is predominantly controlled by the stability of acidic form.