Semiquantum versus semiclassical mechanics for simple nonlinear systems

Quantum mechanics has been formulated in phase space, with the Wigner function as the representative of the quantum density operator, and classical mechanics has been formulated in Hilbert space, with the Groenewold operator as the representative of the classical Liouville density function. Semiclassical approximations to the quantum evolution of the Wigner function have been defined, enabling the quantum evolution to be approached from a classical starting point. Now analogous semiquantum approximations to the classical evolution of the Groenewold operator are defined, enabling the classical evolution to be approached from a quantum starting point. Simple nonlinear systems with one degree of freedom are considered, whose Hamiltonians are polynomials in the Hamiltonian of the simple harmonic oscillator. The behavior of expectation values of simple observables and of eigenvalues of the Groenewold operator are calculated numerically and compared for the various semiclassical and semiquantum approximations.

H-1 NMR spectroscopic studies of the stability of an oxazolidine condensation product

Condensation of (-)-norephedrine with excess formaldehyde under mild conditions leads to formation of the 2:1 condensation product N,N'-methylenebis(4-methyl-5-phenyl)oxazolidine compared with the reaction with 1 mol of formaldehyde, which leads to 4-methyl-5-phenyloxazolidine. H-1 and C-13 NMR spectroscopy was used to monitor the stability of this compound and its decomposition products. The 2:1 condensation product is found to be stable in CDC1(3) but breaks down rapidly in CD3OD to yield a 50:50 mixture of 4-methyl-5-phenyloxazolidine and 3-hydroxymethyl-4-methyl-5-phenyloxazolidine. Upon addition of D2O to this equimolar mixture, the latter compound decomposes to norephedrine and formaldehyde, whereas the former compound is stable. (C) 1997 by John Wiley & Sons, Ltd.

Synthesis, identification, characterization, stability, solubility, and protein binding of ester derivatives of salicylic acid and diflunisal

O-Acyl esters were prepared from salicylic acid and diflunisal by esterification with the appropriate acyl anhydride (in the presence of sulfuric acid at 80 degrees C) or acyl chloride (in the presence of pyridine at 0 degrees C). Synthesis, identification and characterization of these compounds is described. In vitro hydrolysis, solubility and protein binding studies of these O-acyl esters were performed. For the diflunisal esters, the melting points fell as the side chain was increased from ethyl to pentyl. The melting points showed no significant difference as the length of the side chain was increased from pentyl to heptyl. The aspirin analogues showed a similar trend, The relationship between solubility and carbon chain length agreed closely with that for the melting points with carbon chain length. In vitro non-enzymatic hydrolysis studies concluded that: (1) hydrolysis rate constants generally decreased with carbon chain length; (2) the diflunisal esters have shorter half lives compared with their salicylate counterparts; and (3) the in vitro hydrolysis of these compounds was retarded by the presence of bovine serum albumin. Protein binding experiments showed that the strength of binding of the aspirin and diflunisal analogues to bovine serum albumin increased with carbon chain length. (C) 1997 Elsevier Science B.V.

Structural analysis of three His32 mutants of DsbA: Support for an electrostatic role of His32 in DsbA stability

DsbA, a 21-kDa protein from Escherichia coli, is a potent oxidizing disulfide catalyst required for disulfide bond formation in secreted proteins. The active site of DsbA is similar to that of mammalian protein disulfide isomerases, and includes a reversible disulfide bond formed from cysteines separated by two residues (Cys3O-Pro31-His32-Cys33). Unlike most protein disulfides, the active-site disulfide of DsbA is highly reactive and the oxidized form of DsbA is much less stable than the reduced form at physiological pH. His32, one of the two residues between the active-site cysteines, is critical to the oxidizing power of DsbA and to the relative instability of the protein in the oxidized form. Mutation of this single residue to tyrosine, serine, or leucine results in a significant increase in stability (of similar to 5-7 kcal/mol) of the oxidized His32 variants relative to the oxidized wild-type protein. Despite the dramatic changes in stability, the structures of all three oxidized DsbA His32 Variants are very similar to the wild-type oxidized structure, including conservation of solvent atoms near the active-site residue, Cys3O. These results show that the His32 residue does not exert a conformational effect on the structure of DsbA. The destabilizing effect of His32 on oxidized DsbA is therefore most likely electrostatic in nature.

The composite Euler method for stiff stochastic differential equations

In this paper we present the composite Euler method for the strong solution of stochastic differential equations driven by d-dimensional Wiener processes. This method is a combination of the semi-implicit Euler method and the implicit Euler method. At each step either the semi-implicit Euler method or the implicit Euler method is used in order to obtain better stability properties. We give criteria for selecting the semi-implicit Euler method or the implicit Euler method. For the linear test equation, the convergence properties of the composite Euler method depend on the criteria for selecting the methods. Numerical results suggest that the convergence properties of the composite Euler method applied to nonlinear SDEs is the same as those applied to linear equations. The stability properties of the composite Euler method are shown to be far superior to those of the Euler methods, and numerical results show that the composite Euler method is a very promising method. (C) 2001 Elsevier Science B.V. All rights reserved.