Quantum mechanical/molecular mechanical study on the mechanism of the enzymatic Baeyer-Villiger reaction

We report a combined quantum mechanical/molecular mechanical (QM/MM) study on the mechanism of the enzymatic Baeyer-Villiger reaction catalyzed by cyclohexanone monooxygenase (CHMO). In QM/MM geometry optimizations and reaction path calculations, density functional theory (B3LYP/TZVP) is used to describe the QM region consisting of the substrate (cyclohexanone), the isoalloxazine ring of C4a-peroxyflavin, the side chain of Arg-329, and the nicotinamide ring and the adjacent ribose of NADP(+), while the remainder of the enzyme is represented by the CHARMM force field. QM/MM molecular dynamics simulations and free energy calculations at the semiempirical OM3/CHARMM level employ the same QM/MM partitioning. According to the QM/MM calculations, the enzyme-reactant complex contains an anionic deprotonated C4a-peroxyflavin that is stabilized by strong hydrogen bonds with the Arg-329 residue and the NADP(+) cofactor. The CHMO-catalyzed reaction proceeds via a Criegee intermediate having pronounced anionic character. The initial addition reaction has to overcome an energy barrier of about 9 kcal/mol. The formed Criegee intermediate occupies a shallow minimum on the QM/MM potential energy surface and can undergo fragmentation to the lactone product by surmounting a second energy barrier of about 7 kcal/mol. The transition state for the latter migration step is the highest point on the QM/MM energy profile. Gas-phase reoptimizations of the QM region lead to higher barriers and confirm the crucial role of the Arg-329 residue and the NADP(+) cofactor for the catalytic efficiency of CHMO. QM/MM calculations for the CHMO-catalyzed oxidation of 4-methylcyclohexanone reproduce and rationalize the experimentally observed (S)-enantioselectivity for this substrate, which is governed by the conformational preferences of the corresponding Criegee intermediate and the subsequent transition state for the migration step.     

Stability of linear difference equations with unmodelled higher order terms

Dedicated to Gerry Ladas on his sixtieth birthday. We consder the case when the tru linear difference equation may difer from the nominal one. Neither higher order coefficients nor the order of the true equation are konwn: the only information available is that these higher order coefficients ae bounded in l ₁norm. We obtain necessary and sufficient conditionsfor stability of the entire family of such equations.     

Azides of N-substituted aziridine-2-carboxylic acids. Reaction with methyl esters of amino acids

The corresponding azide was obtained by nitrosation of 1-benzylaziridine-2-carboxylic acid hydrazide. Reaction of the azide with methyl esters of amino acids gave N-(1-benzyl-2-aziridinylcarbonyl)-substituted methyl esters of amino acids.Translated from Khimiya Geterotsiklicheskikh Soedinenii, No. 10, pp. 1350–1352, October, 1980.     

Newton-Kantorovich Method and Its Global Convergence

In 1948, L. V. Kantorovich extended the Newton method for solving nonlinear equations to functional spaces. This event cannot be overestimated: the Newton-Kantorovich method became a powerful tool in numerical analysis as well as in pure mathematics. We address basic ideas of the method in historical perspective and focus on some recent applications and extensions of the method and some approaches to overcoming its local ture. Bibliography: 56 titles. __________ Published in Zapiski Nauchnykh Seminarov POMI, Vol. 312, 2004, pp. 256–274.     

Primal-dual nonlinear rescaling method with dynamic scaling parameter update

In this paper we developed a general primal-dual nonlinear rescaling method with dynamic scaling parameter update (PDNRD) for convex optimization. We proved the global convergence, established 1.5-Q-superlinear rate of convergence under the standard second order optimality conditions. The PDNRD was numerically implemented and tested on a number of nonlinear problems from COPS and CUTE sets. We present numerical results, which strongly corroborate the theory. The research of the authors supported by the NSF Grant CCF-0324999     

XPS study of early stages of Al/Au interface formation

The interface formation between Au polycrystalline substrate kept at temperature of liquid nitrogen and Al deposit and its evolution during sample thermal treatments have been investigated by means of XPS. The intermixing of the Al and Au atoms at the interface occurred readily already at temperature of liquid nitrogen and resulted in the appearance of well‐resolved components on the high‐binding‐energy side of the Au(4f) spectra assignable to AlAu intermetallic phase. The sample annealing resulted in the growth of the amount of intermetallic compound formed at liquid nitrogen temperature. The formation of the initial AlAu phase at the Al/Au interface in our experimental conditions can be explained on the basis of its thermodynamic stability. Copyright © 2009 John Wiley & Sons, Ltd.     

Quantization of Linear Poisson Structures and Degrees of Maps

Kontsevich's formula for a deformation quantization of Poisson structures involves a Feynman series of graphs, with the weights given by some complicated integrals (using certain pullbacks of the standard angle form on a circle). We explain the geometric meaning of this series as degrees of maps of some grand configuration spaces; the associativity proof is also interpreted in purely homological terms. An interpretation in terms of degrees of maps shows that any other 1-form on the circle also leads to a star-product and allows one to compare these products.     

Quantum chemical simulation of the interaction of membrane fluorescent probe 4-dimethylaminochalcone with hydroxy groups of the environment

The quantum chemical simulation of the ground and electron-excited states of diverse complexes of fluorescent probe 4-dimethylaminochalcone (DMAC) and water in vacuo was performed by the HF/MP2 and RI-CC2 methods. Molecules of the DMAC probe and water can form five types of stable complexes. The geometries corresponding to the potential energy minimum and dipole moments for two lowest singlet and one lowest triplet states were calculated for each type of the complexes. The partial charges on the DMAC atoms and their changes due to the intramolecular charge transfer upon photoexcitation were determined. The coordination of the water molecule at the carbonyl group of DMAC is preferable in vacuo. The formation of hydrogen bonds between the carbonyl group of DMAC and water molecules decreases the energy of the excited state of the complex ¹(π, π*), due to which the fluorescence yield increases upon photoexcitation. The calculation results are confirmed by the experimental data on studying the fluorescence of the probe in binary mixtures of benzene and alcohols.     

Diassociative Algebras and Milnor’s Invariants for Tangles

We extend Milnor’s μ-invariants of link homotopy to ordered (classical or virtual) tangles. Simple combinatorial formulas for μ-invariants are given in terms of counting trees in Gauss diagrams. Invariance under Reidemeister moves corresponds to axioms of Loday’s diassociative algebra. The relation of tangles to diassociative algebras is formulated in terms of a morphism of corresponding operads.