Enumerating Perfect Matchings in n-Cubes

The perfect matchings in the n-cube have earlier been enumerated for n?≤?6. A dynamic programming approach is here used to obtain the total number of perfect matchings in the 7-cube, which is 391 689 748 492 473 664 721 077 609 089. The number of equivalence classes of perfect matchings is further shown to be 336 in the 5-cube, 356 788 059 in the 6-cube and 607 158 046 495 120 886 820 621 in the 7-cube. The techniques used can be generalized to arbitrary bipartite and general graphs.     

New coverings of t-sets with (t + 1)-sets

The minimum number of k-subsets out of a v-set such that each t-set is contained in at least one k-set is denoted by C(v, k, t). In this article, a computer search for finding good such covering designs, leading to new upper bounds on C(v, k, t), is considered. The search is facilitated by predetermining automorphisms of desired covering designs. A stochastic heuristic search (embedded in the general framework of tabu search) is then used to find appropriate sets of orbits. A table of upper bounds on C(v, t + 1, t) for v 28 and t 8 is given, and the new covering designs are listed. © 1999 John Wiley & Sons, Inc. J. Combin Designs 7: 217–226, 1999     

The directive of the protein: how does cytochrome P450 select the mechanism of dopamine formation?

Dopamine can be generated from tyramine via arene hydroxylation catalyzed by a cytochrome P450 enzyme (CYP2D6). Our quantum mechanical/molecular mechanical (QM/MM) results reveal the decisive impact of the protein in selecting the 'best' reaction mechanism. Instead of the traditional Meisenheimer-complex mechanism, the study reveals a mechanism involving an initial hydrogen atom transfer from the phenolic hydroxyl group of the tyramine to the iron-oxo of the compound I (Cpd I), followed by a ring-π radical rebound that eventually leads to dopamine by keto-enol rearrangement. This mechanism is not viable in the gas phase since the O-H bond activation by Cpd I is endothermic and the process does not form a stable intermediate. By contrast, the in-protein reaction has a low barrier and is exothermic. It is shown that the local electric field of the protein environment serves as a template that stabilizes the intermediate of the H-abstraction step and thereby mediates the catalysis of dopamine formation at a lower energy cost. Furthermore, it is shown that external electric fields can either catalyze or inhibit the process depending on their directionality.     

Solvating,manipulating, damaging,and repairing DNA in a computer

This work highlights four different topics in modeling of DNA: (i) the importance of water and ions together with the structure and function of DNA; the hydration structure around the ions appears to be the determining factor in the ion coordination to DNA, as demonstrated in the results of our MD simulations; (ii) how MD simulations can be used to simulate single molecule manipulation experiments as a complement to reveal the structural dynamics of the studied biomolecules; (iii) how damaged DNA can be studied in computer simulations; and (iv) how repair of damaged DNA can be studied theoretically. © 2006 Wiley Periodicals, Inc. Int J Quantum Chem, 2007     

Platinum(II) and palladium(II) complexes of bisphosphine ligands bearing o-N,N-dimethylanilinyl substituents: a hint of catalytic olefin hydration

Platinum(II) and palladium(II) complexes of the potentially hexadentate P,N-donor ligand family Ar2P-X-PAr2 (X = (CH2)2 [dmape], cyclic-C5H8 [dmapcp]; Ar = o-N,N-dimethylanilinyl) are described. In CH2Cl2, the dmape complexes exist as equilibrium mixtures of MCl2(P,P'-dmape) and [MCl(P,P',N-dmape)]Cl isomers (M = Pd, Pt), governed by deltaH(o) = -19 +/- 4 kJ mol(-1) and deltaS(o) = -100 +/- 30 J mol(-1) K(-1) for M = Pt, and deltaH(o) = -11 +/- 7 kJ mol(-1) and deltaS(o) = -60 +/- 20 J mol(-1) K(-1) for M = Pd. The water-soluble dmapcp complexes exist solely in the [MCl(P,P',N-dmapcp)]Cl form, but the free and coordinated anilinyl rings in these complexes are in slow diastereoselective exchange. X-ray crystal structures for MCl2(P,P'-dmape) (M = Pd, Pt), and the [PdCl(P,P',N-dmape)]+ and [PtCl(P,P',N-dmapcp)]+ cations, are presented. Some of the complexes show marginal activity in water for the catalyzed hydration of maleic to malic acid, giving about 6-7% conversion in 24 h at 100 degrees C and substrate:catalyst loadings of 100:1. Attempts to synthesize a PdCl(P,P',N-dmapm)+ species led instead to isolation of [Pd(mu-Cl)(P,P'-dmapm)]2[PF6]2 (dmapm = Ar2PCH2Ar2).     

The Steiner quadruple systems of order 16

The Steiner quadruple systems of order 16 are classified up to isomorphism by means of an exhaustive computer search. The number of isomorphism classes of such designs is 1,054,163. Properties of the designs—including the orders of the automorphism groups and the structures of the derived Steiner triple systems of order 15—are tabulated. A consistency check based on double counting is carried out to gain confidence in the correctness of the classification.     

Quarter pinched homogeneous spaces of negative curvature

Certain properties of simply connected spaces with quarter pinched sectional curvature K, −4<K≤1, are considered. Additional conditions guaranteeing that the corresponding group of isometries is a symmetric space are given. Published inZapiski Nauchnykh Seminarov POMI, Vol. 234, 1996, pp. 39–40.     

Separation of water-soluble vitamins by reversed-phase high performance liquid chromatography with ultra-violet detection: application to polyvitaminated premixes

Nine water-soluble vitamins: [thiamine (B1), ascorbic acid (C), nicotinamide (PP), pyridoxine (B6), calcium pantothenate (B5), folic acid (B9), cyanocobalamin (B12), riboflavin (B2) and biotin (B8)] were separated on a YMC-Pack Pro C18 column (250 mm x 4.6 mm, 5 microm particle size) in a single run with a gradient elution of mobile phase consisting of 0.025% trifluoroacetic acid pH 2.6 (solvent A) and acetonitrile (solvent B). The separation was achieved within 17 min with a flow rate of 0.8 ml min(-1) and the detection was performed at two wavelengths (210 and 275 nm). The calibration graphs plotted with six concentrations of each vitamin were linear with a regression coefficient R2 > 0.995. The method was applied for the quantification of vitamins B1, C, PP, B6, B5, B9 B2 and B8 in polyvitaminated premixes (premixes) used for the fortification of infant nutrition products. The sample preparation involves an aqueous extraction of vitamins and two different samples dilution were used prior the LC-analysis. The specificity of the method was demonstrated by the retention characteristics, UV spectra and by comparing the peak purity with the standard of each vitamin. The repeatability of the method was evaluated at different level of concentrations on 12 premixes and the coefficients of variation (CVr) were below 6.5%. The values of the intermediate precision (CV1) were below 9.6% (n = 6). The concentrations of vitamins found in premixes with our method were comparable to the declared values, since no bias was found between the two sets of results at 95% confidence. The simplicity of the procedure should make it highly desirable for quality control of premixes in the food industry.