Determination of the Wiener molecular branching index for the general tree

The many applications of the distance matrix, D(G), and the Wiener branching index, W(G), in chemistry are briefly outlined. W(G) is defined as one half the sum of all the entries in D(G). A recursion formula is developed enabling W(G) to be evaluated for any molecule whose graph G exists in the form of a tree. This formula, which represents the first general recursion formula for trees of any kind, is valid irrespective of the valence of the vertices of G or of the degree of branching in G. Several closed expressions giving W(G) for special classes of tree molecules are derived from the general formula. One illustrative worked example is also presented. Finally, it is shown how the presence of an arbitrary number of heteroatoms in tree-like molecules can readily be accommodated within our general formula by appropriately weighting the vertices and edges of G.     

Active site reactant center geometry in the Co(II)-product radical pair state of coenzyme B12-dependent ethanolamine deaminase determined by using orientation-selection electron spin-echo envelope modulation spectroscopy

The distances and orientations among reactant centers in the active site of coenzyme B12-dependent ethanolamine deaminase from Salmonella typhimurium have been characterized in the Co(II)-product radical pair state by using X-band electron paramagnetic resonance (EPR) and two-pulse electron spin-echo envelope modulation (ESEEM) spectroscopies in the disordered solid state. The unpaired electron spin in the product radical is localized on C2. Our approach is based on the orientation-selection created in the EPR spectrum of the biradical by the axial electron-electron dipolar interaction. Simulation of the EPR line shape yielded a best-fit Co(II)-C2 distance of 9.3 A. ESEEM spectroscopy performed at four magnetic field values addressed the hyperfine coupling of the unpaired electron spin on C2 with 2H in the C5' methyl group of 5'-deoxyadenosine and in the beta-2H position at C1 of the radical. Global ESEEM simulations (over the four magnetic fields) were weighted by the orientation dependence of the EPR line shape. A Nelder-Mead direct search fitting algorithm was used to optimize the simulations. The results lead to a partial model of the active site, in which C5' is located a perpendicular distance of 1.6 A from the Co(II)-C2 axis, at distances of 6.3 and 3.5 A from Co(II) and C2, respectively. The van der Waals contact of the C5'-methyl group and C2 indicates that C5' remains close to the radical species during the rearrangement step. The C2-Hs-C5' angle including the strongly coupled hydrogen, Hs, and the C5'-Hs orientation relative to the C1-C2 axis are consistent with a linear hydrogen atom transfer coordinate and an in-line acceptor p-orbital orientation. The trigonal plane of the C2 atom defines sub-spaces within the active site for C5' radical migration and hydrogen atom transfers (side of the plane facing Co(II)) and amine migration (side of the plane facing away from Co(II)).     

Pitzer model parameters for sparingly soluble salts from solubility measurements. The systems TlCl+SrCl2+H2O and TlCl+BaCl2+H2O at 25°C

The solubility of thallium(I) chloride has been determined in aqueous solutions of strontium chloride and barium chloride at concentrations up to 1.5 mol kg^–1. The data were analyzed using Pitzer's equations without making explicit assumption of association to ion pairs by assuming =3 instead of =2, with the ⁽¹⁾ term for TlCl being equivalent to the ⁽²⁾ term for 2-2 electrolytes. Best values of ⁽⁰⁾ and ⁽¹⁾ for TlCl are recommended together with K _s , the activity solubility product. These were used to fit the present solubility data and derive the Pitzer model mixture parameters relevant to the systems, _fTIN and _fTINCl (N=Sr, Ba). Mixture parameters for TlCl+MCl+H₂O systems are also derived to complete the parameter base. The fit of the experimental data was found to be worse when higher-order terms for asymmetrical mixing were included in the analysis. Activity coefficients for thallium(I) chloride in the mixtures are derived.     

Studies on taxol biosynthesis. Preparation of 5α-acetoxytaxa-4(20),11-dien-2α,10β-diol derivatives by deoxygenation of a taxadiene tetra-acetate obtained from Japanese yew

The putative metabolite, 5α-acetoxytaxa-4(20),11-dien-2α,10β-diol (7), which is a promising candidate as a biosynthetic pathway triol in taxol biosynthesis, has been prepared by Barton deoxygenation of the C-14-hydroxyl group of a differentially protected derivative of natural 2α,5α,10β-triacetoxy-14β-(2-methyl)-butyryloxytaxa-4(20),11-diene (8), a major taxoid metabolite isolated from Japanese Yew heart wood. The synthetic protocol devised, is amenable for the preparation of isotopically labeled congeners that will be useful to probe further intermediate steps in the biosynthesis of taxol.     

Comparison of MBPT and coupled-cluster methods with full CI. Importance of triplet excitation and infinite summations

Results from full fourth-order perturbation theory [SDTQ MBPT(4)], and the coupled-cluster single- and double-excitation model (CCSD). are compared with recent full CI results for BH, HF, NH₃, and H₂O. For H₂O, studies include large symmetric displacements of the OH bonds, which offer a severe test for any single-reference MBPT/CC method. In every case. CCSD plus fourth-order triple-excitation terms provide agreement with the full CI to < 2 kcal/mole. SDTQ MBPT(4) has an error 10 kcal/mole for displaced H₂O.     

Dynamic metal-ligand coupling in the infrared MCD spectra of the cobalt(II) tetrahalides

The axial single-crystal magnetic circular dichroism spectra of Cs₃ZnCl₅/Co²⁺ and Cs₃ZnBr₅/Co²⁺ have been measured over the 4000–7000 cm^?1 region of the ⁴A₂ → ⁴T₁ (F) transition at ambient and liquid-helium temperature. The B/D and C/D terms obtained give transition moment ratios, 〈t₂∥m∥t₂〉/〈e∥m∥t₂〉, in accord with the value required (?3^{$\text{1}\text{2}$}/2^{$\text{1}\text{2}$}) by a dynamic ligand-polarisation model for d-electron transition probabilities in tetrahedral metal complexes.     

Theoretical treatment of multiple site reactivity in large molecules

The method of electrostatic potentials is generalized via a double perturbation theory to describe the simultaneous attack of a large molecule by two or more charged species. The interaction term is found to reproduce accurately the full “super-molecule” calculation. The scheme is illustrated by treating the diprotonation of adenine and N7-methyladenine. For adenine, the most stable diprotonated species is found to be the N1, N7 combination, while the N3, N9 couple is predicted for the N7 substituted derivative if N3 is the first protonation site.     

Lateral diffusion of molecules in two-component lipid bilayer: a Monte Carlo simulation study

Lateral diffusion of membrane components makes possible any in-plane membrane reaction and has a key role in signaling in cell membranes. In this report the equilibrium lateral diffusion of intrinsic molecules in an equimolar DMPC/DSPC mixture is simulated using a thoroughly tested two-state model of two-component phospholipid bilayers. The model has been successful in calculating the excess heat capacity function, the most frequent center-to-center distances between DSPC clusters, and the fractal dimensions of gel clusters (Sugar, I. P., Thompson, T. E., Biltonen, R. L. Biophys. J. 1999, 76, 2099-2110). In the gel/fluid mixed phase region, a diffusing intrinsic molecule may change its state from fluid to gel (or from gel to fluid) at any time. A common characterization of the diffusion of intrinsic molecules is given by the simulated average first-passage time curves. We find that these curves can be described as power functions containing two parameters, alpha and beta, except near the percolation threshold of gel/fluid or compositional clusters. We find also that the intrinsic molecules are involved in approximately normal diffusion, i.e., beta approximately 2 in the extreme gel and fluid phase regions, while in the gel/fluid and gel/gel mixed phase regions the diffusion is anomalous, i.e., beta not equal 2. In the mixed phase regions, when the initial local state of the diffusing molecule is not specified, each component is involved in sub-diffusion (beta > 2). In the gel/fluid mixed phase region molecules situated initially inside a fluid cluster are involved in sub-diffusion, but DMPC molecules situated initially inside a gel cluster are involved in super-diffusion (beta < 2). The possibility of anomalous diffusion in membranes apparently arises because the diffusing molecule visits a variety of different environments characterized by its relative proximity to various membrane components. The diffusion is actually anomalous when the components of the bilayer are nonrandomly distributed. The deviation from random distribution is strongly correlated with beta. Similar to the results of the NMR experiments, the calculated relative diffusion coefficient continuously decreases in the gel/fluid mixed phase region with decreasing temperature. In apparent contradiction, diffusion measured by fluorescence recovery after photobleaching (FRAP) demonstrates the existence of a threshold temperature, below which long-range diffusion of FRAP probe molecules is essentially blocked. This threshold temperature is highly correlated with the percolation temperature of gel clusters.