Resistance distance and Laplacian spectrum

The resistance distance r _ij between two vertices v _i and v _j of a (connected, molecular) graph G is equal to the resistance between the respective two points of an electrical network, constructed so as to correspond to G, such that the resistance of any two adjacent points is unity. We show how the matrix elements r _ij can be expressed in terms of the Laplacian eigenvalues and eigenvectors of G. In addition, we determine certain properties of the resistance matrix R=||r _ij ||. AcknowledgementsThis research was supported by the Natural Science Foundation of China and Fujian Province, and by the Ministry of Sciences, Technologies and Development of Serbia, within Project no. 1389. The authors thank Douglas J. Klein (Galveston) for useful comments.     

Prediction of retention times of proteins in hydrophobic interaction chromatography using only their amino acid composition

This paper focuses on the prediction of the dimensionless retention time of proteins (DRT) in hydrophobic interaction chromatography (HIC) by means of mathematical models based, essentially, only on aminoacidic composition. The results show that such prediction is indeed possible. Our main contribution was the design of models that predict the DRT using the minimal information concerning a protein: its aminoacidic composition. The performance is similar to that observed in models that use much more sophisticated information such as the three-dimensional structure of proteins. Three models that, in addition to the amino acid composition, use different assumptions about the amino acids tendency to be exposed to the solvent, were evaluated in 12 proteins with known experimental DRT. In all the cases analyzed, the model that obtained the best results was the one based on a linear estimation of the aminoacidic surface composition. The models were adjusted using a collection of 74 vectors of aminoacidic properties plus a set of 6388 vectors derived from these using two mathematical tools: k-means and self-organizing maps (SOM) algorithms. The best vector was generated by the SOM algorithm and was interpreted as a hydrophobicity scale based partly on the tendency of the amino acids to be hidden in proteins. The prediction error (MSE(JK)) obtained by this model was almost 35% smaller than that obtained by the model that supposes that all the amino acids are completely exposed and 40% smaller than that obtained by the model that uses a simple correction factor considering the general tendency of each amino acid to be exposed to the solvent. In fact, the performance of the best model based on the aminoacidic composition was 5% better than that observed in the model based on the three-dimensional structure of proteins.     

Use of the 13C-NMR chemical shift/charge density linear relationship for recognition and ranking of chemical structures

A novel scheme for computer-aided recognition of chemical structures based on the ¹³C-NMR chemical shift/charge density linear relationship is described. The spectral signals are uniquely assigned to the carbon atoms of each of the compared structures via an automatic assignment procedure. On the basis of this assignment, a factor reflecting the agreement between the spectrum and the molecular structure is defined. This factor has different values for different structures, similar values for similar structures, equal values for equivalent (isomorphic in the graph-theoretical sense) structures, and the lowest value for the structure best corresponding to the ¹³C-NMR spectrum. The potential of this approach for retrieval and ranking of chemical structures is discussed with examples.     

Polarizing a hydrophobic cavity for the efficient binding of organic guests: the case of calix[6]tren, a highly efficient and versatile receptor for neutral or cationic species

The host-guest properties of calix[6]tren 1 have been evaluated. The receptor is based on a calix[6]arene that is covalently capped at the narrow rim by a tren unit. As a result, the system presents a concave hydrophobic cavity with, at its bottom, a grid-like nitrogenous core. Despite its well-defined cavity and opening to the outside at the large rim, 1 did not behave as a good receptor for neutral molecules in chloroform. However, it exhibited efficient endo-complexation of ammonium guests. By contrast, the per-protonated host, 1.4H(+), behaved as a remarkable receptor for small organic molecules. The complexation is driven by a strong charge-dipole interaction and hydrogen bonds between the polar guest and the tetracationic cap of the calixarene. Finally, coordination of Zn(2+) to the tren core led to the asymmetrization of calixarene cavity and to the strong but selective endo-binding of neutral ligands. This study emphasizes the efficiency of a receptor presenting a concave hydrophobic cavity that is polarized at its bottom. The resulting combination of charge-dipole, hydrogen bonding, CH-pi, and van der Waals interactions highly stabilizes the supramolecular architectures. Also, importantly, the tren cap allows the tuning of the polarization, offering either a basic (1), a highly charged and acidic (1.4H(+)), or a coordination (1.Zn(2+)) site. As a result, the system proved to be highly versatile, tunable, and interconvertible in solution by simple addition of protons, bases, or metal ions.     

Preparation and the mechanisms of formation of silver particles of different morphologies in homogeneous solutions

Uniform, well-dispersed silver particles of various morphologies have been prepared by reducing highly acidic silver nitrate solutions with ascorbic acid in the presence of a sodium naphthalene sulfonate-formaldehyde copolymer as dispersing agent. By varying the temperature of the reaction, the free acid content, the addition rate of the reductant, and the aging time, both isometric and anisotropic silver particles could be obtained. It was found that the latter were formed by aggregation of nanosize subunits, which were identified by electron microscopy and X-ray diffractometry.     

On the cycle index of point groups

In this brief work we express the cycle index of the molecular point groups as a function of a limited number of initial geometrical parameters. Such parameters are the number of elements composing the domain D of sites of substitutions in the molecule belonging to the point group G, and the numbers of sites of D lying on the symmetry elements for G.     

Kinetics of the manganese(III)-oxalate reaction in acidic sulphate media

The kinetics of the reaction of manganese(III) with oxalic acid (OA) has been studied in H₂SO₄ solutions. Under the experimental conditions of 6 × 10^–3 <>₀ < 0.4=" mol=">^–3 and [H₂SO₄]₀ 0.2 mol dm^–3 the observed pseudo-first order rate constant k _obs follows the expression

Two-state irreversible thermal denaturation of anionic peanut (Arachis hypogaea L.) peroxidase

Detailed differential scanning calorimetry (DSC), steady-state tryptophan fluorescence and far-UV circular dichroism (CD) studies, together with enzymatic assays, were carried out to monitor the thermal stability of anionic peanut peroxidase (aPrx) at pH 3.0. The spectral parameters were seen to be good complements to the highly sensitive but integral method of DSC. Thus, changes in far-UV CD corresponded to changes in the overall secondary structure of the enzyme, while changes in intrinsic tryptophan fluorescence emission corresponded to changes in the tertiary structure of the enzyme. The results, supported with data concerning changes in enzymatic activity with temperature, show that thermally induced transitions for aPrx are irreversible and strongly dependent upon the scan rate, suggesting that denaturation is under kinetic control. It is shown that the process of aPrx denaturation can be interpreted with sufficient accuracy in terms of the simple kinetic scheme, , where k is a first-order kinetic constant that changes with temperature, as given by the Arrhenius equation; N is the native state, and D is the denatured state. On the basis of this model, the parameters of the Arrhenius equation were calculated.     

Relating Total π-Electron Energy and Resonance Energy of Benzenoid Molecules with Kekulé- and Clar-Structure-Based Parameters

Within classes of isomeric benzenoid hydrocarbons various Kekulé- and Clar-structure-based parameters (Kekulé structure count, Clar cover count, Herndon number, Zhang–Zhang polynomial) are all mutually correlated. This explains why both the total π-electron energy (E), the Dewar resonance energy (DRE), and the topological resonance energy (TRE) are well correlated with all these parameters. Nevertheless, there exists an optimal value of the variable of the Zhang–Zhang polynomial for which it yields the best results. This optimal value is negative-valued for E, around zero for TRE, and positive-valued for DRE. A somewhat surprising result is that TRE and DRE considerably differ in their dependence on Kekulé- and Clar-structure-based parameters.     

Mercury(II) mediated cyclisation of R-1-(1′-hydroxyethyl)-2-(1″-propenyl)-3-alkoxy-4-methoxybenzenes to chiral isochromanes

A protocol has been established for the transformation of chiral ortho 1-hydroxyethyl propenyl benzenes under both anaerobic and oxidative mercury(II) mediated conditions to produce chiral isochromanes. Further transformations of the former products yielded chiral isochromanquinones, while the latter afforded the corresponding chiral 4-hydroxyisochromanquinones.