Quantitative modeling of degree-degree correlation in complex networks.

This paper presents an approach to the modeling of degree-degree correlation in complex networks. Thus, a simple function, Δ(k', k), describing specific degree-to-degree correlations is considered. The function is well suited to graphically depict assortative and disassortative variations within networks. To quantify degree correlation variations, the joint probability distribution between nodes with arbitrary degrees, P(k', k), is used. Introduction of the end-degree probability function as a basic variable allows using group theory to derive mathematical models for P(k', k). In this form, an expression, representing a family of seven models, is constructed with the needed normalization conditions. Applied to Δ(k', k), this expression predicts a nonuniform distribution of degree correlation in networks, organized in two assortative and two disassortative zones. This structure is actually observed in a set of four modeled, technological, social, and biological networks. A regression study performed on 15 actual networks shows that the model describes quantitatively degree-degree correlation variations.

Theoretical prediction of relative and absolute pKa values of aminopyridines.

This work presents a study aimed at the theoretical prediction of pK(a) values of aminopyridines, as a factor responsible for the activity of these compounds as blockers of the voltage-dependent K(+) channels. To cover a large range of pK(a) values, a total of seven substituted pyridines is considered as a calibration set: pyridine, 2-aminopyridine, 3-aminopyridine, 4-aminopyridine, 2-chloropyridine, 3-chloropyridine, and 4-methylpirydine. Using ab initio G1, G2 and G3 extrapolation methods, and the CPCM variant of the Polarizable Continuum Model for solvation, we calculate gas phase and solvation free energies. pK(a) values are obtained from these data using a thermodynamic cycle for describing protonation in aqueous and gas phases. The results show that the relatively inexpensive G1 level of theory is the most accurate at predicting pK(a) values in aminopyridines. The highest standard deviation with respect to the experimental data is 0.69 pK(a) units for absolute values calculations. The difference increases slightly to 0.74 pK(a) units when the pK(a) is computed relative to the pyridine molecule. Considering only compounds at least as basic as pyridine (the values of interest for bioactive aminopyridines) the error falls to 0.10 and 0.12 pK(a) units for the absolute and relative computations, respectively. The technique can be used to predict the effect of electronegative substituents in the pK(a) of 4-AP, the most active aminopyridine considered in this work. Thus, 2-chloro and 3-chloro-4-aminopyridine are taken into account. The results show a decrease of the pK(a), suggesting that these compounds are less active than 4-AP at blocking the K(+) channel.

Thermodynamic conformational analysis and structural stability of the nicotinic analgesic ABT-594.

This work presents a theoretical study of the nicotinic analgesic ABT-594. We describe its neutral (precursor) and protonated (active) forms in vacuum and aqueous solution at the MP2/cc-pVDZ level. A conformational analysis is performed on the two torsional angles describing the orientation of the azetidinyl group and the azetidinylmethoxy moiety. To account for entropic effects, a thermostatistical study of conformational populations at physiological temperature is carried out. In the neutral form, conformer I is found as the most populated in vacuum and solution. Here, the nitrogen of the azetidinyl group is far from the electron pairs of the oxygen and the pyridinic nitrogen. In the protonated form, conformer VIII is the most stable in vacuum and solution. Now, the additional proton on the azetidinyl group is oriented toward the electron lone pairs of oxygen. The structural stability of conformers I and VIII is considered through the atoms in molecules theory. The conformer I, in the neutral forms, is stabilized by an intramolecular hydrogen bond. The preference of conformer VIII in the protonated forms is explained by the higher strength of its intramolecular hydrogen bond over the cation-pi interaction found in conformer I. The effect of the interaction energy with the receptor on the conformational preferences of protonated ABT-594 is simulated. The result is that the population of conformers associated to the rotation of the azetidinyl group increases. So, the molecule can easily adopt the optimal internitrogen separation for interaction with the receptor.

Theoretical analysis of the molecular determinants responsible for the K(+) channel blocking by aminopyridines.

This work presents a theoretical analysis of the molecular determinants responsible for the pharmacological activity (K(+) channel blocking) of aminopyridines. Thus, DFT theory at the B3LYP/cc-pVDZ level is applied to a series of active compounds: 2-aminopyridine, 3-aminopyridine, 4-aminopyridine, 3,4-diaminopyridine, and 4-aminoquinoleine. The two forms present in the biological environment, neutral and cationic (protonated), are considered in vacuum as well as in aqueous solution. The results show pyramidal and planar structures for the neutral and cationic forms, respectively. An analysis of the topology of the electron density show that an increase in conjugation between the pyridine ring and the amine group is responsible for the observed planarity of the protonated forms. By computing the Laplacian of the charge density we found the pyridine nitrogen to be the preferred protonation site, as a consequence of a much higher curvature of the charge density field. Also, from three-dimensional (3D) isoLaplacian diagrams a common reactivity pattern is only found in the charged forms. This reactivity pattern implies that interaction with the biological receptor site is mediated by electrostatic interactions and hydrogen bonding. Development of a physical-mathematical model allows identification of the specific relationship of the pharmacological activity index with the affinity for the receptor and the protonation ability.

Theoretical and experimental study of the acetohydroxamic acid protonation: the solvent effect.

The mechanism of the protonation of acetohydroxamic acid is investigated comparing experimental results and ab initio calculations. Experimentally, the UV spectral curves were recorded at different temperatures, at constant dioxane/water concentration, and at very high concentrations of strong mineral acids. The process is followed by monitoring the changes in the UV curves with increasing acid concentration. The molecular structures and the solvation energies were calculated with the RHF, B3LYP, and MP2 methods. The solvent is treated as a continuum of uniform dielectric constant. The isolated molecule of acetohydroxamic acid exhibits two protonation sites, the carbonyl oxygen and the nitrogen atom. In dioxane/water mixture, the RHF calculations predict the existence of a third cation of low stability, where the proton is bonded to the OH oxygen. With the MP2 ab initio calculations, the free energies of the formation processes in solution of the two most stable cations, CH3COH-NHOH+ (O3H+) and CH3CO-NH2OH+ have been evaluated to be -160.2 kcalmol(-1) and -157.6 kcal mol(-1). The carbonyl site is the most active center in solution and in the gas phase. The carbonyl site is also the most active center in the UV measurements. Experimentally, the ionization constant was found to be pK(O3H+) = -2.21 at 298.15 K, after the elimination of the medium effects using the Cox-Yates equation for hight acidity levels. Experiments and ab initio calculations indicate that K(O3H+) decreases with the temperature.

Modeling of protonation processes in acetohydroxamic acid

This work presents a theoretical study of acetohydroxamic acid and its protonation processes using ab initio methodology at the MP2(FC)/cc-pdVZ level. We find the amide form more stable than the imidic tautomer by less than 1.0 kcal mol(-)(1). For comparison with the experimental data, a three-dimensional conformational study is performed on the most stable tautomer (amide). From this study, the different barriers to rotation and inversion are determined and the intramolecular hydrogen bond between the OH group and the carbonyl oxygen is characterized. The electrostatic potential distribution shows three possible sites for electrophilic attack, but it is shown that only two of them, the carbonyl oxygen and the nitrogen atoms, are actual protonation sites. The protonation energy (proton affinity) is obtained from the results of the neutral and charged species. Proton affinities for the species charged on the carbonyl oxygen and the nitrogen atoms are estimated to be 203.4 and 194.5 kcal mol(-)(1), respectively. The development of a statistical model permits the quantification of DeltaG (gas-phase basicity) for the two protonation processes. In this way, the carbonyl oxygen protonated form is found to be more stable than that of the nitrogen atoms by 8.3 kcal mol(-)(1) at 1 atm and 298.15 K, due to the enthalpic contribution. As temperature increases, the proportion of the nitrogen protonated form increases slightly.

The Torsion-Inversion-Bending Energy Levels in the S1(n, pi*) Electronic State of Acetaldehyde.

The band assignments and analyses of the jet-cooled high-resolution laser-induced fluorescence excitation spectrum of acetaldehyde that results from the S1(n, pi*) electronic state have been extended to +600 cm-1 from the 0(0)0 system origin. The new assignments start at Band #7 and finish at Band #21. Bands #8 and #9, originally assigned to 14(2)0, have now been assigned to 15(3)0. The assignments of the lower energy bands remain unaltered. The origins of the bands that involve the torsional modes nu15 (v = 1 to 4) in combination with the wagging mode nu14 (v = 1 and 2) and the nu10 (v = 1) were determined by analyses with a rigid rotational Hamiltonian. These origins were fitted to a set of levels that were derived from a torsion-wagging-bending Hamiltonian that employed flexible large amplitude coordinates. The resulting potential surface was found to have barriers to torsion and inversion of 712.5 and 638.6 cm-1, respectively, with minima in the potential hypersurface at theta = 59.9 degrees and alpha = 33.5 degrees for the torsion and wagging coordinates. Copyright 1998 Academic Press.

Quantum mechanical study and nuclear magnetic resonance measurements of some alpha-arylcarboxyalkyl acids as anti-inflammatory agents.

The CNDO/2 quantum mechanical conformation method of analysis, charge density and protonation energy calculations, as well as 13C and 1H NMR measurements were carried out for ibufenac, ibuprofen, methylibuprofen, and for a series of alpha-arylpropionic acids. It was found that the nature of the terminal lipophilic residue does not significantly influence the conformation of the alpha-arylcarboxyalkyl acid side chain. The preferred conformational angle, for the torsion of the phenyl-C alpha bond, was found to be 90, 120, and 180 degrees in ibufenac, ibuprofen, and methylibuprofen, respectively. This conformational angle is calculated to be the same in all the alpha-arylpropionic acids. The protonation energies of the alpha-arylpropionic acids are correlated with the anti-inflammatory activity. It was found that the smaller the protonation energy, the larger the anti-inflammatory activity.