Alkane isomers: presence in petroleum ether and complexity.

The presence and absence of alkane isomers in petroleum and petroleum derivatives depend on the complexity of these structures. It was assumed that the more complex the structure is the less probable it is that that the molecule can be detected in any petroleum derivative. Complexity is a vague concept, which has not been defined in quantitative terms yet, and therefore there is no experimental method, which could be used to determine 'complexity'. Mass spectrometry and infrared spectroscopy in combination with gas chromatography were used to identify the various structural isomers of alkanes in petroleum ether. The isomers were categorised in quantitative terms by using topological indices and linear discriminant analysis. It was found that alkanes possessing a more complex, highly branched structure are less probable to be detected in petroleum ether than isomers with a simpler backbone structure. It was proposed that the experimental 'measure' of the complexity of isomer(i) should be proportional to 1/C(i), where C(i), denotes the concentration of isomer(i) in a (primary) petroleum derivative.

A topological account of chirality.

Graph invariants may differentiate structural isomers but are inappropriate to account for stereoisomerism and to distinguish between chiral structures. This work is an attempt to address this problem. A chiral function F satisfying condition F(D) = -F(L), where D and L denote enantiomers of the same structure, has been applied in combination with Randic's index (1)chi(v). The resulting index chi(c) was used to explain the variance in thin-layer chromatographic retention indices.(1)

Distance indices and their hyper-counterparts: intercorrelation and use in the structure-property modeling.

Intercorrelation between the Wiener index, hyper-Wiener index, Harary index, hyper-Harary index, detour index and hyper-detour index is studied on three sets of branched and unbranched alkanes and cycloalkanes with up to eight carbon atoms. First set (S-39) contains all alkanes from ethane to octane (39 molecules), the second set (S-139) 139 cyclic hydrocarbons from cyclopropane to branched and unbranched polycyclic octanes and the third set (S-178) is a combination of the first two sets (178 molecules). It is found that the pairs of distance indices and the corresponding hyper-counterparts are highly intercorrelated for all three sets. The use of the distance indices of both kinds in structure-boiling point modeling was analyzed. Distance indices and hyper-distance indices do not lead to particularly good models for any of the three sets. When used as composite indices they give much-improved models. However, they are most useful when combined with such indices as the number of carbon atoms in a hydrocarbon, Hosoya Z index and/or total walk count index. The following standard errors of estimate are obtained for the best models based on the combination of descriptors: 2.1 degrees C (S-39), 4.4 degrees C (S-139) and 4.1 degrees C (S-178). They compare favorably with the related models in the literature.

Distance-related indexes in the quantitative structure-property relationship modeling.

A comparative study of structure-boiling point modeling for a set of 180 acyclic and cyclic hydrocarbons (DS-180) and two of its subsets (one containing a selection of 76 acyclic and cyclic alkanes (DS-76), and the other containing 104 (DS-104) mono- and polycyclic butanes through octanes) using several known and novel distance-related indices is reported. The distance-related indices used were as follows: Wiener index, hyper-Wiener index, detour index, hyper-detour index, Harary index, Pasaréti index, Vérhalom index, Wiener-sum index, inverse Wiener-sum index and the product-form version of the Wiener index. Additional indices used were the total number of paths, the Hosoya Z index, the total walk count index, the number of carbon atoms, and the number of rings in the hydrocarbon. The best models for predicting the boiling points of 76, 104, and 180 acyclic and cyclic alkanes contain the natural logarithm of the cross-products of the Hosoya and detour index and of the Pasaréti index and the number of rings. This result extends earlier work by us and Rücker and Rücker on the use of the Wiener, detour, and Hosoya indices in modeling boiling points of alkanes and cycloalkanes. It also supports later work by Rücker and Rücker on the use of the descriptor combination for the same purpose.

A compact form of the adjacency matrix

It has been shown that the adjacency matrix can be transformed into a row vector and then into a single number. This number can again be decoded to recover the row vector, and this in turn can be decoded to restore the original adjacency matrix. A special, rather efficient coding scheme was devised for acyclic structures.

Isomer generation: semantic rules for detection of isomorphism

The problem of exhaustive generation of a nonredundant set of structural formulas (graphs) of acyclic alkanes was considered. A technique based on the compressed adjacency matrix (CAM) was proposed. The algorithm generates CAMs, which encode trees numbered according to the Morgan naming algorithm. Out of this set of CAMs those corresponding to the maximal Morgan codes--which in fact are the CAMs of canonically numbered isomers--must be found. CAMs are conceived as "sentences" of a primitive language. Sentences violating the syntactic and semantic rules of this language have to be discarded. In this paper three semantic rules have been proposed. The algorithm devised is efficient, and the decision to retain or to reject the actual structure does not involve any comparison with other structures. It was proved that several subsets of CAMs will not contain any maximal CAM and therefore it is not necessary to generate them. The whole procedure was illustrated by generating CAMs of all acyclic graphs containing nine vertices.

The multiplicative version of the Wiener index

The classical Wiener index, W(G), is equal to the sum of the distances between all pairs of vertexes of a (molecular) graph, G. We now consider a related topological index, pi(G), equal to the product of distances between all pairs of vertexes of G. The basic properties of the pi index are established and its possible physicochemical applications examined. In the case of alkanes, pi and W are highly correlated; a slightly curvilinear correlation exists between In pi and W.

Quantitative structure-activity relationships employing independent quantum chemical indices.

Derivation of quantitative structure-activity relationships between pharmacological potencies and the electronic structure of molecules may often result in chance correlations, because of the large number of quantum chemical indices. Interrelationships between the parameters complicate the interpretation of the results. Quantum chemical indices of benzylamines, tetracyclines, and 1,4-benzodiazepines were transformed into mutually independent components using principal component analysis. The number of essential components was 3, 4, and 3, respectively. The computational efforts needed to develop multivariate linear regression equations between these components and the pharmacological activities were reduced, since the regression coefficients were not affected by the inclusion of new parameters. In each example, the first component, which accounted for the highest part of the total sample variance in the electronic structure, was the most important one in determining pharmacological activity. It seems that besides the electrostatic forces, charge transfer also affected the inhibitory potencies of benzylamines.

Correlation between affinity toward adrenergic receptors and approximate electrostatic potentials of phenylethylamine derivatives. 1. Effects of the side chain.

The molecular electrostatic potential (VN) in the region of the nitrogen lone pair of a series of substituted propylamines is used in a correlation with the dissociation constants of parent phenylethylamine-type ligands obtained on beta-adrenoceptors by Bilezikian et al. It is shown that VN is a more effective index for quantitative structure-activity relationship studies than an optimal set of substituent constants used in additive, linear models. No significant correlation between the total electronic charge on the nitrogen and the binding potencies was obtained in the examined series. Protonation energies of the propylamines have been computed, but no meaningful correlation with the dissociation constants was obtained.

Lorazepam and oxazepam esters. Hydrophobicity, hydrolysis rates and brain appearance.

Six prodrug-type esters of oxazepam and lorazepam, which are potent benzodiazepine tranquillizers, were synthesized in 2-14C-labelled form. Pharmacokinetics of the compounds administered i.p. to mice were compared with respect to the effect of the acyl groups on the brain appearance of the esters and the parent drugs. Brain accumulation of the compounds administered was characterized by the areas under the brain-to-blood concentration ratio-time functions (AUQ). The rates of brain penetration were characterized by the slope of the correlation between i.v. dose and 1 -min brain levels. These slopes as well as AUQ values depended upon hydrophobicity (Rm) according to an optimum function. The lag times of the brain appearance of the parent drugs showed a minimum at about the same Rm at which AUQ values were maximal. The rates of brain appearance of the parent compounds correlated with the hepatic microsomal hydrolysis rate of their esters.

An advanced version of the dynamic receptor pattern generation model: the flux model.

In the recently described simple model of dynamic receptor pattern generation we used a two dimensional hexagonal area of a regular triangular network, formed by a statistically constant distribution of unit electostatic changes in a dynamic equilibrium. A set of 16 trnasition rules was applied to all units simultaneously; the next state of each unit depended only on the previous state of its six nearest neighbours, and the transition of the total pattern into the new one occurred in a single jump. Hence we designated the initial simple model as "jump model". In this paper we described an advanced version of the model, in which simplified rules are applied to one unit after the other in a sequential order, from left to right, starting with the top row of units. In the advanced version the state of a unit depends not only on that of its six nearest neighbours, but also on the state of all units preceding in sequence the one actually considered. This results in flux-like transitions. We therefore designated the advanced version as the "flux model". It is shown that the flux model represents a closer approximation of physical and biological realities than the original jump model.

Decomposition of pharmacological activity indices into mutually independent components using principal component analysis.

Various subsets of pharmacological activity indices of benzodiazepines, of 8-quinolinol derivatives, and of rifamycin B amides were decomposed into mutually independent components by using principal component analysis. The activites not included into the subset were considered as the dependent variables. In three out of the six cases with a fair correlation coefficient (r less than or equal to 0.9) between pairs of primary pharmacological indices, the main component obtained by the decomposition procedure showed significantly higher correlation with the dependent variable than any of the original pharmacological activity indices. Factors, explaining a rather low portion of the total sample variance of the subset, may still account for important secondary effects.

Oxazepam esters. 1. Correlation between hydrolysis rates and brain appearance of oxazepam.

Esters of the centrally acting oxazepam were investigated to find quantitative correlations between the pharmacokinetics of the parent drug and in vitro biotransformation rates and physicochemical properties of its prodrugs. The 14C-labeled aliphatic and omega-phenyl-substituted esters were administered intravenously to mice. Brain levels of the esters and oxazepam were determined and the latter was fitted to a simplified exponential equation. In vitro hydrolysis rate of the esters catalyzed by the hepatic microsomal fraction was measured with a pH stat. Pharmacokinetic constants characterizing the rising part of oxazepam brain levels correlate well with the chromatographic RM values and with in vitro maximal hydrolysis rates of the esters. The hydrolysis is capacity limited in the liver. In a closely related set of aliphatic esters, oxazepam brain penetration also correlates with the steric constant (ES) of its esters.