Milan Šoškić

LINK BETWEEN ORTHOGONAL AND STANDARD MULTIPLE LINEAR REGRESSION MODELS

Several topics in connection with a recently proposed method for the orthogonalization of predictor variables (dominant component analysis) are considered. Applying the sequential regression procedure, it is shown that dominant component analysis and the standard multiple linear regression method are directly related to each other. In addition, it is demonstrated that an earlier proposed iterative procedure for the orthogonalization of a correlated variable can be efficiently replaced by one step regression. It is also shown that the coefficient of determination for an orthogonal descriptor coincides with the corresponding squared semipartial correlation coefficient. Finally, the origin of extra information in an orthogonalized predictor variable is discussed.

Molecular recognition of indole derivatives by polymers imprinted with indole-3-acetic acid: A QSPR study

Three molecularly imprinted polymers (MIPs) were prepared using the phytohormone indole-3-acetic acid (IAA) as a template molecule, 4-vinylpyridine (MIP-1 and MIP-2) or N,N-dimethylaminoethyl methacrylate (MIP-3) as functional monomers, ethylenglycol dimethacrylate as a cross linker and acetonitrile (MIP-1), a methanol-water mixture (MIP-2) or chloroform (MIP-3) as porogens. Retention factors for IAA and 29 indole derivatives were determined by high-performance liquid chromatography, using the molecularly imprinted polymers as stationary phases and acetonitrile as an eluent. High correlations between selectivity factors of above mentioned polymers indicate that their retention mechanisms are basically the same. A quantitative structure-property relationships analysis revealed that the presence of the terminal carboxyl group on the 3-side chain plays an essential role in the binding of the indole derivatives to the polymers. The derivatives without the carboxyl group exhibit a drastically lower affinity toward the polymers. Another factor which favors the binding is electronic density of indole nucleus. Substituents with electro-withdrawing properties enhance the binding, while electro-donating substituents have the opposite effect. The length of the 3-side chain also affects the binding. Indole-3-carboxylic acid having the carboxyl group directly attached to the ring as well as the derivatives whose side chain is longer than that of IAA bind to the polymers with a lower affinity.

Modeling the Octanol−Water Partition Coefficients by an Optimized Molecular Connectivity Index†

A procedure that makes it possible to generate a coherent model for prediction of the octanol-water partition coefficient within the molecular connectivity formalism was put forward. The method is based on the optimization of weights for corresponding skeletal atoms and is similar to the method for calculation of a variable connectivity index proposed by Randić. In contrast to Randićs method, we incorporate in the algorithm the possibility that the contribution of a term describing a carbon-heteroatom bond may be negative. When tested on a set of about 300 structurally diverse organic molecules, our procedure proved to be superior to the standard valence connectivity method. External validation on a smaller set of compounds confirmed the superiority of our procedure with respect to the standard one. Intramolecular interactions, which are operative in more complex compounds, are treated in a similar fashion to that in the Hansch-Leo or Rekker methods, by inclusion of empirical correction factors.

Comparison between the structure–boiling point relationships with different descriptors for condensed benzenoids

We compare the structure–boiling point models for benzenoid hydrocarbons based on three distance descriptors (the detour index, the Wiener sum index and its variant) and two connectivity indices (the vertex- and edge-connectivity indices) with those based on the geometric distance indices. The conclusions of this study are that the best model is based on the edge-connectivity index and that the models based on the geometric distance indices are good but not as good as models based on the connectivity indices.

2-Difluoromethylthio-4,6-bis(monoalkylamino)-1,3,5-triazines as Inhibitors of Hill Reaction: A QSAR Study with Orthogonalized Descriptors

The QSAR models for herbicidal activity of 2-difluoromethylthio-4,6-bis(monoalkylamino)-1,3,5-triazines have been developed, using orthogonalized molecular connectivity indices. The orthogonalization of the descriptor variables were performed by a recently proposed dominant component method and well established principal component analysis. The three parameter model based on dominant component descriptors and four parameter principal component regression model are similar in their statistical properties. However, direct correspondence between dominant component descriptors and original variables makes the former model easier to interpret. The obtained models are simpler than the earlier proposed six parameter model, based on n-octanol/water partition coefficients and Tafts steric substituent constants, but are as accurate as this model.

QSAR study of 1,8-naphthyridin-4-ones as inhibitors of photosystem II.

The effect of substituents on in vitro activity of 20 1,8-naphthyridin-4-ones, a novel class of photosystem II inhibitors, was studied. A four-parameter QSAR model based on the molecular connectivity indices was developed which accounts for about 87% of the variations in inhibitory potencies of these compounds. The model suggests that the position, size, and polarity of substituents are factors that predominantly control their activity. By using physicochemical constants, a quantitative model for both 1,8-naphthyridin-4-ones and structurally related 2-trifluoromethyl-4-hydroxyquinoline derivatives was proposed.

Quantitative structure-activity relationships for N-(indol-3-ylacetyl)amino acids used as sources of auxin in plant tissue culture

The methods of quantitative structure-activity relationship (QSAR) analysis were applied to two sets of N-(indol-3-ylacetyl)amino acids tested in vitro as promoters of unorganized callus growth in cultures derived from Solanum nigrum L. and from soybean (Glycine max L.). Two types of statistical models were developed describing molecular structure: (a) by molecular connectivity indices or (b) by experimentally determined biochemical constants. The parameter structure of those models indicated that the mode of action of the indole-3-acetic acid (IAA) conjugates is similar in both plant systems. Growth-promoting activities decreased with molecular size and with increasing involvement of the amino acid C-α and C-β in branched or cyclic structures. This was more clearly visible when molecular connectivity indices were employed as descriptor variables. The biochemical constants with most accurately describe the auxin-like effect of N-(IAA)amino acids are lipophilicity and resistance to degradation by peroxidase. This suggests that biological activity mostly depends on uptake and metabolic stability. The latter includes hydrolysis to free IAA, but the models do not support the popular hypothesis that this is the only ratedetermining step.

Extension of the Z Matrix to Cycle-Containing and Edge-Weighted Molecular Graphs†

The Hosoya Z matrix is originally defined only for trees. Due to a multitude of possibilities to connect pairs of vertices in a general connected undirected graph, the Z matrix could be generalized in different ways. A possibility to resolve this problem is discussed. For edge-weighted graphs, the Zew matrix based on the novel Z* index is defined. In analogy to path numbers invariants kZ, k = 1, 2, ..., are introduced, and their correlation with boiling points of saturated hydrocarbons is studied.

ON THE RELATION BETWEEN THE P'/P INDEX AND THE WIENER NUMBER

It is shown analytically that the recently introduced P ‘/P index and the Wiener number are closely related graph-theoretical invariants for connected undirected acyclic structures and cycles.

On the Calculation of the Molecular Descriptor χ’/χ

The molecular descriptor χ’/χ was recently introduced by Randic. The explicit formula for calculation of the χ’/χ index is derived. The formula provides an easy method to calculate the χ’/χ index for any connected graph. The advantages of the formula over the algorithm proposed by Randic et al. are pointed out.