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D Bonchev

Publications and source records attributed to D Bonchev.

14 recordsLinked to original sources
PubMed2003

On the complexity of directed biological networks.

Recently there was an increased interest towards network approach to biology and environmental sciences. Networks are believed to be the key to the understanding of the work of biological machine in cells, organs, organisms, and ecosystems. While complexity of undirected networks has been recently analyzed, the assessment of complexity in directed networks has specificity that has not been explored so far. The present paper aims to address the existing gap by discussing the applicability of the available complexity descriptors. New specific measures (vertex accessibility, accessible connectedness, and adjusted average distance) are introduced based on assessment of the reduced accessibility of nodes in directed networks.

Animals↗
PubMed2001

Overall connectivity--a next generation molecular connectivity.

The development of molecular connectivity concept and some of its key elements - Randić's inverse-square-root function and the detailed subgraph characterization - are analyzed. The concept of overall connectivity recently advanced is presented as a next step in unfolding the ideas of molecular connectivity by combining them with those of molecular complexity. Definitions of overall connectivity index, eth-order overall connectivities, and overall connectivity vector are presented along with formulae for calculating these sets of topological indices for several classes of graphs of chemical relevance. Based on sums of adjacencies over all subgraphs (or up to a limiting subgraph size in large molecules), the overall connectivities increase both with molecule size and complexity, as expressed in branching and cyclicity of molecular skeleton. When applied to molecules containing heteroatoms, valence overall connectivities are constructed employing the Kier and Hall scheme. The usefulness of the novel indices is demonstrated by modeling physicochemical properties of alkane compounds. A detailed comparison is made with other models derived for the same set of compounds, proceeding from molecular connectivity, as well as with two other probe connectivity functions--the overall connectivity versions of the second Zagreb index, and a derivative inverse function of this index. The favorable comparisons indicate the need of molecular connectivity paradigm revisiting, and show the potential of the overall connectivity indices for QSPR/QSAR applications.

Alkanes↗
PubMed2001

Overall molecular descriptors. 3. Overall Zagreb indices.

This paper develops further the concept of overall characterization of molecular topology, which is based on calculation of a given graph-invariant for all subgraphs of molecular graph. The new approach defines a cumulative topological descriptor, and an ordered series of terms (eth-order descriptor), which present the sum of the graph-invariant values for all subgraphs having the same number of edges. Alternatively, the terms in the series may be further partitioned, in the manner of molecular connectivity concept of Randić, Kier, and Hall, into contributions of path, cluster, and path-cluster type of subgraphs. The previous publications on the novel approach were based on the simplest graph-invariants--the sum of entries of the adjacency matrix and the distance matrix. Overall connectivity and overall Wiener index were thus defined, along with their respective series of e-order terms. The present study makes use of two other simple functions of vertex degrees, the first and second Zagreb indices. The overall versions of these two indices, very recently constructed, are analyzed in detail. Their potential applicability is verified by deriving multilinear regression models of ten physicochemical properties of alkanes, and comparing them to the results obtained by molecular connectivity and overall connectivity indices.

Chemical Phenomena↗
PubMed2000

Overall connectivities/topological complexities: a new powerful tool for QSPR/QSAR

Earlier attempts to assess the complexity of molecules are analyzed and summarized in a number of definitions of general and topological complexity. A concept which specifies topological complexity as overall connectivity, and generalizes the idea of molecular connectivities of Randic, Kier, and Hall, is presented. Two overall connectivity indices, TC and TC1, are defined as the connectivity (the sum of the vertex degrees) of all connected subgraphs in the molecular graph. The contributions to TC and TC1, which originate from all subgraphs having the same number of edges e, form two sets of eth-order overall connectivities, eTC and eTC1. The total number of subgraphs K is also analyzed as a complexity measure, and the vector of its eth-order components, eK, is examined as well. The TC, TC1, and K indices match very well the increase in molecular complexity with the increase in the number of atoms and, at a constant number of atoms, with the increased degree of branching and cyclicity of the molecular skeleton, as well as with the multiplicity of bonds and the presence of heteroatoms. The potential of the three sets of eth-order complexities for applications to QSPR was tested by the modeling of 10 alkane properties (boiling point, critical temperature, critical pressure, critical volume, molar volume, molecular refraction, heat of formation, heat of vaporization, heat of atomization, and surface tension), in parallel with Kier and Hall's molecular connectivity indices (k)chi. The topological complexity indices were shown to outperform molecular connectivity indices in 44 out of the 50 pairs of models compared, including all models with four and five parameters.

Journal Article↗
PubMed1994

Modeling the anticarcinogenic action of retinoids by making use of the OASIS method. 3. Inhibition of the induction of ornithine decarboxylase by arotinoids.

A series of 15 congeneric aromatic retinoids (arotinoids) was subjected to a study of the conformational dependence of basic molecular descriptors, and the anticarcinogenic potency of the compounds was modeled by the sophisticated OASIS (optimized approach based on structural indices set) method. A high correlation was obtained for both two-variable models and three-variable models. The best models of these two kinds had correlation coefficients of 0.956 vs 0.988 and standard deviations s2 = 0.14 vs 0.04, respectively. The most significant variables were several interatomic and topological distances, which specify the optimum geometric drug-receptor fit. The group of significant electronic descriptors included characteristic pi-bond orders, the electronic charge at one atomic position in the tetrahydronaphthalene ring, the total electronic energy, and two electronic-topological indices. An electrostatic drug-receptor interaction was conjectured on this basis. A contribution of the through-cell membrane transport was inferred from the importance of molecular refraction in the best three-variable model. The models derived were validated by the leave-one-out procedure and by reproducing the activities of five arotinoids not included in the correlation sample.

Anticarcinogenic Agents↗
PubMed1994

The conformational flexibility of aromatic retinoids.

AM1 and PM3 complete geometry optimizations were performed on 19 arotinoids congeneric with (E)-4-[2-(5,6,7,8-tetrahydro-5,5,8,8-tetramethyl-2- naphthalenyl)-1-propenyl] benzoic acid (TTNPB), a very potent agent in carcinoprevention and carcinotherapy. Sixteen TTNPB conformations with close energy were obtained and characterized; four representative conformations were then studied for 14 derivative compounds, for which we found a substantial non-planarity of the two aromatic moieties. Large rotational flexibility of the arotinoid ring fragments was predicted by both methods. Very low barriers (0.4-3.9 kcal/mol) were found for the tetralenyl ring rotation. The two methods also agreed in predicting benzoic acid moiety rotation in a wide range of torsion angle values except those close to 0 or 180 degrees for which the PM3 rotational barriers were found to be considerably lower than the AM1 ones. This high conformational flexibility of arotinoid molecules may facilitate their favorable orientation in the process of fitting to the receptor sites.

Benzoates↗
PubMed1993

Modeling the anticancer action of some retinoid compounds by making use of the OASIS method.

The powerful OASIS (optimized approach based on structural indices set) approach is applied to the anticancer activity of a series of vitamin A analogs. The best three- and four-variable models obtained via the OASIS technique have correlation coefficients of 0.973 vs. 0.990 and standard deviations s2 = 0.11 and 0.05, respectively. The models incorporate the hydrophobicity factor log P, two geometric parameters (topological indices and/or 3-D steric ones), and the molecular dipole moment. For a set of 15 compounds studied here, the activity measured by ED50 was well correlated by models with approximately equal contribution of the through cell membrane transport and the geometric drug-receptor correspondence while weak nonspecific electronic interaction was also found to play some role. Comparison to previous treatments of this data is given and extension to larger sets is discussed.

Antineoplastic Agents↗
PubMed1986

Modelling the interaction of small organic molecules with biomacromolecules. III. Interaction of benzoates with anti-p-(p'-azophenylazo)benzoate antibody.

A novel approach for modelling the biological activity of organic molecules, which requires simultaneous consideration of the influence of all factors (topological, steric, hydrophobic, and electronic) that determine the bioactivity, is used to study the interaction of a series of benzoates with anti-p-(p'-azophenylazo)benzoate antibody. The results obtained suggest that this biological interaction proceeds by a two-step stereospecific mechanism. The first step requires a geometrical correspondence between the benzoates and the cavity in the biomacromolecule, which enables the pharmacophore to come into close contact with the receptor. The second step is the orbitally controlled electronic interaction between the active parts of the benzoates and the antibody. The electronic interaction results from pi-charge transfer from the pharmacophore to the biomacromolecule and from the formation of pi-complexes. A proposed mathematical model for this biological interaction exhibits some statistical advantages over existing models.

Antibodies↗
PubMed1986

Modelling the interaction of small organic molecules with biomacromolecules. I. Interaction of substituted pyridines with anti-3-azopyridine antibody.

An approach is presented for modelling the biological activity of organic molecules. This approach requires a consideration of the influence of all factors (topological, steric, hydrophobic, electronic) which determine the bioactivity. In this work, the interaction between substituted pyridines and antibodies generated by anti-3-azapyridine is studied. The stereoelectronic interactions are responsible for the reaction. Meta-positions to nitrogen are found to be the most probable positions for attack. The most likely reaction products are pi-complexes with charges transfer from the biomolecule to the pyridine derivatives followed by the formation of covalent-type bonds.

Antibodies↗
PubMed1986

Modelling the interaction of small organic molecules with biomacromolecules. II. A generalized concept for biological interactions.

In the first part of this series it was shown that, for interactions between substituted pyridines and anti-3-azopyridine antibody, the maximum biological activity is observed for an optimum electronic correspondence between the reactants. This particular result, together with data in the literature which points to the necessity for geometrical and lipophilic correspondence, supports a generalization for the nature of the biological action of chemical compounds. Accordingly in this paper it is proposed that the affinity towards a given biomacromolecule will be maximum only for those chemicals within a series of compounds which are characterized by optimum values of basic factors which condition the biological activity: geometric, electronic, and/or lipophilic. The practical aspects of the hypothesis should be valuable in molecular pharmacology, drug design, and theory of chemical reactivity.

Aminopyridines↗
PubMedDate not supplied

Novel chirality descriptors derived from molecular topology.

Several series of novel chirality descriptors of chemical organic molecules have been introduced. The descriptors have been developed on the basis of conventional topological descriptors of molecular graphs. They include modified molecular connectivity indices, Zagreb group indices, extended connectivity, overall connectivity, and topological charge indices. These modified descriptors make use of an additional term called chirality correction, which is added to the vertex degrees of asymmetric atoms in a molecular graph. Chirality descriptors can be real or complex numbers. Advantages and drawbacks of different series of chirality descriptors are discussed. These descriptors circumvent the inability of conventional topological indices to distinguish chiral or enantiomeric isomers, which so far has been the major drawback of 2D descriptors as compared to true 3D descriptors (e.g., shape, molecular fields) of molecular structure. These novel chirality descriptors have been implemented in a quantitative structure-activity releationship (QSAR) study of a set of ecdysteroids with a high content of chiral and enantiomeric compounds using the k nearest neighbor QSAR method (kNN) recently developed in this laboratory. We show that the results of this study compare favorably with those obtained with the comparative molecular field analysis (CoMFA) applied to the same dataset. The novel chirality descriptors of molecular structure should find their applications in QSAR studies and related investigations of molecular sdatasets.

Models, Chemical↗
PubMedDate not supplied

The overall Wiener index--a new tool for characterization of molecular topology.

Recently, the concept of overall connectivity of a graph G, TC(G), was introduced as the sum of vertex degrees of all subgraphs of G. The approach of more detailed characterization of molecular topology by accounting for all substructures is extended here to the concept of overall distance OW(G) of a graph G, defined as the sum of distances in all subgraphs of G, as well as the sum of eth-order terms, (e)OW(G), with e being the number of edges in the subgraph. Analytical expressions are presented for OW(G) of several basic classes of graphs. The overall distance is analyzed as a measure of topological complexity in acyclic and cyclic structures. The potential usefulness of the components of this generalized Wiener index in QSPR/QSAR is evaluated by its correlation with a number of properties of C3-C8 alkanes and by a favorable comparison with models based on molecular connectivity indices.

Journal Article↗
PubMedDate not supplied

Topological analysis of long-chain branching patterns in polyolefins.

Patterns in molecular topology and complexity for long-chain branching are quantitatively described. The Wiener number, the topological complexity index, and a new index of 3-starness are used to quantify polymer structure. General formulas for these indices were derived for the cases of 3-arm star, H-shaped, and B-arm comb polymers. The factors affecting complexity in monodisperse polymer systems are ranked as follows: number of arms >> arm length > arm central position approximately equal to arm clustering > total molecular weight approximately equal to backbone molecular weight. Topological indices change rapidly and then plateau as the molecular weight of branches on a polyolefin backbone increases from 0 to 5 kD. Complexity calculations relate 2-arm or 3-arm comb structures to the corresponding 3-arm stars of equivalent complexity but much higher molecular weight. In a subsequent paper, we report the application of topological analysis for developing structure/property relationships for monodisperse polymers. While the focus of the present work is on the description of monodisperse, well-defined architectures, the methods may be extended to the description of polydisperse systems.

Journal Article↗