On a topological interpretation of electronic and vibrational molecular energies

Topological Indices of Hyaluronic Acid-Paclitaxel Conjugates’ Molecular Structure in Cancer Treatment

A large number of medical experiments have confirmed that the features of drugs have a close correlation with their molecular structure. Drug properties can be obtained by studying the molecular structure of corresponding drugs. The calculation of the topological index of a drug structure enables scientists to have a better understanding of the physical chemistry and biological characteristics of drugs. In this paper, we focus on Hyaluronic Acid-Paclitaxel conjugates which are widely used in the manufacture of anticancer drugs. Several topological indices are determined by virtue of the edge-partition method, and our results remedy the lack of medicine experiments, thus providing a theoretical basis for pharmaceutical engineering.

The “ETA” Indices in QSAR/QSPR/QSTR Research

Descriptors are one of the most essential components of predictive Quantitative Structure-Activity/Property/Toxicity Relationship (QSAR/QSPR/QSTR) modeling analysis, as they encode chemical information of molecules in the form of quantitative numbers, which are used to develop mathematical correlation models. The quality of a predictive model not only depends on good modeling statistics, but also on the extraction of chemical features. A significant amount of research since the beginning of QSAR analysis paradigm has led to the introduction of a large number of predictor variables or descriptors. The Extended Topochemical Atom (ETA) indices, developed by the authors' group, successfully address the aspects of molecular topology, electronic information, and different types of bonded interactions, and have been extensively employed for the modeling of different types of activity/property and toxicity endpoints. This chapter provides explicit information regarding the basis, algorithm, and applicability of the ETA indices for a predictive modeling paradigm.

The “ETA” Indices in QSAR/QSPR/QSTR Research

Descriptors are one of the most essential components of predictive Quantitative Structure-Activity/Property/Toxicity Relationship (QSAR/QSPR/QSTR) modeling analysis, as they encode chemical information of molecules in the form of quantitative numbers, which are used to develop mathematical correlation models. The quality of a predictive model not only depends on good modeling statistics, but also on the extraction of chemical features. A significant amount of research since the beginning of QSAR analysis paradigm has led to the introduction of a large number of predictor variables or descriptors. The Extended Topochemical Atom (ETA) indices, developed by the authors' group, successfully address the aspects of molecular topology, electronic information, and different types of bonded interactions, and have been extensively employed for the modeling of different types of activity/property and toxicity endpoints. This chapter provides explicit information regarding the basis, algorithm, and applicability of the ETA indices for a predictive modeling paradigm.

Molecular topology as a novel approach for drug discovery

INTRODUCTION

Molecular topology (MT) has emerged in recent years as a powerful approach for the in silico generation of new drugs. One key part of MT is that, in the process of drug design/discovery, there is no need for an explicit knowledge of a drug's mechanism of action unlike other drug discovery methods.

AREAS COVERED

In this review, the authors introduce the topic by explaining briefly the most common methodology used today in drug design/discovery and address the most important concepts of MT and the methodology followed (QSAR equations, LDA, etc.). Furthermore, the significant results achieved, from this approach, are outlined and discussed.

EXPERT OPINION

The results outlined herein can be explained by considering that MT represents a new paradigm in the field of drug design. This means that it is not only an alternative method to the conventional methods, but it is also independent, that is, it represents a pathway to connect directly molecular structure with the experimental properties of the compounds (particularly drugs). Moreover, the process can be realized also in the reverse pathway, that is, designing new molecules from their topological pattern, what opens almost limitless expectations in new drugs development, given that the virtual universe of molecules is much greater than that of the existing ones.

Model of twelve properties of a set of organic solvents with graph-theoretical and/or experimental parameters

Twelve properties of a highly heterogeneous class of organic solvents have been modeled with a graph-theoretical molecular connectivity modified (MC) method, which allows to encode the core electrons and the hydrogen atoms. The graph-theoretical method uses the concepts of simple, general, and complete graphs, where these last types of graphs are used to encode the core electrons. The hydrogen atoms have been encoded by the aid of a graph-theoretical perturbation parameter, which contributes to the definition of the valence delta, delta(v), a key parameter in molecular connectivity studies. The model of the twelve properties done with a stepwise search algorithm is always satisfactory, and it allows to check the influence of the hydrogen content of the solvent molecules on the choice of the type of descriptor. A similar argument holds for the influence of the halogen atoms on the type of core electron representation. In some cases the molar mass, and in a minor way, special "ad hoc" parameters have been used to improve the model. A very good model of the surface tension could be obtained by the aid of five experimental parameters. A mixed model method based on experimental parameters plus molecular connectivity indices achieved, instead, to consistently improve the model quality of five properties. To underline is the importance of the boiling point temperatures as descriptors in these last two model methodologies.

Design of novel antituberculosis compounds using graph-theoretical and substructural approaches

The increasing resistance of Mycobacterium tuberculosis to the existing drugs has alarmed the worldwide scientific community. In an attempt to overcome this problem, two models for the design and prediction of new antituberculosis agents were obtained. The first used a mixed approach, containing descriptors based on fragments and the topological substructural molecular design approach (TOPS-MODE) descriptors. The other model used a combination of two-dimensional (2D) and three-dimensional (3D) descriptors. A data set of 167 compounds with great structural variability, 72 of them antituberculosis agents and 95 compounds belonging to other pharmaceutical categories, was analyzed. The first model showed sensitivity, specificity, and accuracy values above 80% and the second one showed values higher than 75% for these statistical indices. Subsequently, 12 structures of imidazoles not included in this study were designed, taking into account the two models. In both cases accuracy was 100%, showing that the methodology in silico developed by us is promising for the rational design of antituberculosis drugs.

Complete graph conjecture for inner-core electrons: homogeneous index case

The complete graph conjecture that encodes the inner-core electrons of atoms with principal quantum number n >or= 2 with complete graphs, and especially with odd complete graphs, is discussed. This conjecture is used to derive new values for the molecular connectivity and pseudoconnectivity basis indices of hydrogen-suppressed chemical pseudographs. For atoms with n = 2 the new values derived with this conjecture are coincident with the old ones. The modeling ability of the new homogeneous basis indices, and of the higher-order terms, is tested and compared with previous modeling studies, which are centered on basis indices that are either based on quantum concepts or partially based on this new conjecture for the inner-core electrons. Two similar algorithms have been proposed with this conjecture, and they parallel the two "quantum" algorithms put forward by molecular connectivity for atoms with n > 2. Nine properties of five classes of compounds have been tested: the molecular polarizabilities of a class of organic compounds, the dipole moment, molar refraction, boiling points, ionization energies, and parachor of a series of halomethanes, the lattice enthalpy of metal halides, the rates of hydrogen abstraction of chlorofluorocarbons, and the pED(50) of phenylalkylamines. The two tested algorithms based on the odd complete graph conjecture give rise to a highly interesting model of the nine properties, and three of them can even be modeled by the same set of basis indices. Interesting is the role of some basis indices all along the model.

Prediction of molecular volume and surface of alkanes by molecular topology

Molecular volume and molecular surface are expressed as a function of topological degree in alkane graphs. This allows not only a straightforward approach to calculate such physicochemical magnitudes but also an interpretation of the role of the local vertex invariant (LOVI) or valence degree, delta, as well as the connectivity indices in the prediction of physicochemical properties. The interpretation is based on the concept of molecular accessibility (as introduced by Estrada, J. Phys. Chem. A 2002, 106, 9085) for which precise mathematical definitions are provided.

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.

Molecular connectivity: intermolecular accessibility and encounter simulation

The simple molecular connectivity indices are interpreted as summations of bond accessibilities to bimolecular encounters with another, identical molecule. To transcend this model, a molecule is treated as disjecta membra with each bond modeled as a discrete cell in a dynamic simulation of many molecules. Each bond accessibility is transformed into a cellular automata rule. The dynamics are run for each of 38 alkanes, recording the average number of cell encounters, beta. The beta values show a high correlation with the boiling points. The significance of the bond accessibilities and the concept of intermolecular encounters explaining the molecular connectivity indices is supported by these findings.

Predicting bond lengths in planar benzenoid polycyclic aromatic hydrocarbons: a chemometric approach

Two hundred and twenty-three aromatic carbon-carbon bond lengths in high precision crystal structures containing 22 planar condensed benzenoid polycyclic aromatic hydrocarbons (PB-PAHs) were related to the Pauling pi-bond order, its analogue corrected to crystal packing effects, the number of hexagonal rings around the bond, and the numbers of carbons atoms around the bond at topological distance one and two. Principal Component Analysis (PCA) showed that the bond lengths in PB-PAHs are at least two-dimensional phenomenon, with well pronounced classification into 12 types of bonds, as confirmed with Hierachical Cluster Analysis (HCA). Consequently, Multiple Linear Regression (MLR) and Partial Least Squares (PLS) models were superior to univariate models, reducing the degeneration of the data set and improving the estimation of Julg's structural aromaticity index. The approximate regression models based on topological descriptors only were built for fast and easy prediction of bond lengths and bond orders in PB-PAHs.

3D connectivity indices in QSPR/QSAR studies

Topographic (3D) molecular connectivity indices based on molecular graphs weighted with quantum chemical parameters are used in QSPR and QSAR studies. These descriptors were compared to 2D connectivity indices (vertex and edge ones) and to quantum chemical descriptors in modeling partition coefficient (log P) and antibacterial activity of 2-furylethylene derivatives. In describing log P the 3D connectivity indices produced a significant improvement (more than 29%) in the predictive capacity of the model compared to those derived with topological and quantum chemical descriptors. The best linear discriminant model for classifying antibacterial activity of these compounds was also obtained with the use of 3D connectivity indices. The global percent of good classification obtained with 3D and 2D connectivity as well as quantum chemical descriptors were 94.1, 91.2, and 88.2, respectively. In general, all these models predict correctly the antibacterial activity of a set of nine new 2-furylethylene derivatives. The best result is obtained with 3D connectivity indices that classified correctly 100% of these compounds versus 88.9% obtained with 2D connectivity or quantum chemical descriptors.

Getting discriminant functions of antibacterial activity from physicochemical and topological parameters

Linear discriminant analysis has been demonstrated to be a very useful tool in the selection and design of new drugs. Up to now we have used it through the search of a topological pattern of activity. In this work our goal is to calculate a complete set of physicochemical parameters using semiempirical (quantum chemical) calculations as well as topological indices (TIs) and try to find out any discriminant function for antibacterial activity through the combined use of both types of descriptors. The physicochemical parameters, such as heat of formation, HOMO, LUMO, dipole moment, polarizability, hyperpolarizability, PM3 generated IR vibrational frequencies, etc., were calculated using PM3 Hamiltonian implemented within the MOPAC97 package. Among the TIs, connectivity as well as topological charge indices stands as the most representatives. The obtained results suggest that one of the maxima and minima vibrational frequencies play an important role in the antibacterial activity. These frequencies are associated with the torsional molecular vibration (N3) and the stretching vibration (N5) of X-H groups (X = C, N, O). Furthermore, the differences between the maxima and minima values showed an even better discriminant ability than the values themselves. The additional use of the topological indices provided a clear improvement in the discriminant function and also provided a straightforward way to predict the values of such frequencies, so that the results can be applied to a large set of compounds searching for new candidates as antibacterials.

Excitonic couplings and electronic coherence in bridged naphthalene dimers

The electronic excitations of naphthalene and a family of bridged naphthalene dimers are calculated and analyzed by using the Collective Electronic Oscillator method combined with the oblique Lanczos algorithm. All experimentally observed trends in absorption profiles and radiative lifetimes are reproduced. Each electronic excitation is linked to the corresponding real-space transition density matrix, which represents the motions of electrons and holes created in the molecule by photon absorption. Two-dimensional plots of these matrices help visualize the degree of exciton localization and explain the dependence of the electronic interaction between chromophores on their separation.