From molecular connectivity indices to semiempirical connectivity terms: recent trends in graph theoretical descriptors

Investigation of DNA‐Binding Properties of Organic Molecules Using Quantitative Structure‐Activity Relationship (QSAR) Models

Due to the great potential of DNA as a receptor, many classes of synthetic and naturally occurring molecules exert their anticancer activities through DNA-binding. In the field of antitumor DNA-binding agents, a number of acridine and anthracycline derivatives are in the market as chemotherapeutic agents. However, the clinical application of such classes of compounds has encountered problems such as multi-drug resistance and secondary and/or collateral effects. Thus, there has been increasing interest in discovering and developing small molecules that are capable of DNA-binding, which will be expected to be used either in place of or in conjunction with, the existing compounds. The interest in the application of the QSAR paradigm has steadily increased in recent decades and we hope it may be useful in the design and development of DNA-binding molecules as new anticancer agents. In the present review, an attempt has been made to understand the DNA-binding properties of different compound series and discussed using 27 QSAR models, which reveal a number of interesting points. The most important determinants for the activity in these models are Hammett electronic (sigma and sigma+), hydrophobic, molar refractivity, and Sterimol width parameters.

20-(S)-Camptothecin Analogues as DNA Topoisomerase I Inhibitors: A QSAR Study

The interest in the application of the quantitative structure-activity relationships (QSAR) has steadily increased in recent decades because it has repeatedly proven itself to be a low-cost, high-return investment. Potential use of QSAR models for screening of chemical databases or virtual libraries before their synthesis appears equally attractive to chemical manufacturers, pharmaceutical companies, and government agencies. We hope it may also be useful in the design and development of new camptothecin derivatives as DNA topoisomerase I (topo I) inhibitors. In this paper, two series of camptothecin derivatives were undertaken to correlate DNA topo I inhibition with their hydrophobic and steric properties, to understand their chemical-biological interactions. The resulting QSAR have shown that the inhibitory activity of camptothecin analogues 4 toward DNA topo I is mainly dependent on their hydrophobic and steric descriptors, whereas the same activity of 10,11-methylenedioxy- camptothecin analogues 5 is largely dependent on their hydrophobicity at position-7. Using internal [cross-validation, quality factor (Q), Fischer statistics (F), and Y-randomization tests] and external validation tests both of these QSAR models have been validated. Both series of these camptothecin derivatives are also filtered by Lipinski's rule of five to check their oral bioavailability. On the basis of these QSAR models, five compounds (4-35, 4-36, 5-20, 5-21, and 5-22) have been predicted that may be the next synthetic target. These molecules also fulfill the conditions of Lipinski's rule of five.

QSAR studies on the activation of the human carbonic anhydrase cytosolic isoforms I and II and secretory isozyme VI with amino acids and amines

The first QSAR study on the activation of the human secretory isoform of the metalloenzyme carbonic anhydrase (CA, EC 4.2.1.1), CA VI, with a series of amines and amino acids is reported. A large set of topological indices have been used to obtain several tri-/tetra-parametric models. We compared the CA VI activating QSAR models with those calculated for activation of the cytosolic human isozymes hCA I and hCA II. In addition, the effect of D- and L-amino acids as activators of hCA I, hCA II and of hCA VI as compared to those of structurally related biogenic amines was investigated for obtaining statistically significant and predictive QSAR equations. The obtained models are discussed using a variety of statistical parameters. The best models were obtained for hCA II activation, followed by hCA I, whereas the QSAR models for the activation of hCA VI were statistically weaker.

Implementing Molecular Connectivity Theory, a Basic Tool in Modeling Drugs

The concepts of chain graph, general graph, and complete graph have been used to implement the graph framework of molecular connectivity (MC) theory. Some concepts of this theory have been addressed using "external" theoretical concepts belonging mostly to quantum or structural chemistry, with no direct counterpart in graph theory. Thus, while the concept of chain graph can be used to tackle the cis-trans isomerism problem, the concept of pseudograph, or general graph can be used to tackle the description of the sigma-, pi-, and nonbonding n-electrons. The concept of complete graph can instead be used to tackle the electron core problem of the atoms of a molecule. Graph concepts can also be used to tackle the problem of the hydrogen contribution in hydrogen depleted graphs, which are encoded by the aid of a perturbation parameter, which differentiates between compounds with similar hydrogen-suppressed chemical graphs, like the graphs of CH(3)F and BH(2)F. These concepts have allowed redesign of a central parameter of MC theory, the valence delta, giving MC indices with improved model quality as exemplified here with different properties for each treated topic.

A general QSPR model for the prediction of θ (lower critical solution temperature) in polymer solutions with topological indices

The quantitative structure-property relationship (QSPR) study was performed between topological indices representing the molecular structures and theta (LCST, lower critical solution temperature) with a database of 169 data points including 12 polymers and 67 solvents. A linear 10-parameter model was developed to predict theta (LCST) with squared correlation coefficient (R(2)) of 0.8874 and standard error of estimation (SEE) of 24.57 for the training set of 112 systems. The mean relative error (MRE) for the calculation of theta (LCST) was 3.49%. The stability of the proposed model was validated using Leave-One-Out cross-validation and randomization experiments. The model is generally predictive and requires only topological indices during the predictions with the advantage of the relative ease in calculating descriptors which makes it easy to apply. A satisfactory MRE of 4.95% for a test set of 57 systems indicates that the model would be very useful to obtain reliable estimates of theta (LCST) in polymer solutions before they are actually synthesized.

Matrix metalloproteinases (MMPs): chemical-biological functions and (Q)SARs

Matrix metalloproteinases (MMPs) are a large family of calcium-dependent zinc-containing endopeptidases, which are responsible for the tissue remodeling and degradation of the extracellular matrix (ECM), including collagens, elastins, gelatin, matrix glycoproteins, and proteoglycan. They are regulated by hormones, growth factors, and cytokines, and are involved in ovarian functions. MMPs are excreted by a variety of connective tissue and pro-inflammatory cells including fibroblasts, osteoblasts, endothelial cells, macrophages, neutrophils, and lymphocytes. These enzymes are expressed as zymogens, which are subsequently processed by other proteolytic enzymes (such as serine proteases, furin, plasmin, and others) to generate the active forms. Matrix metalloproteinases are considered as promising targets for the treatment of cancer due to their strong involvement in malignant pathologies. Clinical/preclinical studies on MMP inhibition in tumor models brought positive results raising the idea that the development of strategies to inhibit MMPs may be proved to be a powerful tool to fight against cancer. However, the presence of an inherent flexibility in the MMP active-site limits dramatically the accurate modeling of MMP-inhibitor complexes. The interest in the application of quantitative structure-activity relationships (QSARs) has steadily increased in recent decades and we hope it may be useful in elucidating the mechanisms of chemical-biological interactions for this enzyme. In the present review, an attempt has been made to explore the in-depth knowledge from the classification of this enzyme to the clinical trials of their inhibitors. A total number of 92 QSAR models (44 published and 48 new formulated QSAR models) have also been presented to understand the chemical-biological interactions. QSAR results on the inhibition of various compound series against MMP-1, -2, -3, -7, -8, -9, -12, -13, and -14 reveal a number of interesting points. The most important of these are hydrophobicity and molar refractivity, which are the most important determinants of the activity.

Understanding human rhinovirus infections in terms of QSAR

The human rhinoviruses (HRVs) are the single most important cause of common colds. The widespread nature of this affliction, the economic consequences, and the well-known impracticality of vaccine development due to the large number of HRV serotypes (>100) have justified the search for chemotherapeutic agents. The interest in the application of quantitative structure-activity relationships has steadily increased in recent decades and we hope it may be useful in the search for anti-HRV agents. In the present paper, we have discussed the inhibition of various six compound series against HRV-1A, -1B, -2, -9, -14, -21, -22, -25, -64, and -89 by the formulation of a total number of 14 QSAR. Hydrophobicity is found to be one of the most important determinants of activity. Parabolic correlation with the hydrophobic parameter (Eq. ) is an encouraging example, where the optimal hydrophobicity is well defined. We believe that this may be the predictive model to narrow the synthetic challenges in order to yield very specific HRV-2 inhibitors. On the basis of this model, we have predicted eleven compounds (I-1 to I-11) that may be the next synthetic target. The proposed molecules (I-1 to I-11) also fulfill the conditions of Lipinski's "rule of five".

True prediction of lowest observed adverse effect levels

A database of structurally heterogeneous chemical structures with their experimental values of Lowest Observed Adverse Effect Levels (LOAELs) was modeled using graph theoretical descriptors. Variable selection for multiple linear regression (MLR) and linear discriminant analysis (LDA) was accomplished by the Internal Test Set (ITS) method in order to achieve true predicted LOAEL values. The results obtained can be considered good if we take in count the structural diversity of the training set.

QSAR study on topically acting sulfonamides incorporating GABA moieties: A molecular connectivity approach

A quantitative Structure-activity relationship study (QSAR) on a set of carbonic anhydrase (CA, EC 4.2.1.1) inhibitors is reported using first-order valence connectivity index ((1)chi(v)). The inhibitory activity against three isozymes CAI, CAII (cystolic forms), and CAIV (membrane bound form), some of which are involved in important physiological processes, were considered for this purpose. All the three activities were excellently modeled by (1)chi(v) in multi-parametric regression containing indicator parameters. The results are critically discussed on the basis of various regression parameters.

QSAR studies on benzopyran potassium channel activators

QSAR studies on a series of benzopyrans as potassium channel activators have been carried out using a large set of distance-based topological indices. In addition, the molecular descriptors namely: negentropy and molecular redundancy indices have also been used. The relaxant potency in rat trachea, expressed as pEC(50) was used for biological characterization of the benzopyrans. The results have shown that pEC(50) can be modeled excellently in multiparametric model in that we have to include an indicator parameter. The predictive powers of the proposed models are discussed on the bases of cross-validation parameters.

Modeling of activity of cyclic urea HIV-1 protease inhibitors using regularized-artificial neural networks

Artificial neural networks (ANNs) were used to model both inhibition of HIV-1 protease (K(i)) and inhibition of HIV replication (IC90) for 55 cyclic urea derivatives using constitutional and 2D descriptors. As a preliminary step, linear dependences were established by multiple linear regression (MLR) approaches, selecting the relevant descriptors by genetic algorithm (GA) feature selection. For ANN models non-linear GA feature selection was also applied. Non-linear modeling of K(i) overcame the results of the linear one using four properties, keeping in mind standard Pearson R correlation coefficients (0.931 vs. 0.862) and leave one out (LOO) cross-validation analysis (Q(LOO)2 = 0.703 vs. 0.510). On the other hand, IC90 modeling was insoluble by a linear approach: no predictive model was achieved; however, a non-linear relation was encountered according to statistic results (R = 0.891; Q(LOO)2 = 0.568). The best non-linear models suggested the influence of the presence of nitrogen atoms and the molecular volume distribution in the inhibitor structures on the HIV-1 protease inhibition as well as that the inhibition of HIV replication was dependent on the occurrence of five-member rings. Finally, inhibitors were well distributed regarding its activity levels in a Kohonen self-organizing map built using the input variables of the best non-linear models.

The hydrogen perturbation in molecular connectivity computations

A new algorithm for the delta(v) number, the basic parameter of molecular connectivity indices, is proposed. The new algorithm, which is centered on graph concepts like complete graphs and general graphs, encodes the information of the bonded hydrogen on different atoms through a perturbation parameter that makes use of no new graph concepts. The model quality of the new algorithm is tested with 13 properties of seven different classes of compounds, as well as with composite classes of compounds with the same property and with composite properties of the same class of compounds. Chosen properties and classes of compounds display different percentage of bonded hydrogen atoms, which allow a checking of the importance of this parameter. A comparison is drawn with previous results with zero contribution for the hydrogen perturbation as well as among results obtained by changing the number of compounds of a property but keeping constant the percentage of hydrogen atoms. Results underline the importance of the property as well as the importance of the number of compounds in determining the level of the hydrogen perturbation. Molecular connectivity terms are in some cases more critical than the combination of indices in detecting the perturbation introduced by the hydrogen atoms.

Can topological indices transmit information on properties but not on structures?

A survey of several topological indices (TIs) is provided according to the nature (integers or real numbers) of the local vertex invariants (LOVIs) and of the resulting molecular descriptor (TI). The 1st generation TIs such as the Wiener index when both the LOVIs and the TI are integers have a very high degeneracy. This fact can become an asset for the problem under discussion: when confronted with the "inverse problem" (reverse engineering) such indices lead to a combinatorial explosion of possible solutions. On the other extreme, TIs with very low degeneracy may also offer the possibility to transmit information on properties but not on structures, because they may be too difficult to lend themselves to reverse engineering in a reasonable amount of time. Several such indices are discussed: the novel second-generation index G (derived from the average distance-based connectivity index J in order to include a dependence on graph size and cyclicity), and third-generation indices such as the triplet TI denoted by DN2S(4) or the Kier-Hall index TOTOP. The intercorrelation of these indices is discussed: G is almost linearly-correlated with DN2S(4), and shows a different type of correlation with TOTOP.

Simplex Optimization of Generalized Topological Index (GTI−Simplex): A Unified Approach to Optimize QSPR Models

GTI-simplex is a new methodology that combines the generalized topological indices and the down hill simplex optimization procedure to search for optimized quantitative structure-property relationship models (Chem. Phys. Lett. 2005, 410, 343). In this study, the fundamental role of the graph topological distance inducing a local shell structure on vertexes and a detailed derivation of the GTI-decomposition in terms of the so-called "geodesic-brackets", i.e., functions that mix the local shell structure for different vertexes are presented. Applications of the GTI-simplex to a set of physicochemical properties covering those depending on intramolecular and/or intermolecular interactions are included. GTI-simplex has showed to be a very effective methodology for the description of different properties from a unified point of view. No ad hoc definition for topological index is required to each property as in the traditional use of topological indices or other molecular descriptors to QSAR/QSPR studies.

Linear indices of the 'macromolecular graph's nucleotides adjacency matrix' as a promising approach for bioinformatics studies. Part 1: prediction of paromomycin's affinity constant with HIV-1 psi-RNA packaging region

The design of novel anti-HIV compounds has now become a crucial area for scientists around the world. In this paper a new set of macromolecular descriptors (that are calculated from the macromolecular graph's nucleotide adjacency matrix) of relevance to nucleic acid QSAR/QSPR studies, nucleic acids' linear indices. A study of the interaction of the antibiotic Paromomycin with the packaging region of the HIV-1 psi-RNA has been performed as example of this approach. A multiple linear regression model predicted the local binding affinity constants [Log K (10(-4) M(-1))] between a specific nucleotide and the aforementioned antibiotic. The linear model explains more than 87% of the variance of the experimental Log K (R = 0.93 and s = 0.102 x 10(-4) M(-1)) and leave-one-out press statistics evidenced its predictive ability (q2 = 0.82 and s(cv) = 0.108 x 10(-4) M(-1)). The comparison with other approaches (macromolecular quadratic indices, Markovian Negentropies and 'stochastic' spectral moments) reveals a good behavior of our method.

Prediction of glass transition temperatures of OLED materials using topological indices

The QSPR study was performed between topological indices and glass transition temperatures (T(g)s) of organic light-emitting diode materials based on a diverse set of 80 compounds. A five-parameter correlation with the squared correlation coefficient R2 = 0.9304 and an average absolute error of 7.7 K was obtained through step-wise multi-linear regression analysis with leave-one-out cross-validation. The new model proposed is predictive and requires only topological indices in the calculations and has the advantage of the relative ease in calculating the descriptors, which makes it easier to apply. The predicted results of the new model are comparable to those of the existing equation by using the Comprehensives Descriptors for Structural and Statistical Analysis approach.

Predictability and prediction of lowest observed adverse effect levels in a structurally heterogeneous set of chemicals

A database of chronic lowest observed adverse effect levels (LOAELs) for 234 compounds, previously compiled from different sources (Toxicology Letters79, 131-143 (1995)), was modelled using graph theoretical descriptors. This study reveals that data are not homogeneous. Only those data originating from the U.S. Environmental Protection Agency (EPA) reports could be well modelled by multilinear regression (MLR) and linear discriminant analysis (LDA). In contrast, data available from the specific procedures of the National Toxicology Program (NTP) database introduced noise and did not render good models either alone, or in combination with the EPA data.

A novel method of estimation of lipophilicity using distance-based topological indices: dominating role of equalized electronegativity

Attempt is made to propose yet another method of estimating lipophilicity of a heterogeneous set of 223 compounds. The method is based on the use of equalized electronegativity along with topological indices. It was observed that excellent results are obtained in multiparametric regression upon introduction of indicator parameters. The results are discussed critically on the basis various statistical parameters.

Using variable and fixed topological indices for the prediction of reaction rate constants of volatile unsaturated hydrocarbons with OH radicals

Volatile organic compounds (VOCs) play an important role in different photochemical processes in the troposphere. In order to predict their impact on ozone formation processes a detailed knowledge about their abundance in the atmosphere as well as their reaction rate constants is required. The QSPR models were developed for the prediction of reaction rate constants of volatile unsaturated hydrocarbons. The chemical structure was encoded by constitutional and topological indices. Multiple linear regression models using CODESSA software was developed with the RMS(CV) error of 0.119 log units. The chemical structure was encoded by six topological indices. Additionally, a regression model using a variable connectivity index was developed. It provided worse cross-validation results with an RMS(CV) error of 0.16 log units, but enabled a structural interpretation of the obtained model. We differentiated between three classes of carbon atoms: sp2-hybridized, non-allylic sp3-hybridized and allylic sp3-hybridized. The structural interpretation of the developed model shows that most probably the most important mechanisms are the addition to multiple bonds and the hydrogen atom abstraction at allylic sites.

Encoding the core electrons with graph concepts

The core electron problem of atoms in chemical graph studies has always been considered as a minor problem. Usually, chemical graphs had to encode just a small set of second row atoms, i.e., C, N, O, and F, thus, graph and, in some cases, pseudograph concepts were enough to "graph" encode the molecules at hand. Molecular connectivity theory, together with its side-branch the electrotopological state, introduced two "ad hoc" algorithms for the core electrons of higher-row atoms based, mainly, on quantum concepts alike. Recently, complete graphs, and, especially, odd complete graphs have been introduced to encode the core electrons of higher-row atoms. By the aid of these types of graphs a double-valued algorithm has been proposed for the valence delta, deltav, of any type of atoms of the periodic table with a principal quantum number n > or =2. The new algorithm is centered on an invariant suggested by the hand-shaking theorem, and the values it gives rise to parallel in some way the values derived by the aid of the two old "quantum" algorithms. A thorough comparative analysis of the newly proposed algorithms has been undertaken for atoms of the group 1A-7A of the periodic table. This comparative study includes the electronegativity, the size of the atoms, the first ionization energy, and the electron affinity. The given algorithm has also been tested with sequential complete graphs, while the even complete graphs give rise to conceptual difficulties. QSAR/QSPR studies do not show a clear-cut preference for any of the two values the algorithm gives rise to, even if recent results seem to prefer one of the two values.

Modified Connectivity Indices and Their Application to QSPR Study

A modified adjacency matrix was developed to delineate the chemical graph of a compound, in which the element a(ii) along the diagonal of the matrix reflects the numbers of the lone-pair electrons and pi bonds of the ith atom, and the off-diagonal element a(ij) of the matrix characterizes whether the jth non-hydrogen atom is bonded to the ith non-hydrogen atom as well as the number of hydrogen atoms bonded to the jth non-hydrogen atom. The corresponding vertex-degree matrix can distinguish the non-hydrogen atoms in the compound better than that from the original adjacency matrix. Based on the newly proposed adjacency matrix, modified molecular connectivity indices (mMCIs) were proposed as structural descriptors for organic compounds, which were applied to the QSPR studies on the boiling point temperature, molar volume and molar refraction of alkanes, alkenes and alcohols. The results show that, in most cases, the mMCIs give improved correlations than the original molecular connectivity indices (MCIs), which are particularly suitable to distinguish isomers.

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.

QCODES - fast topological descriptors for macromolecules

A fast iterative algorithm to obtain topological atomic and molecular descriptors, called Qcodes, is presented in this work. Its linear time dependence with the size of the structures and low memory requirement allows practical use for small molecules as well as macromolecular systems. The descriptors are unique and are able to sense small topological changes in atom's neighborhood. These properties make them suitable as atom and molecular identifiers to be used in database searching, force field atom typing, isomorphism, and automorphism algorithms. Examples of descriptors, their convergence behavior, sensitivity, ambiguity, and algorithm's performance are shown in this paper.

Algorithmically compressed data and the topological conjecture for the inner-core electrons

Eight different properties of three classes of compounds, metal halides, halomethanes, and chlorofluorocarbons, have been modeled with the aim to check the validity of the odd complete graph conjecture suggested for encoding the contribution of the inner-core electrons to the molecular connectivity indices. Modeling using this conjecture is compared with modeling using connectivity indices derived by other well-known algorithms. The conjecture of odd complete graph for the inner-core electrons achieves to improve the modeling quality of the molecular connectivity indices and/or of the molecular connectivity terms. The importance of the recently introduced dual molecular connectivity indices and pseudoindices in further refining the modeling quality of the higher-order terms has also been stressed.

Issues in representation of molecular structure the development of molecular connectivity

Significant issues in the representation of molecular structure and the development of the molecular connectivity paradigm are presented. In the molecular connectivity paradigm, molecular structure is represented directly. Kier and Hall developed the method by creating ways to encode electronic information based on the paradigm developed from the Randić branching index. The simple and valence delta values were created to encode atomic and valence-state electronic information through counts of sigma, pi, and lone pair electrons. A family of indices was created to provide a wide range of structure information. The key aspects of the development are presented and discussed in such a way as to reveal, at least in part, the imaginative thinking involved in the process. Possible future roles for molecular connectivity chi indices are discussed.

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.

How far are molecular connectivity descriptors from I(S) molecular pseudoconnectivity descriptors?

A comparison of the characteristics of the molecular connectivity and intrinsic-state pseudoconnectivity indices in modeling different activities and properties of different classes of compounds is performed. Two different activities of chlorofluorocarbons, an activity of 2-Br-2-phenetylamines, an activity of benzimidazoles, and the boiling points of primary amines and primary alcohols are modeled. The simultaneous modeling of these last two classes of compounds is also accomplished. The comparison encompasses also the molar mass as descriptor. Further, the influence of the rescaling procedure on the modeling for the case of benzimidazoles is analyzed as well as the relationship between degeneracy of connectivity values and quality of the modeling. Molecular pseudoconnectivity terms seem to compete advantageously with molecular connectivity terms in the descriptive power of the activity and property of many classes of compounds. In many cases new mixed higher-order connectivity-pseudoconnectivity terms have been detected that consistently improve the quality of the description.

Retro-regression--another important multivariate regression improvement

We review the serious problem associated with instabilities of the coefficients of regression equations, referred to as the MRA (multivariate regression analysis) "nightmare of the first kind". This is manifested when in a stepwise regression a descriptor is included or excluded from a regression. The consequence is an unpredictable change of the coefficients of the descriptors that remain in the regression equation. We follow with consideration of an even more serious problem, referred to as the MRA "nightmare of the second kind", arising when optimal descriptors are selected from a large pool of descriptors. This process typically causes at different steps of the stepwise regression a replacement of several previously used descriptors by new ones. We describe a procedure that resolves these difficulties. The approach is illustrated on boiling points of nonanes which are considered (1) by using an ordered connectivity basis; (2) by using an ordering resulting from application of greedy algorithm; and (3) by using an ordering derived from an exhaustive search for optimal descriptors. A novel variant of multiple regression analysis, called retro-regression (RR), is outlined showing how it resolves the ambiguities associated with both "nightmares" of the first and the second kind of MRA.

On structural interpretation of several distance related topological indices

We consider the role that individual bonds play in bond-additivities in order to better understand the structural basis of various topological indices. In particular we consider indices closely related to the Wiener index (W) and the distance matrix and search for optimal weights of terminal and interior CC bonds in alkanes for a selection of physicochemical properties. It is interesting to note that different properties are associated with different relative roles of the exterior and the interior CC bonds.