Quantitative molecular similarity analysis (QMSA) methods for property estimation: a comparison of property-based,arbitrary, and tailored similarity spaces

Three classes of arbitrary quantitative molecular similarity analysis (QMSA) methods have been computed using atom pairs, topological indices, and physicochemical properties. Tailored QMSA models have been developed using a selected number of TIs chosen by ridge regression. The methods have been applied to the K-nearest neighbor based estimation of log P of two sets of chemicals. Results show that the property-based and tailored QMSA methods are superior to the arbitrary similarity methods in estimating log P of both sets of chemicals     

Quantitative molecular similarity analysis (QMSA) methods for property estimation: A comparison of property-based,arbitrary, and tailored similarity spaces

Three classes of arbitrary quantitative molecular similarity analysis (QMSA) methods have been computed using atom pairs, topological indices, and physicochemical properties. Tailored QMSA models have been developed using a selected number of TIs chosen by ridge regression. The methods have been applied to the K -nearest neighbor based estimation of log P of two sets of chemicals. Results show that the property-based and tailored QMSA methods are superior to the arbitrary similarity methods in estimating log P of both sets of chemicals     

Optimal characterization of structure for prediction of properties

Different topological and physicochemical parameters have been used to predict hydrophobicity (logP, octanol-water) of chemicals. We calculated a hydrogen bonding parameter (HB₁) and a large number of molecular connectivity and complexity indices for a diverse set of 382 molecules. It is known from earlier studies that topological indices (TIs) predict properties of congeneric sets reasonably well. Since HB₁ is an approximate quantifier of hydrogen bonding and has integral values, we used HB₁ to classify the diverse set into strongly and weakly hydrogen bonding subsets. In an attempt to examine the utility of Us in predicting properties of relatively similar groups of molecules, we carried out a correlation of logP with TIs for a subset (n = 139) of the original diverse set (n = 382) with a weak hydrogen bonding ability (HB₁ = 0). Results show that TIs give a better predictive model for the more homogeneous subset as compared to the diverse set of molecules.     

Predicting properties of molecules using graph invariants

Topological indices (TIs) have been used to study structure-activity relationships (SAR) with respect to the physical, chemical, and biological properties of congeneric sets of molecules. Since there are many TIs and many are correlated, it is important that we identify redundancies and extract useful information from TIs into a smaller number of parameters. Moreover, it is important to determine if TIs, or parameters derived from TIs, can be used for global SAR models of diverse sets of chemicals. We calculated seventy-one TIs for three groups of molecules of increasing complexity and diversity: (a) 74 alkanes, (b) 29 alkylbenzenes, and (c) 37 polycyclic aromatic hydrocarbons (PAHs). Principal components analysis (PCA) revealed that a few principal components (PCs) could extract most of the information encoded by the seventy-one TIs. The structural basis of the first few PCs could be derived from their pattern of correlation with individual TIs. For the three sets of molecules, viz. alkanes, alkylbenzenes and PAHs, PCs were able to predict the boiling points reasonably well. Also, for the combined set of 140 chemicals consisting of the alkanes, alkylbenzenes and PAHs, the derived PCs were not as effective in predicting properties as in the case of individual classes of compounds.     

GTI-space: the space of generalized topological indices

A new extension of the generalized topological indices (GTI) approach is carried out to represent “simple” and “composite” topological indices (TIs) in an unified way. This approach defines a GTI-space from which both simple and composite TIs represent particular subspaces. Accordingly, simple TIs such as Wiener, Balaban, Zagreb, Harary and Randić connectivity indices are expressed by means of the same GTI representation introduced for composite TIs such as hyper-Wiener, molecular topological index (MTI), Gutman index and reverse MTI. Using GTI-space approach we easily identify mathematical relations between some composite and simple indices, such as the relationship between hyper-Wiener and Wiener index and the relation between MTI and first Zagreb index. The relation of the GTI-space with the sub-structural cluster expansion of property/activity is also analysed and some routes for the applications of this approach to QSPR/QSAR are also given.     

Molecular Similarity and Risk Assessment: Analog Selection and Property Estimation Using Graph Invariants

Abstract

Four molecular similarity measures have been used to select the nearest neighbor of chemicals in two data sets of 139 hydrocarbons and 15 nitrosamines, respectively. The similarity methods are based on calculated graph invariants which include atom pairs, connectivity indices and information theoretic topological indices. The property of the selected nearest neighbor by each method was taken as the estimate of the property under investigation. The results show that for these data sets, all four methods give reasonable estimates of the properties studied.     

Quantitative structure-activity relationship studies of boron-containing dipeptide proteasome inhibitors using calculated mathematical descriptors

Topological indices (TIs) and atom pairs (APs) were used to develop quantitative structure-activity relationship (QSAR) models of a set of 58 dipeptide boronic acids which are potent inhibitors of proteasome and have found applications in the treatment of various types of cancers. Of the three linear regression methods used for QSAR development, viz., principal components regression (PCR), partial least square (PLS), and ridge regression (RR), the last method gave the most satisfactory models whereas the remaining two methods yielded poor models. RR results obtained in this paper using TIs and APs are comparable to the CoMFA and CoMSIA results reported in the literature with the same set of compounds.     

Comparative study of topological indices of macro/supramolecular RNA complex networks

RNA function annotation is often based on alignment to a previously studied template. In contrast to the study of proteins, there are not many alignment-free methods to predict RNA functions if alignment fails. The use of topological indices (TIs) of RNA complex networks (CNs) to find quantitative structure-activity relationships (QSAR) may be an alternative to incorporate secondary structure or sequence-to-sequence similarity. Here, we introduce new QSAR-like techniques using RNA macromolecular CNs (mmCNs), where nodes are nucleotides, or RNA supramolecular CNs (smCNs), where nodes are RNA sequences. We studied a data set of 198 sequences including 18S-rRNAs (important phylogenetic molecular biomarkers). We constructed three types of RNA mmCNs: sequence-linear (SL), Cartesian-lattice (CL), and sequence-folding CNs (SF-CNs) and two smCNs: sequence-sequence disagreement CN (SSD) and sequence-sequence similarity (SSS-smCN). We reported the first comparative QSAR study with all these CIs and CNs, which includes: (i) spectral moments ( ( i )micro d ( w)) of SL-mmCNs (accuracy = 75.3%), (ii) electrostatic CIs (xi d ) of CL-mmCNs (>90%), (iii) thermodynamic parameters (Delta G, Delta H, Delta S, and T m) of SF-mmCNs (64.7%), (iv) disagreement-distribution moments ( M k ) of the SSD-smCN (79.3%), and (v) node centralities of the SSD-smCN (78.0%). Furthermore, we reported the experimental isolation of a new RNA sequence from Psidum guajava leaf tissue and its QSAR and BLAST prediction to illustrate the practical use of these methods. We also investigated the use of these CNs to explore rRNA diversity on bacteria, plants, and parasites from the Dactylogyrus genus. The HPL-mmCNs model was the best of all found. All the CNs and TIs, except SF-mmCNs, were introduced here by the first time for the QSAR study of RNA, which allowed a comparative study for RNA classification.     

Topological indices for molecular fragments and new graph invariants

Whereas the internal fragment topological index (IFTI) is calculated in the normal manner as for any molecule, the external fragment topological index (EFTI) is calculated so as to reflect the interaction between the excised fragment F and the remainder of the molecule (G-F). For selected topological indices (TIs), a survey of EFTI values, formulas and examples is presented. Some requirements as to the fragment indices are formulated and examined. In the discussion of the results, it is shown that for some TIs regularities exist in the dependence of EFTI values upon the branching of fragment F, or upon the marginal versus central position of the fragment F in the graph G. New vortex invariants can be computed as EFTI values for one-atom fragments over all graph vertices; by iteration, it is in principle possible to devise an infinite number of now vertex invariants.     

Design of topological indices: computer-oriented approach

A novel method is suggested for constructing topological indices (TIs) of molecular graphs which models human logic. This method is described in terms of a block scheme, consisting of the mutually connected elementary blocks. In each block the simple transformations of a molecular graph are fulfilled. A variant of the transformation is selected from the list of possible variants. Every TI is obtained as a result of the sequential execution of a number of operations, corresponding to some ‘walk’ on the block scheme. This walk can be selected both randomly and by the investigator. The suggested method can serve as a basis for the development of the respective computer program which may be used for the automatic construction of any number of TIs of differing nature. By this process one can also obtain the TIs that are unlikely to be constructed manually, due to their complexity. The set of obtained TIs may be used for building the structure–property models. In the case of an unsatisfactory result the obtained set of TIs may be changed using the described generator of TIs. A number of examples of application of the suggested approach for the building QSAR/QSPR models is given.     

Four new topological indices based on the molecular path code

The sequence of all paths pi of lengths i = 1 to the maximum possible length in a hydrogen-depleted molecular graph (which sequence is also called the molecular path code) contains significant information on the molecular topology, and as such it is a reasonable choice to be selected as the basis of topological indices (TIs). Four new (or five partly new) TIs with progressively improved performance (judged by correctly reflecting branching, centricity, and cyclicity of graphs, ordering of alkanes, and low degeneracy) have been explored. (i) By summing the squares of all numbers in the sequence one obtains Sigmaipi(2), and by dividing this sum by one plus the cyclomatic number, a Quadratic TI is obtained: Q = Sigmaipi(2)/(mu+1). (ii) On summing the Square roots of all numbers in the sequence one obtains Sigmaipi(1/2), and by dividing this sum by one plus the cyclomatic number, the TI denoted by S is obtained: S = Sigmaipi(1/2)/(mu+1). (iii) On dividing terms in this sum by the corresponding topological distances, one obtains the Distance-reduced index D = Sigmai{pi(1/2)/[i(mu+1)]}. Two similar formulas define the next two indices, the first one with no square roots: (iv) distance-Attenuated index: A = Sigmai{pi/[i(mu + 1)]}; and (v) the last TI with two square roots: Path-count index: P = Sigmai{pi(1/2)/[i(1/2)(mu + 1)]}. These five TIs are compared for their degeneracy, ordering of alkanes, and performance in QSPR (for all alkanes with 3-12 carbon atoms and for all possible chemical cyclic or acyclic graphs with 4-6 carbon atoms) in correlations with six physical properties and one chemical property.