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.     

Atom-type-based AI topological descriptors: application in structure-boiling point correlations of oxo organic compounds

Structure-boiling point relationships are studied for a series of oxo organic compounds by means of multiple linear regression (MLR) analysis. Excellent MLR models based on the recently introduced Xu index and the atom-type-based AI indices are obtained for the two subsets containing respectively 77 ethers and 107 carbonyl compounds and a combined set of 184 oxo compounds. The best models are tested using the leave-one-out cross-validation and an external test set, respectively. The MLR model produces a correlation coefficient of r = 0.9977 and a standard error of s = 3.99 degrees C for the training set of 184 compounds, and r(cv) = 0.9974 and s(cv) = 4.16 degrees C for the cross-validation set, and r(pred) = 0.9949 and s(pred) = 4.38 degrees C for the prediction set of 21 compounds. For the two subsets containing respectively 77 ethers and 107 carbonyl compounds, the quality of the models is further improved. The standard errors are reduced to 3.30 and 3.02 degrees C, respectively. Furthermore, the results obtained from this study indicate that the boiling points of the studied oxo compound dominantly depend on molecular size and also depend on individual atom types, especially oxygen heteroatoms in molecules due to strong polar interactions between molecules. These excellent structure-boiling point models not only provide profound insights into the role of structural features in a molecule but also illustrate the usefulness of these indices in QSPR/QSAR modeling of complex compounds.     

一个新的拓扑指数用于有机化合物的QSPR/QSAR研究

在分子图的邻接矩阵和距离矩阵的基础上提出了一个新的拓扑指数Xu,该拓扑指数易于计算,对C~2-C~1~6饱和烷烃有较高的结构区分能力,通过适当的处理可方便地推广到含多重键杂原子体系。该指数与饱和烷烃的正常沸点等理化性质,不饱和链烃类化合物的热容以及某些脂肪醇的毒性和疏水性参数均具有较好的性质相关性。绝大多数理化性质与Xu指数均能建立简单线性模型,且相关系数均大于0.99,表明该指数有望在QSPR/QSAR研究中作为一个新的参数而获得推广应用。     

New atom-type-based AI topological indices: Application to QSPR studies of aldehydes and ketones

Multiple linear regression (MLR) analysis based on a combined use of the modified Xu index and the atom-type based AI indices is performed to construct quantitative structure-property models on several data sets of organic compounds including aliphatic aldehydes and/or ketones. For each of the physical properties (the normal boiling points, molar refractions, gas heat capacities at 25 degrees C, water solubility at 25 degrees C, and n-octanol/water partition coefficient at 25 degrees C), high quality QSPR models are obtained, particularly the decrease in the standard error is within the range of 23.6-75.9% relative to the linear models with the modified Xu index alone. For individual subsets containing only aldehydes or ketones, in the majority of cases the quality of the model can be further improved. The significant improvement verifies the efficiency of the present approach and also indicates the usefulness of these indices for application to a wide range of physical properties. The results indicate that the physical properties studied are dominated by molecular size but atom types have smaller influences, especially the oxygen atom seems to be most important due to intermolecular polar interactions. The final models are validated to be statistically reliable using the leave-one-out cross-validation and/or an external test set.     

一个新的连接性指数对脂肪醇的QSPR/QSAR研究

在分子拓扑理论的基础上 ,提出了一个新的连接性指数nχz,并用 nχz 研究了脂肪醇化合物在水中的溶解度 (Sw)、正辛醇 /水分配系数 (Kow)及对水生生物急性毒性 (-LC50 ) ,给出了相关方程 ,研究结果表明 ,相关性良好 ,新方法计算方便 ,物理意义明确 ,预测值与相应的实验值较吻合     

一种新的分子拓扑指数及其在QSPR/QSAR研究中的应用

通过引入量子数、键参数,认为分子的性质与其中各原子的电负性、价电子数、成键电子数、价层主量子数及各化学键的键长有关,提出了一种新的分子拓扑指数mAY.采用该拓扑指数对饱和烷烃、烷基苯、烷氧氯硅烷、卤代苯、含氮杂环化合物、碱金属卤化物及卤化锡的性质/活性进行了相关关系的研究.结果表明,mAY与有机物和无机物的性质/活性间具有良好的相关性.     

Quantum topological molecular descriptors in QSAR analysis of organophosphorus compounds

A Quantitative structure–activity relationship study is performed on a set of organophosphorus compounds to reveal structural and quantum‐chemical features influencing the toxic effect. The properties derived from the topological analysis of the electron density have been used to model the toxicity data. A multiple linear regression analysis in conjunction with genetic algorithm is used in the study, followed by subsequent validation of the results. Obtained QSAR models are beneficial for virtual screening of toxicity for new compounds of interest. Because toxicity of organophosphorus compounds is dependent on conformational properties, a conformational search has been performed before optimization of geometries. All quantum‐chemical calculations are carried out at DFT/B3LYP level of theory with 6‐311++G(d,p) basis set. Frequency calculations are performed after full geometry optimization. Ab initio wave functions were obtained for further analysis and evaluation of quantum topological properties of target molecules. © 2011 Wiley Periodicals, Inc. Int J Quantum Chem, 2012     

On the topological sub-structural molecular design (TOSS-MODE) in QSPR/QSAR and drug design research

A recently introduced graph-theoretical approach to the study of structure-property-activity relationships is presented. The theoretical approach and the computational strategy for the use of the TOSS-MODE approach are given with details. Several QSPR and QSAR applications are reviewed including the study of physical properties of organic compounds, diamagnetic susceptibilities, and biological properties. The applications of the TOSS-MODE approach to discrimination of active/inactive compounds, the virtual screening of compounds with a desired property from databases of chemical structures, identification of active/inactive fragments and its relationships with 2D/3D pharmacophores, and to the design of novel compounds with desired biological activities are also reviewed.