Garcia-Jacas Cesar R, Marrero-Ponce Yovani, Barigye Stephen J, Valdes-Martini Jose R, Rivera-Borroto Oscar M, Olivero-Verbel Jesus
Unit of Computer-Aided Molecular "Biosilico" Discovery and Bioinformatic Research (CAMD-BIR Unit), Faculty of Chemistry-Pharmacy. Universidad Central "Martha Abreu" de Las Villas, Santa Clara, 54830, Villa Clara, Cuba.
Curr Drug Metab. 2014;15(4):441-69. doi: 10.2174/1389200215666140605124506.
The present manuscript introduces, for the first time, a novel 3D-QSAR alignment free method (QuBiLS-MIDAS) based on tensor concepts through the use of the three-linear and four-linear algebraic forms as specific cases of n-linear maps. To this end, the k(th) three-tuple and four-tuple spatial-(dis)similarity matrices are defined, as tensors of order 3 and 4, respectively, to represent 3Dinformation among "three and four" atoms of the molecular structures. Several measures (multi-metrics) to establish (dis)-similarity relations among "three and four" atoms are discussed, as well as, normalization schemes proposed for the n-tuple spatial-(dis)similarity matrices based on the simple-stochastic and mutual probability algebraic transformations. To consider specific interactions among atoms, both for the global and local indices, n-tuple path and length cut-off constraints are introduced. This algebraic scaffold can also be seen as a generalization of the vector-matrix-vector multiplication procedure (which is a matrix representation of the traditional linear, quadratic and bilinear forms) for the calculation of molecular descriptors and is thus a new theoretical approach with a methodological contribution. A variability analysis based on Shannon's entropy reveals that the best distributions are achieved with the ternary and quaternary measures corresponding to the bond and dihedral angles. In addition, the proposed indices have superior entropy behavior than the descriptors calculated by other programs used in chemo-informatics studies, such as, DRAGON, PADEL, Mold2, and so on. A principal component analysis shows that the novel 3D n-tuple indices codify the same information captured by the DRAGON 3D-indices, as well as, information not codified by the latter. A QSAR study to obtain deeper criteria on the contribution of the novel molecular parameters was performed for the binding affinity to the corticosteroid-binding globulin, using Cramer's steroid database. The achieved results reveal superior statistical parameters for the Bond Angle and Dihedral Angle approaches, consistent with the results obtained in variability analysis. Finally, the obtained QuBiLS-MIDAS models yield superior performances than all 3D-QSAR methods reported in the literature using the 31 steroids as training set, and for the popular division of Cramer's database in training (1-21) and test (22-31) sets, comparable to superior results in the prediction of the activity of the steroids are obtained. From the results achieved, it can be suggested that the proposed QuBiLS-MIDAS N-tuples indices are a useful tool to be considered in chemo-informatics studies.
本手稿首次介绍了一种基于张量概念的新型3D-QSAR无对齐方法（QuBiLS-MIDAS），该方法通过使用三线性和四线性代数形式作为n线性映射的具体实例。为此，分别定义了第k个三元组和四元组空间（不）相似性矩阵，作为三阶和四阶张量，以表示分子结构中“三个和四个”原子之间的三维信息。讨论了几种用于建立“三个和四个”原子之间（不）相似性关系的度量（多指标），以及基于简单随机和互概率代数变换为n元组空间（不）相似性矩阵提出的归一化方案。为了考虑原子之间的特定相互作用，对于全局和局部指标，引入了n元组路径和长度截止约束。这种代数框架也可以看作是向量-矩阵-向量乘法过程（它是传统线性、二次和双线性形式的矩阵表示）的推广，用于计算分子描述符，因此是一种具有方法学贡献的新理论方法。基于香农熵的变异性分析表明，与键角和二面角对应的三元和四元度量可实现最佳分布。此外，所提出的指标比化学信息学研究中使用的其他程序（如DRAGON、PADEL、Mold2等）计算的描述符具有更好的熵行为。主成分分析表明，新型3D n元组指标编码了DRAGON 3D指标捕获的相同信息，以及后者未编码的信息。使用克莱默类固醇数据库，进行了一项QSAR研究，以获得关于新型分子参数贡献的更深入标准，用于与皮质类固醇结合球蛋白的结合亲和力。所取得的结果表明，键角和二面角方法具有更好的统计参数，这与变异性分析中获得的结果一致。最后，使用31种类固醇作为训练集，所获得的QuBiLS-MIDAS模型比文献中报道的所有3D-QSAR方法具有更好的性能，并且对于克莱默数据库在训练集（1-21）和测试集（22-31）中的常见划分，在类固醇活性预测方面获得了可比的优异结果。从所取得的结果可以看出，所提出的QuBiLS-MIDAS N元组指标是化学信息学研究中值得考虑的有用工具。
