Universidad de San Buenaventura - Cartagena - Facultad de Ciencias de la Salud - Grupo de Investigación Microbiología & Ambiente (GIMA) - Calle Real de Ternera, Diagonal 32, No. 30-966, Cartagena, Código postal: 1300 10 - Colombia.
Universidad San Francisco de Quito (USFQ), Grupo de Medicina Molecular y Traslacional (MeM&T), Colegio de Ciencias de la Salud (COCSA), Escuela de Medicina, Edificio de Especialidades Médicas, Av. Interoceánica Km 12 ½ -Cumbayá, Quito 170157, Ecuador.
Curr Top Med Chem. 2019;19(11):944-956. doi: 10.2174/1568026619666190510093651.
Recently, some authors have defined new molecular descriptors (MDs) based on the use of the Graph Discrete Derivative, known as Graph Derivative Indices (GDI). This new approach about discrete derivatives over various elements from a graph takes as outset the formation of subgraphs. Previously, these definitions were extended into the chemical context (N-tuples) and interpreted in structural/physicalchemical terms as well as applied into the description of several endpoints, with good results.
A generalization of GDIs using the definitions of Higher Order and Mixed Derivative for molecular graphs is proposed as a generalization of the previous works, allowing the generation of a new family of MDs.
An extension of the previously defined GDIs is presented, and for this purpose, the concept of Higher Order Derivatives and Mixed Derivatives is introduced. These novel approaches to obtaining MDs based on the concepts of discrete derivatives (finite difference) of the molecular graphs use the elements of the hypermatrices conceived from 12 different ways (12 events) of fragmenting the molecular structures. The result of applying the higher order and mixed GDIs over any molecular structure allows finding Local Vertex Invariants (LOVIs) for atom-pairs, for atoms-pairs-pairs and so on. All new families of GDIs are implemented in a computational software denominated DIVATI (acronym for Discrete DeriVAtive Type Indices), a module of KeysFinder Framework in TOMOCOMD-CARDD system.
QSAR modeling of the biological activity (Log 1/K) of 31 steroids reveals that the GDIs obtained using the higher order and mixed GDIs approaches yield slightly higher performance compared to previously reported approaches based on the duplex, triplex and quadruplex matrix. In fact, the statistical parameters for models obtained with the higher-order and mixed GDI method are superior to those reported in the literature by using other 0-3D QSAR methods.
It can be suggested that the higher-order and mixed GDIs, appear as a promissory tool in QSAR/QSPRs, similarity/dissimilarity analysis and virtual screening studies.
最近，一些作者基于图离散导数的使用定义了新的分子描述符（MD），称为图导数指数（GDI）。这种关于图中各种元素的离散导数的新方法以子图的形成为起点。在此之前，这些定义被扩展到化学环境中（N-元组），并从结构/物理化学角度进行解释，并应用于多个终点的描述，取得了良好的效果。
提出一种使用分子图的高阶导数和混合导数的 GDIs 广义化，作为对以前工作的推广，允许生成一组新的 MD。
提出了对以前定义的 GDIs 的扩展，为此，引入了高阶导数和混合导数的概念。这些基于分子图离散导数（有限差分）概念获得 MD 的新方法使用从分子结构的 12 种不同碎片方式（12 个事件）构思的超矩阵元素。将高阶和混合 GDIs 应用于任何分子结构的结果允许找到原子对、原子对-对等等的局部顶点不变量（LOVI）。所有新的 GDI 族都在一个名为 DIVATI（离散导数类型指数的缩写）的计算软件中实现，这是 TOMOCOMD-CARDD 系统中 KeysFinder 框架的一个模块。
对 31 种甾体生物活性（Log 1/K）的 QSAR 建模表明，使用高阶和混合 GDIs 方法获得的 GDIs 与以前基于双联体、三联体和四联体矩阵的报告方法相比，性能略有提高。事实上，使用高阶和混合 GDI 方法获得的模型的统计参数优于使用其他 0-3D QSAR 方法在文献中报告的参数。
可以认为，高阶和混合 GDIs 是 QSAR/QSPR、相似性/差异性分析和虚拟筛选研究中的一种有前途的工具。
