Mycobacterium tuberculosis is an organism that causes tuberculosis (TB), a common infectious disease that has a high death and morbidity rate. Topological indices are mathematical tools used to describe the structural properties of molecules or networks. They provide a quantitative measure of the connectivity and complexity of a system, and play a crucial role in numerous area such as biochemistry and bioinformatics. The purpose of topological indices is to simplify complex structures into numerical values that can be easily analyzed and compared. QSPR modeling is a technique in chemistry that relates the structure of a chemical compound to its physical or chemical properties. It is used to predict properties like boiling points, solubilities, toxicities, and even biological activities of compounds. This saves time, resources, and enables researchers to make informed decisions in drug discovery, material science, and many other areas. In this study, we conducted an analysis of several drugs used for the treatment of tuberculosis. We focused on computing the reducible topological indices based on their degrees. Several techniques and approaches are employed. To perform calculations, we used edge partition methodology, analytical techniques, theoretical graph utilities, and degree counting method. Additionally, we examined six physicochemical properties of these drugs. To establish quantitative structure-property relationship models and evaluate their effectiveness, we employed linear, quadratic, and logarithmic regression analysis. By analyzing the reducible topological indices and physicochemical properties, we aimed to gain a deeper understanding of the drugs’ characteristics and their potential impact on tuberculosis treatment. This study established a significant relationship between the defined indices with two key properties: molar mass and collision cross section. The correlation coefficients for molar mass range from 0.7 to 0.9, while the collision cross section range from 0.8 to 0.9. These results demonstrate a strong association between the indices and the properties under investigation. Furthermore, it is worth noting that both molar mass and collision cross section satisfy the requirements for p-value and F-test value across all indices. This indicates the statistical significance of the observed correlations and the reliability of our findings.

中文翻译：

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通过 QSPR 研究分析抗结核药物的可还原分子描述符和热力学方面的作用

结核分枝杆菌是一种导致结核病 (TB) 的生物体，结核病是一种死亡率和发病率很高的常见传染病。拓扑指数是用于描述分子或网络结构特性的数学工具。它们提供了系统连接性和复杂性的定量测量，并在生物化学和生物信息学等众多领域发挥着至关重要的作用。拓扑指数的目的是将复杂的结构简化为易于分析和比较的数值。 QSPR 建模是一种化学技术，它将化合物的结构与其物理或化学性质联系起来。它用于预测化合物的沸点、溶解度、毒性甚至生物活性等特性。这节省了时间、资源，并使研究人员能够在药物发现、材料科学和许多其他领域做出明智的决策。在这项研究中，我们对几种用于治疗结核病的药物进行了分析。我们专注于根据度数计算可约拓扑指数。采用了多种技术和方法。为了进行计算，我们使用了边划分方法、分析技术、理论图实用程序和度计数方法。此外，我们还检查了这些药物的六种理化特性。为了建立定量的结构-性质关系模型并评估其有效性，我们采用了线性、二次和对数回归分析。通过分析可约拓扑指数和理化性质，我们的目的是更深入地了解药物的特性及其对结核病治疗的潜在影响。这项研究在定义的指数与两个关键属性之间建立了显着的关系：摩尔质量和碰撞截面。摩尔质量的相关系数范围为 0.7 至 0.9，而碰撞截面范围为 0.8 至 0.9。这些结果表明指数与所调查的属性之间存在很强的关联性。此外，值得注意的是，摩尔质量和碰撞截面都满足以下要求：p-值和F-所有指数的测试值。这表明观察到的相关性的统计显着性和我们的研究结果的可靠性。