Statistical parameters for the Complexity.

A topological index is a numerical value derived from the structure of a molecule or graph that provides useful information about the molecule’s physical, chemical, or biological properties. These indices are especially important in chemo-informatics and QSAR/QSPR (Quantitative Structure-Activity Relationship/Quantitative Structure-Property Relationship) studies, where they are used to predict a wide range of properties without the need for experimental measurements. In essence, a topological index is a way to quantify the molecular structure in a form that can be used in mathematical models to estimate the molecule’s behavior, activity, or properties. In terms of chemical graph theory and chemo-informatics, entropy-based indices quantify the structural complexity or disorder in a molecule’s connectivity. These indices are useful for modeling and predicting molecular properties and biological activities. In this paper, we established a QSPR analysis of colorectal drugs between entropy indices and their physical properties and developed a relationship. Through a comprehensive analysis of these drugs, we gain essential insights into their molecular properties, which are vital for predicting their behavior and effectiveness in treating colorectal cancer. These models are compared with existing degree-based models, highlighting the superior performance of our approach. The QSPR study is performed using curvilinear regression models including linear, quadratic, cubic exponential and logarithmic models. Additionally, we propose the integration of machine learning (ML) techniques to further enhance the predictive accuracy and robustness of our models. By leveraging advanced ML algorithms, we aim to uncover more complex, non-linear relationships between topological indices and drug efficacy, potentially leading to more accurate predictions and better-informed drug design strategies.

拓扑指数（topological index）是由分子或图的结构衍生出的数值，可提供该分子物理、化学或生物学性质的有效信息。这类指数在化学信息学（chemo-informatics）以及定量构效关系（Quantitative Structure-Activity Relationship，QSAR）/定量构性关系（Quantitative Structure-Property Relationship，QSPR）研究中尤为关键：无需开展实验测量，即可借助它们预测分子的多种性质。简言之，拓扑指数是一种将分子结构量化为可用于数学模型的形式，以预估分子行为、活性或性质的方法。在化学图论与化学信息学领域，基于熵的指数（entropy-based indices）可量化分子连接性中的结构复杂度或无序程度，这类指数在建模与预测分子性质及生物活性方面具有重要应用价值。本文针对结直肠癌治疗药物，开展了基于熵指数与药物物理性质间的QSPR分析，并构建了二者的关联关系。通过对这类药物的全面分析，我们深入掌握了其分子性质，这对于预测药物的行为及结直肠癌治疗疗效至关重要。将所构建的模型与现有的基于度的模型进行对比后，结果凸显了本研究方法的优异性能。本次QSPR分析采用了曲线回归模型，涵盖线性、二次、三次指数及对数回归模型。此外，本研究提出融合机器学习（ML）技术，以进一步提升模型的预测精度与鲁棒性。通过运用先进的机器学习算法，本研究旨在揭示拓扑指数与药物疗效间更为复杂的非线性关联，有望实现更精准的预测，并为药物设计策略提供更科学的参考依据。