Statistical parameters for the Polarizability

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）是一种由分子或图的结构衍生而来的数值，可提供有关分子物理、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）与QSAR/QSPR（定量构效关系/定量构性关系，Quantitative Structure-Activity Relationship/Quantitative Structure-Property Relationship）研究中尤为关键，此类研究无需开展实验测量即可预测多种分子特性。从本质而言，拓扑指数是将分子结构量化为可用于数学模型的形式，以此估算分子的行为、活性或特性。在化学图论与化学信息学领域，基于熵的指数可量化分子连接性中的结构复杂度或无序程度。这类指数可用于建模并预测分子特性与生物活性。本研究针对结直肠癌治疗药物，开展了熵指数与物理特性间的QSPR分析，并构建了二者的相关关系模型。通过对这类药物的全面分析，我们获取了其分子特性的关键见解，这对于预测它们治疗结直肠癌的行为与有效性至关重要。将所提模型与现有基于度的模型进行对比后可见，本方法的性能更优。本QSPR研究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，我们提出将机器学习（ML, machine learning）技术融入模型，以进一步提升预测精度与模型鲁棒性。借助先进的机器学习算法，我们旨在揭示拓扑指数与药物疗效间更复杂的非线性关系，有望实现更精准的预测，并为合理药物设计策略提供更充分的决策依据。