Exploring entropy measures with topological indices on colorectal cancer drugs using curvilinear regression analysis and machine learning approaches

Abstract

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.

Fig 1. Molecular structures of anti-colorectal cancer drugs.

Fig 2. Flowchart for regression analysis using entropy measure.

Fig 3. Residual plot for Molecular Weight for Ent_ABC.

Fig 4. Comparison of correlation between entropy index Ent_ABC and physio-chemical properties for the colorectal cancer drugs.

Fig 5. Comparison of correlation between entropy index Ent_F and physio-chemical properties for the colorectal cancer drugs.

Fig 6. Comparison of correlation between entropy index Ent_GA and physio-chemical properties for the colorectal cancer drugs.

Fig 7. Comparison of correlation between entropy index Ent_H and physio-chemical properties for the colorectal cancer drugs.

Fig 8. Comparison of correlation between entropy index Ent_ISI and physio-chemical properties for the colorectal cancer drugs.

Fig 9. Comparison of correlation between entropy index EntM1 and physio-chemical properties for the colorectal cancer drugs.

Fig 10. Comparison of correlation between entropy index EntM2 and physio-chemical properties for the colorectal cancer drugs.

Fig 11. Comparison of correlation between entropy index Ent_S and physio-chemical properties for the colorectal cancer drugs.

Fig 12. Comparison of correlation between entropy index Ent_SO and physio-chemical properties for the colorectal cancer drugs.

Fig 13. Comparison of correlation between entropy index Ent_R and physio-chemical properties for the colorectal cancer drugs.

Fig 14. Molecular structure for Erbitux and Larotrectinib.