<p>Amylose, a vital polysaccharide component of starch, plays a significant role in plant energy storage and has important implications in nutrition and health. In this study, the structural characteristics of amylose are analyzed using Sombor indices, a relatively recent method in topological molecular analysis. Leveraging Euclidean geometry, this work introduces the first area-based Sombor index, offering a novel perspective on the molecular connectivity and spatial configuration of amylose. The third and fifth Sombor indices are derived from perimeter-based geometric principles, introducing a new level of complexity to the topological characterization. In contrast, the second, fourth, and sixth indices are developed using angular-based formulations, enabling a more refined structural interpretation. To assess the relationship between these indices and the physicochemical properties of amylose, regression analysis was performed using supervised machine learning techniques. This statistical modeling uncovered meaningful correlations, enhancing our understanding of how molecular topology relates to chemical behavior. Additionally, Analysis of Variance (ANOVA) was applied to determine the statistical significance of each index. Correlation analyses revealed strong interrelationships among the indices. The results indicate that among all considered Sombor-based indices, SO<InlineEquation ID="IEq1"> <EquationSource Format="TEX">\(_4\)</EquationSource> </InlineEquation> and SO<InlineEquation ID="IEq2"> <EquationSource Format="TEX">\(_5\)</EquationSource> </InlineEquation> are the most effective predictors of amylose’s structural and functional properties. In particular, SO<InlineEquation ID="IEq3"> <EquationSource Format="TEX">\(_5\)</EquationSource> </InlineEquation> exhibited the highest predictive accuracy and model robustness, while SO<InlineEquation ID="IEq4"> <EquationSource Format="TEX">\(_4\)</EquationSource> </InlineEquation> also demonstrated consistent performance, affirming their applicability in molecular modeling. This research underscores the potential of Sombor indices as reliable topological descriptors for molecular classification and offers valuable insights into the physiochemical behavior of amylose. The findings open new directions for applying topological analysis to the study of biopolymers and polysaccharides, with implications in materials science, biochemistry, and food technology.</p>

Data-driven regression analysis of amylose using Sombor molecular descriptors

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2025年12月22日

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Zeeshan Saleem Mufti,
Muhammad Asim,
A. S. Shflot,
Syed Tauseef Saeed,
Jihad Younis

摘要

Amylose, a vital polysaccharide component of starch, plays a significant role in plant energy storage and has important implications in nutrition and health. In this study, the structural characteristics of amylose are analyzed using Sombor indices, a relatively recent method in topological molecular analysis. Leveraging Euclidean geometry, this work introduces the first area-based Sombor index, offering a novel perspective on the molecular connectivity and spatial configuration of amylose. The third and fifth Sombor indices are derived from perimeter-based geometric principles, introducing a new level of complexity to the topological characterization. In contrast, the second, fourth, and sixth indices are developed using angular-based formulations, enabling a more refined structural interpretation. To assess the relationship between these indices and the physicochemical properties of amylose, regression analysis was performed using supervised machine learning techniques. This statistical modeling uncovered meaningful correlations, enhancing our understanding of how molecular topology relates to chemical behavior. Additionally, Analysis of Variance (ANOVA) was applied to determine the statistical significance of each index. Correlation analyses revealed strong interrelationships among the indices. The results indicate that among all considered Sombor-based indices, SO \(_4\) and SO \(_5\) are the most effective predictors of amylose’s structural and functional properties. In particular, SO \(_5\) exhibited the highest predictive accuracy and model robustness, while SO \(_4\) also demonstrated consistent performance, affirming their applicability in molecular modeling. This research underscores the potential of Sombor indices as reliable topological descriptors for molecular classification and offers valuable insights into the physiochemical behavior of amylose. The findings open new directions for applying topological analysis to the study of biopolymers and polysaccharides, with implications in materials science, biochemistry, and food technology.