Fusarium wilt is a soil-borne disease that leads to wilting, yellowing, and sometimes death of various plant species. This article examines the correlations between physicochemical properties and molecular invariants of the chemical structures of molecular biocontrol agents used to mitigate Fusarium wilt, a plant disease. The study considers effective agents like fungicides (thiophanate-methyl, azoxystrobin, trifloxystrobin, fludioxonil, and metalaxyl), soil fumigants (chloropicrin, metam sodium, and 1,3-dichloropropene), and molecular biocontrol agents (methionine and adenosine). This is the first review of QSPR studies on plant diseases in the literature. For the chemical structures of these molecular biocontrol agents, we have calculated M-polynomials of various molecular invariants, including the Zagreb-type indices, atom-bond connectivity index, harmonic index, Sombor index, forgotten index, and symmetric division degree index. The relationships identified through regression analysis provide insights into their effectiveness and optimization. Our findings highlight the best regression coefficients, which have the lowest RMSE and the maximum F-statistics values for significant correlations. Using these regression coefficients, we can predict the behavior of bioagents.

Hantavirus Pulmonary Syndrome (HPS) is a severe rodent-borne viral disease that can rapidly progress from influenza-like symptoms to life-threatening cardiopulmonary failure, while therapeutic options remain limited. This study develops a quantitative structure–property relationship (QSPR) framework for a curated set of fourteen HPS-related drug candidates using key physicochemical endpoints. Molecular structures are modeled as graphs, and degree-based topological descriptors are systematically derived via the M-polynomial techniques. Linear, quadratic, power, and logistic regression models are fitted to quantify structure–property relations, and model quality is assessed using R, \(R^{2}\), RMSE, SE, and F-statistics, with internal predictivity evaluated through leave-one-out cross-validation (LOOCV) using \(Q^{2}\). Results indicate that selected degree-based descriptors capture meaningful variation in the considered physicochemical properties and support reproducible, computation-driven screening of candidate compounds. In future directions, integrating pharmacokinetic and toxicity-oriented computational assessment is expected to further enhance the practical relevance of the proposed framework. Graphical Abstract

This work applies quantitative structure–property relationship analysis to examine molecular characteristics linked to stiffness person syndrome (SPS), a rare neurological condition marked by persistent muscle rigidity and spasmodic episodes. Topological indices such as Zagreb indices and their modification are employed to examine their correlations with key physicochemical properties. Linear, quadratic, exponential growth, and power curve fitting models are applied to identify the best correlations, focusing on the maximum F‐statistic and the coefficient of determination R ² . Furthermore, heatmap‐based correlation analysis is performed to visually quantify the strength and direction of correlations between the calculated topological indices and selected physicochemical parameters. In addition to classical regression techniques, gradient boosting, a powerful ensemble machine learning method, is utilized to enhance predictive accuracy and evaluate the contribution of each descriptor toward property estimation. Additionally, M‐polynomials are calculated, and their corresponding graphs are plotted to assess the structural features of potential therapeutic agents. The findings offer significant insights into the role of graph‐theoretical methods in drug discovery, advancing the computational design of targeted treatments for SPS.

This study presents a computational QSPR framework for the analysis of protein-associated small molecular graphs by using machine learning under limited sample conditions. Protein related molecules were modeled as molecular graphs, and their structural characteristics were quantified using topological indices, physicochemical properties, and molecular complexity descriptors. To address the high dimensionality relative to the sample size (n = 20), univariate feature selection was employed to retain the most informative descriptors, and model performance was rigorously evaluated using Leave-One-Out Cross-Validation (LOOCV). An Artificial Neural Network (ANN) optimized with the L-BFGS algorithm was benchmarked against Support Vector Regression (SVR) to assess predictive robustness. The results demonstrate excellent predictive accuracy for mass related properties such as molecular weight, while revealing inherent limitations of topological descriptors for complex physicochemical properties including isoelectric point and hydrophobicity. The reporting of cross-validation uncertainty confirms the model stability and mitigates overfitting concerns, establishing the proposed framework as a reliable and interpretable approach for small-sample QSPR modeling with therapeutic relevance.

Machine learning is increasingly used to explore structure–property relationships in dendrimer‐drug systems; however, its integration with topology‐based structural compatibility analysis remains limited. This study presents a learning‐driven framework to evaluate the topology‐based structural compatibility of perylene diimide core dendrimers with antiviral, antioxidant, and imaging agents. Within a quantitative structure–property relationship framework, linear regression, Gaussian process regression (GPR), and artificial neural networks are employed to identify dominant graph‐theoretic topological indices and to capture linear and nonlinear structure–property relationships. These insights are combined with a structure‐based compatibility analysis that ranks dendrimer generations without altering drug identity or ordering. Generation‐wise compatibility is computed using standardized Euclidean distance after global normalization, and ranking stability is assessed through monotonic and magnitude analysis. Results show class‐dependent descriptor relevance, with GPR achieving test‐set R ² values above 0.94 for molecular weight, exact mass, monoisotopic mass, and heavy atom count. The generation‐wise compatibility analysis further reveals distinct topology‐based structural compatibility patterns across the investigated drug classes, highlighting the value of integrating machine learning with graph‐theoretic analysis for rational nanocarrier design and the computational assessment of potential encapsulation suitability.