Physics-Informed Machine Learning for Predicting β-D-Galactosidase Stability in Eucalyptus Sawdust-Reinforced Pectin Biohydrogels

Abstract

Predicting the long-term stability of immobilized enzymes remains challenging due to the complex physicochemical interactions within immobilization matrices. In this study, a Physics-Informed Machine-Learning (PIML) framework was developed to investigate the deactivation behavior of β-D-galactosidase immobilized in pectin-based biohydrogels reinforced with eucalyptus sawdust (ES). The approach combines first-order deactivation kinetics with Gaussian process regression (GPR), integrating mechanistic interpretability with data-driven prediction. Structural descriptors of hydrogel rigidity, hydrogen-bond interactions, and diffusion behavior were incorporated to characterize the immobilization environment. The PIML framework provided a physically plausible representation of the experimental data while avoiding non-monotonic deactivation artifacts commonly observed in unconstrained machine learning models. Leave-one-condition-out validation yielded RMSE, MAE, and R2 values of 0.164, 0.119, and 0.625, respectively, indicating moderate predictive robustness under partially extrapolative conditions. External validation using independent, literature-derived datasets revealed reasonable transferability across thermal and storage stability regimes but substantially lower performance in operational reuse systems, suggesting the involvement of additional mechanisms, such as enzyme leakage and support degradation. The optimized formulation containing 5 wt % ES at pH 4.0 increased the estimated enzymatic half-life by 36.9%. These findings demonstrate the potential of physically constrained low-data machine learning for biocatalyst design while highlighting important transferability limitations across distinct immobilization architectures.