Commutative algebra neural network reveals genetic origins of diseases.

Genetic mutations can disrupt protein structure, stability, and solubility, contributing to a wide range of diseases. Existing predictive models often lack interpretability and fail to integrate physical and chemical interactions critical to molecular mechanisms. Moreover, current approaches treat disease association, stability changes, and solubility alterations as separate tasks, limiting model generalizability. In this study, we introduce a unified framework based on multiscale commutative algebra to capture intrinsic physical and chemical interactions for the first time. Leveraging Persistent Stanley-Reisner Theory, we extract multiscale algebraic invariants to build a Commutative Algebra neural Network (CANet). Integrated with transformer features and auxiliary physical features, we apply CANet to tackle three key domains for the first time: disease-associated mutations, mutation-induced protein stability changes, and solubility changes upon mutations. Across six benchmark tasks, CANet and its gradient boosting tree counterpart, CATree, consistently attain state-of-the-art performance, achieving up to 7.5% improvement in predictive accuracy. Our approach offers multiscale, mechanistic, interpretable,and generalizable models for predicting disease-mutation associations.