A commutative algebra-based learning framework, termed CAL, for protein B-factor prediction, that achieves robust and consistent performance across diverse datasets and is competitive with existing state-of-the-art methods.
Abstract
Protein flexibility, commonly quantified by B-factors, is closely related to protein structure and function. However, accurate B-factor prediction remains challenging due to the multiscale nature of protein structures and the complexity of atomic interactions. In this work, we propose a commutative algebra-based learning framework, termed CAL, for protein B-factor prediction. Unlike many biomolecular prediction tasks that rely primarily on global structural representations, B-factor prediction requires an accurate characterization of the local geometric environments surrounding individual atoms. To address this challenge, CAL employs commutative algebra theory to construct localized algebraic descriptors at multiple spatial scales. On a benchmark dataset of 364 proteins, CAL improves prediction accuracy by 34.5\% over the classical Gaussian network model (GNM). Extensive experiments demonstrate that CAL achieves robust and consistent performance across diverse datasets and is competitive with existing state-of-the-art methods. Furthermore, by integrating CAL with machine learning, we develop a blind prediction model capable of cross-protein B-factor prediction. Overall, CAL provides an effective, efficient, and mathematically principled framework for protein flexibility prediction and offers a powerful approach for analyzing and predicting localized structural properties in complex biomolecular systems.
Motivation With the rapid development of AI methods that predict protein structures from sequence, understanding the structure-function relation increasingly depends on quantitative structural descriptors that are both biologically meaningful and scalable to large datasets. Here, we introduce mathematical topology metrics that quantify the entanglement complexity of a tertiary protein structure while respecting uncrossability constraints. Results By employing only three such metrics across all protein structures in the Protein Data Bank, we represent the proteome structural space in a continuous three-dimensional space. Distances within this space capture structural similarity and correlate with functional similarity. We find that the mathematical entanglement based landscape of protein structural space diversifies with the evolutionary expansion of protein function across species. Moreover, this continuous representation reproduces CATH classifications with high accuracy for major structural classes. These results indicate that these metrics efficiently encode structural features linked to protein function and provide a more informative description than conventional metrics. Availability Data used in this study are available in the Protein Data Bank. Details of the machine learning model used can be found in https://github.com/roshitac/CATH_Classification-. Contact Banu.Ozkan@asu.edu, Eleni.Panagiotou@asu.edu Supplementary information Supplementary data are available at Journal Name online.
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