Persistent Sheaf Laplacian Analysis of Protein Flexibility

TL;DR

This paper introduces the persistent sheaf Laplacian (PSL), a topological data analysis tool, to model and predict protein flexibility with improved accuracy over classical models, aiding protein analysis and drug discovery.

Contribution

The paper presents the novel PSL method for analyzing protein flexibility, demonstrating significant accuracy improvements in B-factor prediction over existing models.

Findings

PSL increases B-factor prediction accuracy by 32% compared to GNM.

PSL effectively captures local topology and geometry of proteins.

Extensive validation confirms PSL's robustness and effectiveness.

Abstract

Protein flexibility, measured by the B-factor or Debye-Waller factor, is essential for protein functions such as structural support, enzyme activity, cellular communication, and molecular transport. Theoretical analysis and prediction of protein flexibility are crucial for protein design, engineering, and drug discovery. In this work, we introduce the persistent sheaf Laplacian (PSL), an effective tool in topological data analysis, to model and analyze protein flexibility. By representing the local topology and geometry of protein atoms through the multiscale harmonic and non-harmonic spectra of PSLs, the proposed model effectively captures protein flexibility and provides accurate, robust predictions of protein B-factors. Our PSL model demonstrates an increase in accuracy of 32% compared to the classical Gaussian network model (GNM) in predicting B-factors for a dataset of 364 proteins. Additionally, we construct a blind machine learning prediction method utilizing global and local protein features. Extensive computations and comparisons validate the effectiveness of the proposed PSL model for B-factor predictions.