Persistent topological Laplacian analysis of SARS-CoV-2 variants

TL;DR

This paper introduces persistent topological Laplacians (PTLs) as a novel topological data analysis tool to study SARS-CoV-2 protein structures, capturing structural changes and aiding in mutation impact predictions.

Contribution

It demonstrates the effectiveness of PTLs in analyzing protein structural evolution and mutation effects, surpassing persistent homology in this context.

Findings

PTLs effectively capture structural changes in SARS-CoV-2 variants.

PTLs outperform persistent homology in analyzing protein structures.

PTL-based machine learning predicts mutation impacts on variants.

Abstract

Topological data analysis (TDA) is an emerging field in mathematics and data science. Its central technique, persistent homology, has had tremendous success in many science and engineering disciplines. However, persistent homology has limitations, including its incapability of describing the homotopic shape evolution of data during filtration. Persistent topological Laplacians (PTLs), such as persistent Laplacian and persistent sheaf Laplacian, were proposed to overcome the drawback of persistent homology. In this work, we examine the modeling and analysis power of PTLs in the study of the protein structures of the severe acute respiratory syndrome coronavirus 2 (SARS-CoV-2) spike receptor binding domain (RBD) and its variants, i.e., Alpha, Beta, Gamma, BA.1, and BA.2. First, we employ PTLs to study how the RBD mutation-induced structural changes of RBD-angiotensin-converting enzyme 2 (ACE2) binding complexes are captured in the changes of spectra of the PTLs among SARS-CoV-2 variants. Additionally, we use PTLs to analyze the binding of RBD and ACE2-induced structural changes of various SARS-CoV-2 variants. Finally, we explore the impacts of computationally generated RBD structures on PTL-based machine learning, including deep learning, and predictions of deep mutational scanning datasets for the SARS-CoV-2 Omicron BA.2 variant. Our results indicate that PTLs have advantages over persistent homology in analyzing protein structural changes and provide a powerful new TDA tool for data science.