Persistent topological Laplacian analysis of SARS-CoV-2 variants

Area of Science:

• Mathematics and Data Science
• Computational Biology
• Structural Biology

Background:

• Persistent homology, a core technique in topological data analysis (TDA), has limitations in handling heterogeneous data and quantitative structural changes.
• Existing methods struggle with qualitative assessments (e.g., ring size) and non-topological changes in protein binding.

Approach:

• This study investigates Persistent Topological Laplacians (PTLs) as an advancement over persistent homology.
• PTLs were applied to analyze structural changes in the SARS-CoV-2 spike receptor binding domain (RBD) across variants.
• The research examined RBD-angiotensin-converting enzyme 2 (ACE2) binding complexes and computationally generated RBD structures.

Key Points:

• PTLs effectively capture mutation-induced structural changes in SARS-CoV-2 RBD-ACE2 binding complexes.
• Analysis of spectral changes in PTLs revealed insights into variant-specific binding dynamics.
• The study explored the impact of PTLs on topological deep learning and deep mutational scanning predictions for Omicron BA.2.

Conclusions:

• Persistent topological Laplacians demonstrate superior capabilities compared to persistent homology for protein structure analysis.
• PTLs offer a powerful and versatile new tool for topological data analysis in scientific research.
• This work highlights the potential of PTLs in understanding viral evolution and protein interactions.