Speakers - CARWC2025

Abstract

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics, and transport is one of the most challenging tasks in biological science. In the present work, persistent homology is introduced for the first time to extract molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification, and classification.

With the introduction of the filtration process, persistent homology is capable of reintroducing the geometric information associated with topological features like isolated components, loops, rings, circles, pockets, holes, and cavities. The most successful applications of persistent homology in the literature have been about qualitative characterizations or classifications in the past. Indeed, there is hardly any successful quantitative model based on topology in the literature, because topological invariants preclude geometric description. It is interesting and desirable to develop quantitative models based on persistent homology analysis.

To further exploit persistent homology for quantitative modeling, protein folding is proposed, which is an essential process for proteins to assume well-defined structure and function. It has been shown from basic observation that well-folded proteins, especially well-folded globular proteins, have abundant non-covalent bonds due to hydrogen bonds and van der Waals interactions, which translates into higher numbers of topological invariants, particularly, a large measurement of the first Betti number.

Additionally, the funnel theory of protein folding states that a well-folded protein, i.e., the native structure, has the lowest free energy. In contrast, unfolded protein structures have fewer topological invariants and higher free energies. Based on this analysis, a persistent homology-based model is proposed to characterize protein topological evolution and predict protein folding stability. The correlation of the negative accumulated bar length of the first Betti number to the protein total energy for a series of protein configurations generated by the steered molecular dynamics. As such, the evolution of topological invariants in the protein folding/unfolding process is tracked. The persistent homology-based model is found and established to provide an excellent quantitative prediction of protein total energy during the protein folding/unfolding process.