Persistent homology analysis of protein structure, flexibility and folding

TL;DR

This paper introduces persistent homology as a novel topological method to analyze protein structures, flexibility, and folding, providing new insights and quantitative predictions that align well with molecular dynamics simulations.

Contribution

The work is the first to apply persistent homology to extract molecular topological fingerprints for protein analysis, including folding and flexibility prediction.

Findings

Accurate prediction of optimal cutoff distances in elastic network models.

Quantitative modeling of protein flexibility using accumulated bar length.

Consistent topological predictions with molecular dynamics simulations.

Abstract

Proteins are the most important biomolecules for living organisms. The understanding of protein structure, function, dynamics and transport is one of most challenging tasks in biological science. In the present work, persistent homology is, for the first time, introduced for extracting molecular topological fingerprints (MTFs) based on the persistence of molecular topological invariants. MTFs are utilized for protein characterization, identification and classification. The method of slicing is proposed to track the geometric origin of protein topological invariants. Both all-atom and coarse-grained representations of MTFs are constructed. A new cutoff-like filtration is proposed to shed light on the optimal cutoff distance in elastic network models. Based on the correlation between protein compactness, rigidity and connectivity, we propose an accumulated bar length generated from persistent topological invariants for the quantitative modeling of protein flexibility. To this end, a correlation matrix based filtration is developed. This approach gives rise to an accurate prediction of the optimal characteristic distance used in protein B-factor analysis. Finally, MTFs are employed to characterize protein topological evolution during protein folding and quantitatively predict the protein folding stability. An excellent consistence between our persistent homology prediction and molecular dynamics simulation is found. This work reveals the topology-function relationship of proteins.