Persistent homology analysis of protein structure, flexibility, and folding

• Published in: International journal for numerical methods in biomedical engineering Vol. 30; no. 8; pp. 814 - 844
• Main Authors: Xia, Kelin, Wei, Guo-Wei
• Format: Journal Article
• Language: English
• Published: England Blackwell Publishing Ltd 01.08.2014; Wiley Subscription Services, Inc
• Subjects: Algorithms; computational topology; Fullerenes - chemistry; Models, Molecular; Molecular Dynamics Simulation; molecular topological fingerprint; persistent homology; Protein Folding; Protein Structure, Secondary; protein topological evolution; protein topology-function relationship; Structural Homology, Protein; Thermodynamics; protein topological evolution; protein topology-function relationship; molecular topological fingerprint; computational topology; persistent homology
• ISSN: 2040-7939; 2040-7947; 2040-7947
• DOI: 10.1002/cnm.2655

SUMMARYProteins 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, 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. On the basis of 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. Copyright © 2014 John Wiley & Sons, Ltd. Topological tools often incur too much reduction of the original geometric information, while geometric tools are frequently inundated with too much structural detail and can be computationally too expensive to be practical. Persistent homology bridges between geometry and topology, and offers an effective strategy for biomolecular analysis. This work introduces molecular topological fingerprints (MTFs) based on persistent homology analysis of topological invariants to reveal the topology‐function relationship of macromolecules as shown in the illustration, where the MTFs of a beta barrel (top left), a protein (top right), and its unfolded conformation (middle) are depicted in the bottom from the left to the right, respectively.