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.

本研究首次引入持久同调理论以及分子拓扑学概念，基于分子拓扑不变量持久性提出分子拓扑指纹（MTFs），并通过 MTFs 实现了对蛋白质的表征、识别和分类等任务，研究还建议了一种新型的截止距离过滤方法，并提出了基于持久同调不变量的累积条形图用于定量建模蛋白质的柔性，并利用 MTFs 量化预测蛋白质的拓扑演变与折叠稳定性，结果表明，我们的持久同调预测结果与分子动力学模拟结果高度一致，揭示了蛋白质的拓扑 - 功能关系。