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Stretched-exponential protein refolding kinetics, first observed decades ago, were attributed to a nonnative ensemble of structures with parallel, non-interconverting folding pathways. However, the structural origin of the large energy barriers preventing interconversion between these folding pathways is unknown. Here, we combine simulations with limited proteolysis (LiP) and cross-linking (XL) mass spectrometry (MS) to study the protein phosphoglycerate kinase (PGK). Simulations recapitulate its stretched-exponential folding kinetics and reveal that misfolded states involving changes of entanglement underlie this behavior: either formation of a nonnative, noncovalent lasso entanglement or failure to form a native entanglement. These misfolded states act as kinetic traps, requiring extensive unfolding to escape, which results in a distribution of free energy barriers and pathway partitioning. Using LiP-MS and XL-MS, we propose heterogeneous structural ensembles consistent with these data that represent the potential long-lived misfolded states PGK populates. This structural and energetic heterogeneity creates a hierarchy of refolding timescales, explaining stretched-exponential kinetics. 

One-third of protein domains in the CATH database contain a recently discovered tertiary topological motif: non-covalent lasso entanglements, in which a segment of the protein backbone forms a loop closed by non-covalent interactions between residues and is threaded one or more times by the N- or C-terminal backbone segment. Unknown is how frequently this structural motif appears across the proteomes of organisms. And the correlation of these motifs with various classes of protein function and biological processes have not been quantified. Here, using a combination of protein crystal structures, AlphaFold2 predictions, and Gene Ontology terms we show that in E. coli, S. cerevisiae and H. sapiens that 71%, 52% and 49% of globular proteins contain one-or-more non-covalent lasso entanglements in their native fold, and that some of these are highly complex with multiple threading events. Further, proteins containing these tertiary motifs are consistently enriched in certain functions and biological processes across these organisms and depleted in others, strongly indicating an influence of evolutionary selection pressures acting positively and negatively on the distribution of these motifs. Together, these results demonstrate that non-covalent lasso entanglements are widespread and indicate they may be extensively utilized for protein function and subcellular processes, thus impacting phenotype.