Cooperativity and modularity in protein folding

Accurate prediction of protein folding mechanisms by simple structure-based statistical mechanical models

Recent breakthroughs in highly accurate protein structure prediction using deep neural networks have made considerable progress in solving the structure prediction component of the 'protein folding problem'. However, predicting detailed mechanisms of how proteins fold into specific native structures remains challenging, especially for multidomain proteins constituting most of the proteomes. Here, we develop a simple structure-based statistical mechanical model that introduces nonlocal interactions driving the folding of multidomain proteins. Our model successfully predicts protein folding processes consistent with experiments, without the limitations of protein size and shape. Furthermore, slight modifications of the model allow prediction of disulfide-oxidative and disulfide-intact protein folding. These predictions depict details of the folding processes beyond reproducing experimental results and provide a rationale for the folding mechanisms. Thus, our physics-based models enable accurate prediction of protein folding mechanisms with low computational complexity, paving the way for solving the folding process component of the 'protein folding problem'.

The Wako-Saitô-Muñoz-Eaton Model for Predicting Protein Folding and Dynamics

Despite the recent advances in the prediction of protein structures by deep neutral networks, the elucidation of protein-folding mechanisms remains challenging. A promising theory for describing protein folding is a coarse-grained statistical mechanical model called the Wako-Saitô-Muñoz-Eaton (WSME) model. The model can calculate the free-energy landscapes of proteins based on a three-dimensional structure with low computational complexity, thereby providing a comprehensive understanding of the folding pathways and the structure and stability of the intermediates and transition states involved in the folding reaction. In this review, we summarize previous and recent studies on protein folding and dynamics performed using the WSME model and discuss future challenges and prospects. The WSME model successfully predicted the folding mechanisms of small single-domain proteins and the effects of amino-acid substitutions on protein stability and folding in a manner that was consistent with experimental results. Furthermore, extended versions of the WSME model were applied to predict the folding mechanisms of multi-domain proteins and the conformational changes associated with protein function. Thus, the WSME model may contribute significantly to solving the protein-folding problem and is expected to be useful for predicting protein folding, stability, and dynamics in basic research and in industrial and medical applications.

Thermodynamics and folding landscapes of large proteins from a statistical mechanical model

Statistical mechanical models that afford an intermediate resolution between macroscopic chemical models and all-atom simulations have been successful in capturing folding behaviors of many small single-domain proteins. However, the applicability of one such successful approach, the Wako-Saitô-Muñoz-Eaton (WSME) model, is limited by the size of the protein as the number of conformations grows exponentially with protein length. In this work, we surmount this size limitation by introducing a novel approximation that treats stretches of 3 or 4 residues as blocks, thus reducing the phase space by nearly three orders of magnitude. The performance of the 'bWSME' model is validated by comparing the predictions for a globular enzyme (RNase H) and a repeat protein (IκBα), against experimental observables and the model without block approximation. Finally, as a proof of concept, we predict the free-energy surface of the 370-residue, multi-domain maltose binding protein and identify an intermediate in good agreement with single-molecule force-spectroscopy measurements. The bWSME model can thus be employed as a quantitative predictive tool to explore the conformational landscapes of large proteins, extract the structural features of putative intermediates, identify parallel folding paths, and thus aid in the interpretation of both ensemble and single-molecule experiments.

Unified understanding of folding and binding mechanisms of globular and intrinsically disordered proteins

Extensive experimental and theoretical studies have advanced our understanding of the mechanisms of folding and binding of globular proteins, and coupled folding and binding of intrinsically disordered proteins (IDPs). The forces responsible for conformational changes and binding are common in both proteins; however, these mechanisms have been separately discussed. Here, we attempt to integrate the mechanisms of coupled folding and binding of IDPs, folding of small and multi-subdomain proteins, folding of multimeric proteins, and ligand binding of globular proteins in terms of conformational selection and induced-fit mechanisms as well as the nucleation–condensation mechanism that is intermediate between them. Accumulating evidence has shown that both the rate of conformational change and apparent rate of binding between interacting elements can determine reaction mechanisms. Coupled folding and binding of IDPs occurs mainly by induced-fit because of the slow folding in the free form, while ligand binding of globular proteins occurs mainly by conformational selection because of rapid conformational change. Protein folding can be regarded as the binding of intramolecular segments accompanied by secondary structure formation. Multi-subdomain proteins fold mainly by the induced-fit (hydrophobic collapse) mechanism, as the connection of interacting segments enhances the binding (compaction) rate. Fewer hydrophobic residues in small proteins reduce the intramolecular binding rate, resulting in the nucleation–condensation mechanism. Thus, the folding and binding of globular proteins and IDPs obey the same general principle, suggesting that the coarse-grained, statistical mechanical model of protein folding is promising for a unified theoretical description of all mechanisms.