How simple models explain complex protein folding behaviors

Abstract

Understanding complex protein folding behaviors requires simplified models that capture the essential features of the folding process. Protein folding involves a delicate interplay between short-range (secondary) and long-range (tertiary) interactions, which together dictate the thermodynamic and kinetic properties of the system. In this study, we employ a mean-field framework to investigate these interactions using three progressively refined models. The regular model considers only short-range, nearest-neighbor interactions and reveals a cooperative folding transition driven by localized secondary interactions, consistent with standard two-state folding behavior. The Bryngelson–Wolynes (BW) model incorporates stochastic nonlocal interactions, demonstrating long-range cooperativity and introducing energy landscape ruggedness that shifts the folding transition. The modified Bryngelson–Wolynes (M-BW) model integrates both short-range and long-range effects, leading to the emergence of a hysteresis loop characteristic of first-order-like phase transitions, even in finite systems. These results suggest that the interplay between secondary and tertiary interactions is sufficient to induce phase transition-like properties in proteins. By providing a unified framework, this study highlights how simplified models can elucidate the complex dynamics of protein folding, misfolding, and aggregation, offering critical insights into the underlying mechanisms of these fundamental biological processes.