Molecular mechanisms for cooperative folding of proteins

The folding of single-domain globular proteins exhibits the character of first-order or two-state thermodynamics. The origin of such high cooperativity in relatively small polymer systems is still not well understood. Recently, the statistical mechanics of protein folding has been studied extensively with simple protein models such as short cubic-lattice chains with contact-based interactions. While many valuable insights about protein folding were gained with such models, some concerns have also arisen, viz. that they lack the character of protein backbones whose interactions would limit the folding patterns of proteins. Here, a comparative study of the conventional cubic-lattice chain model and a fine-grained more realistic lattice protein model with both backbone and side-chain interactions is carried out. It is found that, even though both types of models exhibit a cooperative two-state folding transition to the native structure with optimized force fields, the character and origin of cooperativity of the two models are different. In the simple contact-based model, the free-energy barrier occurs at the low end of the energy scale, and the cooperativity arises from a concerted formation of native contacts among many residues in a compact state. In the other more complicated model, the free-energy barrier occurs in the intermediate energy region, and the folding cooperativity arises from collective orientational arrangements of locally structured units in semi-open conformational states. On the basis of these results, two limiting molecular mechanisms for protein folding emerge, which can be used for analyzing the folding process of real proteins.