Characterization of foldable protein models: Thermodynamics, folding kinetics and force field

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Abstract
We propose three analytical models that describe the characteristics of proteins that can be folded into unique native structures. Model I is characterized by a mean-field single-residue energy which favors the native state and has a large energy gap between the native and non-native states; Model II involves mean-field cooperative interactions among the residues in the native states, and Model III is characterized by the mean-field single-residue energy at a low degree of folding and by the cooperative interactions among native residues at a high degree of folding. The thermodynamics of all three protein models exhibit two-state transition behavior, in which the non-native state is dominated by large entropy while the native state is determined by low energy. The folding kinetics of the models are studied by means of the master equation method. While the kinetics of folding of all three models are driven by the energetic biases of individual residues which favor the native state, the different interaction modes lead to different folding rates. It is found that the models with long-range cooperativity (i.e., Models II and III) fold several orders of magnitude faster than the model with only localized interactions (Model I). The intramolecular interactions that are responsible for the different properties of these models are examined, and the ways that these models may be used for developing the force fields for realistic proteins are discussed.