Analyses of simulations of three-dimensional lattice proteins in comparison with a simplified statistical mechanical model of protein folding

Folding and unfolding simulations of three-dimensional lattice proteins were analyzed using a simplified statistical mechanical model in which their amino acid sequences and native conformations were incorporated explicitly. Using this statistical mechanical model, under the assumption that only interactions between amino acid residues within a local structure in a native state are considered, the partition function of the system can be calculated for a given native conformation without any adjustable parameter. The simulations were carried out for two different native conformations, for each of which two foldable amino acid sequences were considered. The native and non-native contacts between amino acid residues occurring in the simulations were examined in detail and compared with the results derived from the theoretical model. The equilibrium thermodynamic quantities (free energy, enthalpy, entropy, and the probability of each amino acid residue being in the native state) at various temperatures obtained from the simulations and the theoretical model were also examined in order to characterize the folding processes that depend on the native conformations and the amino acid sequences. Finally, the free energy landscapes were discussed based on these analyses.