MONTE-CARLO SIMULATION OF A FIRST-ORDER TRANSITION FOR PROTEIN-FOLDING

The first-order transition of a model protein from the statistically-coiled state to the native globular state is studied by an entropy sampling Monte Carolo (ESMC) method. The model protein, containing 38 residues with a specific sequence, is constructed on the (210) lattice (Kolinski, A.; Skolnick, J. J. Chem. Phys. 1991, 94, 3978). With a potential function that includes both local chain states and long-range interresidue interactions, the protein adopts a unique lowest-energy beta-sheet structure. The ESMC simulations directly produce the relative entropy of different energy states for the model protein. The free energy of the molecule is then calculated on the basis of thermodynamic relations. At the transition temperature, the free energy of the protein exhibits two pronounced minima, one at the coil state and the other at the globular state, separated by a wide free energy barrier. This result indicates that the folding/unfolding of the model protein involves a first-order transition. It is found that the free energy barrier in the transition process arises because the entropy increases slower than the energy when the protein initially unfolds from the native state. Therefore, the cooperative, i.e. all-or-none, behavior of the folding/unfolding transition of the model protein can be attributed to a conformational entropy effect. There is a distribution of low-energy conformations within the globular state. The simulation results suggest that, under a general interaction scheme that pertains to those of proteins, relatively small heteropolymers can undergo a first-order transition between coiled and globular native states. This work provides a theoretical basis for the commonly used two-state model in protein folding/unfolding experiments.