Experimental and theoretical studies of protein folding-unfolding

Recently, a mean field theory of protein folding-unfolding based on the generalization of the Ising model has been developed. In this work, we apply this theory to obtain averaged coupling energy between two neighbor units in protein and denaturation free energy of protein units. The free energy change of protein folding is found to be 6.0, 5.1, 11.4 kcal mol^-1 from absorption, fluorescence, and circular dichroism, respectively; the respective coupling energies of cyt c induced with acid are estimated to be around 10% of the average free energy of protein. The denaturation free energies per molar are determined to be -3400 kcal mol^-1 M^-1 from absorption, -1260 kcal mol^-1 M^-1 from fluorescence, and -3180 kcal mol^-1 M^-1 from circular dichroism. Fused silica (a hydrophilic surface) is found to play a role to unfold protein and provide a denaturation free energy of -4.05 kcal mole^-1. For the case in which protein is denatured by acid on a fused silica surface, the average coupling energy is found to be 85% smaller than the one estimated in bulk solution; the denaturation free energy per molar is found to be 3260 kcal mol^-1 M^-1. Another purpose of this paper is to generalize our original kinetic model of protein folding-unfolding by explicitly taking into account the correlation between protein units. We show that at equilibrium, this new model also yields the same equilibrium as that obtained from our model of thermodynamics of protein folding-unfolding.