Statistical mechanics of protein folding, unfolding and fluctuation.

Conformational fluctuations of globular proteins in the native state and the processes of folding and unfolding are studied from the statistical mechanical point of view. 1) It is pointed out that the formation of the native specific conformation of a globular protein is not a result of random sampling of minimum energy conformations. This fact provides a motivation for the study of the processes of folding, or the paths of folding, of proteins. The processes of folding and unfolding are shown to be statistical mechanical in nature. 2) The conformational (folding and unfolding) transitions in globular proteins are compared with the helix-coil transitions in polypeptides. The gradedness of the latter transition is shown to be due to the fact that the phenomenon is of an essentially one-dimensional system. The former transition is characterized ideally by the fact that it is of the all-or-none type. 3) A lattice model of proteins is introduced. "A protein molecule" is defined as a chain of noninteresting units of a given length on a two-dimensional square lattice. The copolymeric character of protein molecules is incorporated into the model by specificities of interunit interactions. 4) This model proved powerful for studying the statistical mechanical characterization of protein denaturation and fluctuations. The specificities of interunit interactions were shown to be the primary factors responsible for the all-or-none type transition from native to denatured states of globular proteins. 5) The model is studied by the Monte Carlo method of Metropolis et al., which simulates a kinetic process approximately. The method is shown to be a promising tool in finding the native conformation of proteins from their amino acid sequence. 6) A new theoretical method is developed to study phenomenologically the processes of protein folding and unfolding and the conformational fluctuations in the native state. An important role is played by a quantity S(H): the entropy of a protein molecule in solution in the conformational states with a given value of enthalpy H. Qualitative character of the S-H curve, such as whether it is convex or concave determines characteristics of the conformational transition in a globular protein such as whether or not it is of the all-or-none type. 7) The concept of an ideal process of protein folding and unfolding is introduced and defined by three statements. The S-H curve is calculated for this ideal process. The curve is shown to be concave, indicating that the transition is of the all-or-none type. This conclusion is drawn essentially from the globularity and specificity of the native conformational of proteins. 8) Residual structures in the denatured state and conformational fluctuations in the native state are discussed. In order to discuss the latter, an independent fluctuating site model is introduced, in which it is assumed that there are several independent fluctuating sites, each localized in some part of the protein molecule...