Structural changes and fluctuations of proteins. I. A statistical thermodynamic model

A general theory of the structural changes and fluctuations of proteins has been proposed based on statistical thermodynamic considerations at the chain level. The "structure" of protein was assumed to be characterized by the state of secondary bonds between unique pairs of specific sites on peptide chains. Every secondary bond changes between the bonded and unbonded states by thermal agitation and the "structure" is continuously fluctuating. The free energy of the "structural state" that is defined by the fraction of secondary bonds in the bonded state has been expressed by the bond energy, the cooperative interaction between bonds, the mixing entropy of bonds, and the entropy of polypeptide chains. The most probable "structural state" can be simply determined by graphical analysis and the effect of temperature or solvent composition on it is discussed. The temperature dependence of the free energy, the probability distribution of structural states and the specific heat have been calculted for two examples of structural change. The theory predicts two different types of structural changes from the ordered to disorderd state, a "structured transition" and a "gradual structural change" with rising temperature. In the "structural transition", the probability distribution has two maxima in the temperature range of transition. In the "gradual structural change", the probabilty distribution has only one maximum during the change. A considerable fraction of secondary bonds is in the unbounded state and is always fluctuating even in the ordered state at room temperature. Such structural flucutations in a single protein molecule have been discussed quantitatively. The theory is extended to include small molecules which bind to the protein molecule and affect the structural state. The changes of structural state caused by specific and non-specific binding and allosteric effects are explained in a unified manner.