Influence of specific contacts on the stability and structure of proteins. Theory for the perturbation of a harmonic system.

The question of how specific contacts within a protein influence its stability and structure is examined within a formal theoretical framework. A mathematical model is developed in which the potential energy of a protein is taken as a harmonic expansion of all of its internal or normal coordinates. With classical statistical mechanics the properties of the system can be derived from this potential energy function. A few new contacts are then introduced as additional energy terms, each having a quadratic dependence on a single internal coordinate. These terms are added as perturbations to the original potential energy, and the attendant changes in the properties of the system are obtained. Exact expressions can be derived for changes in the enthalpy, entropy, and for any arbitrary internal degree of freedom. These quantities are expressed in terms of the parameters of the potential energy functions of the new contacts, and the mean square displacements and positional correlation functions of the internal coordinates. These results provide qualitative insights into the role of contacts in stabilizing a particular conformation. Estimates are given for the entropy of formation of a hydrogen bond in a protein. A criterion is proposed for determining whether a contact is essential to the stability of a protein conformation. This model may be applicable to many experimental systems in which mutant or modified proteins are available that differ by one or a few amino acids. The results may also be useful in thermodynamic analyses of computer simulations.