On the physics of thermal-stability changes upon mutations of a protein

It is of great interest from both scientific and practical viewpoints to theoretically predict the thermal-stability changes upon mutations of a protein. However, such a prediction is an intricate task. Up to now, significantly many approaches for the prediction have been reported in the literature. They always include parameters which are adjusted so that the prediction results can be best fitted to the experimental data for a sufficiently large set of proteins and mutations. The inclusion is necessitated to achieve satisfactorily high prediction performance. A problem is that the resulting values of the parameters are often physically meaningless, and the physicochemical factors governing the thermal-stability changes upon mutations are rather ambiguous. Here, we develop a new measure of the thermal stability. Protein folding is accompanied by a large gain of water entropy (the entropic excluded-volume (EV) effect), loss of protein conformational entropy, and increase in enthalpy. The enthalpy increase originates primarily from the following: The energy increase due to the break of protein-water hydrogen bonds (HBs) upon folding cannot completely be cancelled out by the energy decrease brought by the formation of protein intramolecular HBs. We develop the measure on the basis of only these three factors and apply it to the prediction of the thermal-stability changes upon mutations. As a consequence, an approach toward the prediction is obtained. It is distinguished from the previously reported approaches in the following respects: The parameters adjusted in the manner mentioned above are not employed at all, and the entropic EV effect, which is ascribed to the translational displacement of water molecules coexisting with the protein in the system, is fully taken into account using a molecular model for water. Our approach is compared with one of the most popular approaches, FOLD-X, in terms of the prediction performance not only for single mutations but also for double, triple, and higher-fold (up to sevenfold) mutations. It is shown that on the whole our approach and FOLD-X exhibit almost the same performance despite that the latter uses the adjusting parameters. For multiple mutations, however, our approach is far superior to FOLD-X. Five multiple mutations for staphylococcal nuclease lead to highly enhanced stabilities, but we find that this high enhancement arises from the entropic EV effect. The neglect of this effect in FOLD-X is a principal reason for its ill success. A conclusion is that the three factors mentioned above play essential roles in elucidating the thermal-stability changes upon mutations.