Physicochemical origin of high correlation between thermal stability of a protein and its packing efficiency: a theoretical study for staphylococcal nuclease mutants

There is an empirical rule that the thermal stability of a protein is related to the packing efficiency or core volume of the folded state and the protein tends to exhibit higher stability as the backbone and side chains are more closely packed. Previously, the wild type and its nine mutants of staphylococcal nuclease were compared by examining their folded structures. The results obtained were as follows: The stability was not correlated with the number of intramolecular hydrogen bonds, intramolecular electrostatic interaction energy, or degree of burial of the hydrophobic surface; though the empirical rule mentioned above held, it was not the proximate cause of higher stability; and the number of van der Waals contacts NvdW, or equivalently, the intramolecular van der Waals interaction energy was an important factor governing the stability. Here we revisit the wild type and its nine mutants of staphylococcal nuclease using our statistical-mechanical theory for hydration of a protein. A molecular model is employed for water. We show that the pivotal factor is the magnitude of the water-entropy gain upon folding. The gain originates from an increase in the total volume available to the translational displacement of water molecules coexisting with the protein in the system. The magnitude is highly correlated with the denaturation temperature Tm. Moreover, the apparent correlation between NvdW and Tm as well as the empirical rule is interpretable (i.e., their physicochemical meanings can be clarified) on the basis of the water-entropy effect.