Revised Manuscript Received May 29, 1990 e energetics of virtually all binding functions in proteins is the culmination of a set of molecular interactions. For example, removal of a single molecular contact by a point mutation causes relatively small reductions (typically 0.5—5 kcal/mol) in the free energy of transition-state stabilization [for reviews see Fersht (1987) and Wells and Estell (1988)], protein-protein interactions (Laskowski et al., 1983, 1989; Ackers & Smith, 1985), or protein stability [for review see Matthews (1987)] compared to the overall free energy asso-ciated with these functional properties (usually 5-20 kcal/mol). Thus, it is possibleto modulate protein function by mutation at many contact sites. In fact, to design large changes in function will often require mutation of more than one functional residue.

There is now a large data base for free energy changes that result when single mutants are combined. A review of these data shows that, in the majority of cases, the sum of the free energy changes derived from the single mutations is nearly equal to the free energy change measured in the multiple mutant. However, there are two major exceptions where such simple additivity breaks down. The first is where the mutated residues interact with each other, by direct contact or indirectly through electrostatic interactions or structural perturbations, so that they no longer behave independently. The second is where the mutation causes a change in mechanism or rate-limiting step of the reaction. It is important to note that the additive effects discussed here do not change the molecularity of their respective reactions. When the molecularity of the reaction changes [as in comparing the free energy of binding of one linked substrate (AB) versus the sum of two fragments (A plus B)], large deviations from simple additivity can result from entropic effects (Jencks, 1981). Although thefocus here is on enzyme activity, similar conclusions may be drawnfrom mutations affecting protein-protein interactions, protein-DNA recognition, or protein stability. Some practical examples and applications are discussed.