The quantitative effect of a second mutation on a mutant enzyme may be antagonistic, absent, partially additive, additive, or synergistic with respect to the first mutation. Depending on which kinetic or thermodynamic parameter of an enzyme is measured, the same two mutations can interact differently in the double mutant. Additive effects of two mutations on an equilibrium constant, such as the dissociation constant of the enzyme-substrate complex (Ks), occur when noninteracting residues which facilitate the same step (substrate binding) are mutated. Partially additive effects result from the cooperative interaction with the substrate of the two residues mutated, and synergistic effects result from the anticooperative interaction with the substrate of the two residues mutated. An alternative explanation for synergy is extensive unfolding of the enzyme. Antagonistic effects on an equilibrium constant such as Ks result from opposing structural effects of the two mutations on substrate binding. No additional effect of the second mutation in the double mutant represents a limiting case of either partial additivity or synergy. The interactions of the effects of two mutations on a rate constant such as kcat have the same explanations as those given above for equilibrium constants since the binding of a rate-limiting transition state is occurring. However, due to kinetic complexity, the following exceptions and additions exist. Additive effects of two mutations on kcat occur when non-interacting residues which facilitate the same step are mutated, provided this step is rate limiting. If the affected step is not rate limiting then synergistic effects of the two mutations are observed as each mutation causes the step to become progressively more rate limiting. Additive effects on kcat also occur when the two mutations affect consecutive steps, provided one of them is rate limiting. Partially additive effects on kcat also occur when noninteracting residues facilitating consecutive, non-rate-limiting steps are mutated. These concepts, when applied to published data on double mutants of Δ5-3-ketosteroid isomerase, staphylococcal nuclease, tyrosyl-tRNA synthetase, glutathione reductase, and subtilisin, provide deeper insights into the independent, cooperative, anti-cooperative, or antagonistic interactions of amino acid residues in the binding of substrates, activators, and inhibitors and in promoting catalysis.
