Inverse thinking about double mutants of enzymes.

The quantitative effect of a second damaging mutation on a mutated enzyme may be additive, partially additive, synergistic, antagonistic, or absent, in the double mutant. Each of these five possible types of interactions has its own mechanistic explanation [Mildvan, A. S., Weber, D. J., and Kuliopulos, A. (1992) Arch. Biochem. Biophys. 294, 327-340]. Additive effects indicate independent functioning of the two residues in the process being studied, such as catalysis (k(cat)) or substrate binding (K(S)). Departures from additivity reflect interaction of the two residues. Thus, partial additivity indicates cooperativity, synergy indicates anticooperativity, and antagonism indicates opposing structural effects of the two mutations. No additional effects represent limiting cases of either partial additivity or antagonism. A significant conceptual simplification is achieved by applying inverse thinking, namely, by using the parameters of the double mutant rather than those of the wild-type enzyme as the reference point. To explain partially additive effects on k(cat), inverse thinking starts with the k(cat) of the double mutant. Restoring only one residue increases k(cat) by the factor A. Restoring only the other residue increases k(cat) by the factor B. Restoring both residues is shown to increase k(cat) by a factor greater than A x B, with the excess directly measuring the cooperativity. Similarly, inverse thinking provides simpler and more intuitive explanations of synergistic and antagonistic effects, as illustrated by specific examples.