A double-mutant cycle involves wild-type protein, two single mutants and the corresponding double mutant protein. If the change in free energy associated with a structural or functional property of the protein upon a double mutation differs from the sum of changes in free energy due to the single mutations, then the residues at the two positions are coupled. Such coupling reflects either direct or indirect interactions between these residues. Double-mutant cycle analysis can be used to measure the strength of intramolecular and intermolecular pairwise interactions in proteins or protein-ligand complexes with known structure. Double-mutant cycles can also be employed to characterize structures that are inaccessible to NMR and X-ray crystallography, such as those of transition states for protein folding, ligand binding and enzyme catalysis, or of membrane proteins. Multidimensional mutant cycle analysis can be used to measure higher-order cooperativity between intramolecular or intermolecular interactions. In the absence of coupling between residues, prediction of mutational effects is possible by assuming their additivity.