Harmonic mean relationship between affinity for wild-type receptors and alanine-scan mutants

Alanine-scanning mutagenesis involves systematic substitution of a single alanine for other amino acid constituents of a ligand or receptor protein. The sequential process generates a discrete set of "mutant" proteins, each member of which differs from the native 'wild-type' receptor (R(wt)) or ligand by the single amino acid (alpha) substitution with alanine (R(Ala)). The Ala mapsto alpha substitutions are made for amino acids suspected of being important for binding of ligand to receptor. Binding assays are then used to measure the affinity for R(wt) and mutants, quantified by the ligand-receptor equilibrium constant (K(eq)) or its reciprocal, the dissociation constant (K(d)=1/K(eq)). However, the relationship betweenR(wt)K(d) and R(Ala)K(d) values is not obvious. Neither the arithmetic mean nor the geometric mean (based on a simplified relationship between K(d) and the thermodynamic standard free energy change) of the R(Ala)K(d) values turns out to be adequate. The harmonic mean was found to be a good estimator when applied to the published data from 14 alanine-scan studies. This result is consonant with the present understanding of ligand-receptor interactions.