Miyazawa-Jernigan Contact Potentials and Carter-Wolfenden Vapor-to-Cyclohexane and Water-to-Cyclohexane Scales as Parameters for Calculating Amino Acid Pair Distances

Abstract

The difference between amino acid chemical properties that correlate to the exchangeability of protein sequence residues is often analysed using approach proposed by Grantham (1974). His difference formula, i.e., matrix, for calculating the distances between amino acid pairs of the protein consists of three essential amino acid physicochemical properties – composition, polarity and volume, that are significantly correlated to the substitution frequencies of the protein residues. Miyata et al. (1979) re-evaluated this concept, and showed that the degree of amino acid difference is just as adequately explained by only two physicochemical factors, volume and polarity. Miyazawa-Jernigan relative partition/hydrophobic energies (ε = Δe _ir ), and Carter-Wolfenden vapor-to-cyclohexane scale (G _v>c = ΔG_v>c) are two alternative amino acid physicochemical parameters that are strongly correlated to their polarity and volume/mass, respectively. We show that the Miyazawa-Jernigan residue contact potential could be used instead of the Grantham polarity and composition parameters to derive an updated Miyata matrix. This substitution permits Miyata matrix correction for the amino acid parameters of: contact energies, repulsive packing energies, secondary structure energies, and Grantham’s composition property. Distance values calculated between both (classic and updated) Miyata matrices exhibit a strong correlation of r = 0.91. The possibility of analyzing residue distances based on Carter-Wolfenden water-to-cyclohexane (w > c) and vapor-to-cyclohexane (v > c) scales instead of the amino acid polarity and volume parameters is also discussed, and a new distance matrix is derived.