Nature of Driving Force for Protein Folding: A Result From Analyzing the Statistical Potential

In a statistical approach to protein structure analysis, Miyazawa and Jernigan derived a 20×20 matrix of inter-residue contact energies between different types of amino acids. Using the method of eigenvalue decomposition, we find that the Miyazawa-Jernigan matrix can be accurately reconstructed from its first two principal component vectors as Mᵢⱼ0ex0ex=0ex0exC₀+C₁(qᵢ+qⱼ)+C₂qᵢqⱼ, with constant C's, and 20 q values associated with the 20 amino acids. This regularity is due to hydrophobic interactions and a force of demixing, the latter obeying Hildebrand's solubility theory of simple liquids.