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

Abstract

In a statistical approach to protein structure analysis, Miyazawa and Jernigan derived a $20\ifmmode\times\else\texttimes\fi{}20$ 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 ${M}_{\mathrm{ij}}{\phantom{\rule{0ex}{0ex}}=\phantom{\rule{0ex}{0ex}}C}_{0}{+C}_{1}({q}_{i}{+q}_{j}){+C}_{2}{q}_{i}{q}_{j}$, 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.