Statistical potentials extracted from protein structures: How accurate are they?

'Statistical potentials' are energies widely used in computer algorithms to fold, dock, or recognize protein structures. They are derived from: (1) observed pairing frequencies of the 20 amino acids in databases of known protein structures, and (2) approximations and assumptions about the physical process that these quantities measure. Using exact lattice models, we construct a rigorous test of those assumptions and approximations. We find that statistical potentials often correctly rank-order the relative strengths of interresidue interactions, but they do not reflect the true underlying energies because of systematic errors arising from the neglect of excluded volume in proteins. We find that complex residue-residue distance dependences observed in statistical potentials, even those among charged groups, can be largely explained as an indirect consequence of the burial of non-polar groups. Our results suggest that current statistical potentials may have limited value in protein folding algorithms and wherever they are used to provide energy-like quantities.