Lattice protein folding with two and four-body statistical potentials

The cooperative folding of proteins implies a description by multibody potentials. Such multibody potentials can be generalized from common two-body statistical potentials through a relation to probability distributions of residue clusters via the Boltzmann condition. In this exploratory study, we compare a four-body statistical potential, defined by the Delaunay tessellation of protein structures, to the Miyazawa-Jernigan (MJ) potential for protein structure prediction, using a lattice chain growth algorithm. We use the four-body potential as a discriminatory function for conformational ensembles generated with the MJ potential and examine performance on a set of 22 proteins of 30-76 residues in length. We find that the four-body potential yields comparable results to the two-body MJ potential, namely, an average coordinate root-mean-square deviation (cRMSD) value of 8 Å for the lowest energy configurations of all-α proteins, and somewhat poorer cRMSD values for other protein classes. For both two and four-body potentials, superpositions of some predicted and native structures show a rough overall agreement. Formulating the four-body potential using larger data sets and direct, but costly, generation of conformational ensembles with multibody potentials may offer further improvements.