UNITED-RESIDUE FORCE-FIELD FOR OFF-LATTICE PROTEIN-STRUCTURE SIMULATIONS - III - ORIGIN OF BACKBONE HYDROGEN-BONDING COOPERATIVITY IN UNITED-RESIDUE POTENTIALS

Based on the dipole model of peptide groups developed in our earlier w ork [Liwo et al., Prot. Sci., 2, 1697 (1993)], a cumulant expansion of the average free energy of the system of freely rotating peptide-grou p dipoles tethered to a fixed cr-carbon trace is derived. A graphical approach is presented to find all nonvanishing terms in the cumulants. In particular, analytical expressions for three-and four-body (correl ation) terms in the averaged interaction potential of united peptide g roups are derived. These expressions are similar to the cooperative fo rces in hydrogen bonding introduced by Kolinski and Skolnick [J. Chem. Phys., 97, 9412 (1992)]. The cooperativity arises here naturally from the higher order terms in the power-series expansion (in the inverse of the temperature) for the average energy. Test calculations have sho wn that addition of the derived four-body term to the statistical unit ed-residue potential of our earlier work [Liwo et al., J. Comput. Chem ., 18, 849, 874 (1997)] greatly improves its performance in folding po ly-L-alanine into an alpha-helix. (C) 1998 John Wiley & Sons, Inc.