Does compactness induce secondary structure in proteins? A study of poly-alanine chains computed by distance geometry

A few years ago, lattice model studies indicated that compactness could induce polymer chains to develop protein-like secondary structures. Subsequent off-lattice studies have found the amounts of induced structure to be relatively small. Here we use distance geometry to generate random conformations of compact poly-alanine chains of various chain lengths. The poly-alanine chains are subjected only to compactness and excluded volume constraints; no other energies or conformational propensities are included in the chain generation procedure. We find that compactness leads to considerable stabilization of secondary structure, but the absolute amount of secondary structure depends strongly on the criteria used to define helices and sheets. By loose criteria, much secondary structure arises from compactness, but by strict criteria, little does. The stabilization free energy of secondary structure provided by compactness, however, appears to be independent of criteria. Since real helices and sheets in proteins can be identified by strict criteria, we introduced small energy perturbations to compact poly-alanine chains using the AMBER force field. Small refinements produced good α-helices. For β-sheets, however, larger refinements are necessary. Compactness appears to impart stability, but not much structural specificity, to secondary structures in proteins. Compactness acts more like diffusion as a force, a result of ensemble statistics, than like pair interactions such as hydrogen bonding.