Cooperativity in amide hydrogen bonding chains. Relation between energy, position, and H-bond chain length in peptide and protein folding models

The individual H-bond energies have been calculated at the B3LYP/D95** level for linear chains of H-bonding formamides containing from 2 to 15 monomeric units. The cooperative effect upon the strongest H-bonds (those nearest the center of the 15-formamide chain) approaches 200% that of the dimer. The cooperative interaction far exceeds that expected for electrostatic interactions. The large variation in the calculated H-bonding enthalpies cannot readily be modeled using pairwise nearest-neighbor potentials. The energetic data obtained from the DFT calculations have been empirically fit using parameters based upon the chain length (n) and the H-bond type (k) which corresponds to the position of the H-bond in the chain (k = 1 for terminal, 2 for penultimate H-bonds, etc.). Each type (k) of H-bond asymptotically approaches a limiting interaction energy specific for that type. As k becomes larger, the initial H-bond for that type becomes more stable, but the cooperative contribution to that type becomes less. The results are discussed with respect to their utility for improving the modeling of peptide structure and protein folding.