Discrete Breathers in Peptide Chain and Secondary Structures of Protein Backbone

The role of the rigidity of a peptide chain in its equilibrium dynamics is investigated within the framework of a microscopic model. The stacking interaction characterizing the chain rigidity is found to be repulsive for both types of protein secondary structure (α-helix and anti-parallel β-sheet) mainly encountered in natural proteins. A discrete breather (DB) or else intrinsic localized oscillation associated with the changes of torsional (dihedral) angles is shown to exist in α-helix and in parallel β-sheet but not in anti-parallel β-sheet. Since β-proteins are known to contain predominantly anti-parallel β-sheets one can conclude that such proteins do not support the excitation of the DB as opposed to α-proteins. This conclusion agrees well with the results of recent experiments of Xie et al. on far infrared laser spectroscopy of proteins.