  The role of the rigidity of a peptide chain in its equilibrium dynamics is
investigated within a realistic model with stringent microscopically derived
coupling interaction potential and effective on-site potential. The coupling
interaction characterizing the chain rigidity and the effective on-site
potentials are calculated for three main types of protein secondary structure.
The coupling interaction is found to be surprisingly weak for all of them but
different in character: repulsive for alpha-helix and anti-parallel beta-sheet
structures and attractive for parallel beta-sheet structure. The effective
on-site potential is found to be a hard one for alpha-helix and anti-parallel
beta-sheet and a soft one for parallel beta-sheet. In all three types of
protein secondary structures a stable zig-zag shape discrete breather (DB)
associated with the oscillations of torsional (dihedral) angles can exist due
to weakness of the coupling interaction. However, since the absorption of far
infrared radiation (IR) by proteins is known to require the existence of rather
long chains of hydrogen bonds that takes place only in alpha-helicies, then one
can conclude that the excitation of a DB in such a way is possible in
alpha-helix and seems to be hardly possible in beta-sheet structures. The
interpretation of the recent experiments of Xie et al. on far IR laser pulse
spectroscopy of proteins is suggested. The frequency of a DB in an the
alpha-helix is obtained in the region of 115 cm^{-1} in accordance with these
experiments.

Soft Condensed Matter;Pattern Formation and Solitons;Biomolecules