  The consequences of recent experimental finding that hydrogen bonds of the
anti-parallel $\beta $-sheet in nonspecific binding site of serine proteases
become significantly shorter and stronger synchronously with the catalytic act
are examined. We investigate the effect of the transformation of an ordinary
hydrogen bond into a low-barrier one on the crankshaft motion a peptide group
in the anti-parallel $\beta $-sheet. For this purpose we make use of a
realistic model of the peptide chain with stringent microscopically derived
coupling interaction potential and effective on-site potential. The coupling
interaction characterizing the peptide chain rigidity is found to be
surprisingly weak and repulsive in character. The effective on-site potential
is found to be a hard one, i.e., goes more steep than a harmonic one. At
transformation of the ordinary hydrogen bond into the low-barrier one the
frequency of crankshaft motion of the corresponding peptide group in the
anti-parallel $\beta $-sheet is roughly doubled.
