  We consider six different secondary structures of proteins and construct two
types of Go-type off-lattice models: with the steric constraints and without.
The basic aminoacid-aminoacid potential is Lennard Jones for the native
contacts and a soft repulsion for the non-native contacts. The interactions are
chosen to make the target secondary structure be the native state of the
system. We provide a thorough equilibrium and kinetic characterization of the
sequences through the molecular dynamics simulations with the Langevin noise.
Models with the steric constraints are found to be better folders and to be
more stable, especially in the case of the $\beta$-structures. Phononic spectra
for vibrations around the native states have low frequency gaps that correlate
with the thermodynamic stability. Folding of the secondary structures proceeds
through a well defined sequence of events. For instance, $\alpha$-helices fold
from the ends first. The closer to the native state, the faster establishment
of the contacts. Increasing the system size deteriorates the folding
characteristics. We study the folding times as a function of viscous friction
and find a regime of moderate friction with the linear dependence. We also
consider folding when one end of a structure is pinned which imitates
instantaneous conditions when a protein is being synthesized. We find that,
under such circumstances, folding of helices is faster and of the
$\beta$-sequences slower.
