  In this article the configurational space of two simple protein models
consisting of polymers composed of a periodic sequence of four different kinds
of monomers is studied as a function of temperature. In the protein models,
hydrogen bond interactions, electrostatic repulsion, and covalent bond
vibrations are modeled by discontinuous step, shoulder and square-well
potentials, respectively. The protein-like chains exhibit a secondary alpha
helix structure in their folded states at low temperatures, and allow a natural
definition of a configuration by considering which beads are bonded. Free
energies and entropies of configurations are computed using the parallel
tempering method in combination with hybrid Monte Carlo sampling of the
canonical ensemble of the discontinuous potential system. The probability of
observing the most common configuration is used to analyze the nature of the
free energy landscape, and it is found that the model with the least number of
possible bonds exhibits a funnel-like free energy landscape at low enough
temperature for chains with fewer than 30 beads. For longer proteins, the
landscape consists of several minima, where the configuration with the lowest
free energy changes significantly by lowering the temperature and the
probability of observing the most common configuration never approaches one due
to the degeneracy of the lowest accessible potential energy.
