Free Energy Landscape of Protein-like Chains with Discontinuous Potentials

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.