Parallel tempering Monte Carlo simulation of met-enkephalin and WW-domain proteins

Efficient sampling of low-energy conformational states remains a central challenge in protein folding simulations. In this study, we investigated the performance and limitations of standard Monte Carlo (MC) and parallel tempering Monte Carlo (PTMC) methods in exploring protein energy landscapes using two representative systems: the small peptide Met-enkephalin and the FBP28 WW-Domain protein. For Met-enkephalin, standard MC simulations achieved equilibrium at higher temperatures but showed insufficient sampling in low-energy regions. In contrast, PTMC significantly improved sampling efficiency across a wide temperature range, particularly in the low-energy regime, enabling robust exploration of the energy landscape. PTMC successfully identified the global minimum structure of Met-enkephalin with an energy of -11.23 kcal/mol and a root-mean-square deviation of 1.18 Å from the reference structure. The applicability of PTMC to larger proteins was further examined through extensive simulations of the WW-Domain, revealing pronounced energy fluctuations and folding–unfolding transitions at higher temperatures, while sampling at lower temperatures remained limited. The number of visits per unit energy range for two consecutive temperatures have also monitored to check the exchange rate and conformational sampling of the entire landscape. The average energy and specific heat with respect to temperature have also calculated to check the folding unfolding transition of WW-Domain. These results demonstrated the superiority of PTMC over standard MC for protein folding studies; however, they also highlighted challenges associated with larger protein systems.