Free energy calculations for peptides via deterministic global optimization

The αBB algorithm is a deterministically based global optimization method that has been successfully used to locate the global minimum energy conformations of peptide systems. The goal of this procedure is to identify the native conformation of a given peptide by identifying the structure possessing the global minimum potential energy. However, a rigorous conformational search should locate the structure exhibiting the global minimum free energy. In this work, novel methods are developed for locating free energy global minimum conformations and clusters of peptides. These methods are based on an harmonic approximation for entropic effects, which requires the ability to generate a dense ensemble of distinct low energy local minima. Two approaches, both based on the general concepts of the αBB branch and bound framework, are used to generate these ensembles. In performing these calculations, potential-energy contributions were modeled using an all-atom force field. In addition, hydration effects were also considered by utilizing a solvent-accessible volume of hydration shell model. The free energy analysis was applied to both the unsolvated and solvated forms of met- and leu-enkephalin. It was found that both methods produce dense, Boltzmann-type, distributions of low-energy metastable states. The inclusion of entropic effects was also found to influence the prediction of free energy global minima. In addition, a statistical treatment of the thermodynamics of folding showed that the transition temperature, which signified a collapse from high energy, extended structures to a ground-statelike ensemble, could be identified.