Adaptive umbrella sampling of the potential energy: modified updating procedure of the umbrella potential and application to peptide folding

Abstract

Adaptive umbrella sampling of the potential energy is used as a search method to determine the structures and thermodynamics of peptides in solution. It leads to uniform sampling of the potential energy, so as to combine sampling of low-energy conformations that dominate the properties of the system at room temperature with sampling of high-energy conformations that are important for transitions between different minima. A modification of the procedure for updating the umbrella potential is introduced to increase the number of transitions between folded and unfolded conformations. The method does not depend on assumptions about the geometry of the native state. Two peptides with 12 and 13 residues, respectively, are studied using the CHARMM polar-hydrogen energy function and the analytical continuum solvent potential for treatment of solvation. In the original adaptive umbrella sampling simulations of the two peptides, two and six transitions occur between folded and unfolded conformations, respectively, over a simulation time of 10 ns. The modification increases the number of transitions to 6 and 12, respectively, in the same simulation time. The precision of estimates of the average effective energy of the system as a function of temperature and of the contributions to the average effective energy of folded conformations obtained with the adaptive methods is discussed.