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

Adaptive umbrella sampling of the potential energy is used as a search meth od to determine the structures and thermodynamics of peptides in solution. It leads to uniform sampling of the potential energy, so as to combine samp ling of low-energy conformations that dominate the properties of the system at room temperature with sampling of high-energy conformations that are im portant for transitions between different minima. A modification of the pro cedure for updating the umbrella potential is introduced to increase the nu mber of transitions between folded and unfolded conformations. The method d oes not depend on assumptions about the geometry of the native state. Tno p eptides with 12 and 13 residues, respectively, are studied using the CHARMM polar-hydrogen energy function and the analytical continuum solvent potent ial for treatment of solvation. In the original adaptive umbrella sampling simulations of the two peptides, two and sh transitions occur between folde d and unfolded conformations, respectively, over a simulation time of 10 ns . The modification increases the number of transitions to 6 and 12, respect ively. in the same simulation time. The precision of estimates of the avera ge effective energy of the system as a function of temperature and of the c ontributions to the average effective energy of folded conformations obtain ed with the adaptive methods is discussed.