Probability distributions for complex systems: Adaptive umbrella sampling of the potential energy

An adaptive umbrella sampling molecular dynamics algorithm based on the potential energy is introduced to reduce the simulation time required for deriving equilibrium properties of molecular systems. The potential energy, in contrast to the commonly used umbrella potentials, is of particular interest for complex systems because it does not depend on assumptions about the geometry nor on a knowledge of the important conformations and transition states that are involved in the equilibration. The method is illustrated by applying it to the threonine dipeptide and to met-Enkephalin. For the threonine dipeptide, potentials of mean force for all dihedral angles of the system are derived from a single 10 ns run. The accuracy of the potentials is confirmed by comparison with previous results. Met-Enkephalin is found to sample several different conformations at 300 K. Three representative structures are used to cluster the dominant conformations. Equilibrium distributions of dihedral angles and the distance between the two termini are calculated. The precision of the results is analyzed, and the utility of the proposed adaptive umbrella sampling method is discussed.