  Umbrella sampling is an efficient method for the calculation of free energy
changes of a system along well-defined reaction coordinates. However, when
multiple parallel channels along the reaction coordinate or hidden barriers in
directions perpendicular to the reaction coordinate exist, it is difficult for
conventional umbrella sampling methods to generate sufficient sampling within
limited simulation time. Here we propose an efficient approach to combine
umbrella sampling with the integrated tempering sampling method. The umbrella
sampling method is applied to conformational degrees of freedom which possess
significant barriers and are chemically more relevant. The integrated tempering
sampling method is employed to facilitate the sampling of other degrees of
freedom in which statistically non-negligible barriers may exist. The combined
method is applied to two model systems and show significantly improved sampling
efficiencies as compared to standalone conventional umbrella sampling or
integrated tempering sampling approaches. Therefore, the combined approach will
become a very efficient method in the simulation of biomolecular processes
which often involve sampling of complex rugged energy landscapes.
