Integrated tempering enhanced sampling method as the infinite switching limit of simulated tempering

A fast and accurate sampling method is in high demand, in order to bridge the large gaps between molecular dynamic simulations and experimental observations. Recently, an integrated tempering enhanced sampling (ITS) method has been proposed and successfully applied to various biophysical examples, significantly accelerating conformational sampling. The mathematical validation for its effectiveness has not been elucidated yet. Here we show that the integrated tempering enhanced sampling method can be viewed as a reformulation of the infinite switching limit of the simulated tempering method over a mixed potential. Moreover, we demonstrate that the efficiency of simulated tempering molecular dynamics improves as the frequency of switching between the temperatures is increased, based on the large deviation principle of empirical distributions. Our theory provides the theoretical justification of the advantage of ITS. Finally, we illustrate the utility of the infinite switching simulated tempering method through several numerical examples.