A Gaussian kernel Monte Carlo resampling method to construct smooth free energy surface from discrete simulation data

Constructing a free energy surface based on discrete molecular simulation data is a common practice in computational chemistry and biophysics. As a general strategy, histogram-based methods have substantial limitations in producing smooth free energy surfaces from sparse samples. Most histogram-free methods allow for possible smooth global free energy surface mapping but likely lead to significantly compromised local features. This issue is particularly severe when both the global shape and the local free energy transition need to be quantitatively depicted, as often aimed for in general ensemble simulation studies. In this work, we introduce a Gaussian kernel Monte Carlo (GKMC) resampling method to robustly construct a smooth free energy surface from discrete simulation data. In GKMC resampling, the target free energy surface is mapped as the sum of local Gaussian basis functions; the height of each Gaussian basis function is recursively obtained through MC resampling of the simulation data. In this work, the GKMC resampling method is illustrated based on the data from a generalized orthogonal space tempering simulation study of deca-alanine peptide conformational changes in aqueous solution. As revealed in the case study, smooth free energy surfaces that can accurately represent simulated probability distributions could be robustly generated through the GKMC resampling strategy. Because data noise can be effectively removed, local free energy features could be displayed in an informative way. Notably, without impacting the global free energy shape, local free energy smoothness can be conveniently adjusted via the choice of the Gaussian kernel function width. As demonstrated, GKMC resampling is a robust approach for high-quality free energy surface construction.