Back-mapping based sampling: Coarse grained free energy landscapes as a guideline for atomistic exploration

One ongoing topic of research in MD simulations is how to enable sampling to chemically and biologically relevant time scales. We address this question by introducing a back-mapping based sampling (BMBS) that combines multiple aspects of different sampling techniques. BMBS uses coarse grained (CG) free energy surfaces (FESs) and dimensionality reduction to initiate new atomistic simulations. These new simulations are started from atomistic conformations that were back-mapped from CG points all over the FES in order to sample the entire accessible phase space as fast as possible. In the context of BMBS, we address relevant back-mapping related questions like where to start the back-mapping from and how to judge the atomistic ensemble that results from the BMBS. The latter is done with the use of the earth mover's distance, which allows us to quantitatively compare distributions of CG and atomistic ensembles. By using this metric, we can also show that the BMBS is able to correct inaccuracies of the CG model. In this paper, BMBS is applied to a just recently introduced neural network (NN) based approach for a radical coarse graining to predict free energy surfaces for oligopeptides. The BMBS scheme back-maps these FESs to the atomistic scale, justifying and complementing the proposed NN based CG approach. The efficiency benefit of the algorithm scales with the length of the oligomer. Already for the heptamers, the algorithm is about one order of magnitude faster in sampling compared to a standard MD simulation.