LINES: Log-Probability Estimation via Invertible Neural Networks for Enhanced Sampling.

It is very challenging to sample a molecular process with large activation energies using molecular dynamics simulations. Current enhanced sampling methodologies, such as umbrella sampling and metadynamics, rely on the identification of appropriate reaction coordinates for a system. In this paper, we developed a method for log-probability estimation via invertible neural networks for enhanced sampling (LINES). This iterative scheme utilizes a normalizing flow machine learning model to learn the underlying free energy surface (FES) of a system as a function of molecular coordinates and then applies a gradient-based optimization method to the learned normalizing flow to identify reaction coordinates. A biasing potential is then evaluated over a tabulated grid of the reaction coordinate values, which can be applied to the next round of simulations for enhanced sampling, resulting in more efficient sampling. We tested the accuracy and efficiency of the LINES method in sampling the FES using the alanine dipeptide system. We also demonstrated the effectiveness of identification of reaction coordinates through simulation of cyclobutanol unbinding from β-cyclodextrin and the folding/unfolding of CLN025─a variant of the peptide Chignolin. The LINES method can be extended to the study of large-scale protein systems with complex nonlinear reaction pathways.