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 CLN025a variant of the peptide
Chignolin. The LINES method can be extended to the study of large-scale
protein systems with complex nonlinear reaction pathways.
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