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

Abstract

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.

Recent advances in protein conformation sampling by combining machine learning with molecular simulation

“…By substituting the DenseNet architecture within the VDE network with more sophisticated and advanced architectures, more complicated systems can be investigated. The LINES method [60] employed a state-of-the-art flow-based machine learning model (Fig. 1(c)) to learn a dimensionpreserving transformation from conformational space to latent space.…”

“…These outlined works have provided useful methodologies for optimizing the selection of collective variables (CVs), thereby enhancing the exploration efficiency in model potentials and simple systems. However, these methods [57,[60][61][62] have limitations in terms of the number of latent coordinates (usually equivalent to the number of CVs) that the networks are designed to encode. The few number of CVs may limit the application of these methods on large proteins with complex conformational landscapes.…”

Chasing collective variables using temporal data-driven strategies

“…The temporal information of the simulation trajectories is, however, ignored in classical AEs. A number of strategies have been put forth to take time explicitly into account in NN-based models, which includes, but is not limited to variational approach for Markov processes networks (VAMPnets) (Mardt et al, 2018 ), time-lagged AEs (TAEs) (Hernández et al, 2018 ; Wehmeyer and Noé, 2018 ), modified TAEs (Chen et al, 2019 a ), past–future information bottleneck (PIB) (Wang et al, 2019 ) and log-probability estimation via invertible NN for enhanced sampling (LINES) (Odstrcil et al, 2022 ). As we will show in our numerical experiments, the variables that can maximise the explained variances do not always necessarily coincide with the important DOFs of the process of interest.…”

Prediction of the Peptide–TIM3 Binding Site in Inhibiting TIM3–Galectin 9 Binding Pathways

“…Machine learning can be leveraged here to identify reaction coordinates when given a list of molecular coordinates that may or may not be important to the reaction pathway. − However, these machine learning methods often rely on already observing the reaction of interest before predicting a reaction coordinate that accelerates the reaction, which can be impractical if there is a large ensemble of conformations for the molecular system. Our recently developed approach Log-Probability Estimation via Invertible Neural Networks for Enhanced Sampling (LINES) circumvents this issue by predicting reaction coordinates based on gradients of the free-energy surface (FES) with respect to each molecular coordinate instead of the molecular coordinate values themselves. LINES represents an attractive alternative that has foundations in local optimization methods, meaning that the reaction pathways are predicted before the reaction entirely occurs, improving the convergence rate of the reaction coordinate prediction.…”