Multiscale Reweighted Stochastic Embedding: Deep Learning of Collective Variables for Enhanced Sampling

Abstract

Machine learning methods provide a general framework for automatically finding and representing the essential characteristics of simulation data. This task is particularly crucial in enhanced sampling simulations. There we seek a few generalized degrees of freedom, referred to as collective variables (CVs), to represent and drive the sampling of the free energy landscape. In theory, these CVs should separate different metastable states and correspond to the slow degrees of freedom of the studied physical process. To this aim, we propose a new method that we call multiscale reweighted stochastic embedding (MRSE). Our work builds upon a parametric version of stochastic neighbor embedding. The technique automatically learns CVs that map a high-dimensional feature space to a low-dimensional latent space via a deep neural network. We introduce several new advancements to stochastic neighbor embedding methods that make MRSE especially suitable for enhanced sampling simulations: (1) weight-tempered random sampling as a landmark selection scheme to obtain training data sets that strike a balance between equilibrium representation and capturing important metastable states lying higher in free energy; (2) a multiscale representation of the high-dimensional feature space via a Gaussian mixture probability model; and (3) a reweighting procedure to account for training data from a biased probability distribution. We show that MRSE constructs low-dimensional CVs that can correctly characterize the different metastable states in three model systems: the Müller-Brown potential, alanine dipeptide, and alanine tetrapeptide.

Enhancing the Inhomogeneous Photodynamics of Canonical Bacteriophytochrome

“…Conversely, not all metastable states can be observed just by looking at the Φ dihedral angle. This indicates the importance of selecting a set of CVs that can describe the studied systems while losing as little information as possible . We cannot answer the question if the Φ dihedral is the only required degree of freedom to quantitatively describe the BV-BphP photoisomerization in experimental conditions.…”

“…This indicates the importance of selecting a set of CVs that can describe the studied systems while losing as little information as possible. 82 We cannot answer the question if the Φ dihedral is the only required degree of freedom to quantitatively describe the BV-BphP photoisomerization in experimental conditions. However, it is clear that by biasing both dihedral angles, we are able to provide a detailed thermodynamic characterization of Pr and Pfr.…”

SGOOP-d: Estimating Kinetic Distances and Reaction Coordinate Dimensionality for Rare Event Systems from Biased/Unbiased Simulations

“…In this final section, we demonstrate our method on a more complicated molecular system, namely the peptide Ace-Ala 3 -Nme with a much larger number of metastable states, and an even larger number of state-to-state transitions . Simulation details are provided in the Supporting Information.…”

“…Simulation details are provided in the Supporting Information. As discussed in ref , the three dihedral angles ϕ 1 , ϕ 2 , and ϕ 3 are sufficient to characterize the 2 3 = 8 dominant metastable states corresponding to the positive and negative parts of the Ramachandran diagram for the three central Alanine residues. The RC components used in computing SGOOP-d distances are calculated as a linear combination of cosines and sines of these three dihedral angles, thereby amounting to a total of six order parameters.…”

Discover, Sample, and Refine: Exploring Chemistry with Enhanced Sampling Techniques

“…In parallel, like several other groups, − we have proposed different strategies to identify useful CVs. The use of neural network-based collective variables has allowed efficient CVs to be defined as nonlinear combinations of a relatively large set of molecular descriptors once the initial and final states of the reactive process are known beforehand. ,− Thus, they are not suitable to explore in a blind way the reaction space.…”