Reaction Coordinates for Conformational Transitions using Linear Discriminant Analysis on Positions

Abstract

In this work, we demonstrate that Linear Discriminant Analysis (LDA) applied to atomic positions in two different states of a biomolecule produces a good reaction coordinate between those two states. Atomic coordinates of a macromolecule are a direct representation of a macromolecular configuration, and yet they have not been used in enhanced sampling studies due to a lack of rotational and translational invariance. We resolve this issue using the technique of our prior work, where a molecular configuration is considered a member of an equivalence class in size-and-shape space, which is the set of all configurations that can be translated and rotated to a single point within a reference multivariate Gaussian distribution characterizing a single molecular state. The reaction coordinates produced by LDA applied to positions are shown to be good reaction coordinates both in terms of characterizing the transition between two states of a system within a long molecular dynamics (MD) simulation, and also ones that allow us to readily produce free energy estimates along that reaction coordinate using enhanced sampling MD techniques.

11 pages, 5 figures (plus 2 SI pages and 3 SI figures)

References in corpus (6)

• Well-Tempered Metadynamics: A Smoothly Converging and Tunable Free-Energy Method
• Machine learning for molecular simulation
• Nonlinear Discovery of Slow Molecular Modes using State-Free Reversible VAMPnets
• A self-learning algorithm for biased molecular dynamics
• Collective Variables for the Study of Crystallization
• Assessing models of force-dependent unbinding rates via infrequent metadynamics