Reaction Coordinates for Conformational Transitions using Linear Discriminant Analysis on Positions

TL;DR

This paper introduces a method using Linear Discriminant Analysis on atomic positions, accounting for invariance to rotations and translations, to generate effective reaction coordinates for conformational transitions in biomolecules, facilitating enhanced sampling.

Contribution

The work demonstrates that LDA applied to properly aligned atomic positions can serve as a robust reaction coordinate for biomolecular conformational changes, addressing previous invariance issues.

Findings

LDA-based reaction coordinates effectively characterize conformational transitions.

The method enables accurate free energy estimation along the reaction coordinate.

Application to MD simulations shows good performance in transition analysis.

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.