Reaction Coordinates for Conformational Transitions Using Linear Discriminant Analysis on Positions

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 are not 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, whereby 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.

Automated summary

In this work, we show that applying Linear Discriminant Analysis (LDA) to atomic positions is an effective way to obtain a good reaction coordinate between two different states of a biomolecule. The lack of rotational and translational invariance has prevented the use of atomic coordinates in enhanced sampling studies. However, by considering molecular configurations as members of equivalence classes in size-and-shape space, we overcome this issue and produce reaction coordinates that effectively characterize the transition between two states and allow for free energy estimation using enhanced sampling MD techniques.