Path Similarity Analysis: a Method for Quantifying Macromolecular Pathways

TL;DR

The paper introduces Path Similarity Analysis (PSA), a novel method using geometric path metrics to quantitatively compare macromolecular transition paths in high-dimensional space, aiding the assessment of sampling algorithms.

Contribution

PSA utilizes Hausdorff and Fréchet metrics to quantify path similarity and introduces Hausdorff-pair maps for atomic-scale analysis, advancing the comparison of complex molecular transition paths.

Findings

PSA successfully compares multiple transition ensembles of adenylate kinase.

Differences in transition paths are linked to specific atomic interactions like salt bridges.

PSA can be integrated with existing analysis methods for complex systems.

Abstract

Diverse classes of proteins function through large-scale conformational changes; sophisticated enhanced sampling methods have been proposed to generate these macromolecular transition paths. As such paths are curves in a high-dimensional space, they have been difficult to compare quantitatively, a prerequisite to, for instance, assess the quality of different sampling algorithms. The Path Similarity Analysis (PSA) approach alleviates these difficulties by utilizing the full information in 3N-dimensional trajectories in configuration space. PSA employs the Hausdorff or Fr\'echet path metrics---adopted from computational geometry---enabling us to quantify path (dis)similarity, while the new concept of a Hausdorff-pair map permits the extraction of atomic-scale determinants responsible for path differences. Combined with clustering techniques, PSA facilitates the comparison of many paths, including collections of transition ensembles. We use the closed-to-open transition of the enzyme adenylate kinase (AdK)---a commonly used testbed for the assessment enhanced sampling algorithms---to examine multiple microsecond equilibrium molecular dynamics (MD) transitions of AdK in its substrate-free form alongside transition ensembles from the MD-based dynamic importance sampling (DIMS-MD) and targeted MD (TMD) methods, and a geometrical targeting algorithm (FRODA). A Hausdorff pairs analysis of these ensembles revealed, for instance, that differences in DIMS-MD and FRODA paths were mediated by a set of conserved salt bridges whose charge-charge interactions are fully modeled in DIMS-MD but not in FRODA. We also demonstrate how existing trajectory analysis methods relying on pre-defined collective variables, such as native contacts or geometric quantities, can be used synergistically with PSA, as well as the application of PSA to more complex systems such as membrane transporter proteins.