Principal nested shape space analysis of molecular dynamics data

Dryden, Ian L.; Kim, Kwang-Rae; Laughton, Charles A.; Le, Huiling

Abstract

Molecular dynamics simulations produce huge datasets of temporal sequences of molecules. It is of interest to summarize the shape evolution of the molecules in a succinct, low-dimensional representation. However, Euclidean techniques such as principal components analysis (PCA) can be problematic as the data may lie far from in a flat manifold. Principal nested spheres gives a fundamentally different decomposition of data from the usual Euclidean sub-space based PCA (Jung et al., 2012). Sub-spaces of successively lower dimension are fitted to the data in a backwards manner, with the aim of retaining signal and dispensing with noise at each stage. We adapt the methodology to 3D sub-shape spaces and provide some practical fitting algorithms. The methodology is applied to cluster analysis of peptides, where different states of the molecules can be identified. Also, the temporal transitions between cluster states are explored.

Citation

Dryden, I. L., Kim, K.-R., Laughton, C. A., & Le, H. (2019). Principal nested shape space analysis of molecular dynamics data. Annals of Applied Statistics, 13(4), 2213-2234. https://doi.org/10.1214/19-AOAS1277

• Journal Article Type: Article
• Acceptance Date: Jun 10, 2019
• Online Publication Date: Nov 28, 2019
• Publication Date: Nov 28, 2019
• Deposit Date: Jun 17, 2019
• Publicly Available Date: Jun 17, 2019
• Journal: Annals of Applied Statistics
• Print ISSN: 1932-6157
• Electronic ISSN: 1941-7330
• Publisher: Institute of Mathematical Statistics (IMS)
• Peer Reviewed: Peer Reviewed
• Volume: 13
• Issue: 4
• Pages: 2213-2234
• DOI: https://doi.org/10.1214/19-AOAS1277
• Keywords: dimension reduction; manifold; principal components analysis; principal nested spheres; Riemannian; shape
• Public URL: https://nottingham-repository.worktribe.com/output/2196717
• Publisher URL: https://projecteuclid.org/euclid.aoas/1574910042
• Contract Date: Jun 17, 2019