  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, Dryden and Marron, 2012, Biometrika). 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.
