Dynamic Feature Extraction from Molecular Mechanics Trajectories

With the recent advancements in distributed computing, it is now possible to simulate molecular dynamics of large systems over unprecedented time scales. However, due to the sheer size of the generated trajectories, it is no longer possible to reliably extract relevant chemical and biological information from a simulation through visual inspection alone a single trajectory alone may consist of well over a thousand of atoms, charted over hundreds of time points. Currently, Markov state models are being used to compute a discretization of the conformational space of large proteins. However, one current challenge lies in understanding the transitions between the states. To address this problem, we consider restoring the dynamic systems perspective and look for methods capable of detecting transition mechanisms in this context. Since physical interactions between atoms are typically proportional to distances between corresponding atoms, we are particularly interested in analyzing pairwise atomic distances. Unfortunately, the space of pairwise distances scales with the number of atoms squared. It is therefore desirable to develop methods that reduce the dimensionality of the space into readily interpretable coordinates that largely account for variations in the data. While offering a promise of fewer dimensions, conventional methods, such as Principal Components Analysis (PCA), often produce difficult to interpret coordinates, as each of the coordinates mixes a significant number of atoms that makes it difficult to definitely attribute motion along a principal component to motion in real space. Furthermore, the assumption of linearity is weak in the context molecular dynamics. Similar problems arise for factor analysis. Finally, many of these techniques are not readily applicable to time series data because measurements taken close in time cannot be considered independent samples from the distribution of atomic configurations. Here we seek to address this issue by proposing an unsupervised feature selection method for a system of time series that incorporates basic time dependent relationships within the system. For the application, we will be working with pairwise distances from single molecular dynamics trajectories; however, this method should be applicable to other feature spaces and possibly other fields.