Extracting collective motions underlying nucleosome dynamics via nonlinear manifold learning

The identification of effective collective variables remains a challenge in molecular simulations of complex systems. Here, we use a nonlinear manifold learning technique known as the diffusion map to extract key dynamical motions from a complex biomolecular system, namely the nucleosome: a DNA-protein complex consisting of 147 base pairs of DNA wrapped around a disc-shaped group of eight histone proteins. We show that diffusion maps are effective at extracting collective variables previously found through a detailed free energy analysis in addition to revealing more subtle features involving looping conformations, in which DNA bulges away from the histone complex. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and its characteristic slow modes.