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 known as the nucleosome: a DNA-protein complex consisting of a DNA segment wrapped around a disc-shaped group of eight histone proteins. We show that without any a priori information, diffusion maps can identify and extract meaningful collective variables that characterize the motion of the nucleosome complex. We find excellent agreement between the collective variables identified by the diffusion map and those obtained manually using a free energy-based analysis. Notably, diffusion maps are shown to also identify subtle features of nucleosome dynamics that did not appear in those manually specified collective variables. For example, diffusion maps identify the importance of looped conformations in which DNA bulges away from the histone complex that are important for the motion of DNA around the nucleosome. This work demonstrates that diffusion maps can be a promising tool for analyzing very large molecular systems and for identifying their characteristic slow modes.