Dimensionality Estimation of Protein Dynamics Using Polymer Models.

Molecular dynamics (MD) simulation is a powerful technique for sampling the conformational landscape of natively folded proteins (NFPs) and structurally dynamic intrinsically disordered proteins (IDPs). NFPs and IDPs can be viewed as nonlinear dynamical systems that exercise available degrees of freedom to explore their energetically-accessible conformation landscape. Dimensionality estimators have emerged as useful tools to characterize nonlinear dynamical systems in other domains, but their application to MD simulation has been limited due to thermal noise and a lack of ground-truth data. We develop a series of increasingly complex biopolymer models which exhibit a range of dynamics we seek to characterize in MD simulations (stochastic dynamics, helical structures, partially folded states, and correlated motions) and are of known dimensionality. We utilize the maximum-likelihood dimension (MLD) estimator to investigate the effects of thermal noise and noise-smoothing techniques on the estimates obtained from the polymer models and MD simulations of two NFPs and two IDPs. We find that under certain noise/smoothing conditions, the MLD over/under-estimates the true dimensionality of the models in a predictable manner, allowing us to relate differences between MLD estimates to differences between NFP and IDP motions for classification of biomolecular systems based on their dynamics.