Predicting NMR Relaxation Using a First-Principles Brownian Dynamics Approach

Interpreting time-resolved magnetic resonance experiments, sensitive to slow motions in molecules, requires access to at least the microsecond time scale. Today, all-atom classical molecular dynamics simulations allow exploration of such a long time scale; however, this comes at the price of a considerable computational effort. Stochastic models, based on a hierarchical distinction of the coordinates into relevant (treated explicitly) and irrelevant (treated as generators of fluctuation and dissipation), offer a relatively low-cost solution to this problem. In the past, ad hoc but essentially phenomenological approaches based on Langevin or Fokker-Planck equations have been employed, which are good in catching relevant differences among (even complex) molecular systems, but lack of predictive power since a map between such parameters and atomistic details is not always clear or defined. Recently, a rigorous derivation of a stochastic description of the dynamics of a macromolecule from the complete equations of motion has been provided. In this paper, a computational strategy based on the solution of the Brownian dynamics equations associated with the original model is discussed for the calculation and interpretation of nuclear magnetic resonance relaxation data. The approach merges the ability of stochastic approaches to perform a targeted complexity reduction of the system with the flexibility of molecular dynamics simulations in describing at the atomistic level the time evolution of the system. By expressing the stochastic dynamics in the relevant natural internal coordinates and exploiting the acceleration power of GPU-based hardware, the proposed approach lays the foundations for an effective interpretation of long-time dynamics of generic semiflexible complex molecules.