# Predicting NMR Relaxation Using a First-Principles Brownian Dynamics Approach

## TL;DR

This paper introduces a new method using Brownian dynamics to predict NMR relaxation, combining efficiency with atomistic detail for studying slow molecular motions.

## Contribution

A first-principles Brownian dynamics approach is proposed for NMR relaxation prediction, merging stochastic modeling with atomistic simulations.

## Key findings

- The method enables long-time dynamics analysis of semiflexible molecules with reduced computational cost.
- GPU acceleration and natural internal coordinates enhance the efficiency and accuracy of the simulations.
- The approach provides a rigorous framework for interpreting NMR relaxation data from molecular dynamics.

## Abstract

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.