Motional clustering in supra-τ_c conformational exchange influences NOE cross-relaxation rate

Biomolecular spin relaxation processes, such as the NOE, are commonly modeled by rotational τ_c-tumbling combined with fast motions on the sub-τ_c timescale. Motions on the supra-τ_c timescale, in contrast, are considered to be completely decorrelated to the molecular tumbling and therefore invisible. Here, we show how supra-τ_c dynamics can nonetheless influence the NOE build-up between methyl groups. This effect arises because supra-τ_c motions can cluster the fast-motion ensembles into discrete states, affecting distance averaging as well as the fast-motion order parameter and hence the cross-relaxation rate. We present a computational approach to estimate methyl-methyl cross-relaxation rates from extensive (>100×τ_c) all-atom molecular dynamics (MD) trajectories on the example of the 723-residue protein Malate Synthase G. The approach uses Markov state models (MSMs) to resolve transitions between metastable states and thus to discriminate between sub-τ_c and supra-τ_c conformational exchange. We find that supra-τ_c exchange typically increases NOESY cross-peak intensities. The methods described in this work extend the theory of modeling sub-μs dynamics in spin relaxation and thus contribute to a quantitative estimation of NOE cross-relaxation rates from MD simulations, eventually leading to increased precision in structural and functional studies of large proteins.