Enhancing NMR derived ensembles with kinetics on multiple timescales

Abstract

Nuclear magnetic resonance (NMR) has the unique advantage of elucidating the structure and dynamics of biomolecules in solution at physiological temperatures, where they are in constant movement on timescales from picoseconds to milliseconds. Such motions have been shown to be critical for enzyme catalysis, allosteric regulation, and molecular recognition. With NMR being particularly sensitive to these timescales, detailed information about the kinetics can be acquired. However, nearly all methods of NMR-based biomolecular structure determination neglect kinetics, which introduces a large approximation to the underlying physics, limiting both structural resolution and the ability to accurately determine molecular flexibility. Here we present the Kinetic Ensemble approach that uses a hierarchy of interconversion rates between a set of ensemble members to rigorously calculate Nuclear Overhauser Effect (NOE) intensities. It can be used to simultaneously refine both temporal and structural coordinates. By generalizing ideas from the extended model free approach, the method can analyze the amplitudes and kinetics of motions anywhere along the backbone or side chains. Furthermore, analysis of a large set of crystal structures suggests that NOE data contains a surprising amount of high-resolution information that is better modeled using our approach. The Kinetic Ensemble approach provides the means to unify numerous types of experiments under a single quantitative framework and more fully characterize and exploit kinetically distinct protein states. While we apply the approach here to the protein ubiquitin and cross validate it with previously derived datasets, the approach can be applied to any protein for which NOE data is available.

Using molecular dynamics trajectories to predict nuclear spin relaxation behaviour in large spin systems

“…For the three-spin subsystem of the glucose ring, the agreement with the analytical model using pure rotational diffusion is good (Figure 3, left panel) -rotational correlation time in the analytical model was the only fitting parameter. Within the experimental error, the fitted value of 78 ps agrees well with ~100 ps reported from 13 C relaxation analysis of data from a 100 mM sucrose sample in D2O [24], particularly if corrections for differences in H2O vs D2O viscosity are made (a reduction of ~10%). This suggests that isotropic rotational diffusion approximates the dynamics of the relatively rigid glucose ring well.…”

“…However, most models used to interpret spin relaxation data make spartan approximations about local mobility [10,11] and use isolated spin pair models. More elaborate treatments of NMR [12][13][14][15] and EPR [16,17] relaxation using MD simulations recently emerged, but they still mostly use spin pair approximations; the work from one of our groups is also in this category [18,19]. What is needed is a software framework that would be able to directly convert an MD trajectory into a relaxation superoperator [20] for an arbitrary spin system.…”

“…We tested the proposed methods on aqueous sucrose (GLYCAM06 force field [22]) with OPC [5] and TIP5P [23] water. Conformational mobility in sucrose is well researched, particularly by 13 C spin relaxation measurements interpreted using isolated spin-pair approximations [24][25][26]. Here, we will focus on the less straightforward but more informative 1 H-1 H nuclear Overhauser effect (NOE) that probes the contacts between the H1 anomeric proton (Figure 1) of glucose and H11,12 protons of fructose positioned across the glycosidic bond connecting glucose and fructose residues.…”

Conformational ensembles of intrinsically disordered proteins and flexible multidomain proteins

“…Many experiments report on distances, which are straightforward to calculate from ensembles. For example, NOEs are often calculated simply as an −6 -weighted ensemble-average of interatomic distances , with the approximation that dynamics do not contribute to the NOE intensity (Brüschweiler et al, 1992;Peter et al, 2001;Smith et al, 2020). Distance-based experiments that require chemical labeling, such as smFRET, PRE, and DEER, introduce an additional challenge, as label dynamics must be taken into account in the forward model (Steinhoff and Hubbell, 1996;Tombolato et al, 2006a,b;Salmon et al, 2010;Polyhach et al, 2011;Sindbert et al, 2011;Kalinin et al, 2012;Reichel et al, 2018;Borgia et al, 2018;Tesei et al, 2021a;Klose et al, 2021).…”

“…However, for certain types of biophysical experiments, time-dependent dynamics must be taken into account. For example, NMR relaxation experiments report on molecular motions which can only be calculated from a time-series of structures or models of the dynamics, such as the Lipari-Szabo model-free approach (Lipari and Szabo, 1982;Brüschweiler et al, 1992;Peter et al, 2001;Salvi et al, 2016;Smith et al, 2020;Kümmerer et al, 2021). Additionally, many biological processes do not happen at equilibrium, but rather involve transitions from one state to another.…”