The nuclear Overhauser effect from a quantitative perspective

The nuclear Overhauser enhancement or effect (NOE) is the most important measure in liquid-state NMR with macromolecules. Thus, the NOE is the subject of numerous reviews and books. Here, the NOE is revisited in light of our recently introduced measurements of exact nuclear Overhauser enhancements (eNOEs), which enabled the determination of multiple-state 3D protein structures. This review encompasses all relevant facets from the theoretical considerations to the use of eNOEs in multiple-state structure calculation. Important aspects include a detailed presentation of the relaxation theory relevant for the nuclear Overhauser effect, the estimation of the correction for spin diffusion, the experimental determination of the eNOEs, the conversion of eNOE rates into distances and validation of their quality, the distance-restraint classification and the protocols for calculation of structures and ensembles.

Towards a true protein movie: a perspective on the potential impact of the ensemble-based structure determination using exact NOEs

Confined by the Boltzmann distribution of the energies of the states, a multitude of structural states are inherent to biomolecules. For a detailed understanding of a protein's function, its entire structural landscape at atomic resolution and insight into the interconversion between all the structural states (i.e. dynamics) are required. Whereas dedicated trickery with NMR relaxation provides aspects of local dynamics, and 3D structure determination by NMR is well established, only recently have several attempts been made to formulate a more comprehensive description of the dynamics and the structural landscape of a protein. Here, a perspective is given on the use of exact NOEs (eNOEs) for the elucidation of structural ensembles of a protein describing the covered conformational space.

The experimental accuracy of the uni-directional exact NOE

We have established protocols to calculate exact NOEs (eNOE) from NOE data. eNOEs lend unprecedented precision to the calculation of distance restraints used for structure calculation. Moreover, as eNOEs are averaged quantities over all conformations of a molecule, they may contain accessible information of the sampled conformational space. In practice, a prerequisite for an exact interpretation is the evaluation of both NOESY cross-peak buildups. For large molecular sizes, the fraction of NOEs which can only be obtained from one cross peak typically increases. Distance restraints derived from such NOEs must be used with a tolerance for errors associated with the broken symmetry of the individual magnetization transfer pathways. The correct choice of upper and lower limits is particularly important for multiple-state ensemble calculation, where too narrow tolerances may lead to incorrect spatial sampling. In order to dissect these pathways in heavy-atom resolved 3D NOESY experiments, we analyze 2D [(1)H, (1)H]-NOESY experiments, which are the fundamental building blocks of the former. In combination with an analysis of excitation and inversion profiles of pulses on heavy atoms and relaxation effects during HXQC elements, we derive a rule for the correct choice of upper and lower distance limits derived from such uni-directional NOEs. We show that normalization of the cross- to the diagonal-peak intensities of the spins of magnetization destination rather than origin leads to similar errors of the distance restraints. This opens up the prospect of extended collection of unidirectional eNOEs.

Protein Motional Details Revealed by Complementary Structural Biology Techniques

Proteins depend on defined molecular plasticity for their functionality. How to comprehensively capture dynamics correctly is of ubiquitous biological importance. Approaches commonly used to probe protein dynamics include model-free elucidation of site-specific motion by NMR relaxation, molecular dynamics (MD)-based approaches, and capturing the substates within a dynamic ensemble by recent eNOE-based multiple-structure approaches. Even though MD is sometimes combined with ensemble-averaged NMR restraints, these approaches have largely been developed and used individually. Owing to the different underlying concepts and practical requirements, it has remained unclear how they compare, and how they cross-validate and complement each other. Here, we extract and compare the differential information contents of MD simulations, NMR relaxation measurements, and eNOE-based multi-state structures for the SH3 domain of chicken α-spectrin. The data show that a validated, consistent, and detailed picture is feasible both for timescales and actual conformational states sampled in the dynamic ensemble. This includes the biologically important side-chain plasticity, for which experimentally cross-validated assessment is a significant challenge.

Reducing the measurement time of exact NOEs by non-uniform sampling

We have previously reported on the measurement of exact NOEs (eNOEs), which yield a wealth of additional information in comparison to conventional NOEs. We have used these eNOEs in a variety of applications, including calculating high-resolution structures of proteins and RNA molecules. The collection of eNOEs is challenging, however, due to the need to measure a NOESY buildup series consisting of typically four NOESY spectra with varying mixing times in a single measurement session. While the 2D version can be completed in a few days, a fully sampled 3D-NOESY buildup series can take 10 days or more to acquire. This can be both expensive as well as problematic in the case of samples that are not stable over such a long period of time. One potential method to significantly decrease the required measurement time of eNOEs is to use non-uniform sampling (NUS) to decrease the number of points measured in the indirect dimensions. The effect of NUS on the extremely tight distance restraints extracted from eNOEs may be very pronounced. Therefore, we investigated the fidelity of eNOEs measured from three test cases at decreasing NUS densities: the 18.4 kDa protein human Pin1, the 4.1 kDa WW domain of Pin1 (both in 3D), and a 4.6 kDa 14mer RNA UUCG tetraloop (2D). Our results show that NUS imparted negligible error on the eNOE distances derived from good quality data down to 10% sampling for all three cases, but there is a noticeable decrease in the eNOE yield that is dependent upon the underlying sparsity, and thus complexity, of the sample. For Pin1, this transition occurred at roughly 40% while for the WW domain and the UUCG tetraloop it occurred at lower NUS densities of 20% and 10%, respectively. We rationalized these numbers through reconstruction simulations under various conditions. The extent of this loss depends upon the number of scans taken as well as the number of peaks to be reconstructed. Based on these findings, we have created guidelines for choosing an optimal NUS density depending on the number of peaks needed to be reconstructed in the densest region of a 2D or 3D NOESY spectrum.

NOE-Derived Methyl Distances from a 360 kDa Proteasome Complex

Nuclear magnetic resonance spectroscopy is the prime tool to probe structure and dynamics of biomolecules at atomic resolution. A serious challenge for that method is the size limit imposed on molecules to be studied. Standard studies are typically restricted to ca. 30-40 kDa. More recent developments lead to spin relaxation measurements in methyl groups in single proteins or protein complexes as large as a mega-Dalton, which directly allow the extraction of angular information or experiments with paramagnetic samples. However, these probes are all of indirect nature in contrast to the most intuitive and easy-to-interpret structural/dynamics restraint, the internuclear distance, which can be measured by nuclear Overhauser enhancement (NOE). Herein, we demonstrate time-averaged distance measurements on the 360 kDa half proteasome from Thermoplasma acidophilium. The approach is based on exact quantification of the NOE (eNOE). Our findings open up an avenue for such measurements on very large molecules. These restraints will help in a detailed determination of conformational changes upon perturbation such as ligand binding.

Optimization and validation of multi-state NMR protein structures using structural correlations

Recent advances in the field of protein structure determination using liquid-state NMR enable the elucidation of multi-state protein conformations that can provide insight into correlated and non-correlated protein dynamics at atomic resolution. So far, NMR-derived multi-state structures were typically evaluated by means of visual inspection of structure superpositions, target function values that quantify the violation of experimented restraints and root-mean-square deviations that quantify similarity between conformers. As an alternative or complementary approach, we present here the use of a recently introduced structural correlation measure, PDBcor, that quantifies the clustering of protein states as an additional measure for multi-state protein structure analysis. It can be used for various assays including the validation of experimental distance restraints, optimization of the number of protein states, estimation of protein state populations, identification of key distance restraints, NOE network analysis and semiquantitative analysis of the protein correlation network. We present applications for the final quality analysis stages of typical multi-state protein structure calculations.

Advances in the exact nuclear Overhauser effect 2018-2022

The introduction of the exact nuclear Overhauser enhancement (eNOE) methodology to solution-state nuclear magnetic resonance (NMR) spectroscopy results in tighter distance restraints from NOEs than in convention analysis. These improved restraints allow for higher resolution in structure calculation and even the disentanglement of different conformations of macromolecules. While initial work primarily focused on technical development of the eNOE, structural studies aimed at the elucidation of spatial sampling in proteins and nucleic acids were published in parallel prior to 2018. The period of 2018-2022 saw a continued series of technical innovation, but also major applications addressing biological questions. Here, we review both aspects, covering topics from the implementation of non-uniform sampling of NOESY buildups, novel pulse sequences, adaption of the eNOE to solid-state NMR, advances in eNOE data analysis, and innovations in structural ensemble calculation, to applications to protein, RNA, and DNA structure elucidation.