Explicit models of motions to analyze NMR relaxation data in proteins

Nuclear Magnetic Resonance (NMR) is a tool of choice to characterize molecular motions. In biological macromolecules, pico- to nano-second motions, in particular, can be probed by nuclear spin relaxation rates which depend on the time fluctuations of the orientations of spin interaction frames. For the past 40 years, relaxation rates have been successfully analyzed using the Model Free (MF) approach which makes no assumption on the nature of motions and reports on the effective amplitude and time-scale of the motions. However, obtaining a mechanistic picture of motions from this type of analysis is difficult at best, unless complemented with molecular dynamics (MD) simulations. In spite of their limited accuracy, such simulations can be used to obtain the information necessary to build explicit models of motions designed to analyze NMR relaxation data. Here, we present how to build such models, suited in particular to describe motions of methyl-bearing protein side-chains and compare them with the MF approach. We show on synthetic data that explicit models of motions are more robust in the presence of rotamer jumps which dominate the relaxation in methyl groups of protein side-chains. We expect this work to motivate the use of explicit models of motion to analyze MD and NMR data

Understanding the Methyl-TROSY effect over a wide range of magnetic fields

The use of relaxation interference in the methyl Transverse Relaxation-Optimized SpectroscopY (TROSY) experiment has opened new avenues for the study of large proteins and protein assemblies in nuclear magnetic resonance. So far, the theoretical description of the methyl-TROSY experiment has been limited to the slow-tumbling approximation, which is correct for large proteins on high field spectrometers. In a recent paper, favorable relaxation interference was observed in the methyl groups of a small protein at a magnetic field as low as 0.33 T, well outside the slow-tumbling regime. Here, we present a model to describe relaxation interference in methyl groups over a broad range of magnetic fields, not limited to the slow-tumbling regime. We predict that the type of multiple-quantum transitions that show favorable relaxation properties change with the magnetic field. Under the condition of fast methyl-group rotation, methyl-TROSY experiments can be recorded over the entire range of magnetic fields from a fraction of 1 T up to 100 T

Relaxation par RMN multi-champs dans les biomolécules

La relaxation des spins nucléaires est un phénomène fondamental en Résonance Magnétique Nucléaire (RMN). Au cours d’une expérience, elle conduit à des pertes de polarisation affectant la qualité des spectres. Afin de développer de nouvelles séquences d’impulsion, il est essentiel de prendre en compte ses effets, voire de les optimiser, comme dans le cas des expériences de type TROSY (Transverse Relaxation Optimized SpectroscopY). Après une brève introduction à la théorie de la relaxation en phase liquide, nous détaillons comment cette théorie a été implémentée dans le but de calculer efficacement les vitesses de relaxation d’un grand nombre de systèmes de spins. La théorie de la relaxation nous a permis de comprendre le spectre de groupes méthyl dans la protéine Ubiquitine, et enregistré avec une évolution zéro quantum à bas champs et une détection à haut champs en utilisant un spectromètre RMN à deux champs. Cela nous a conduits à étendre le champ d’application de la théorie du methyl-TROSY. Par ailleurs, nous avons introduit le concept de TROSY à deux-champs. Il repose non seulement sur la sélection d’opérateur de spin ayant des propriétés de relaxation favorables, mais également sur la sélection adéquate des champs magnétiques pour l’évolution sous l’effet du déplacement chimique tout en conservant la sensibilité des hauts champs pour la détection. La mesure des vitesses de relaxation, constitue un outil de choix pour la caractérisation de la dynamique sur des échelles de temps allant de la pico- à la seconde, et plus. Nous présentons ici des outils pour analyser la dépendance en champs magnétique de vitesses de relaxation enregistrées sur une large gamme de champs magnétiques. Enfin, nous présentons quelques modèles de mouvements prenant en compte la nature des mouvements dans les protéines. En particulier, nous montrons l’existence d’un mécanisme de relaxation associé à des différences de CSA (Chemical Shift Anisotropy) dans les chaînes latérales aliphatiques.Nuclear spin relaxation is a fundamental phenomenon in Nuclear Magnetic Resonance (NMR). During the course of an experiment, it leads to polarization losses that can be detrimental to the spectrum quality. Taking spin relaxation into account when developing NMR pulse sequences appears essential, and can reveal itself beneficial, as shown in TRansverse Optimized SpectroscopY (TROSY) type of experiments. After a brief introduction to nuclear spin relaxation theory in liquid, we will detail how it has been implemented to efficiently compute relaxation rates of arbitrary spin systems. Nuclear spin relaxation theory has been used to understand the spectrum of methyl groups in the protein Ubiquitin recorded with zero-quantum evolution at low field and signal detection at high field using a two-field NMR spectrometer. This led us to extend the methyl-TROSY theory beyond its original conditions of application. In addition, we introduced the concept of two-field TROSY which relies not only on the selection of spin quantum operators with favorable relaxation properties, but also on the proper selection of the magnetic field for chemical shift labeling while retaining high-field high-sensitivity detection. Relaxation measurements report on dynamic properties over timescales ranging from pico- to seconds and more is unique. Here, we present tools to analyze the field-dependence of relaxation rates recorded while moving the sample inside the bore of the spectrometer to extend the range of available magnetic fields. Finally, we discuss models of motions adapted to the nature of internal motions in protons. We reveal the existence of a rotamer Chemical Shift Anisotropy (CSA) dependent relaxation mechanism in aliphatic side-chains

NMR relaxation in biomolecules over orders of magnitude of magnetic field

Nuclear spin relaxation is a fundamental phenomenon in Nuclear Magnetic Resonance (NMR). During the course of an experiment, it leads to polarization losses that can be detrimental to the spectrum quality. Taking spin relaxation into account when developing NMR pulse sequences appears essential, and can reveal itself beneficial, as shown in TRansverse Optimized SpectroscopY (TROSY) type of experiments. After a brief introduction to nuclear spin relaxation theory in liquid, we will detail how it has been implemented to efficiently compute relaxation rates of arbitrary spin systems. Nuclear spin relaxation theory has been used to understand the spectrum of methyl groups in the protein Ubiquitin recorded with zero-quantum evolution at low field and signal detection at high field using a two-field NMR spectrometer. This led us to extend the methyl-TROSY theory beyond its original conditions of application. In addition, we introduced the concept of two-field TROSY which relies not only on the selection of spin quantum operators with favorable relaxation properties, but also on the proper selection of the magnetic field for chemical shift labeling while retaining high-field high-sensitivity detection. Relaxation measurements report on dynamic properties over timescales ranging from pico- to seconds and more is unique. Here, we present tools to analyze the field-dependence of relaxation rates recorded while moving the sample inside the bore of the spectrometer to extend the range of available magnetic fields. Finally, we discuss models of motions adapted to the nature of internal motions in protons. We reveal the existence of a rotamer Chemical Shift Anisotropy (CSA) dependent relaxation mechanism in aliphatic side-chains.La relaxation des spins nucléaires est un phénomène fondamental en Résonance Magnétique Nucléaire (RMN). Au cours d’une expérience, elle conduit à des pertes de polarisation affectant la qualité des spectres. Afin de développer de nouvelles séquences d’impulsion, il est essentiel de prendre en compte ses effets, voire de les optimiser, comme dans le cas des expériences de type TROSY (Transverse Relaxation Optimized SpectroscopY). Après une brève introduction à la théorie de la relaxation en phase liquide, nous détaillons comment cette théorie a été implémentée dans le but de calculer efficacement les vitesses de relaxation d’un grand nombre de systèmes de spins. La théorie de la relaxation nous a permis de comprendre le spectre de groupes méthyl dans la protéine Ubiquitine, et enregistré avec une évolution zéro quantum à bas champs et une détection à haut champs en utilisant un spectromètre RMN à deux champs. Cela nous a conduits à étendre le champ d’application de la théorie du methyl-TROSY. Par ailleurs, nous avons introduit le concept de TROSY à deux-champs. Il repose non seulement sur la sélection d’opérateur de spin ayant des propriétés de relaxation favorables, mais également sur la sélection adéquate des champs magnétiques pour l’évolution sous l’effet du déplacement chimique tout en conservant la sensibilité des hauts champs pour la détection. La mesure des vitesses de relaxation, constitue un outil de choix pour la caractérisation de la dynamique sur des échelles de temps allant de la pico- à la seconde, et plus. Nous présentons ici des outils pour analyser la dépendance en champs magnétique de vitesses de relaxation enregistrées sur une large gamme de champs magnétiques. Enfin, nous présentons quelques modèles de mouvements prenant en compte la nature des mouvements dans les protéines. En particulier, nous montrons l’existence d’un mécanisme de relaxation associé à des différences de CSA (Chemical Shift Anisotropy) dans les chaînes latérales aliphatiques

Optimizing frequency sampling in CEST experiments

For the past decade chemical exchange saturation transfer (CEST) experiments have been successfully applied to study exchange processes in biomolecules involving sparsely populated, transiently formed conformers. Initial implementations focused on extensive sampling of the CEST frequency domain, requiring significant measurement times. Here we show that the lengthy sampling schemes often used are not optimal and that reduced frequency sampling schedules can be developed without a priori knowledge of the exchange parameters, that only depend on the chosen B1 field, and, to a lesser extent, on the intrinsic transverse relaxation rates of ground state spins. The reduced sampling approach described here can be used synergistically with other methods for reducing measurement times such as those that excite multiple frequencies in the CEST dimension simultaneously, or make use of non-uniform sampling of indirectly detected time domains, to further decrease measurement times. The proposed approach is validated by analysis of simulated and experimental datasets

Two-Field Transverse Relaxation-Optimized Spectroscopy for the Study of Large Biomolecules – an in Silico Investigation

Biomolecular NMR spectroscopy has greatly benefited from the development of TROSY-type pulse sequences, in pair with specific labeling. The selection of spin operators with favorable relaxation properties has led to an increase in the resolution and sensitivity of spectra of large biomolecules. However, nuclei with a large chemical shift anisotropy (CSA) contribution to relaxation can still suffer from large linewidths at conventional magnetic fields (higher than 9 T). Here, we introduce the concept of two-field TROSY (2F-TROSY) where the chemical shifts of nuclei with large CSA is labeled at low fields (ca. 2 T) dramatically reducing the contribution of CSA to relaxation. Signal detection is performed at high field (> 9 T) on a nucleus with efficient TROSY interference to yield high-resolution and sensitivity. We use comprehensive numerical simulations to demonstrate the power of this approach on aromatic 13C-19F spin pairs for which a TROSY pulse sequence has recently been published. We predict that the 2F- TROSY experiment shall yield good quality spectra for large proteins (global tumbling correlation times as high as 100 ns) with one order of magnitude higher sensitivity than the single-field experiment. </div

Determination of Protein ps-ns Motions by High-Resolution Relaxometry

International audienc

Comprehensive analysis of relaxation decays from high-resolution relaxometry

Relaxometry consists in measuring relaxation rates over orders of magnitude of magnetic fields to probe motions of complex systems. High-resolution relaxometry (HRR) experiments can be performed on conventional high-field NMR magnets equipped with a sample shuttle. During the experiment, the sample shuttle transfers the sample between the high-field magnetic center and a chosen position in the stray field for relaxation during a variable delay, thus using the stray field as a variable field. As the relaxation delay occurs outside of the probe, HRR experiments cannot rely on the control of cross-relaxation pathways, which is standard in high-field relaxation pulse sequences. Thus, decay rates are not pure relaxation rates, which may impair a reliable description of the dynamics. Previously, we took into account cross-relaxation effects in the analysis of high- resolution relaxometry data by applying a correction factor to relaxometry decay rates in order to estimate relaxation rates. These correction factors were obtained from the iterative simulation of the relaxation decay while the sample lies outside of the probe and a preceding analysis of relaxation rates which relies on the approximation of a priori multi-exponential decays by mono-exponential functions. However, an analysis protocol matching directly experimental and simulated relaxometry decays should be more self consistent. Here, we introduce Matching INtensities for the Optimization of Timescales and Amplitudes of motions Under Relaxometry (MINOTAUR), a framework for the analysis of high-resolution relaxometry that takes as input the intensity decays at all fields. This approach uses the full relaxation matrix to calculate intensity decays, allowing complex relaxation pathways to be taken into account. Therefore, it eliminates the need for a correction of decay rates and for fitting multi-exponential decays with mono-exponential functions. The MINOTAUR software is designed as a flexible framework where relaxation matrices and spectral density functions corresponding to various models of motions can be defined on a case-by-case basis. The agreement with our previous analyses of protein side-chain dynamics from carbon-13 relaxation is excellent, while providing a more robust analysis tool. We expect MINOTAUR to become the tool of choice for the analysis of high-resolution relaxometry

How Wide Is the Window Opened by High-Resolution Relaxometry on the Internal Dynamics of Proteins in Solution?

Here we apply the detectors approach to probe the amount of information in high-resolution relaxometry measurements in biological macromolecules in solution. We show that high-resolution relaxometry provides new relevant information in the nanosecond range and that the additional range of information is all the more large as the overall rotational diffusion is slow

Inhibitor-3 inhibits Protein Phosphatase 1 via a metal binding dynamic protein–protein interaction

Protein phosphatase 1 (PP1) is regulated by intrinsically disordered proteins like inhibitor-3, I3. The authors show that I3 does not inhibit PP1 by forming a rigid complex but instead by binding dynamically with its active site metals, showing how flexibility is used in biology