Nanosecond time scale motions in proteins revealed by high-resolution NMR relaxometry

Exploring weak ligand-protein interactions by relaxometry of long-lived spin order

Relaxation times of nuclear spins often serve as a valuable source of information on the dynamics of various biochemical processes. Measuring relaxation as a function of the external magnetic field turned out to be extremely useful for the studies of weak ligand-protein interactions. We demonstrate that observing the relaxation of the long-lived spin order instead of longitudinal magnetization extends the capability of this approach. We studied the field-dependent relaxation of the longitudinal magnetization and the singlet order (SO) of methylene protons in alanine-glycine dipeptide and citrate in the presence of human serum albumin (HSA). As a result, SO relaxation proved to be more sensitive to ligand-protein interaction, providing higher relaxation contrast for various HSA concentrations. To assess the parameters of the binding process in more details, we utilized a simple analytical relaxation model to fit the experimental field dependences for both SO and T1 relaxation. We also tested the validity of our approach in the experiments with trimethylsilylpropanoic acid (TSP) used as a competitor in ligand binding with HSA.

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C' CSA-13C'-13Cα DD CCR rate [Formula: see text] and present a novel 3D version of the transverse [Formula: see text] CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.

Unraveling motion in proteins by combining NMR relaxometry and molecular dynamics simulations: A case study on ubiquitin

Nuclear magnetic resonance (NMR) relaxation experiments shine light onto the dynamics of molecular systems in the picosecond to millisecond timescales. As these methods cannot provide an atomically resolved view of the motion of atoms, functional groups, or domains giving rise to such signals, relaxation techniques have been combined with molecular dynamics (MD) simulations to obtain mechanistic descriptions and gain insights into the functional role of side chain or domain motion. In this work, we present a comparison of five computational methods that permit the joint analysis of MD simulations and NMR relaxation experiments. We discuss their relative strengths and areas of applicability and demonstrate how they may be utilized to interpret the dynamics in MD simulations with the small protein ubiquitin as a test system. We focus on the aliphatic side chains given the rigidity of the backbone of this protein. We find encouraging agreement between experiment, Markov state models built in the χ1/χ2 rotamer space of isoleucine residues, explicit rotamer jump models, and a decomposition of the motion using ROMANCE. These methods allow us to ascribe the dynamics to specific rotamer jumps. Simulations with eight different combinations of force field and water model highlight how the different metrics may be employed to pinpoint force field deficiencies. Furthermore, the presented comparison offers a perspective on the utility of NMR relaxation to serve as validation data for the prediction of kinetics by state-of-the-art biomolecular force fields.

Using NMR diffusion data to validate MD models of disordered proteins: Test case of N-terminal tail of histone H4

MD simulations can provide uniquely detailed models of intrinsically disordered proteins (IDPs). However, these models need careful experimental validation. The coefficient of translational diffusion Dtr, measurable by pulsed field gradient NMR, offers a potentially useful piece of experimental information related to the compactness of the IDP's conformational ensemble. Here, we investigate, both experimentally and via the MD modeling, the translational diffusion of a 25-residue N-terminal fragment from histone H4 (N-H4). We found that the predicted values of Dtr, as obtained from mean-square displacement of the peptide in the MD simulations, are largely determined by the viscosity of the MD water (which has been reinvestigated as a part of our study). Beyond that, our analysis of the diffusion data indicates that MD simulations of N-H4 in the TIP4P-Ew water give rise to an overly compact conformational ensemble for this peptide. In contrast, TIP4P-D and OPC simulations produce the ensembles that are consistent with the experimental Dtr result. These observations are supported by the analyses of the 15N spin relaxation rates. We also tested a number of empirical methods to predict Dtr based on IDP's coordinates extracted from the MD snapshots. In particular, we show that the popular approach involving the program HYDROPRO can produce misleading results. This happens because HYDROPRO is not intended to predict the diffusion properties of highly flexible biopolymers such as IDPs. Likewise, recent empirical schemes that exploit the relationship between the small-angle x-ray scattering-informed conformational ensembles of IDPs and the respective experimental Dtr values also prove to be problematic. In this sense, the first-principle calculations of Dtr from the MD simulations, such as demonstrated in this work, should provide a useful benchmark for future efforts in this area.

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 and more generally applicable as it can accommodate deviations from mono-exponential decays. 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.

A dual-core NMR system for field-cycling singlet assisted diffusion NMR

Long-lived singlet spin order offers the possibility to extend the spin memory by more than an order of magnitude. This enhancement can be used, among other applications, to assist NMR diffusion experiments in porous media where the extended lifetime of singlet spin order can be used to gain information about structural features of the medium as well as the dynamics of the imbibed phase. Other than offering the possibility to explore longer diffusion times of the order of many minutes that, for example, gives unprecedented access to tortuosity in structures with interconnected pores, singlet order has the important advantage to be immune to the internal field gradients generated by magnetic susceptibility inhomogeneities. These inhomogeneities, however, are responsible for very short T₂ decay constants in high magnetic field and this precludes access to the singlet order in the first instance. To overcome this difficulty and take advantage of singlet order in diffusion experiments in porous media, we have here developed a dual-core system with radiofrequency and 3-axis pulsed field gradients facilities in low magnetic field, for preparation and manipulation of singlet order and a probe, in high magnetic field, for polarisation and detection. The system operates in field-cycling and can be used for a variety of NMR experiments including diffusion tensor imaging (both singlet assisted and not). In this paper we present and discuss the new hardware and its calibration, and demonstrate its capabilities through a variety of examples.

Computer-aided drug design approaches applied to screen natural product's structural analogs targeting arginase in Leishmania spp

Introduction: Leishmaniasis is a disease with high mortality rates and approximately 1.5 million new cases each year. Despite the new approaches and advances to fight the disease, there are no effective therapies. Methods: Hence, this study aims to screen for natural products' structural analogs as new drug candidates against leishmaniasis. We applied Computer-aided drug design (CADD) approaches, such as virtual screening, molecular docking, molecular dynamics simulation, molecular mechanics-generalized Born surface area (MM-GBSA) binding free estimation, and free energy perturbation (FEP) aiming to select structural analogs from natural products that have shown anti-leishmanial and anti-arginase activities and that could bind selectively against the Leishmania arginase enzyme. Results: The compounds 2H-1-benzopyran, 3,4-dihydro-2-(2-methylphenyl)-(9CI), echioidinin, and malvidin showed good results against arginase targets from three parasite species and negative results for potential toxicities. The echioidinin and malvidin ligands generated interactions in the active center at pH 2.0 conditions by MM-GBSA and FEP methods. Conclusions: This work suggests the potential anti-leishmanial activity of the compounds and thus can be further in vitro and in vivo experimentally validated.

Modern Manufacturing Enables Magnetic Field Cycling Experiments and Parahydrogen-Induced Hyperpolarization with a Benchtop NMR

Benchtop NMR (btNMR) spectrometers are revolutionizing the way we use NMR and lowering the cost drastically. Magnetic field cycling (MFC) experiments with precise timing and control over the magnetic field, however, were hitherto not available on btNMRs, although some systems exist for high-field, high-resolution NMR spectrometers. Still, the need and potential for btNMR MFC is great─e.g., to perform and analyze parahydrogen-induced hyperpolarization, another method that has affected analytical chemistry and NMR beyond expectations. Here, we describe a setup that enables MFC on btNMRs for chemical analysis and hyperpolarization. Taking full advantage of the power of modern manufacturing, including computer-aided design, three-dimensional printing, and microcontrollers, the setup is easy to reproduce, highly reliable, and easy to adjust and operate. Within 380 ms, the NMR tube was shuttled reliably from the electromagnet to the NMR isocenter (using a stepper motor and gear rod). We demonstrated the power of this setup by hyperpolarizing nicotinamide using signal amplification by reversible exchange (SABRE), a versatile method to hyperpolarize a broad variety of molecules including metabolites and drugs. Here, the standard deviation of SABRE hyperpolarization was between 0.2 and 3.3%. The setup also allowed us to investigate the field dependency of the polarization and the effect of different sample preparation protocols. We found that redissolution of the activated and dried Ir catalyst always reduced the polarization. We anticipate that this design will greatly accelerate the ascension of MFC experiments for chemical analysis with btNMR─adding yet another application to this rapidly developing field.

DHFR Mutants Modulate Their Synchronized Dynamics with the Substrate by Shifting Hydrogen Bond Occupancies

Antibiotic resistance is a global health problem in which mutations occurring in functional proteins render drugs ineffective. The working mechanisms of the arising mutants are seldom apparent; a methodology to decipher these mechanisms systematically would render devising therapies to control the arising mutational pathways possible. Here we utilize C_α-C_β bond vector relaxations obtained from moderate length MD trajectories to determine conduits for functionality of the resistance conferring mutants of Escherichia coli dihydrofolate reductase. We find that the whole enzyme is synchronized to the motions of the substrate, irrespective of the mutation introducing gain-of-function or loss-of function. The total coordination of the motions suggests changes in the hydrogen bond dynamics with respect to the wild type as a possible route to determine and classify the mode-of-action of individual mutants. As a result, nine trimethoprim-resistant point mutations arising frequently in evolution experiments are categorized. One group of mutants that display the largest occurrence (L28R, W30G) work directly by modifying the dihydrofolate binding region. Conversely, W30R works indirectly by the formation of the E139-R30 salt bridge which releases energy resulting from tight binding by distorting the binding cavity. A third group (D27E, F153S, I94L) arising as single, resistance invoking mutants in evolution experiment trajectories allosterically and dynamically affects a hydrogen bonding motif formed at residues 59-69-71 which in turn modifies the binding site dynamics. The final group (I5F, A26T, R98P) consists of those mutants that have properties most similar to the wild type; these only appear after one of the other mutants is fixed on the protein structure and therefore display clear epistasis. Thus, we show that the binding event is governed by the entire enzyme dynamics while the binding site residues play gating roles. The adjustments made in the total enzyme in response to point mutations are what make quantifying and pinpointing their effect a hard problem. Here, we show that hydrogen bond dynamics recorded on sub-μs time scales provide the necessary fingerprints to decipher the various mechanisms at play.

How does it really move? Recent progress in the investigation of protein nanosecond dynamics by NMR and simulation

Nuclear magnetic resonance (NMR) spin relaxation experiments currently probe molecular motions on timescales from picoseconds to nanoseconds. The detailed interpretation of these motions in atomic detail benefits from complementarity with the results from molecular dynamics (MD) simulations. In this mini-review, we describe the recent developments in experimental techniques to study the backbone dynamics from ¹⁵N relaxation and side-chain dynamics from ¹³C relaxation, discuss the different analysis approaches from model-free to dynamics detectors, and highlight the many ways that NMR relaxation experiments and MD simulations can be used together to improve the interpretation and gain insights into protein dynamics.

Explicit Models of Motion to Understand Protein Side-Chain Dynamics

Nuclear magnetic relaxation is widely used to probe protein dynamics. For decades, most analyses of relaxation in proteins have relied successfully on the model-free approach, forgoing mechanistic descriptions of motion. Model-free types of correlation functions cannot describe a large carbon-13 relaxation dataset in protein side chains. Here, we use molecular dynamics simulations to design explicit models of motion and solve Fokker-Planck diffusion equations. These models of motion provide better agreement with relaxation data, mechanistic insight, and a direct link to configuration entropy.

Convergent views on disordered protein dynamics from NMR and computational approaches

Intrinsically disordered proteins (IDPs) or intrinsically disordered regions (IDRs) is a class of biologically important proteins exhibiting specific biophysical characteristics. They lack a hydrophobic core, and their conformational behavior is strongly influenced by electrostatic interactions. IDPs and IDRs are highly dynamic, and a characterization of the motions of IDPs and IDRs is essential for their physically correct description. NMR together with molecular dynamics simulations are the methods best suited to such a task because they provide information about dynamics of proteins with atomistic resolution. Here, we present a study of motions of a disordered C-terminal domain of the delta subunit of RNA polymerase from Bacillus subtilis. Positively and negatively charged residues in the studied domain form transient electrostatic contacts critical for the biological function. Our study is focused on investigation of ps-ns dynamics of backbone of the delta subunit based on analysis of amide 15N NMR relaxation data and molecular dynamics simulations. In order to extend an informational content of NMR data to lower frequencies, which are more sensitive to slower motions, we combined standard (high-field) NMR relaxation experiments with high-resolution relaxometry. Altogether, we collected data reporting the relaxation at 12 different magnetic fields, resulting in an unprecedented data set. Our results document that the analysis of such data provides a consistent description of dynamics and confirms the validity of so far used protocols of the analysis of dynamics of IDPs also for a partially folded protein. In addition, the potential to access detailed description of motions at the timescale of tens of ns with the help of relaxometry data is discussed. Interestingly, in our case, it appears to be mostly relevant for a region involved in the formation of temporary contacts within the disordered region, which was previously proven to be biologically important.

Modeling Molecular Interactions with Wetting and Non-Wetting Rock Surfaces by Combining Electron Paramagnetic Resonance and NMR Relaxometry

Three types of natural rocks─Bentheimer and Berea sandstones, as well as Liège Chalk─have been aged by immersion in a bitumen solution for extended periods of time in two steps, changing the surface conditions from water-wet to oil-wet. NMR relaxation dispersion measurements were carried out on water and oil constituents, with saturated and aromatic molecules considered individually. In order to separate the different relaxation mechanisms discussed in the literature, ¹H and ¹⁹F relaxation times were compared to ²H for fully deuterated liquids: while ²H relaxes predominantly by quadrupolar coupling, which is an intramolecular process, the remaining nuclei relax by dipolar coupling, which potentially consists of intra- and intermolecular contributions. The wettability change becomes evident in an increase of relaxation rates for oil and a corresponding decrease for water. However, this expected behavior dominates only for the spin-lattice relaxation rate R₁ at very low field strengths and for the spin-spin relaxation rate R₂, while high-field longitudinal relaxation shows a much weaker or even reverse trend. This is attributed in part to a change of radical concentration on the pore surface upon coverage of the native rock surface by bitumen as well as by the change of surface chemistry and roughness. EPR and DNP measurements quantify the change of volume vs surface radical concentration in the rocks, and an improved understanding of the role of relaxation via paramagnetic centers is obtained. By means of comparing different fluids and nuclei in combination with a defined wettability change of natural rocks, a refined model for molecular dynamics in conjunction with NMR relaxation dispersion is proposed.

Nanobody Paratope Ensembles in Solution Characterized by MD Simulations and NMR

Variable domains of camelid antibodies (so-called nanobodies or V_HH) are the smallest antibody fragments that retain complete functionality and therapeutic potential. Understanding of the nanobody-binding interface has become a pre-requisite for rational antibody design and engineering. The nanobody-binding interface consists of up to three hypervariable loops, known as the CDR loops. Here, we structurally and dynamically characterize the conformational diversity of an anti-GFP-binding nanobody by using molecular dynamics simulations in combination with experimentally derived data from nuclear magnetic resonance (NMR) spectroscopy. The NMR data contain both structural and dynamic information resolved at various timescales, which allows an assessment of the quality of protein MD simulations. Thus, in this study, we compared the ensembles for the anti-GFP-binding nanobody obtained from MD simulations with results from NMR. We find excellent agreement of the NOE-derived distance maps obtained from NMR and MD simulations and observe similar conformational spaces for the simulations with and without NOE time-averaged restraints. We also compare the measured and calculated order parameters and find generally good agreement for the motions observed in the ps–ns timescale, in particular for the CDR3 loop. Understanding of the CDR3 loop dynamics is especially critical for nanobodies, as this loop is typically critical for antigen recognition.

High Resolution 31P Field Cycling NMR Reveals Unsuspected Features of Enzyme-Substrate-Cofactor Dynamics

The dynamic interactions of enzymes and substrates underpins catalysis, yet few techniques can interrogate the dynamics of protein-bound ligands. Here we describe the use of field cycling NMR relaxometry to measure the dynamics of enzyme-bound substrates and cofactors in catalytically competent complexes of GMP reductase. These studies reveal new binding modes unanticipated by x-ray crystal structures and reaction-specific dynamic networks. Importantly, this work demonstrates that distal interactions not usually considered part of the reaction coordinate can play an active role in catalysis. The commercialization of shuttling apparatus will make field cycling relaxometry more accessible and expand its use to additional nuclei, promising more intriguing findings to come.

Conformational Dynamics of Intrinsically Disordered Proteins Regulate Biomolecular Condensate Chemistry

Motions in biomolecules are critical for biochemical reactions. In cells, many biochemical reactions are executed inside of biomolecular condensates formed by ultradynamic intrinsically disordered proteins. A deep understanding of the conformational dynamics of intrinsically disordered proteins in biomolecular condensates is therefore of utmost importance but is complicated by diverse obstacles. Here we review emerging data on the motions of intrinsically disordered proteins inside of liquidlike condensates. We discuss how liquid–liquid phase separation modulates internal motions across a wide range of time and length scales. We further highlight the importance of intermolecular interactions that not only drive liquid–liquid phase separation but appear as key determinants for changes in biomolecular motions and the aging of condensates in human diseases. The review provides a framework for future studies to reveal the conformational dynamics of intrinsically disordered proteins in the regulation of biomolecular condensate chemistry.

Detection of Metabolite-Protein Interactions in Complex Biological Samples by High-Resolution Relaxometry: Toward Interactomics by NMR

Metabolomics, the systematic investigation of metabolites in biological fluids, cells, or tissues, reveals essential information about metabolism and diseases. Metabolites have functional roles in a myriad of biological processes, as substrates and products of enzymatic reactions but also as cofactors and regulators of large numbers of biochemical mechanisms. These functions involve interactions of metabolites with macromolecules. Yet, methods to systematically investigate these interactions are still scarce to date. In particular, there is a need for techniques suited to identify and characterize weak metabolite-macromolecule interactions directly in complex media such as biological fluids. Here, we introduce a method to investigate weak interactions between metabolites and macromolecules in biological fluids. Our approach is based on high-resolution NMR relaxometry and does not require any invasive procedure or separation step. We show that we can detect interactions between small and large molecules in human blood serum and quantify the size of the complex. Our work opens the way for investigations of metabolite (or other small molecules)-protein interactions in biological fluids for interactomics or pharmaceutical applications.

Unveiling protein dynamics in solution with field-cycling NMR relaxometry

Field-cycling NMR relaxometry is a well-established technique that can give information on molecular structure and dynamics of biological systems. It provides the nuclear relaxation rates as a function of the applied magnetic field, starting from fields as low as ~ 10^-4 T up to about 1-3 T. The profiles so collected, called nuclear magnetic relaxation dispersion (NMRD) profiles, can be extended to include the relaxation rates at the largest fields achievable with high resolution NMR spectrometers. By exploiting this wide range of frequencies, the NMRD profiles can provide information on motions occurring on time scales from 10^-6 to 10^-9 s. ¹H NMRD measurements have proved very useful also for the characterization of paramagnetic proteins, because they can help characterise a number of parameters including the number, distance and residence time of water molecules coordinated to the paramagnetic center, the reorientation correlation times and the electron spin relaxation time, and the electronic structure at the metal site.

Impact of dynamic sub-populations within grafted chains on the protein binding and colloidal stability of PEGylated nanoparticles

Polyethylene glycol grafting has played a central role in preparing the surfaces of nano-probes for biological interaction, to extend blood circulation times and to modulate protein recognition and cellular uptake. However, the role of PEG graft dynamics and conformation in determining surface recognition processes is poorly understood primarily due to the absence of a microscopic picture of the surface presentation of the polymer. Here a detailed NMR analysis reveals three types of dynamic ethylene glycol units on PEG-grafted SiO2 nanoparticles (NPs) of the type commonly evaluated as long-circulating theranostic nano-probes; a narrow fraction with fast dynamics associated with the chain ends; a broadened fraction spectrally overlapped with the former arising from those parts of the chain experiencing some dynamic restriction; and a fraction too broad to be observed in the spectrum arising from units closer to the surface/graft which undergo slow motion on the NMR timescale. We demonstrate that ethylene glycol units transition between fractions as a function of temperature, core size, PEG chain length and surface coverage and demonstrate how this distribution affects colloidal stability and protein uptake. The implications of the findings for biological application of grafted nanoparticles are discussed in the context of accepted models for surface ligand conformation.

How wide is the window opened by high-resolution relaxometry on the internal dynamics of proteins in solution?

The dynamics of molecules in solution is usually quantified by the determination of timescale-specific amplitudes of motions. High-resolution nuclear magnetic resonance (NMR) relaxometry experiments-where the sample is transferred to low fields for longitudinal (T₁) relaxation, and back to high field for detection with residue-specific resolution-seeks to increase the ability to distinguish the contributions from motion on timescales slower than a few nanoseconds. However, tumbling of a molecule in solution masks some of these motions. Therefore, we investigate to what extent relaxometry improves timescale resolution, using the "detector" analysis of dynamics. Here, we demonstrate improvements in the characterization of internal dynamics of methyl-bearing side chains by carbon-13 relaxometry in the small protein ubiquitin. We show that relaxometry data leads to better information about nanosecond motions as compared to high-field relaxation data only. Our calculations show that gains from relaxometry are greater with increasing correlation time of rotational diffusion.

Broadband Dynamics of Ubiquitin by Anionic and Cationic Nanoparticle Assisted NMR Spin Relaxation

The quantitative and comprehensive description of the internal dynamics of proteins is critical for understanding their function. Nanoparticle-assisted ¹⁵ N NMR spin relaxation spectroscopy is a new method for the observation of picosecond to microsecond dynamics of proteins when transiently interacting with the surface of the nanoparticles (NPs). The method is applied here to the protein ubiquitin in the presence of anionic and cationic silica NPs (SNPs) of different sizes. The backbone dynamics profiles are reproducible and strikingly similar to each other, indicating that specific protein-SNP interactions are unimportant. The dynamics profiles closely match the sub-nanosecond dynamics S² values observed by model-free analysis of standard ¹⁵ N relaxation of ubiquitin in free solution, indicating that the bulk of the ubiquitin backbone dynamics in solution is confined to sub-nanosecond timescales and, hence, it is dynamically more restrained than previous NMR studies have suggested.

Surprising absence of strong homonuclear coupling at low magnetic field explored by two-field nuclear magnetic resonance spectroscopy

Strong coupling of nuclear spins, which is achieved when their scalar coupling 2 π J is greater than or comparable to the difference Δ ω in their Larmor precession frequencies in an external magnetic field, gives rise to efficient coherent longitudinal polarization transfer. The strong coupling regime can be achieved when the external magnetic field is sufficiently low, as Δ ω is reduced proportional to the field strength. In the present work, however, we demonstrate that in heteronuclear spin systems these simple arguments may not hold, since heteronuclear spin-spin interactions alter the Δ ω value. The experimental method that we use is two-field nuclear magnetic resonance (NMR), exploiting sample shuttling between the high field, at which NMR spectra are acquired, and the low field, where strong couplings are expected and at which NMR pulses can be applied to affect the spin dynamics. By using this technique, we generate zero-quantum spin coherences by means of a nonadiabatic passage through a level anticrossing and study their evolution at the low field. Such zero-quantum coherences mediate the polarization transfer under strong coupling conditions. Experiments performed with a 13 C -labeled amino acid clearly show that the coherent polarization transfer at the low field is pronounced in the 13 C spin subsystem under proton decoupling. However, in the absence of proton decoupling, polarization transfer by coherent processes is dramatically reduced, demonstrating that heteronuclear spin-spin interactions suppress the strong coupling regime, even when the external field is low. A theoretical model is presented, which can model the reported experimental results.

Impact of the Solvent Quality on the Local Dynamics of Soft and Swollen Polymer Nanoparticles Functionalized with Polymer Chains

Grafting polymer chains on the surface of nanoparticles (NPs) is a strategy used to control the interaction between the NPs and their environment. The fate of the resulting particles in a given environment is strongly influenced by the solvent-polymer interaction. The solvent quality affects the behavior, conformation, and dynamics of the grafted polymer chains. However, when this polymer grafting strategy is used to functionalized polymer particles, the influence of solvent quality becomes even more complex; when the grafted polymer chains and the polymer nanoparticles are tethered together, the effect of the solvent quality on the behavior and dynamics of the system depends on the solvent interaction with both polymer components. To explore the relationship between the solvent quality and the dynamics of polymer-functionalized soft polymer NPs, we designed a system based on cross-linked polystyrene (PS) NPs grafted with a canopy of poly(methyl acrylate) (PMA). PS and PMA, two immiscible polymers, can be selectively solvated by using binary mixtures of solvents. NMR spectroscopy was used to address the effect of those selective solvents on the local mobility of the PS-PMA core-canopy NPs and revealed an interplay between the local mobility of the core and the local mobility of the canopy. A selective reduction of the solvent quality for the PMA canopy resulted in the expected reduction of the local mobility of the PMA chains, but also in the slower dynamics of the PS core. Similarly, a selective reduction of the solvent quality for the PS core resulted in a slower dynamics for both the PS core and the PMA canopy.

A temperature-controlled sample shuttle for field-cycling NMR

We present a design for a temperature-controlled sample shuttle for use in NMR measurements at variable magnetic field strength. Accurate temperature control was achieved using a mixture of water-ethylene glycol as a heat transfer fluid, reducing temperature gradients across the sample to < 0.05 °C and minimising convection. Using the sample shuttle, we show how the longitudinal (T₁) and singlet order (T_S) relaxation time constants were measured for two molecules capable of supporting long-lived states, with new record lifetimes observed at low field and above ambient temperatures.

Microscopic Understanding of the Effect of Ionic Liquid on Protein from Molecular Simulation Studies

We have performed molecular dynamics (MD) simulations of the protein α-lactalbumin in aqueous solution containing the ionic liquid (IL) 1-butyl-3-methyl imidazolium tetrafluoroborate ([BMIM][BF₄]) as the cosolvent at different concentrations. Attempts have been made to obtain quantitative understanding of the effects of the IL on the conformational features of the protein as well as the distributions of the IL and water around it. The calculations revealed enhanced rigidity of the protein with reduced conformational fluctuations and increasingly correlated local motions in the presence of the IL. Nonuniform relative population of the BMIM⁺ and BF₄^- ions at the protein surface with respect to that in the bulk solution has been observed. It is demonstrated that exchange of water by the IL around the protein results in rearrangement of the hydrogen bond network at the interface with breaking of protein-water hydrogen bonds and formation of protein-IL hydrogen bonds. Importantly, it is found that the protein forms increased number of stronger salt bridges in the presence of IL. This shows that the formation of a greater number of such stronger salt bridges is the origin behind the enhanced rigidity of the protein in the presence of the IL.

Theoretical and computational framework for the analysis of the relaxation properties of arbitrary spin systems. Application to high-resolution relaxometry

A wide variety of nuclear magnetic resonance experiments rely on the prediction and analysis of relaxation processes. Recently, innovative approaches have been introduced where the sample travels through a broad range of magnetic fields in the course of the experiment, such as dissolution dynamic nuclear polarization or high-resolution relaxometry. Understanding the relaxation properties of nuclear spin systems over orders of magnitude of magnetic fields is essential to rationalize the results of these experiments. For example, during a high-resolution relaxometry experiment, the absence of control of nuclear spin relaxation pathways during the sample transfers and relaxation delays leads to systematic deviations of polarization decays from an ideal mono-exponential decay with the pure longitudinal relaxation rate. These deviations have to be taken into account to describe quantitatively the dynamics of the system. Here, we present computational tools to (1) calculate analytical expressions of relaxation rates for a broad variety of spin systems and (2) use these analytical expressions to correct the deviations arising in high-resolution relaxometry experiments. These tools lead to a better understanding of nuclear spin relaxation, which is required to improve the sensitivity of many pulse sequences, and to better characterize motions in macromolecules.

Boosting the resolution of low-field [Formula: see text] relaxation experiments on intrinsically disordered proteins with triple-resonance NMR

Improving our understanding of nanosecond motions in disordered proteins requires the enhanced sampling of the spectral density function obtained from relaxation at low magnetic fields. High-resolution relaxometry and two-field NMR measurements of relaxation have, so far, only been based on the recording of one- or two-dimensional spectra, which provide insufficient resolution for challenging disordered proteins. Here, we introduce a 3D-HNCO-based two-field NMR experiment for measurements of protein backbone [Formula: see text] amide longitudinal relaxation rates. The experiment provides accurate longitudinal relaxation rates at low field (0.33 T in our case) preserving the resolution and sensitivity typical for high-field NMR spectroscopy. Radiofrequency pulses applied on six different radiofrequency channels are used to manipulate the spin system at both fields. The experiment was demonstrated on the C-terminal domain of [Formula: see text] subunit of RNA polymerase from Bacillus subtilis, a protein with highly repetitive amino-acid sequence and very low dispersion of backbone chemical shifts.

Protein Dynamics from Accurate Low-Field Site-Specific Longitudinal and Transverse Nuclear Spin Relaxation

Nuclear magnetic relaxation provides invaluable quantitative site-specific information on the dynamics of complex systems. Determining dynamics on nanosecond time scales requires relaxation measurements at low magnetic fields incompatible with high-resolution NMR. Here, we use a two-field NMR spectrometer to measure carbon-13 transverse and longitudinal relaxation rates at a field as low as 0.33 T (proton Larmor frequency 14 MHz) in specifically labeled side chains of the protein ubiquitin. The use of radiofrequency pulses enhances the accuracy of measurements as compared to high-resolution relaxometry approaches, where the sample is moved in the stray field of the superconducting magnet. Importantly, we demonstrate that accurate measurements at a single low magnetic field provide enough information to characterize complex motions on low nanosecond time scales, which opens a new window for the determination of site-specific nanosecond motions in complex systems such as proteins.

Reducing bias in the analysis of solution-state NMR data with dynamics detectors

Nuclear magnetic resonance (NMR) is sensitive to dynamics on a wide range of correlation times. Recently, we have shown that analysis of relaxation rates via fitting to a correlation function with a small number of exponential terms could yield a biased characterization of molecular motion in solid-state NMR due to limited sensitivity of experimental data to certain ranges of correlation times. We introduced an alternative approach based on "detectors" in solid-state NMR, for which detector responses characterize motion for a range of correlation times and reduce potential bias resulting from the use of simple models for the motional correlation functions. Here, we show that similar bias can occur in the analysis of solution-state NMR relaxation data. We have thus adapted the detector approach to solution-state NMR, specifically separating overall tumbling motion from internal motions and accounting for contributions of chemical exchange to transverse relaxation. We demonstrate that internal protein motions can be described with detectors when the overall motion and the internal motions are statistically independent. We illustrate the detector analysis on ubiquitin with typical relaxation data sets recorded at a single high magnetic field or at multiple high magnetic fields and compare with results of model-free analysis. We also compare our methodology to LeMaster's method of dynamics analysis.

15N transverse relaxation measurements for the characterization of µs-ms dynamics are deteriorated by the deuterium isotope effect on 15N resulting from solvent exchange

¹⁵N R₂ relaxation measurements are key for the elucidation of the dynamics of both folded and intrinsically disordered proteins (IDPs). Here we show, on the example of the intrinsically disordered protein α-synuclein and the folded domain PDZ2, that at physiological pH and near physiological temperatures amide-water exchange can severely skew Hahn-echo based ¹⁵N R₂ relaxation measurements as well as low frequency data points in CPMG relaxation dispersion experiments. The nature thereof is the solvent exchange with deuterium in the sample buffer, which modulates the ¹⁵N chemical shift tensor via the deuterium isotope effect, adding to the apparent relaxation decay which leads to systematic errors in the relaxation data. This results in an artificial increase of the measured apparent ¹⁵N R₂ rate constants-which should not be mistaken with protein inherent chemical exchange contributions, R_ex, to ¹⁵N R₂. For measurements of ¹⁵N R₂ rate constants of IDPs and folded proteins at physiological temperatures and pH, we recommend therefore the use of a very low D₂O molar fraction in the sample buffer, as low as 1%, or the use of an external D₂O reference along with a modified ¹⁵N R₂ Hahn-echo based experiment. This combination allows for the measurement of R_ex contributions to ¹⁵N R₂ originating from conformational exchange in a time window from µs to ms.

Analysis of NMR Spin-Relaxation Data Using an Inverse Gaussian Distribution Function

Spin relaxation in solution-state NMR spectroscopy is a powerful approach to explore the conformational dynamics of biological macromolecules. Probability distribution functions for overall or internal correlation times have been used previously to model spectral density functions central to spin-relaxation theory. Applications to biological macromolecules rely on transverse relaxation rate constants, and when studying nanosecond timescale motions, sampling at ultralow frequencies is often necessary. Consequently, appropriate distribution functions necessitate spectral density functions that are accurate and convergent as frequencies approach zero. In this work, the inverse Gaussian probability distribution function is derived from general properties of spectral density functions at low and high frequencies for macromolecules in solution, using the principle of maximal entropy. This normalized distribution function is first used to calculate the correlation function, followed by the spectral density function. The resulting model-free spectral density functions are finite at a frequency of zero and can be used to describe distributions of either overall or internal correlation times using the model-free ansatz. To validate the approach, ¹⁵N spin-relaxation data for the bZip transcription factor domain of the Saccharomyces cerevisiae protein GCN4, in the absence of cognate DNA, were analyzed using the inverse Gaussian probability distribution for intramolecular correlation times. The results extend previous models for the conformational dynamics of the intrinsically disordered, DNA-binding region of the bZip transcription factor domain.

Simple and Robust Study of Backbone Dynamics of Crystalline Proteins Employing 1H-15N Dipolar Coupling Dispersion

We report a new solid-state multidimensional NMR approach based on the cross-polarization with variable-contact pulse sequence [ Paluch , P. ; Pawlak , T. ; Amoureux , J.-P. ; Potrzebowski , M. J. J. Magn. Reson. 233 , 2013 , 56 ], with ¹H inverse detection and very fast magic angle spinning (ν_R = 60 kHz), dedicated to the measurement of local molecular motions of ¹H-¹⁵N vectors. The introduced three-dimensional experiments, ¹H-¹⁵N-¹H and hCA(N)H, are particularly useful for the study of molecular dynamics of proteins and other complex structures. The applicability and power of this methodology have been revealed by employing as a model sample the GB-1 small protein doped with Na₂CuEDTA. The results clearly prove that the dispersion of ¹H-¹⁵N dipolar coupling constants well correlates with higher order structure of the protein. Our approach complements the conventional studies and offers a fast and reasonably simple method.

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

Many of the functions of biomacromolecules can be rationalized by the characterization of their conformational energy landscapes: the structures of the dominant states, transitions between states and motions within states. Nuclear magnetic resonance (NMR) spectroscopy is the technique of choice to study internal motions in proteins. The determination of motions on picosecond to nanosecond timescales requires the measurement of nuclear spin relaxation rates at multiple magnetic fields. High sensitivity and resolution are obtained only at high magnetic fields, so that, until recently, site-specific relaxation rates in biomolecules were only measured over a narrow range of high magnetic fields. This limitation was particularly striking for the quantification of motions on nanosecond timescales, close to the correlation time for overall rotational diffusion. High-resolution relaxometry is an emerging technique to investigate picosecond-nanosecond motions of proteins. This approach uses a high-field NMR spectrometer equipped with a sample shuttle device, which allows for the measurement of the relaxation rate constants at low magnetic fields, while preserving the sensitivity and resolution of a high-field NMR spectrometer. The combined analysis of high-resolution relaxometry and standard high-field relaxation data provides a more accurate description of the dynamics of proteins, in particular in the nanosecond range. The purpose of this chapter is to describe how to perform high-resolution relaxometry experiments and how to analyze the rates measured with this technique.

Optimized "detectors" for dynamics analysis in solid-state NMR

Relaxation in nuclear magnetic resonance (NMR) results from stochastic motions that modulate anisotropic NMR interactions. Therefore, measurement of relaxation-rate constants can be used to characterize molecular-dynamic processes. The motion is often characterized by Markov processes using an auto-correlation function, which is assumed to be a sum of multiple decaying exponentials. We have recently shown that such a model can lead to severe misrepresentation of the real motion, when the real correlation function is more complex than the model. Furthermore, multiple distributions of motion may yield the same set of dynamics data. Therefore, we introduce optimized dynamics "detectors" to characterize motions which are linear combinations of relaxation-rate constants. A detector estimates the average or total amplitude of motion for a range of motional correlation times. The information obtained through the detectors is less specific than information obtained using an explicit model, but this is necessary because the information contained in the relaxation data is ambiguous, if one does not know the correct motional model. On the other hand, if one has a molecular dynamics trajectory, one may calculate the corresponding detector responses, allowing direct comparison to experimental NMR dynamics analysis. We describe how to construct a set of optimized detectors for a given set of relaxation measurements. We then investigate the properties of detectors for a number of different data sets, thus gaining an insight into the actual information content of the NMR data. Finally, we show an example analysis of ubiquitin dynamics data using detectors, using the DIFRATE software.

Field-cycling NMR experiments in an ultra-wide magnetic field range: relaxation and coherent polarization transfer

An experimental method is described allowing fast field-cycling Nuclear Magnetic Resonance (NMR) experiments over a wide range of magnetic fields from 5 nT to 10 T. The method makes use of a hybrid technique: the high field range is covered by positioning the sample in the inhomogeneous stray field of the NMR spectrometer magnet. For fields below 2 mT a magnetic shield is mounted on top of the spectrometer; inside the shield the magnetic field is controlled by a specially designed coil system. This combination allows us to measure T1-relaxation times and nuclear Overhauser effect parameters over the full range in a routine way. For coupled proton-carbon spin systems relaxation with a common T1 is found at low fields, where the spins are "strongly coupled". In some cases, experiments at ultralow fields provide access to heteronuclear long-lived spin states. Efficient coherent polarization transfer is seen for proton-carbon spin systems at ultralow fields as follows from the observation of quantum oscillations in the polarization evolution. Applications to analysis and the manipulation of heteronuclear spin systems are discussed.

Atomic resolution conformational dynamics of intrinsically disordered proteins from NMR spin relaxation

Nuclear magnetic resonance (NMR) spectroscopy is one of the most powerful experimental approaches for investigating the conformational behaviour of intrinsically disordered proteins (IDPs). IDPs represent a significant fraction of all proteomes, and, despite their importance for understanding fundamental biological processes, the molecular basis of their activity still remains largely unknown. The functional mechanisms exploited by IDPs in their interactions with other biomolecules are defined by their intrinsic dynamic modes and associated timescales, justifying the considerable interest over recent years in the development of technologies adapted to measure and describe this behaviour. NMR spin relaxation delivers information-rich, site-specific data reporting on conformational fluctuations occurring throughout the molecule. Here we review recent progress in the use of ¹⁵N relaxation to identify local backbone dynamics and long-range chain-like motions in unfolded proteins.

Anion induced conformational preference of Cα NN motif residues in functional proteins

Among different ligand binding motifs, anion binding C^α NN motif consisting of peptide backbone atoms of three consecutive residues are observed to be important for recognition of free anions, like sulphate or biphosphate and participate in different key functions. Here we study the interaction of sulphate and biphosphate with C^α NN motif present in different proteins. Instead of total protein, a peptide fragment has been studied keeping C^α NN motif flanked in between other residues. We use classical force field based molecular dynamics simulations to understand the stability of this motif. Our data indicate fluctuations in conformational preferences of the motif residues in absence of the anion. The anion gives stability to one of these conformations. However, the anion induced conformational preferences are highly sequence dependent and specific to the type of anion. In particular, the polar residues are more favourable compared to the other residues for recognising the anion.

Ultra-wide range field-dependent measurements of the relaxivity of Gd1-xEuxVO4 nanoparticle contrast agents using a mechanical sample-shuttling relaxometer

The current trend for Magnetic Resonance Imaging points towards higher magnetic fields. Even though sensitivity and resolution are increased in stronger fields, T1 contrast is often reduced, and this represents a challenge for contrast agent design. Field-dependent measurements of relaxivity are thus important to characterize contrast agents. At present, the field-dependent curves of relaxivity are usually carried out in the field range of 0 T to 2 T, using fast field cycling relaxometers. Here, we employ a high-speed sample shuttling device to switch the magnetic fields experienced by the nuclei between virtually zero field, and the center of any commercial spectrometer. We apply this approach on rare-earth (mixed Gadolinium-Europium) vanadate nanoparticles, and obtain the dispersion curves from very low magnetic field up to 11.7 T. In contrast to the relaxivity profiles of Gd chelates, commonly used for clinical applications, which display a plateau and then a decrease for increasing magnetic fields, these nanoparticles provide maximum contrast enhancement for magnetic fields around 1–1.5 T. These field-dependent curves are fitted using the so-called Magnetic Particle (MP) model and the extracted parameters discussed as a function of particle size and composition. We finally comment on the new possibilities offered by this approach.

19 F NMR transverse and longitudinal relaxation filter experiments for screening: a theoretical and experimental analysis

Ligand-based ¹⁹ F NMR screening represents an efficient approach for performing binding assays. The high sensitivity of the methodology to receptor binding allows the detection of weak affinity ligands. The observable NMR parameters that are typically used are the ¹⁹ F transverse relaxation rate and isotropic chemical shift. However, there are few cases where the ¹⁹ F longitudinal relaxation rate should also be used. A theoretical and experimental analysis of the ¹⁹ F NMR transverse and longitudinal relaxation rates at different magnetic fields is presented along with proposed methods for improving the sensitivity and dynamic range of these experiments applied to fragment-based screening. Copyright © 2016 John Wiley & Sons, Ltd.