Quantitative analysis of conformational exchange contributions to 1H-15N multiple-quantum relaxation using field-dependent measurements. Time scale and structural characterization of exchange in a calmodulin C-terminal domain mutant

Multiple-quantum spin relaxation is a sensitive probe for correlated conformational exchange dynamics on microsecond to millisecond time scales in biomolecules. We measured differential 1H-15N multiple-quantum relaxation rates for the backbone amide groups of the E140Q mutant of the C-terminal domain of calmodulin at three static magnetic field strengths. The differential multiple-quantum relaxation rates range between -88.7 and 92.7 s(-1), and the mean and standard deviation are 7.0 +/- 24 s(-1), at a static magnetic field strength of 14.1 T. Together with values of the 1H and 15N chemical shift anisotropies (CSA) determined separately, the field-dependent data enable separation of the different contributions from dipolar-dipolar, CSA-CSA, and conformational exchange cross-correlated relaxation mechanisms to the differential multiple-quantum relaxation rates. The procedure yields precise quantitative information on the dominant conformational exchange contributions observed in this protein. The field-dependent differences between double- and zero-quantum relaxation rates directly benchmark the rates of conformational exchange, showing that these are fast on the chemical shift time scale for the large majority of residues in the protein. Further analysis of the differential 1H-15N multiple-quantum relaxation rates using previously determined exchange rate constants and populations, obtained from 15N off-resonance rotating-frame relaxation data, enables extraction of the product of the chemical shift differences between the resonance frequencies of the 1H and 15N spins in the exchanging conformations, deltasigma(H)deltasigma(N). Thus, information on the 1H chemical shift differences is obtained, while circumventing complications associated with direct measurements of conformational exchange effects on 1H single-quantum coherences in nondeuterated proteins. The method significantly increases the information content available for structural interpretation of the conformational exchange process, partly because deltasigma(H)deltasigma(N) is a signed quantity, and partly because two chemical shifts are probed simultaneously. The present results support the hypothesis that the exchange in the calcium-loaded state of the E140Q mutant involves conformations similar to those of the wild-type apo (closed) and calcium-loaded (open) states.     

Multiple-quantum relaxation dispersion NMR spectroscopy probing millisecond time-scale dynamics in proteins: theory and application

New relaxation dispersion experiments are presented that probe millisecond time-scale dynamical processes in proteins. The experiments measure the relaxation of (1)H-(15)N multiple-quantum coherence as a function of the rate of application of either (1)H or (15)N refocusing pulses during a constant time relaxation interval. In contrast to the dispersion profiles generated from more conventional (15)N((1)H) single-quantum relaxation experiments that depend on changes in (15)N((1)H) chemical shifts between exchanging states, (1)H-(15)N multiple-quantum dispersions are sensitive to changes in the chemical environments of both (1)H and (15)N spins. The resulting multiple-quantum relaxation dispersion profiles can, therefore, be quite different from those generated by single-quantum experiments, so that an analysis of both single- and multiple-quantum profiles together provides a powerful approach for obtaining robust measures of exchange parameters. This is particularly the case in applications to protonated proteins where other methods for studying exchange involving amide proton spins are negatively influenced by contributions from neighboring protons. The methodology is demonstrated on protonated and perdeuterated samples of a G48M mutant of the Fyn SH3 domain that exchanges between folded and unfolded states in solution.     

Characterization of conformational exchange of a histidine side chain: protonation, rotamerization, and tautomerization of His61 in plastocyanin from Anabaena variabilis

A model describing conformational exchange of His 61 in plastocyanin from Anabaena variabilis is presented. A detailed picture of the exchange dynamics has been obtained using solution NMR relaxation measurements, chemical shift titrations, and structural information provided by a high-resolution crystal structure of the protein. A three-site model for chemical exchange that involves interconversion among the tautomeric and protonated forms of the histidine side chain with rates that are fast on the NMR chemical shift time scale can account for all of the data. In general, in the limit of fast exchange, it is not possible to obtain separate measures of chemical shift differences and populations of the participating states using NMR. However, we show here that when the data mentioned above are combined, it is possible to extract values of all of the parameters that characterize the exchange process, including rates, populations, and chemical shift changes, and to provide cross-validations that establish their accuracy. The methodology is generally applicable to the study of histidine side chain dynamics, which can play an important functional role in many protein systems.     

Time scales of slow motions in ubiquitin explored by heteronuclear double resonance

Understanding how proteins function at the atomic level relies in part on a detailed characterization of their dynamics. Ubiquitin, a small single-domain protein, displays rich dynamic properties over a wide range of time scales. In particular, several regions of ubiquitin show the signature of chemical exchange, including the hydrophobic patch and the β4-α2 loop, which are both involved in many interactions. Here, we use multiple-quantum relaxation techniques to identify the extent of chemical exchange in ubiquitin. We employ our recently developed heteronuclear double resonance method to determine the time scales of motions that give rise to chemical exchange. Dispersion profiles are obtained for the backbone NH(N) pairs of several residues in the hydrophobic patch and the β4-α2 loop, as well as the C-terminus of helix α1. We show that a single time scale (ca. 50 μs) can be used to fit the data for most residues. Potential mechanisms for the propagation of motions and the possible extent of correlation of these motions are discussed.     

A simple method to predict protein flexibility using secondary chemical shifts

Protein motions play a critical role in many biological processes, such as enzyme catalysis, allosteric regulation, antigen-antibody interactions, and protein-DNA binding. NMR spectroscopy occupies a unique place among methods for investigating protein dynamics due to its ability to provide site-specific information about protein motions over a large range of time scales. However, most NMR methods require a detailed knowledge of the 3D structure and/or the collection of additional experimental data (NOEs, T1, T2, etc.) to accurately measure protein dynamics. Here we present a simple method based on chemical shift data that allows accurate, quantitative, site-specific mapping of protein backbone mobility without the need of a three-dimensional structure or the collection and analysis of NMR relaxation data. Further, we show that this chemical shift method is able to quantitatively predict per-residue RMSD values (from both MD simulations and NMR structural ensembles) as well as model-free backbone order parameters.     

The phases of polymers as determined by NMR

Nuclear magnetic resonance (NMR) spectroscopy has been used to study the morphology and dynamics in semicrystalline polymers. Dynamics may be observed through NMR relaxation rates that are sensitive to motions in the 1–10⁸ Hz range, or through modulation of anisotropic magnetic interactions, such as the chemical shift and dipole-dipole interactions. Morphological structure may be inferred through NMR measurements of polymer dynamics or investigated directly through studies of the magnetic interactions. Here, we discuss the study of morphological structure in semicrystalline polymers using NMR, and review results on poly(ethylene terephthalate) that address the question of the number of phases in this semicrystalline polymer.This work was funded by the Office of Naval Research.     

Hydration dynamics and time scales of coupled water-protein fluctuations

We report experimental and theoretical studies on water and protein dynamics following photoexcitation of apomyoglobin. Using site-directed mutation and with femtosecond resolution, we experimentally observed relaxation dynamics with a biphasic distribution of time scales, 5 and 87 ps, around the site Trp7. Theoretical studies using both linear response and direct nonequilibrium molecular dynamics (MD) calculations reproduced the biphasic behavior. Further constrained MD simulations with either frozen protein or frozen water revealed the molecular mechanism of slow hydration processes and elucidated the role of protein fluctuations. Observation of slow water dynamics in MD simulations requires protein flexibility, regardless of whether the slow Stokes shift component results from the water or protein contribution. The initial dynamics in a few picoseconds represents fast local motions such as reorientations and translations of hydrating water molecules, followed by slow relaxation involving strongly coupled water-protein motions. We observed a transition from one isomeric protein configuration to another after 10 ns during our 30 ns ground-state simulation. For one isomer, the surface hydration energy dominates the slow component of the total relaxation energy. For the other isomer, the slow component is dominated by protein interactions with the chromophore. In both cases, coupled water-protein motion is shown to be necessary for observation of the slow dynamics. Such biologically important water-protein motions occur on tens of picoseconds. One significant discrepancy exists between theory and experiment, the large inertial relaxation predicted by simulations but clearly absent in experiment. Further improvements required in the theoretical model are discussed.     

Weak and Transient Protein Interactions Determined by Solid‐State NMR

Despite their roles in controlling many cellular processes, weak and transient interactions between large structured macromolecules and disordered protein segments cannot currently be characterized at atomic resolution by X‐ray crystallography or solution NMR. Solid‐state NMR does not suffer from the molecular size limitations affecting solution NMR, and it can be applied to molecules in different aggregation states, including non‐crystalline precipitates and sediments. A solid‐state NMR approach based on high magnetic fields, fast magic‐angle sample spinning, and deuteration provides chemical‐shift and relaxation mapping that enabled the characterization of the structure and dynamics of the transient association between two regions in an 80 kDa protein assembly. This led to direct verification of a mechanism of regulation of E. coli DNA metabolism.     

Protein tyrosine phosphatase oligomerization studied by a combination of 15N NMR relaxation and 129Xe NMR. Effect of buffer containing arginine and glutamic acid

15N NMR relaxation and 129Xe NMR chemical shift measurements offer complementary information to study weak protein-protein interactions. They have been applied to study the oligomerization equilibrium of a low-molecular-weight protein tyrosine phosphatase in the presence of 50 mM arginine and 50 mM glutamic acid. These experimental conditions are shown to enhance specific protein-protein interactions while decreasing nonspecific aggregation. In addition, 129Xe NMR chemical shifts become selective reporters of one particular oligomer in the presence of arginine and glutamic acid, indicating that a specific Xe binding site is created in the oligomerization process. It is suggested that the multiple effects of arginine and glutamic acid are related to their effective excluded volume that favors specific protein association and the destabilization of partially unfolded forms that preferentially interact with xenon and are responsible for nonspecific protein aggregation.     

New probes of ligand flexibility in drug design: transferred (13)C CSA-dipolar cross-correlated relaxation at natural abundance

Understanding the impact of molecular flexibility remains an important outstanding problem in rational drug design. Toward this end, we present new NMR relaxation methods that describe ligand flexibility at the atomic level. Specifically, we measure natural abundance (13)C cross-correlated relaxation parameters for ligands in rapid exchange between the free and receptor-bound states. The rapid exchange transfers the bound state relaxation parameters to the free state, such that a comparison of relaxation rates in the absence and presence of protein receptor yields site-specific information concerning the bound ligand flexibility. We perform these measurements for aromatic carbons, which are highly prevalent in drug-like molecules and demonstrate significant cross-correlated relaxation between the (13)C-(1)H dipole-dipole (DD) and (13)C chemical shift anisotropy (CSA) relaxation mechanisms. Our use of natural abundance measurements addresses the practical difficulties of obtaining isotope-labeled ligands in pharmaceutical research settings. We demonstrate our methods on a small ligand of the 42 kDa kinase domain of the p38 MAP kinase. We show that exchange-transferred cross-correlated relaxation measurements are not only sensitive probes of bound ligand flexibility but also offer complementary advantages over standard R(1) = 1/T(1) and R(2) = 1/T(2) measurements. The ligand flexibility profiles obtained from the relaxation data can help assess the influence of dynamics on ligand potency or pharmacokinetic properties or both, and thereby include inherent molecular flexibility in drug design.     

Site-specific variations of carbonyl chemical shift anisotropies in proteins

By combining molecular dynamics (MD) simulation with a novel extended density functional theory method, we calculate site-specific carbonyl chemical shift tensors in the SMN Tudor domain. We formulate a simple model for the C' chemical shift anisotropy (CSA) based solely on the isotropic chemical shift. Using this simple chemical shift tensor model and the MD simulation, an accurate prediction of transverse C'/N-H cross-correlated relaxation rates can be obtained.     

Temperature- and solvation-dependent dynamics of liquid sulfur dioxide studied through the ultrafast optical Kerr effect

The ultrafast dynamics of liquid sulphur dioxide have been studied over a wide temperature range and in solution. The optically heterodyne-detected and spatially masked optical Kerr effect (OKE) has been used to record the anisotropic and isotropic third-order responses, respectively. Analysis of the anisotropic response reveals two components, an ultrafast nonexponential relaxation and a slower exponential relaxation. The slower component is well described by the Stokes-Einstein-Debye equation for diffusive orientational relaxation. The simple form of the temperature dependence and the agreement between collective (OKE) and single molecule (e.g., NMR) measurements of the orientational relaxation time suggests that orientational pair correlation is not significant in this liquid. The relative contributions of intermolecular interaction-induced and single-molecule orientational dynamics to the ultrafast part of the spectral density are discussed. Single-molecule librational-orientational dynamics appear to dominate the ultrafast OKE response of liquid SO2. The temperature-dependent OKE data are transformed to the frequency domain to yield the Raman spectral density for the low-frequency intermolecular modes. These are bimodal with the lowest-frequency component arising from diffusive orientational relaxation and a higher-frequency component connected with the ultrafast time-domain response. This component is characterized by a shift to higher frequency at lower temperature. This result is analyzed in terms of a harmonic librational oscillator model, which describes the data accurately. The observed spectral shifts with temperature are ascribed to increasing intermolecular interactions with increasing liquid density. Overall, the dynamics of liquid SO2 are found to be well described in terms of molecular orientational relaxation which is controlled over every relevant time range by intermolecular interactions.     

Using Cross-Correlated Spin Relaxation to Characterize Backbone Dihedral Angle Distributions of Flexible Protein Segments

Crucial to the function of proteins is their existence as conformational ensembles sampling numerous and structurally diverse substates. Despite this widely accepted notion there is still a high demand for meaningful and reliable approaches to characterize protein ensembles in solution. As it is usually conducted in solution, NMR spectroscopy offers unique possibilities to address this challenge. Particularly, cross-correlated relaxation (CCR) effects have long been established to encode both protein structure and dynamics in a compelling manner. However, this wealth of information often limits their use in practice as structure and dynamics might prove difficult to disentangle. Using a modern Maximum Entropy (MaxEnt) reweighting approach to interpret CCR rates of Ubiquitin, we demonstrate that these uncertainties do not necessarily impair resolving CCR-encoded structural information. Instead, a suitable balance between complementary CCR experiments and prior information is found to be the most crucial factor in mapping backbone dihedral angle distributions. Experimental and systematic deviations such as oversimplified dynamics appear to be of minor importance. Using Ubiquitin as an example, we demonstrate that CCR rates are capable of characterizing rigid and flexible residues alike, indicating their unharnessed potential in studying disordered proteins.     

Predicting chemical shifts with graph neural networks

Inferring molecular structure from Nuclear Magnetic Resonance (NMR) measurements requires an accurate forward model that can predict chemical shifts from 3D structure. Current forward models are limited to specific molecules like proteins and state-of-the-art models are not differentiable. Thus they cannot be used with gradient methods like biased molecular dynamics. Here we use graph neural networks (GNNs) for NMR chemical shift prediction. Our GNN can model chemical shifts accurately and capture important phenomena like hydrogen bonding induced downfield shift between multiple proteins, secondary structure effects, and predict shifts of organic molecules. Previous empirical NMR models of protein NMR have relied on careful feature engineering with domain expertise. These GNNs are trained from data alone with no feature engineering yet are as accurate and can work on arbitrary molecular structures. The models are also efficient, able to compute one million chemical shifts in about 5 seconds. This work enables a new category of NMR models that have multiple interacting types of macromolecules.

This model can predict chemical shifts on proteins and small molecules purely from atom elements and coordinates. It can capture important phenomena like hydrogen bonding induced downfield shift, thus can be used to infer intermolecular interactions.     

Microsecond time-scale conformational exchange in proteins: using long molecular dynamics trajectory to simulate NMR relaxation dispersion data

With the advent of ultra-long MD simulations it becomes possible to model microsecond time-scale protein dynamics and, in particular, the exchange broadening effects (R(ex)) as probed by NMR relaxation dispersion measurements. This new approach allows one to identify the exchanging species, including the elusive "excited states". It further helps to map out the exchange network, which is potentially far more complex than the commonly assumed 2- or 3-site schemes. Under fast exchange conditions, this method can be useful for separating the populations of exchanging species from their respective chemical shift differences, thus paving the way for structural analyses. In this study, recent millisecond-long MD trajectory of protein BPTI (Shaw et al. Science 2010, 330, 341) is employed to simulate the time variation of amide (15)N chemical shifts. The results are used to predict the exchange broadening of (15)N lines and, more generally, the outcome of the relaxation dispersion measurements using Carr-Purcell-Meiboom-Gill sequence. The simulated R(ex) effect stems from the fast (~10-100 μs) isomerization of the C14-C38 disulfide bond, in agreement with the prior experimental findings (Grey et al. J. Am. Chem. Soc. 2003, 125, 14324).     

Explanation of spin-lattice relaxation rates of spin labels obtained with multifrequency saturation recovery EPR

Electron paramagnetic resonance (EPR) pulsed saturation recovery (pSR) measurements of spin-lattice relaxation rates have been made on nitroxide-containing fatty acids embedded in lipid bilayers by Hyde and co-workers. The data have been collected for a number of spin-labeled fatty acids at several microwave spectrometer frequencies (from 2 to 35 GHz). We compare these spin-lattice relaxation rates to those predicted by the Redfield theory incorporating several mechanisms. The dominant relaxation mechanism at low spectrometer frequencies is the electron-nuclear dipolar (END) process, with spin rotation (SR), chemical shift anisotropy (CSA), and a generalized spin diffusion (GSD) mechanism all contributing. The use of a wide range of spectrometer frequencies makes clear that the dynamics cannot be modeled adequately by rigid-body isotropic rotational motion. The dynamics of rigid-body anisotropic rotational motion is sufficient to explain the experimental relaxation rates within the experimental error. More refined models of the motion could have been considered, and our analysis does not rule them out. However, the results demonstrate that measurements at only two suitably chosen spectrometer frequencies are sufficient to distinguish anisotropic from isotropic motion. The results presented demonstrate that the principal mechanisms responsible for anisotropically driven spin-lattice relaxation are well understood in the liquids regime.     

Anesthetic modulation of protein dynamics: insight from an NMR study

Mistic (membrane integrating sequence for translation of integral membrane protein constructs) comprises the four-alpha-helix bundle scaffold found in the transmembrane domains of the Cys-loop receptors that are plausible targets for general anesthetics. Nuclear magnetic resonance (NMR) studies of anesthetic halothane interaction with Mistic in dodecyl phosphocholine (DPC) micelles provide an experimental basis for understanding molecular mechanisms of general anesthesia. Halothane was found to interact directly with Mistic, mostly in the interfacial loop regions. Although the presence of halothane had little effect on Mistic structure, (15)N NMR relaxation dispersion measurements revealed that halothane affected Mistic's motion on the microsecond-millisecond time scale. Halothane shifted the equilibrium of chemical exchange in some residues and made the exchange faster or slower in comparison to the original state in the absence of halothane. The motion on the microsecond-millisecond time scale in several residues disappeared in response to the addition of halothane. Most of the residues experiencing halothane-induced dynamics changes also exhibited profound halothane-induced changes in chemical shift, suggesting that dynamics modification of these residues might result from their direct interaction with halothane molecules. Allosteric modulation by halothane also contributed to dynamics changes, as reflected in residues I52 and Y82 where halothane introduction brought about dynamics changes but not chemical shift changes. The study suggests that inhaled general anesthetics could act on proteins via altering protein motion on the microsecond-millisecond time scale, especially motion in the flexible loops that link different alpha helices. The validation of anesthetic effect on protein dynamics that are potentially correlated with protein functions is a critical step in unraveling the mechanisms of anesthetic action on proteins.     

Probing polar solvation dynamics in proteins: a molecular dynamics simulation analysis

Measurements of time-resolved Stokes shifts on picosecond to nanosecond time scales have been used to probe the polar solvation dynamics of biological systems. Since it is difficult to decompose the measurements into protein and solvent contributions, computer simulations are useful to aid in understanding the details of the molecular behavior. Here we report the analysis of simulations of the electrostatic interactions of the rest of the protein and the solvent with 11 residues of the immunoglobulin binding domain B1 of protein G. It is shown that the polar solvation dynamics are position-dependent and highly heterogeneous. The contributions due to interactions with the protein and with the solvent are determined. The solvent contributions are found to vary from negligible after a few picoseconds to dominant on a scale of hundreds of picoseconds. The origin for the latter is found to involve coupled hydration and protein conformational dynamics. The resulting microscopic picture demonstrates that a wide range of possibilities have to be considered in the interpretation of time-resolved Stokes shift measurements.     

Nuclear spin relaxation due to chemical shift anisotropy of gas-phase 129Xe

Nuclear spin relaxation provides detailed dynamical information on molecular systems and materials. Here, first-principles modeling of the chemical shift anisotropy (CSA) relaxation time for the prototypic monoatomic (129)Xe gas is carried out, both complementing and predicting the results of NMR measurements. Our approach is based on molecular dynamics simulations combined with pre-parametrized ab initio binary nuclear shielding tensors, an "NMR force field". By using the Redfield relaxation formalism, the simulated CSA time correlation functions lead to spectral density functions that, for the first time, quantitatively determine the experimental spin-lattice relaxation times T(1). The quality requirements on both the Xe-Xe interaction potential and binary shielding tensor are investigated in the context of CSA T(1). Persistent dimers Xe(2) are found to be responsible for the CSA relaxation mechanism in the low-density limit of the gas, completely in line with the earlier experimental findings.     

Determination of carbon-13 chemical shielding tensor in the liquid state by combining NMR relaxation experiments and quantum chemical calculations

Based on multifield NMR relaxation measurements and quantum chemistry calculations, a strategy aiming at the determination of the chemical shielding tensor (CST) in the liquid state is described. Brownian motions in the liquid state restrict the direct observation of CST to a third of its trace (isotropic shift), and even if CST can be probed indirectly through some spin relaxation rates (specific longitudinal relaxation rates, dipolar chemical shift anisotropy (CSA) cross-correlation rates), an insufficient number of experimental parameters prevents its complete determination. This lack of information can be compensated by using quantum chemical calculations so as to obtain the molecular CST orientation even if a relatively modest level of computation is used. As relaxation parameters involve a dynamic part, a prerequisite is the determination of the molecular anisotropic reorientation which can be obtained independently from dipolar cross-relaxation rates. A polycyclic molecule exhibiting a well-characterized anisotropic reorientation serves as an example for such a study, and some (but not all) carbon-13 chemical shielding tensors can be accurately determined. A comparison with solid-state NMR data and numerous chemical quantum calculations are presented.