Geometric Approximation: A New Computational Approach To Characterize Protein Dynamics from NMR Adiabatic Relaxation Dispersion Experiments

On the geometric phase effects on time evolution of the density matrix during modulated radiofrequency pulses

In this work the effect of the geometric phase on time evolution of the density matrix was evaluated during nonadiabatic radiofrequency (RF) pulses with Sine amplitude modulation (AM) and Cosine frequency modulation (FM) functions of the RAFF (Relaxations Along a Fictitious Field) family, and the polarization between two energy level ½ spin system coupled by dipolar interaction was evaluated during the application of RF irradiation. The dependencies of the diagonal density matrix elements and the polarization on the rotational correlation times and the time during RF pulses were evaluated. The general treatment of the density matrix elements along with the polarization generated during RF pulses was unavailable thus far, and for the first time was here derived for the nonadiabatic case of the RAFF pulses. The current formalism could be extended to other AM and FM RF waveforms, including the adiabatic RF pulses which are widely used in magnetic resonance (MR). We demonstrate that the sub-geometric phases (SGP) influence the density matrix elements and thus the polarization generated during the application of RF AM and FM pulses. The corrections to describe the SGP influence of the density matrix elements developed in this work could be essential for determination of MR fundamental parameters necessary for evaluation of tissue contrasts in vivo in MRI and for protein dynamics characterization in high resolution NMR, where AM and FM RF pulses are frequently utilized.

Complete solution for rotating frame relaxation functions during adiabatic pulses

During adiabatic full passage (AFP) radiofrequency (RF) pulses the relaxation functions are conventionally treated in the Tilting Doubly Rotating Frame (TDRF), or the second rotating frame (SRF) of reference. Such a description is adequate when during the adiabatic passage the magnetization M is perfectly aligned with the time dependent effective magnetic field, B(1)eff(t), leading to T1ρ(t) relaxation, or evolves on a plane perpendicular to B(1)eff(t), leading to T2ρ(t) relaxation. Time evolution of B(1)eff(t) results in formation of a fictitious magnetic field, which is typically neglected during the AFP pulses operating in adiabatic regime, i.e., given that the adiabatic condition |γ-1dα(1)(t)/dt| ≪ B(1)eff(t) is well satisfied. Here α(1)(t) is the angle between B(1)eff(t) and the axis of quantization of the first rotating frame (FRF) z', and dα(1)(t)/dt is the angular velocity. When the fictitious field component cannot be neglected, for the adequate description of relaxation during AFP pulses the solutions for the relaxation functions in a multi-fold rotating frame are necessary. Such a general treatment is currently unavailable for adiabatic RF pulses. Here, we obtain the solution for the relaxation functions in the Tilting Triply Rotating Frame (TTRF) during the Hyperbolic Secant (HS) pulses of the HSn family, HS1 and HS4, where n is the stretching factor. We show that the contribution to the relaxations originating from the non-negligible magnitude of the fictitious field depends on the pulse modulation functions of the AFP pulses and the parameters of the pulses. The corrections to describe the relaxations are given, which may be relevant in specific experimental setups especially for high-resolution NMR.

Role of pH in Modulating RNA-Protein Interactions in TRBP2-dsRBD2: An Interplay between Conformational Dynamics and Electrostatic Interactions

Understanding RNA-protein interactions is crucial for uncovering the mechanisms of cellular processes and can provide insights into the basis of various diseases, paving the way for the development of targeted therapeutic interventions. Exposure to stress conditions, such as hypoxia, leads to a drop in intracellular pH, which, in turn, alters the ionization states of amino acid residues and RNA bases, affecting the charge distribution and electrostatic interactions between RNA and proteins. In addition, pH also perturbs the structure and dynamics of proteins via the disruption of H-bonds and ionic interactions. Thus, it is crucial to ascertain the role of pH in modulating such interactions. We have previously shown the role of conformational dynamics in the RNA-protein interaction in TAR RNA-binding protein (TRBP) double-stranded RNA-binding domains (dsRBD) 1 and 2 using solution-state NMR spectroscopy. The current study provides insights into the effect of pH on interactions between TRBP2-dsRBD2 and a dsRNA. Remarkably, it was observed that a unit decrease in pH leads to an increase in the flexibility of TRBP2-dsRBD2 in RNA-binding residues, as seen in NMR dynamics experiments, in addition to altering the charge distribution on the protein surface. This led us to propose a dynamics-driven model where the two effects of pH, electrostatic and conformational flexibility, counterbalance each other. Thus, it can be concluded that the overall binding affinity between the protein and RNA is governed by a delicate balance between its conformational dynamics and electrostatic interactions.

Existence of Singularities in NMR Relaxation Dispersion Profiles: Implications for Hidden Dynamics

It is common for NMR relaxation dispersion experiments to suggest an absence of dynamics despite anecdotal indications of conformational dynamics. We explore the potential explanations and approaches to this conundrum. Some inconsistencies have been observed between two relaxation dispersion experiments, Carr-Purcell-Meiboom-Gill (CPMG) and adiabatic relaxation dispersion experiments, in recent dynamic studies of different biomolecules. Theoretical analyses show that such seemingly paradoxical results might come from a complex exchange topology that is concealed by the application of the simple two-site exchange model for interpretation of the relaxation dispersion data. Scenarios are explored and revealed in which the presence of complex millisecond conformational exchange could suppress the amplitude of CPMG relaxation dispersion profiles, even when the exchange rates are within the detectable range of the experiments. With experimental errors, the suppressed relaxation dispersion profiles could lead to the conclusion of "no millisecond conformational exchange". However, such hidden dynamics can potentially be detected by adiabatic relaxation dispersion experiments. Finally, we demonstrate some advantages of adiabatic relaxation dispersion experiments over conventional relaxation dispersion experiments and a simplified computational approach to analyze the adiabatic relaxation dispersion profiles.

Differential conformational dynamics in two type-A RNA-binding domains drive the double-stranded RNA recognition and binding

Trans-activation response (TAR) RNA-binding protein (TRBP) has emerged as a key player in the RNA interference pathway, wherein it binds to different pre-microRNAs (miRNAs) and small interfering RNAs (siRNAs), each varying in sequence and/or structure. We hypothesize that TRBP displays dynamic adaptability to accommodate heterogeneity in target RNA structures. Thus, it is crucial to ascertain the role of intrinsic and RNA-induced protein dynamics in RNA recognition and binding. We have previously elucidated the role of intrinsic and RNA-induced conformational exchange in the double-stranded RNA-binding domain 1 (dsRBD1) of TRBP in shape-dependent RNA recognition. The current study delves into the intrinsic and RNA-induced conformational dynamics of the TRBP-dsRBD2 and then compares it with the dsRBD1 study carried out previously. Remarkably, the two domains exhibit differential binding affinity to a 12-bp dsRNA owing to the presence of critical residues and structural plasticity. Furthermore, we report that dsRBD2 depicts constrained conformational plasticity when compared to dsRBD1. Although, in the presence of RNA, dsRBD2 undergoes induced conformational exchange within the designated RNA-binding regions and other residues, the amplitude of the motions remains modest when compared to those observed in dsRBD1. We propose a dynamics-driven model of the two tandem domains of TRBP, substantiating their contributions to the versatility of dsRNA recognition and binding.

The Landau-Zener-Stückelberg-Majorana transition in the T2 ≪ T1 limit

Landau-Zener-Stückelberg-Majorana (LZSM) transitions occur between quantum states when parameters in the system's Hamiltonian are varied continuously and rapidly. In magnetic resonance, losses in adiabatic rapid passage can be understood using the physics of LZSM transitions. Most treatments of LZSM transitions ignore the T2 dephasing of coherences, however. Motivated by ongoing work in magnetic resonance force microscopy, we employ the Bloch equations, coordinate transformation, and the Magnus expansion to derive expressions for the final magnetization following a rapid field sweep at fixed irradiation intensity that include T2 losses. Our derivation introduces an inversion-function, Fourier transform method for numerically evaluating highly oscillatory integrals. Expressions for the final magnetization are given for low and high irradiation intensity, valid in the T2≪T1 limit. Analytical results are compared to numerical simulations and nuclear magnetic resonance experiments. Our relatively straightforward calculation reproduces semiquantitatively the well known LZSM result in the T2→0 limit.

On the geometric phases during radio frequency pulses with sine and cosine amplitude and frequency modulation

In this work, we describe the formation of geometric phases during nonadiabatic frequency swept (FS) radio frequency (RF) pulses with sine amplitude modulation and cosine frequency modulation functions. The geometric phases during the FS pulse were analyzed using a Schrödinger equation formalism, and the unified analytical expression for the geometric phase was derived. We present the solutions for sub-geometric phase components incorporated in spinor wavefunctions for the RF Hamiltonian of spin ½ nuclei. We demonstrate that the geometric phases during sine/cosine RF pulses are opposite in signs for different initial conditions of the spinor and that geometric phases can accumulate in correspondence to different magnetization trajectories. The derived formalism could be extended for the evaluation of the geometric phases during a wide class of amplitude- and frequency-modulated pulses used in MRI and in high-resolution NMR.

Towards autonomous analysis of chemical exchange saturation transfer experiments using deep neural networks

Macromolecules often exchange between functional states on timescales that can be accessed with NMR spectroscopy and many NMR tools have been developed to characterise the kinetics and thermodynamics of the exchange processes, as well as the structure of the conformers that are involved. However, analysis of the NMR data that report on exchanging macromolecules often hinges on complex least-squares fitting procedures as well as human experience and intuition, which, in some cases, limits the widespread use of the methods. The applications of deep neural networks (DNNs) and artificial intelligence have increased significantly in the sciences, and recently, specifically, within the field of biomolecular NMR, where DNNs are now available for tasks such as the reconstruction of sparsely sampled spectra, peak picking, and virtual decoupling. Here we present a DNN for the analysis of chemical exchange saturation transfer (CEST) data reporting on two- or three-site chemical exchange involving sparse state lifetimes of between approximately 3-60 ms, the range most frequently observed via experiment. The work presented here focuses on the ¹H CEST class of methods that are further complicated, in relation to applications to other nuclei, by anti-phase features. The developed DNNs accurately predict the chemical shifts of nuclei in the exchanging species directly from anti-phase ¹H^N CEST profiles, along with an uncertainty associated with the predictions. The performance of the DNN was quantitatively assessed using both synthetic and experimental anti-phase CEST profiles. The assessments show that the DNN accurately determines chemical shifts and their associated uncertainties. The DNNs developed here do not contain any parameters for the end-user to adjust and the method therefore allows for autonomous analysis of complex NMR data that report on conformational exchange.

Inherent conformational plasticity in dsRBDs enables interaction with topologically distinct RNAs

Many double-stranded RNA-binding domains (dsRBDs) interact with topologically distinct dsRNAs in biological pathways pivotal to viral replication, cancer causation, neurodegeneration, and so on. We hypothesized that the adaptability of dsRBDs is essential to target different dsRNA substrates. A model dsRBD and a few dsRNAs, slightly different in shape from each other, were used to test the systematic shape dependence of RNA on the dsRBD-binding using nuclear magnetic resonance (NMR) spectroscopy and molecular modeling. NMR-based titrations showed a distinct binding pattern for the dsRBD with the topologically distinct dsRNAs. The line broadening upon RNA binding was observed to cluster in the residues lying in close proximity, thereby suggesting an RNA-induced conformational exchange in the dsRBD. Further, while the intrinsic microsecond dynamics observed in the apo-dsRBD were found to quench upon binding with the dsRNA, the microsecond dynamics got induced at residues spatially proximal to quench sites upon binding with the dsRNA. This apparent relay of conformational exchange suggests the significance of intrinsic dynamics to help adapt the dsRBD to target various dsRNA-shapes. The conformational pool visualized in MD simulations for the apo-dsRBD reported here has also been observed to sample the conformations seen previously for various dsRBDs in apo- and in dsRNA-bound state structures, further suggesting the conformational adaptability of the dsRBDs. These investigations provide a dynamic basis for the substrate promiscuity for dsRBD proteins.

Improved design of frequency-swept pulse sequences

Frequency-swept pulses are extensively used in magnetic resonance spectroscopic techniques for the robust manipulation of spins across wide ranges of offset frequencies in the presence of B₁ field variations. Nevertheless, designing pulse sequences consisting of multiple frequency-swept pulses can be challenging, as they often require specific timings and parameter tweaking. In the present work we discuss a simple and general approach for constructing such sequences. We present new and improved pulse sequences for applications including broadband B₁-tolerant CPMG (CHORUS-CPMG), broadband chirped excitation with suppression of homonuclear J-modulation (PROCHORUS), and the further compression of frequency-swept pulse sequences by superposition of pulses which reduces pulse sequence durations by 25-40%. All sequence design strategies are accompanied by mathematical presentations, experimental results, and supporting simulations.

Sensitive Oxidation of Sorbitol-Mediated Fe2+ by H2O2: A Reliable TD-NMR Method for Clinical Blood Glucose Detection

The clinical challenge of high-accuracy blood glucose detection schemes is to overcome the detection error caused by the background interferences in different individuals. H₂O₂ as the specific product of glucose oxidation can be involved in the Fe²⁺/Fe³⁺ conversion and detected by the time-domain nuclear magnetic resonance (TD-NMR) method sensitively. But, in clinical applications, the oxidation of Fe²⁺ is susceptible to the complex sample substrates. In this work, we sorted out two kinds of possible interference mechanisms of Fe²⁺ oxidation in the NMR blood glucose detection method and proposed a feasible scheme that uses sorbitol to weaken the adverse effects of interference. We found that sorbitol-mediated Fe²⁺ can greatly enhance the sensitivity of the T₂ value to H₂O₂. The chain reaction caused by sorbitol can significantly amplify the efficiency of Fe²⁺ oxidation at the same concentration of H₂O₂. Thereby, we can achieve the higher dilution multiple of serum samples to reduce the amount of interfering substances involved in the Fe²⁺/Fe³⁺ conversion. We justified the accuracy and availability of our method by successfully detecting and confirming the correlation between the T₂ decrease and glucose concentration of the serum samples collected from 16 subjects. The sorbitol-Fe²⁺ glucose detection method with high sensitivity can be further combined with miniature NMR analyzers to satisfy the calibration requirements of glucose monitoring in diabetic patients instead of frequent medical visits.

Advances in the study of GPCRs by 19F NMR

Crystallography and cryo-electron microscopy have advanced atomic resolution perspectives of inactive and active states of G protein-coupled receptors (GPCRs), alone and in complex with G proteins or arrestin. ¹⁹F NMR can play a role in ascertaining activation mechanisms and understanding the complete energy landscape associated with signal transduction. Fluorinated reporters are introduced biosynthetically via fluorinated amino acid analogs or chemically, via thiol-specific fluorinated reporters. The chemical shift sensitivity of these reporters makes it possible to discern details of conformational ensembles. In addition to spectroscopic details, paramagnetic species can be incorporated through orthogonal techniques to obtain distance information on fluorinated reporters, while T₂-and T₁-based relaxation experiments provide details on exchange kinetics in addition to fluctuations within a given state.

The Role of Conformational Dynamics in the Recognition and Regulation of Ubiquitination

The ubiquitination pathway is central to many cell signaling and regulatory events. One of the intriguing aspects of the pathway is the combinatorial sophistication of substrate recognition and ubiquitin chain building determinations. The abundant structural and biological data portray several characteristic protein folds among E2 and E3 proteins, and the understanding of the combinatorial complexity that enables interaction with much of the human proteome is a major goal to developing targeted and selective manipulation of the pathway. With the commonality of some folds, there are likely other aspects that can provide differentiation and recognition. These aspects involve allosteric effects and conformational dynamics that can direct recognition and chain building processes. In this review, we will describe the current state of the knowledge for conformational dynamics across a wide timescale, address the limitations of present approaches, and illustrate the potential to make new advances in connecting dynamics with ubiquitination regulation.

Achieving pure spin effects by artifact suppression in methyl adiabatic relaxation experiments

Recent methyl adiabatic relaxation dispersion experiments provide examination of conformational dynamics across a very wide timescale (102-105 s-1) and, particularly, provide insight into the hydrophobic core of proteins and allosteric effects associated with modulators. The experiments require efficient decoupling of 1H and 13C spin interactions, and some artifacts have been discovered, which are associated with the design of the proton decoupling scheme. The experimental data suggest that the original design is valid; however, pulse sequences with either no proton decoupling or proton decoupling with imperfect pulses can potentially exhibit complications in the experiments. Here, we demonstrate that pulse imperfections in the proton decoupling scheme can be dramatically alleviated by using a single composite π pulse and provide pure single-exponential relaxation data. It allows the opportunity to access high-quality methyl adiabatic relaxation dispersion data by removing the cross-correlation between dipole-dipole interaction and chemical shift anisotropy. The resulting high-quality data is illustrated with the binding of an allosteric modulator (G2BR) to the ubiquitin conjugating enzyme Ube2g2.

Protein Dynamics revealed by NMR Relaxation Methods

Structural biology often focuses primarily on three-dimensional structures of biological macromolecules, deposited in the Protein Data Bank (PDB). This resource is a remarkable entity for the world-wide scientific and medical communities, as well as the general public, as it is a growing translation into three-dimensional space of the vast information in genomic databases, e.g. GENBANK. There is, however, significantly more to understanding biological function than the three-dimensional coordinate space for ground-state structures of biomolecules. The vast array of biomolecules experiences natural dynamics, interconversion between multiple conformational states, and molecular recognition and allosteric events that play out on timescales ranging from picoseconds to seconds. This wide range of timescales demands ingenious and sophisticated experimental tools to sample and interpret these motions, thus enabling clearer insight into functional annotation of the PDB. NMR spectroscopy is unique in its ability to sample this range of timescales at atomic resolution and in physiologically relevant conditions using spin relaxation methods. The field is constantly expanding to provide new creative experiments, to yield more detailed coverage of timescales, and to broaden the power of interpretation and analysis methods. This review highlights the current state of the methodology and examines the extension of analysis tools for more complex experiments and dynamic models. The future for understanding protein dynamics is bright, and these extended tools bring greater compatibility with developments in computational molecular dynamics, all of which will further our understanding of biological molecular functions. These facets place NMR as a key component in integrated structural biology.

Probing the Broad Time Scale and Heterogeneous Conformational Dynamics in the Catalytic Core of the Arf-GAP ASAP1 via Methyl Adiabatic Relaxation Dispersion

Methyl-TROSY is one of the most powerful NMR spectroscopic tools for studying structures and conformational dynamics of large protein complexes in solution. In studying conformational dynamics, side chains usually display heterogeneous dynamics, including collective and local motions, that can be difficult to detect and analyze by conventional relaxation dispersion (RD) approaches. The combination of NH-based heteronuclear adiabatic relaxation dispersion (HARD) experiments and a geometric approximation (geoHARD) has been shown to have several advantages over conventional RD in revealing conformational dynamics over a broad time scale. Here, we demonstrate a new technique that has been developed to detect both heterogeneous and wide time scale conformational dynamics in the hydrophobic interior of large macromolecules utilizing methyl-geoHARD. It is shown that methyl-geoHARD will be feasible at ultrahigh magnetic fields (>1 GHz), when this technology becomes available. For the ZA domain of Arf-GAP ASAP1, with a global correlational time of 24 ns at 15 °C, a wide range of conformational dynamics (exhibiting chemical exchange rates (kex) between 102 and 105 s-1) are observed in the methyl groups of isoleucine, leucine, and valine. The dynamics include collective and independent local motions. Furthermore, portions of the collective motions have been confirmed by single-quantum Carr-Purcell-Meiboom-Gill (SQ-CPMG) RD experiments; however, motions outside of the detectable CPMG window (400-8000 s-1) cannot be accurately determined by SQ-CPMG experiments. The methyl-geoHARD experiment allows the dissection of heterogeneous conformational dynamics and pinpoints important motions that, potentially, can be correlated with important biological functions and recognition.

Chemical Exchange

The phenomenon of chemical or conformational exchange in NMR spectroscopy has enabled detailed characterization of time-dependent aspects of biomolecular function, including folding, molecular recognition, allostery, and catalysis, on timescales from microsecond to second. Importantly, NMR methods based on a variety of spin relaxation parameters have been developed that provide quantitative information on interconversion kinetics, thermodynamic properties, and structural features of molecular states populated to a fraction of a percent at equilibrium and otherwise unobservable by other NMR approaches. The ongoing development of more sophisticated experimental techniques and the necessity to apply these methods to larger and more complex molecular systems engenders a corresponding need for theoretical advances describing such techniques and facilitating data analysis in applications. This review surveys current aspects of the theory of chemical exchange, as utilized in ZZ-exchange; Hahn and Carr-Purcell-Meiboom-Gill (CPMG) spin-echo; and R_1ρ, chemical exchange saturation transfer (CEST), and dark state saturation transfer (DEST) spin-locking experiments. The review emphasizes theoretical results for kinetic topologies with more than two interconverting states, both to obtain compact analytical forms suitable for data analysis and to establish conditions for distinguishability between alternative kinetic schemes.

Conformational Dynamics and Allostery in E2:E3 Interactions Drive Ubiquitination: gp78 and Ube2g2

Conformational dynamics plays a fundamental role in molecular recognition and activity in enzymes. The ubiquitin-conjugating enzyme (E2) Ube2g2 functions with the ubiquitin ligase (E3) gp78 to assemble poly-ubiquitin chains on target substrates. Two domains in gp78, RING and G2BR, bind to two distant regions of Ube2g2, and activate it for ubiquitin (Ub) transfer. G2BR increases the affinity between the RING and Ube2g2 by 50-fold, while the RING catalyzes the transfer of Ub from the Ube2g2∼Ub conjugate. How G2BR and RING activate Ube2g2 is unclear. In this work, conformational dynamics in Ube2g2 revealed a clear correlation of binding G2BR and RING with the sequential progression toward Ub transfer. The interrelationship of the existence and exchange between ground and excited states leads to a dynamic energy landscape model, in which redistribution of populations contributes to allostery and activation. These findings provide insight into gp78's modulation of conformational exchange in Ube2g2 to stimulate ubiquitination.

Application of geometric approximation to the CPMG experiment: Two- and three-site exchange

The Carr-Purcell-Meiboom-Gill (CPMG) experiment is one of the most classical and well-known relaxation dispersion experiments in NMR spectroscopy, and it has been successfully applied to characterize biologically relevant conformational dynamics in many cases. Although the data analysis of the CPMG experiment for the 2-site exchange model can be facilitated by analytical solutions, the data analysis in a more complex exchange model generally requires computationally-intensive numerical analysis. Recently, a powerful computational strategy, geometric approximation, has been proposed to provide approximate numerical solutions for the adiabatic relaxation dispersion experiments where analytical solutions are neither available nor feasible. Here, we demonstrate the general potential of geometric approximation by providing a data analysis solution of the CPMG experiment for both the traditional 2-site model and a linear 3-site exchange model. The approximate numerical solution deviates less than 0.5% from the numerical solution on average, and the new approach is computationally 60,000-fold more efficient than the numerical approach. Moreover, we find that accurate dynamic parameters can be determined in most cases, and, for a range of experimental conditions, the relaxation can be assumed to follow mono-exponential decay. The method is general and applicable to any CPMG RD experiment (e.g. N, C', C^α, H^α, etc.) The approach forms a foundation of building solution surfaces to analyze the CPMG experiment for different models of 3-site exchange. Thus, the geometric approximation is a general strategy to analyze relaxation dispersion data in any system (biological or chemical) if the appropriate library can be built in a physically meaningful domain.

General expressions for R1ρ relaxation for N-site chemical exchange and the special case of linear chains

Exploration of dynamic processes in proteins and nucleic acids by spin-locking NMR experiments has been facilitated by the development of theoretical expressions for the R_1ρ relaxation rate constant covering a variety of kinetic situations. Herein, we present a generalized approximation to the chemical exchange, R_ex, component of R_1ρ for arbitrary kinetic schemes, assuming the presence of a dominant major site population, derived from the negative reciprocal trace of the inverse Bloch-McConnell evolution matrix. This approximation is equivalent to first-order truncation of the characteristic polynomial derived from the Bloch-McConnell evolution matrix. For three- and four-site chemical exchange, the first-order approximations are sufficient to distinguish different kinetic schemes. We also introduce an approach to calculate R_1ρ for linear N-site schemes, using the matrix determinant lemma to reduce the corresponding 3N×3N Bloch-McConnell evolution matrix to a 3×3 matrix. The first- and second order-expansions of the determinant of this 3×3 matrix are closely related to previously derived equations for two-site exchange. The second-order approximations for linear N-site schemes can be used to obtain more accurate approximations for non-linear N-site schemes, such as triangular three-site or star four-site topologies. The expressions presented herein provide powerful means for the estimation of R_ex contributions for both low (CEST-limit) and high (R_1ρ-limit) radiofrequency field strengths, provided that the population of one state is dominant. The general nature of the new expressions allows for consideration of complex kinetic situations in the analysis of NMR spin relaxation data.