Deuterium spin probes of side-chain dynamics in proteins. 2. Spectral density mapping and identification of nanosecond time-scale side-chain motions

Quantitative analysis of the slow exchange process by 19F NMR in the presence of scalar and dipolar couplings: applications to the ribose 2'-19F probe in nucleic acids

Solution NMR spectroscopy is a particularly powerful technique for characterizing the functional dynamics of biomolecules, which is typically achieved through the quantitative characterization of chemical exchange processes via the measurement of spin relaxation rates. In addition to the conventional nuclei such as 15N and 13C, which are abundant in biomolecules, fluorine-19 (19F) has recently garnered attention and is being widely used as a site-specific spin probe. While 19F offers the advantages of high sensitivity and low background, it can be susceptible to artifacts in quantitative relaxation analyses due to a multitude of dipolar and scalar coupling interactions with nearby 1H spins. In this study, we focused on the ribose 2'-19F spin probe in nucleic acids and investigated the effects of 1H-19F spin interactions on the quantitative characterization of slow exchange processes on the millisecond time scale. We demonstrated that the 1H-19F dipolar coupling can significantly affect the interpretation of 19F chemical exchange saturation transfer (CEST) experiments when 1H decoupling is applied, while the 1H-19F interactions have a lesser impact on Carr-Purcell-Meiboom-Gill relaxation dispersion applications. We also proposed a modified CEST scheme to alleviate these artifacts along with experimental verifications on self-complementary RNA systems. The theoretical framework presented in this study can be widely applied to various 19F spin systems where 1H-19F interactions are operative, further expanding the utility of 19F relaxation-based NMR experiments.

Accuracy and Reproducibility of Lipari-Szabo Order Parameters From Molecular Dynamics

The Lipari-Szabo generalized order parameter probes the picosecond to nanosecond time scale motions of a protein and is useful for rationalizing a multitude of biological processes such as protein recognition and ligand binding. Although these fast motions are an important and intrinsic property of proteins, it remains unclear what simulation conditions are most suitable to reproduce methyl symmetry axis side chain order parameter data (Saxis2) from molecular dynamics simulations. In this study, we show that, while Saxis2 tends to converge within tens of nanoseconds, it is essential to run 10 to 20 replicas starting from configurations close to the experimental structure to obtain the best agreement with experimental Saxis2 values. Additionally, in a comparison of force fields, AMBER ff14SB outperforms CHARMM36m in accurately capturing these fast time scale motions, and we suggest that the origin of this performance gap is likely attributed to differences in side chain torsional parametrization and not due to differences in the global protein conformations sampled by the force fields. This study provides insight into obtaining accurate and reproducible Saxis2 values from molecular simulations and underscores the necessity of using replica simulations to compute equilibrium properties.

Deuterium spin relaxation of fractionally deuterated ribonuclease H using paired 475 and 950 MHz NMR spectrometers

Deuterium (2H) spin relaxation of 13CH2D methyl groups has been widely applied to investigate picosecond-to-nanosecond conformational dynamics in proteins by solution-state NMR spectroscopy. The B0 dependence of the 2H spin relaxation rates is represented by a linear relationship between the spectral density function at three discrete frequencies J(0), J(ωD) and J(2ωD). In this study, the linear relation between 2H relaxation rates at B0 fields separated by a factor of two and the interpolation of rates at intermediate frequencies are combined for a more robust approach for spectral density mapping. The general usefulness of the approach is demonstrated on a fractionally deuterated (55%) and alternate 13C-12C labeled sample of E. coli RNase H. Deuterium relaxation rate constants (R1, R1ρ, RQ, RAP) were measured for 57 well-resolved 13CH2D moieties in RNase H at 1H frequencies of 475 MHz, 500 MHz, 900 MHz, and 950 MHz. The spectral density mapping of the 475/950 MHz data combination was performed independently and jointly to validate the expected relationship between data recorded at B0 fields separated by a factor of two. The final analysis was performed by jointly analyzing 475/950 MHz rates with 700 MHz rates interpolated from 500/900 MHz data to yield six J(ωD) values for each methyl peak. The J(ω) profile for each peak was fit to the original (τM, Sf2, τf) or extended model-free function (τM, Sf2, Ss2, τf, τs) to obtain optimized dynamic parameters.

Parsing Dynamics of Protein Backbone NH and Side-Chain Methyl Groups using Molecular Dynamics Simulations

Experimental NMR spectroscopy and theoretical molecular dynamics (MD) simulations provide complementary insights into protein conformational dynamics and hence into biological function. The present work describes an extensive set of backbone NH and side-chain methyl group generalized order parameters for the Escherichia coli ribonuclease HI (RNH) enzyme derived from 2-μs microsecond MD simulations using the OPLS4 and AMBER-FF19SB force fields. The simulated generalized order parameters are compared with values derived from NMR 15N and 13CH2D spin relaxation measurements. The squares of the generalized order parameters, S2 for the N-H bond vector and Saxis2 for the methyl group symmetry axis, characterize the equilibrium distribution of vector orientations in a molecular frame of reference. Optimal agreement between simulated and experimental results was obtained by averaging S2 or Saxis2 calculated by dividing the simulated trajectories into 50 ns blocks (∼five times the rotational diffusion correlation time for RNH). With this procedure, the median absolute deviations (MAD) between experimental and simulated values of S2 and Saxis2 are 0.030 (NH) and 0.061 (CH3) for OPLS4 and 0.041 (NH) and 0.078 (CH3) for AMBER-FF19SB. The MAD between OPLS4 and AMBER-FF19SB are 0.021 (NH) and 0.072 (CH3). The generalized order parameters for the methyl group symmetry axis can be decomposed into contributions from backbone fluctuations, between-rotamer dihedral angle transitions, and within-rotamer dihedral angle fluctuations. Analysis of the simulation trajectories shows that (i) backbone and side chain conformational fluctuations exhibit little correlation and that (ii) fluctuations within rotamers are limited and highly uniform with values that depend on the number of dihedral angles considered. Low values of Saxis2, indicative of enhanced side-chain flexibility, result from between-rotamer transitions that can be enhanced by increased local backbone flexibility.

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.

Extein residues regulate the catalytic function of Spl DnaX intein enzyme by restricting the near-attack conformations of the active-site residues

Intein enzymes catalyze the splicing of their flanking polypeptide chains and have found tremendous biotechnological applications. Their terminal residues form the catalytic core and participate in the splicing reaction. Hence, the neighboring N- and C-terminal extein residues influence the catalytic rate. As these extein residues vary depending on the substrate identity, we tested the influence of 20 amino acids at these sites in the Spl DnaX intein and observed significant variation of spliced product as well as N- and C-terminus cleavage product formation. We investigated the dependence of these reactions on the extein residues by molecular dynamics (MD) simulations on eight extein variants, and found that the conformational sampling of the active-site residues of the intein enzyme differed among these extein variants. We found that the extein variants that sample higher population of near-attack conformers (NACs) of the active-site residues undergo higher product formation in our activity assays. Ground state conformers that closely resemble the transition state are referred to as NACs. Very good correlation was observed between the NAC populations from the MD simulations of eight extein variants and the corresponding product formation from our activity assays. Furthermore, this molecular detail enabled us to elucidate the mechanistic roles of several conserved active-site residues in the splicing reaction. Overall, this study shows that the catalytic power of Spl DnaX intein enzyme, and most likely other inteins, depends on the efficiency of formation of NACs in the ground state, which is further modulated by the extein residues.

Fitting Force Field Parameters to NMR Relaxation Data

We present an approach to optimize force field parameters using time-dependent data from NMR relaxation experiments. To do so, we scan parameters in the dihedral angle potential energy terms describing the rotation of the methyl groups in proteins and compare NMR relaxation rates calculated from molecular dynamics simulations with the modified force fields to deuterium relaxation measurements of T4 lysozyme. We find that a small modification of C^γ methyl groups improves the agreement with experiments both for the protein used to optimize the force field and when validating using simulations of CI2 and ubiquitin. We also show that these improvements enable a more effective a posteriori reweighting of the MD trajectories. The resulting force field thus enables more direct comparison between simulations and side-chain NMR relaxation data and makes it possible to construct ensembles that better represent the dynamics of proteins in solution.

Aromatic ring flips in differently packed ubiquitin protein crystals from MAS NMR and MD

Probing the dynamics of aromatic side chains provides important insights into the behavior of a protein because flips of aromatic rings in a protein's hydrophobic core report on breathing motion involving a large part of the protein. Inherently invisible to crystallography, aromatic motions have been primarily studied by solution NMR. The question how packing of proteins in crystals affects ring flips has, thus, remained largely unexplored. Here we apply magic-angle spinning NMR, advanced phenylalanine 1H-13C/2H isotope labeling and MD simulation to a protein in three different crystal packing environments to shed light onto possible impact of packing on ring flips. The flips of the two Phe residues in ubiquitin, both surface exposed, appear remarkably conserved in the different crystal forms, even though the intermolecular packing is quite different: Phe4 flips on a ca. 10-20 ns time scale, and Phe45 are broadened in all crystals, presumably due to µs motion. Our findings suggest that intramolecular influences are more important for ring flips than intermolecular (packing) effects.

Proton TOCSY NMR relaxation rates quantitate protein side chain mobility in the Pin1 WW domain

Protein side chain dynamics play a vital role in many biological processes, but differentiating mobile from rigid side chains remains a technical challenge in structural biology. Solution NMR spectroscopy is ideally suited for this but suffers from limited signal-to-noise, signal overlap, and a need for fractional ¹³C or ²H labeling. Here we introduce a simple strategy measuring initial ¹H relaxation rates during a ¹H TOCSY sequence like DIPSI-2, which can be appended to the beginning of any multi-dimensional NMR sequence that begins on ¹H. The TOCSY RF field compels all ¹H atoms to behave similarly under the influence of strong coupling and rotating frame cross-relaxation, so that differences in relaxation rates are due primarily to side chain mobility. We apply the scheme to a thermostable mutant Pin1 WW domain and demonstrate that the observed ¹H relaxation rates correlate well with two independent NMR measures of side-chain dynamics, cross-correlated ¹³C relaxation rates in ¹³C^βH₂ methylene groups and maximum observable ³J couplings sensitive to the χ₁ side chain dihedral angle (³J_Hα,Hβ, ³J_N,Hβ, and ³J_CO,Hβ). The most restricted side chains belong to Trp26 and Asn40, which are closely packed to constitute the folding center of the WW domain. None of the other conserved aromatic residues is as immobile as the first tryptophan side chain of the WW domain. The proposed ¹H relaxation methodology should make it relatively easy to measure side chain dynamics on uniformly ¹⁵N- or ¹³C-labeled proteins, so long as chemical shift assignments are obtainable.

How does a small molecule bind at a cryptic binding site?

Protein-protein interactions (PPIs) are ubiquitous biomolecular processes that are central to virtually all aspects of cellular function. Identifying small molecules that modulate specific disease-related PPIs is a strategy with enormous promise for drug discovery. The design of drugs to disrupt PPIs is challenging, however, because many potential drug-binding sites at PPI interfaces are “cryptic”: When unoccupied by a ligand, cryptic sites are often flat and featureless, and thus not readily recognizable in crystal structures, with the geometric and chemical characteristics of typical small-molecule binding sites only emerging upon ligand binding. The rational design of small molecules to inhibit specific PPIs would benefit from a better understanding of how such molecules bind at PPI interfaces. To this end, we have conducted unbiased, all-atom MD simulations of the binding of four small-molecule inhibitors (SP4206 and three SP4206 analogs) to interleukin 2 (IL2)—which performs its function by forming a PPI with its receptor—without incorporating any prior structural information about the ligands’ binding. In multiple binding events, a small molecule settled into a stable binding pose at the PPI interface of IL2, resulting in a protein–small-molecule binding site and pose virtually identical to that observed in an existing crystal structure of the IL2-SP4206 complex. Binding of the small molecule stabilized the IL2 binding groove, which when the small molecule was not bound emerged only transiently and incompletely. Moreover, free energy perturbation (FEP) calculations successfully distinguished between the native and non-native IL2–small-molecule binding poses found in the simulations, suggesting that binding simulations in combination with FEP may provide an effective tool for identifying cryptic binding sites and determining the binding poses of small molecules designed to disrupt PPI interfaces by binding to such sites.

Small-molecule drugs typically function by binding to and modulating the biological activity of their protein targets. Drug-binding sites resemble pockets or grooves on the surface of the target protein, and are generally present even when the drug is not bound. In the case of “cryptic” binding sites, however, the pocket or groove only takes shape during the drug-binding process, prior to which the geometric features of a typical binding site are absent. Cryptic sites commonly occur at protein-protein interfaces, for example, so targeting such sites could facilitate the design of drugs capable of modulating specific protein-protein interactions—an approach with great therapeutic potential. In practice, targeting cryptic sites is typically difficult, in part because much less is known about how small molecules bind to cryptic sites than to conventional sites. In the work reported here, we used molecular dynamics simulations to study the process of a drug binding at a cryptic binding site, and showed that simulations are capable of predicting the location and geometry of a drug binding. The improved understanding of how small molecules bind at cryptic sites afforded by approaches like the one presented here could aid the rational design of small molecules that target such sites.

Double Mutant of Chymotrypsin Inhibitor 2 Stabilized through Increased Conformational Entropy

The conformational heterogeneity of a folded protein can affect not only its function but also stability and folding. We recently discovered and characterized a stabilized double mutant (L49I/I57V) of the protein CI2 and showed that state-of-the-art prediction methods could not predict the increased stability relative to the wild-type protein. Here, we have examined whether changed native-state dynamics, and resulting entropy changes, can explain the stability changes in the double mutant protein, as well as the two single mutant forms. We have combined NMR relaxation measurements of the ps-ns dynamics of amide groups in the backbone and the methyl groups in the side chains with molecular dynamics simulations to quantify the native-state dynamics. The NMR experiments reveal that the mutations have different effects on the conformational flexibility of CI2: a reduction in conformational dynamics (and entropy estimated from this) of the native state of the L49I variant correlates with its decreased stability, while increased dynamics of the I57V and L49I/I57V variants correlates with their increased stability. These findings suggest that explicitly accounting for changes in native-state entropy might be needed to improve the predictions of the effect of mutations on protein stability.

How Much Entropy Is Contained in NMR Relaxation Parameters?

Solution-state NMR relaxation experiments are the cornerstone to study internal protein dynamics at an atomic resolution on time scales that are faster than the overall rotational tumbling time τ_R. Since the motions described by NMR relaxation parameters are connected to thermodynamic quantities like conformational entropies, the question arises how much of the total entropy is contained within this tumbling time. Using all-atom molecular dynamics simulations of the T4 lysozyme, we found that entropy buildup is rather fast for the backbone, such that the majority of the entropy is indeed contained in the short-time dynamics. In contrast, the contribution of the slow dynamics of side chains on time scales beyond τ_R on the side-chain conformational entropy is significant and should be taken into account for the extraction of accurate thermodynamic properties.

Model-Free or Not?

Relaxation in nuclear magnetic resonance is a powerful method for obtaining spatially resolved, timescale-specific dynamics information about molecular systems. However, dynamics in biomolecular systems are generally too complex to be fully characterized based on NMR data alone. This is a familiar problem, addressed by the Lipari-Szabo model-free analysis, a method that captures the full information content of NMR relaxation data in case all internal motion of a molecule in solution is sufficiently fast. We investigate model-free analysis, as well as several other approaches, and find that model-free, spectral density mapping, LeMaster's approach, and our detector analysis form a class of analysis methods, for which behavior of the fitted parameters has a well-defined relationship to the distribution of correlation times of motion, independent of the specific form of that distribution. In a sense, they are all "model-free." Of these methods, only detectors are generally applicable to solid-state NMR relaxation data. We further discuss how detectors may be used for comparison of experimental data to data extracted from molecular dynamics simulation, and how simulation may be used to extract details of the dynamics that are not accessible via NMR, where detector analysis can be used to connect those details to experiments. We expect that combined methodology can eventually provide enough insight into complex dynamics to provide highly accurate models of motion, thus lending deeper insight into the nature of biomolecular dynamics.

Observation of Sub-Microsecond Protein Methyl-Side Chain Dynamics by Nanoparticle-Assisted NMR Spin Relaxation

Amino-acid side-chain properties in proteins are key determinants of protein function. NMR spin relaxation of side chains is an important source of information about local protein dynamics and flexibility. However, traditional solution NMR relaxation methods are most sensitive to sub-nanosecond dynamics lacking information on slower ns-μs time-scale motions. Nanoparticle-assisted NMR spin relaxation (NASR) of methyl-side chains is introduced here as a window into these ns-μs dynamics. NASR utilizes the transient and nonspecific interactions between folded proteins and slowly tumbling spherical nanoparticles (NPs), whereby the increase of the relaxation rates reflects motions on time scales from ps all the way to the overall tumbling correlation time of the NPs ranging from hundreds of ns to μs. The observed motional amplitude of each methyl group can then be expressed by a model-free NASR S² order parameter. The method is demonstrated for ²H-relaxation of CH₂D methyl moieties and cross-correlated relaxation of CH₃ groups for proteins Im7 and ubiquitin in the presence of anionic silica-nanoparticles. Both types of relaxation experiments, dominated by either quadrupolar or dipolar interactions, yield highly consistent results. Im7 shows additional dynamics on the intermediate time scales taking place in a functionally important loop, whereas ubiquitin visits the majority of its conformational substates on the sub-ns time scale. These experimental observations are in good agreement with 4-10 μs all-atom molecular dynamics trajectories. NASR probes side-chain dynamics on a much wider range of motional time scales than previously possible, thereby providing new insights into the interplay between protein structure, dynamics, and molecular interactions that govern protein function.

Fitting Side-Chain NMR Relaxation Data Using Molecular Simulations

Proteins display a wealth of dynamical motions that can be probed using both experiments and simulations. We present an approach to integrate side-chain NMR relaxation measurements with molecular dynamics simulations to study the structure and dynamics of these motions. The approach, which we term ABSURDer (average block selection using relaxation data with entropy restraints), can be used to find a set of trajectories that are in agreement with relaxation measurements. We apply the method to deuterium relaxation measurements in T4 lysozyme and show how it can be used to integrate the accuracy of the NMR measurements with the molecular models of protein dynamics afforded by the simulations. We show how fitting of dynamic quantities leads to improved agreement with static properties and highlight areas needed for further improvements of the approach.

Entropy-Entropy Compensation between the Protein, Ligand, and Solvent Degrees of Freedom Fine-Tunes Affinity in Ligand Binding to Galectin-3C

Molecular recognition is fundamental to biological signaling. A central question is how individual interactions between molecular moieties affect the thermodynamics of ligand binding to proteins and how these effects might propagate beyond the immediate neighborhood of the binding site. Here, we investigate this question by introducing minor changes in ligand structure and characterizing the effects of these on ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and computational approaches including molecular dynamics (MD) simulations and grid inhomogeneous solvation theory (GIST). We studied a congeneric series of ligands with a fluorophenyl-triazole moiety, where the fluorine substituent varies between the ortho, meta, and para positions (denoted O, M, and P). The M and P ligands have similar affinities, whereas the O ligand has 3-fold lower affinity, reflecting differences in binding enthalpy and entropy. The results reveal surprising differences in conformational and solvation entropy among the three complexes. NMR backbone order parameters show that the O-bound protein has reduced conformational entropy compared to the M and P complexes. By contrast, the bound ligand is more flexible in the O complex, as determined by ¹⁹F NMR relaxation, ensemble-refined X-ray diffraction data, and MD simulations. Furthermore, GIST calculations indicate that the O-bound complex has less unfavorable solvation entropy compared to the other two complexes. Thus, the results indicate compensatory effects from ligand conformational entropy and water entropy, on the one hand, and protein conformational entropy, on the other hand. Taken together, these different contributions amount to entropy-entropy compensation among the system components involved in ligand binding to a target protein.

Simultaneous measurement of 1HC/N-R2's for rapid acquisition of backbone and sidechain paramagnetic relaxation enhancements (PREs) in proteins

Paramagnetic relaxation enhancements (PREs) are routinely used to provide long-range distance restraints for the determination of protein structures, to resolve protein dynamics, ligand-protein binding sites, and lowly populated species, using Nuclear Magnetic Resonance Spectroscopy (NMR). Here, we propose a simultaneous ¹H-¹⁵ N, ¹H-¹³C SESAME based pulse scheme for the rapid acquisition of ¹H^C/N-R₂ relaxation rates for the determination of backbone and sidechain PREs of proteins. The ¹H^N-R₂ rates from the traditional and our approach on Ubiquitin (UBQ) are well correlated (R² = 0.99), revealing their potential to be used quantitatively. Comparison of the S57C UBQ calculated and experimental PREs provided backbone and side chain Q factors of 0.23 and 0.24, respectively, well-fitted to the UBQ NMR structure, showing that our approach can be used to acquire accurate PRE rates from the functionally important sites of proteins but in at least half the time as traditional methods.

A CEST NMR experiment to obtain glycine 1Hα chemical shifts in 'invisible' minor states of proteins

Chemical exchange saturation transfer (CEST) experiments are routinely used to study protein conformational exchange between a 'visible' major state and 'invisible' minor states because they can detect minor states with lifetimes varying from ~ 3 to ~ 100 ms populated to just ~ 0.5%. Consequently several ¹H, ¹⁵N and ¹³C CEST experiments have been developed to study exchange and obtain minor state chemical shifts at almost all backbone and sidechain sites in proteins. Conspicuously missing from this extensive set of CEST experiments is a ¹H CEST experiment to study exchange at glycine (Gly) ¹H^α sites as the existing ¹H CEST experiments that have been designed to study dynamics in amide ¹H-¹⁵N spin systems and methyl ¹³CH₃ groups with three equivalent protons while suppressing ¹H-¹H NOE induced dips are not suitable for studying exchange in methylene ¹³CH₂ groups with inequivalent protons. Here a Gly ¹H^α CEST experiment to obtain the minor state Gly ¹H^α chemical shifts is presented. The utility of this experiment is demonstrated on the L99A cavity mutant of T4 Lysozyme (T4L L99A) that undergoes conformational exchange between two compact conformers. The CEST derived minor state Gly ¹H^α chemical shifts of T4L L99A are in agreement with those obtained previously using CPMG techniques. The experimental strategy presented here can also be used to obtain methylene proton minor state chemical shifts from protein sidechain and nucleic acid backbone sites.

Automated assignment of methyl NMR spectra from large proteins

As structural biology trends towards larger and more complex biomolecular targets, a detailed understanding of their interactions and underlying structures and dynamics is required. The development of methyl-TROSY has enabled NMR spectroscopy to provide atomic-resolution insight into the mechanisms of large molecular assemblies in solution. However, the applicability of methyl-TROSY has been hindered by the laborious and time-consuming resonance assignment process, typically performed with domain fragmentation, site-directed mutagenesis, and analysis of NOE data in the context of a crystal structure. In response, several structure-based automatic methyl assignment strategies have been developed over the past decade. Here, we present a comprehensive analysis of all available methods and compare their input data requirements, algorithmic strategies, and reported performance. In general, the methods fall into two categories: those that primarily rely on inter-methyl NOEs, and those that utilize methyl PRE- and PCS-based restraints. We discuss their advantages and limitations, and highlight the potential benefits from standardizing and combining different methods.

Dynamics of proteins in solution

The dynamics of proteins in solution includes a variety of processes, such as backbone and side-chain fluctuations, interdomain motions, as well as global rotational and translational (i.e. center of mass) diffusion. Since protein dynamics is related to protein function and essential transport processes, a detailed mechanistic understanding and monitoring of protein dynamics in solution is highly desirable. The hierarchical character of protein dynamics requires experimental tools addressing a broad range of time- and length scales. We discuss how different techniques contribute to a comprehensive picture of protein dynamics, and focus in particular on results from neutron spectroscopy. We outline the underlying principles and review available instrumentation as well as related analysis frameworks.

Interplay between Conformational Entropy and Solvation Entropy in Protein-Ligand Binding

Understanding the driving forces underlying molecular recognition is of fundamental importance in chemistry and biology. The challenge is to unravel the binding thermodynamics into separate contributions and to interpret these in molecular terms. Entropic contributions to the free energy of binding are particularly difficult to assess in this regard. Here we pinpoint the molecular determinants underlying differences in ligand affinity to the carbohydrate recognition domain of galectin-3, using a combination of isothermal titration calorimetry, X-ray crystallography, NMR relaxation, and molecular dynamics simulations followed by conformational entropy and grid inhomogeneous solvation theory (GIST) analyses. Using a pair of diastereomeric ligands that have essentially identical chemical potential in the unbound state, we reduced the problem of dissecting the thermodynamics to a comparison of the two protein-ligand complexes. While the free energies of binding are nearly equal for the R and S diastereomers, greater differences are observed for the enthalpy and entropy, which consequently exhibit compensatory behavior, ΔΔ H°(R - S) = -5 ± 1 kJ/mol and - TΔΔ S°(R - S) = 3 ± 1 kJ/mol. NMR relaxation experiments and molecular dynamics simulations indicate that the protein in complex with the S-stereoisomer has greater conformational entropy than in the R-complex. GIST calculations reveal additional, but smaller, contributions from solvation entropy, again in favor of the S-complex. Thus, conformational entropy apparently dominates over solvation entropy in dictating the difference in the overall entropy of binding. This case highlights an interplay between conformational entropy and solvation entropy, pointing to both opportunities and challenges in drug design.

Minute Additions of DMSO Affect Protein Dynamics Measurements by NMR Relaxation Experiments through Significant Changes in Solvent Viscosity

Studies of protein-ligand binding often rely on dissolving the ligand in dimethyl sulfoxide (DMSO) to achieve sufficient solubility, and then titrating the ligand solution into the protein solution. As a result, the final protein-ligand solution contains small amounts of DMSO in the buffer. Here we report how the addition of DMSO impacts studies of protein conformational dynamics. We used 15 N NMR relaxation to compare the rotational diffusion correlation time (τC ) of proteins in aqueous buffer with and without DMSO. We found that τC scales with the viscosity of the water-DMSO mixture, which depends sensitively on the amount of DMSO and varies by a factor of 2 across the relevant concentration range. NMR relaxation studies of side chains dynamics are commonly interpreted using τC as a fixed parameter, obtained from backbone 15 N relaxation data acquired on a separate sample. Model-free calculations show that errors in τC , arising from mismatched DMSO concentration between samples, lead to significant errors in order parameters. Our results highlight the importance of determining τC for each sample or carefully matching the DMSO concentrations between samples.

Characterization of Internal Protein Dynamics and Conformational Entropy by NMR Relaxation

Recent studies suggest that the fast timescale motion of methyl-bearing side chains may play an important role in mediating protein activity. These motions have been shown to encapsulate the residual conformational entropy of the folded state that can potentially contribute to the energetics of protein function. Here, we provide an overview of how to characterize these motions using nuclear magnetic resonance (NMR) spin relaxation methods. The strengths and limitations of several techniques are highlighted in order to assist with experimental design. Particular emphasis is placed on the practical aspects of sample preparation, data collection, data fitting, and statistical analysis. Additionally, discussion of the recently refined "entropy meter" is presented and its use in converting NMR observables to conformational entropy is illustrated. Taken together, these methods should yield new insights into the complex interplay between structure and dynamics in protein function.

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.

Narrowing the gap between experimental and computational determination of methyl group dynamics in proteins

A synergistic analysis of methyl NMR relaxation data and MD simulations identifies ways to improve studies of protein dynamics.

Enhanced spectral density mapping through combined multiple-field deuterium 13CH2D methyl spin relaxation NMR spectroscopy

Quadrupolar relaxation of ²H (D) nuclear spins is a powerful probe of conformational dynamics in biological macromolecules. Deuterium relaxation rate constants are determined by the spectral density function for reorientation of the C-D bond vector at zero, single-quantum, and double-quantum ²H frequencies. In the present work, ²H relaxation rate constants were measured for an E. coli ribonuclease H [U-²H, ¹⁵N] ILV-[¹³CH₂D] sample using 400, 500, 800, and 900 MHz NMR spectrometers and analyzed by three approaches to determine spectral density values. First, data recorded at each static magnetic field were analyzed independently. Second, data recorded at 400 and 800 MHz were analyzed jointly and data recorded at other fields were analyzed independently. Third, data recorded at 400 and 500 MHz were interpolated to 450 MHz, and the resulting two pairs of data, corresponding to 400 MHz/800 MHz and 450 MHz/900 MHz, were analyzed jointly. The second and third approaches rely on the identity between the double quantum frequency at the lower field and the single quantum frequency at the higher field. Spectral density values for 32 of the 48 resolvable ILV methyl resonances were fit by the Lipari-Szabo model-free formalism and used to validate the three methods. The three spectral density mapping methods performed equally well in cross validation with data recorded at 700 MHz. However, the third method yielded approximately 10-15% more precise estimates of model-free parameters and consequently provides a general strategy for analysis of ²H spin relaxation data in biological macromolecules.

Measurement of 15N longitudinal relaxation rates in 15NH4+ spin systems to characterise rotational correlation times and chemical exchange

Many chemical and biological processes rely on the movement of monovalent cations and an understanding of such processes can therefore only be achieved by characterising the dynamics of the involved ions. It has recently been shown that 15N-ammonium can be used as a proxy for potassium to probe potassium binding in bio-molecules such as DNA quadruplexes and enzymes. Moreover, equations have been derived to describe the time-evolution of 15N-based spin density operator elements of 15NH4+ spin systems. Herein NMR pulse sequences are derived to select specific spin density matrix elements of the 15NH4+ spin system and to measure their longitudinal relaxation in order to characterise the rotational correlation time of the 15NH4+ ion as well as report on chemical exchange events of the 15NH4+ ion. Applications to 15NH4+ in acidic aqueous solutions are used to cross-validate the developed pulse sequence while measurements of spin-relaxation rates of 15NH4+ bound to a 41kDa domain of the bacterial Hsp70 homologue DnaK are presented to show the general applicability of the derived pulse sequence. The rotational correlation time obtained for 15N-ammonium bound to DnaK is similar to the correlation time that describes the rotation about the threefold axis of a methyl group. The methodology presented here provides, together with the previous theoretical framework, an important step towards characterising the motional properties of cations in macromolecular systems.

Dynamically Coupled Residues within the SH2 Domain of FYN Are Key to Unlocking Its Activity

Src kinase activity is controlled by various mechanisms involving a coordinated movement of kinase and regulatory domains. Notwithstanding the extensive knowledge related to the backbone dynamics, little is known about the more subtle side-chain dynamics within the regulatory domains and their role in the activation process. Here, we show through experimental methyl dynamic results and predicted changes in side-chain conformational couplings that the SH2 structure of Fyn contains a dynamic network capable of propagating binding information. We reveal that binding the phosphorylated tail of Fyn perturbs a residue cluster near the linker connecting the SH2 and SH3 domains of Fyn, which is known to be relevant in the regulation of the activity of Fyn. Biochemical perturbation experiments validate that those residues are essential for inhibition of Fyn, leading to a gain of function upon mutation. These findings reveal how side-chain dynamics may facilitate the allosteric regulation of the different members of the Src kinase family.

NMR studies of dynamic biomolecular conformational ensembles

Multidimensional heteronuclear NMR approaches can provide nearly complete sequential signal assignments of isotopically enriched biomolecules. The availability of assignments together with measurements of spin relaxation rates, residual spin interactions, J-couplings and chemical shifts provides information at atomic resolution about internal dynamics on timescales ranging from ps to ms, both in solution and in the solid state. However, due to the complexity of biomolecules, it is not possible to extract a unique atomic-resolution description of biomolecular motions even from extensive NMR data when many conformations are sampled on multiple timescales. For this reason, powerful computational approaches are increasingly applied to large NMR data sets to elucidate conformational ensembles sampled by biomolecules. In the past decade, considerable attention has been directed at an important class of biomolecules that function by binding to a wide variety of target molecules. Questions of current interest are: "Does the free biomolecule sample a conformational ensemble that encompasses the conformations found when it binds to various targets; and if so, on what time scale is the ensemble sampled?" This article reviews recent efforts to answer these questions, with a focus on comparing ensembles obtained for the same biomolecules by different investigators. A detailed comparison of results obtained is provided for three biomolecules: ubiquitin, calmodulin and the HIV-1 trans-activation response RNA.

Site-specific analysis of heteronuclear Overhauser effects in microcrystalline proteins

Relaxation parameters such as longitudinal relaxation are susceptible to artifacts such as spin diffusion, and can be affected by paramagnetic impurities as e.g. oxygen, which make a quantitative interpretation difficult. We present here the site-specific measurement of [(1)H](13)C and [(1)H](15)N heteronuclear rates in an immobilized protein. For methyls, a strong effect is expected due to the three-fold rotation of the methyl group. Quantification of the [(1)H](13)C heteronuclear NOE in combination with (13)C-R 1 can yield a more accurate analysis of side chain motional parameters. The observation of significant [(1)H](15)N heteronuclear NOEs for certain backbone amides, as well as for specific asparagine/glutamine sidechain amides is consistent with MD simulations. The measurement of site-specific heteronuclear NOEs is enabled by the use of highly deuterated microcrystalline protein samples in which spin diffusion is reduced in comparison to protonated samples.

Monitoring side-chain dynamics of proteins using (2)H relaxation

Nuclear magnetic resonance (NMR) is a powerful technique capable of monitoring a wide range of motions in proteins on a per residue basis. A variety of (2)H relaxation experiments have been developed for monitoring side-chain methyl group motions on the picosecond-nanosecond timescale. These experiments enable determination of the order parameter, S (2) axis, which reports on the rigidity of the C-CH3 bond for side-chain methyl groups. The application of a commonly used subset of these experiments is described in this chapter. It is intended to serve as a practical guide to investigators interested in monitoring side-chain motions.

The nuclear Overhauser effect from a quantitative perspective

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

Indirect use of deuterium in solution NMR studies of protein structure and hydrogen bonding

A description of the utility of deuteration in protein NMR is provided with an emphasis on quantitative evaluation of the effects of deuteration on a number of NMR parameters of proteins: (1) chemical shifts, (2) scalar coupling constants, (3) relaxation properties (R1 and R2 rates) of nuclei directly attached to one or more deuterons as well as protons of methyl groups in a highly deuterated environment, (4) scalar relaxation of 15N and 13C nuclei in 15N-D and 13C-D spin systems as a measure of hydrogen bonding strength, and (5) NOE-based applications of deuteration in NMR studies of protein structure. The discussion is restricted to the 'indirect' use of deuterium in the sense that the description of NMR parameters and properties of the nuclei affected by nearby deuterons (15N, 13C, 1H) is provided rather than those of deuterium itself.

Integrated description of protein dynamics from room-temperature X-ray crystallography and NMR

Detailed descriptions of atomic coordinates and motions are required for an understanding of protein dynamics and their relation to molecular recognition, catalytic function, and allostery. Historically, NMR relaxation measurements have played a dominant role in the determination of the amplitudes and timescales (picosecond-nanosecond) of bond vector fluctuations, whereas high-resolution X-ray diffraction experiments can reveal the presence of and provide atomic coordinates for multiple, weakly populated substates in the protein conformational ensemble. Here we report a hybrid NMR and X-ray crystallography analysis that provides a more complete dynamic picture and a more quantitative description of the timescale and amplitude of fluctuations in atomic coordinates than is obtainable from the individual methods alone. Order parameters (S(2)) were calculated from single-conformer and multiconformer models fitted to room temperature and cryogenic X-ray diffraction data for dihydrofolate reductase. Backbone and side-chain order parameters derived from NMR relaxation experiments are in excellent agreement with those calculated from the room-temperature single-conformer and multiconformer models, showing that the picosecond timescale motions observed in solution occur also in the crystalline state. These motions are quenched in the crystal at cryogenic temperatures. The combination of NMR and X-ray crystallography in iterative refinement promises to provide an atomic resolution description of the alternate conformational substates that are sampled through picosecond to nanosecond timescale fluctuations of the protein structure. The method also provides insights into the structural heterogeneity of nonmethyl side chains, aromatic residues, and ligands, which are less commonly analyzed by NMR relaxation measurements.

Dynamics of exocyclic groups in the Escherichia coli O91 O-antigen polysaccharide in solution studied by carbon-13 NMR relaxation

Carbon-13 relaxation data are reported for exocyclic groups of hexopyranosyl sugar residues in the repeating unit within the Escherichia coli O91 O-antigen polysaccharide in a dilute D2O solution. The measurements of T 1, T 2 and heteronuclear nuclear Overhauser enhancements were carried out at 310 K at two magnetic fields (16.4 T, 21.1 T). The data were analyzed using the standard and extended Lipari-Szabo models, as well as a conformational jump model. The extended version of the Lipari-Szabo and the two-site jump models were most successful for the hydroxymethyl groups of Gal and GlcNAc sugar residues. Different dynamics was found for the hydroxymethyl groups associated with different configurations (D-gluco, D-galacto) of the sugar residues, the latter being faster than the former.

Isotope labeling methods for relaxation measurements

Nuclear magnetic spin relaxation has emerged as a powerful technique for probing molecular dynamics. Not only is it possible to use it for determination of time constant(s) for molecular reorientation but it can also be used to characterize internal motions on time scales from picoseconds to seconds. Traditionally, uniformly (15)N labeled samples have been used for these experiments but it is clear that this limits the applications. For instance, sensitivity for large systems is dramatically increased if dynamics is probed at methyl groups and structural characterization of low-populated states requires measurements on (13)Cα, (13)Cβ or (13)CO or (1)Hα. Unfortunately, homonuclear scalar couplings may lead to artifacts in the latter types of experiments and selective isotopic labeling schemes that only label the desired position are necessary. Both selective and uniform labeling schemes for measurements of relaxation rates for a large number of positions in proteins are discussed in this chapter.

Is buffer a good proxy for a crowded cell-like environment? A comparative NMR study of calmodulin side-chain dynamics in buffer and E. coli lysate

Biophysical studies of protein structure and dynamics are typically performed in a highly controlled manner involving only the protein(s) of interest. Comparatively fewer such studies have been carried out in the context of a cellular environment that typically involves many biomolecules, ions and metabolites. Recently, solution NMR spectroscopy, focusing primarily on backbone amide groups as reporters, has emerged as a powerful technique for investigating protein structure and dynamics in vivo and in crowded “cell-like” environments. Here we extend these studies through a comparative analysis of Ile, Leu, Val and Met methyl side-chain motions in apo, Ca²⁺-bound and Ca²⁺, peptide-bound calmodulin dissolved in aqueous buffer or in E. coli lysate. Deuterium spin relaxation experiments, sensitive to pico- to nano-second time-scale processes and Carr-Purcell-Meiboom-Gill relaxation dispersion experiments, reporting on millisecond dynamics, have been recorded. Both similarities and differences in motional properties are noted for calmodulin dissolved in buffer or in lysate. These results emphasize that while significant insights can be obtained through detailed “test-tube” studies, experiments performed under conditions that are “cell-like” are critical for obtaining a comprehensive understanding of protein motion in vivo and therefore for elucidating the relation between motion and function.

SRLS analysis of 15N relaxation from bacteriophage T4 lysozyme: a tensorial perspective that features domain motion

Bacteriophage T4L lysozyme (T4L) comprises two domains connected by a helical linker. Several methods detected ns domain motion associated with the binding of the peptidoglycan substrate. An ESR study of nitroxide-labeled T4L, based on the slowly relaxing local structure (SRLS) approach, detected ns local motion involving the nitroxide and the helix housing it. (15)N−H spin relaxation data from T4L acquired at magnetic fields of 11.7 and 18.8 T, and 298 K, were analyzed previously with the model-free (MF) method. The results did not detect domain motion. SRLS is the generalization of MF. Here, we apply it to the same data analyzed previously with MF. The restricted local N−H motion is described in terms of tilted axial local ordering (S) and local diffusion (D(2)) tensors; dynamical coupling to the global tumbling is accounted for. We find that D(2,⊥) is 1.62 × 10(7) (1.56 × 10(7)) s(−1) for the N-terminal (C-terminal) domain. This dynamic mode represents domain motion. For the linker D(2,⊥) is the same as the rate of global tumbling, given by (1.46 ± 0.04) × 10(7) s(−1). D(2,∥) is 1.3 × 10(9), 1.8 × 10(9) and 5.3 × 10(9) s(−1) for the N-terminal domain, the C-terminal domain, and the linker, respectively. This dynamic mode represents N−H bond vector fluctuations. The principal axis of D(2) is virtually parallel to the N−H bond. The order parameter, S(0)(2), is 0.910 ± 0.046 for most N−H bonds. The principal axis of S is tilted from the C(i−1)(α) −C(i)(α) axis by −2° to 6° for the N-, and C-terminal domains, and by 2.5° for the linker. The tensorial-perspective-based and mode-coupling-based SRLS picture provides new insights into the structural dynamics of bacteriophage T4 lysozyme.

Exposing the Moving Parts of Proteins with NMR Spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool for investigating the dynamics of biomolecules since it provides a description of motion that is comprehensive, site-specific, and relatively non-invasive. In particular, the study of protein dynamics has benefited from sustained methodological advances in NMR that have expanded the scope and time scales of accessible motion. Yet, many of these advances may not be well known to the more general physical chemistry community. Accordingly, this Perspective provides a glimpse of some of the more powerful methods in liquid state NMR that are helping reshape our understanding of functional motions of proteins.

Is a malleable protein necessarily highly dynamic? The hydrophobic core of the nuclear coactivator binding domain is well ordered

The nuclear coactivator binding domain of CREB binding protein folds into remarkably different structures in complex with different ligands. To understand the mechanism of the structural adaptability in the nuclear coactivator binding domain (NCBD), we have compared the dynamics of the hydrophobic core of NCBD in the ligand-free state and in a well-folded complex with the ligand activator for thyroid hormone and retinoid receptors using multiple NMR methods including methyl chemical shifts, coupling constants, and methyl order parameters. From all NMR measures, the aliphatic side chains in the hydrophobic core are slightly more dynamic in the free protein than in the complex, but have mobility comparable to the hydrophobic cores of average folded proteins. Urea titration monitored by NMR reveals that all parts of the protein, including the side-chain packing in the hydrophobic core, denatures in a single cooperative process. The molten globule characteristics of NCBD are thus restricted to a slowly fluctuating tertiary structure. Consequently, the conformational plasticity of the protein is most likely related to its low overall stability rather than an intrinsically flexible protein structure. The well-defined structure supports a model of molecular recognition dominated by conformational selection, whereas only minor structural adjustments are necessary after the association.

Electrostatics of hydrogen exchange for analyzing protein flexibility

Electrostatic interactions at the protein-aqueous interface modulate the reactivity of solvent-exposed backbone amides by a factor of at least a billion fold. The brief (∼10 ps) lifetime of the peptide anion formed during the hydroxide-catalyzed exchange reaction helps enable the experimental rates to be robustly predictable by continuum dielectric methods. Since this ability to predict the structural dependence of exchange reactivity also applies to the protein amide hydrogens that are only rarely exposed to the bulk solvent phase, electrostatic analysis of the experimental exchange rates provides an effective assessment of whether a given model ensemble is consistent with the properly weighted Boltzmann conformational distribution of the protein native state.

Probing side-chain dynamics in proteins by the measurement of nine deuterium relaxation rates per methyl group

We demonstrate the feasibility of the measurement of up to nine deuterium spin relaxation rates in 13CHD2 and 13CH2D methyl isotopomers of small proteins. In addition to five measurable 2H relaxation rates in a 13CH2D methyl group (Millet, O.; Muhandiram, D. R.; Skrynnikov, N. R.; Kay, L. E. J. Am. Chem. Soc. 2002, 124, 6439-48), the measurement of additional four rates of (nearly) single-exponentially decaying magnetization terms in methyl groups of the 13CHD2 variety is reported. Consistency relationships between 2H spin relaxation rates measured in the two different types of methyl groups are derived and verified experimentally for a subset of methyl-containing side chains in the protein ubiquitin. A detailed comparison of methyl-bearing side-chain dynamics parameters obtained from relaxation measurements in 13CH2D and 13CHD2 methyls of ubiquitin at 10, 27, and 40 °C reveals that transverse 2H relaxation rates in 13CHD2 groups are reliable and accurate reporters of the amplitudes of methyl 3-fold axis motions (S(axis)2) for protein molecules with global molecular tumbling times τ(C) >~9 ns. For smaller molecules, simple correction of transverse 2H relaxation rates in 13CHD2 groups is sufficient for the derivation of robust measures of order. Residue-specific distributions of S(axis)2 are consistent with atomic-detail molecular dynamics (MD) results. Both 13CHD2- and 13CH2D-derived S(axis)2 values are in good overall agreement with those obtained from 1 μs MD simulations at all the three temperatures, although some differences in the site-specific temperature dependence between MD- and 2H-relaxation-derived S(axis)2 values are observed.