Amplitudes and time scales of picosecond-to-microsecond motion in proteins studied by solid-state NMR: a critical evaluation of experimental approaches and application to crystalline ubiquitin

Solid-state NMR provides insight into protein motion over time scales ranging from picoseconds to seconds. While in solution state the methodology to measure protein dynamics is well established, there is currently no such consensus protocol for measuring dynamics in solids. In this article, we perform a detailed investigation of measurement protocols for fast motions, i.e. motions ranging from picoseconds to a few microseconds, which is the range covered by dipolar coupling and relaxation experiments. We perform a detailed theoretical investigation how dipolar couplings and relaxation data can provide information about amplitudes and time scales of local motion. We show that the measurement of dipolar couplings is crucial for obtaining accurate motional parameters, while systematic errors are found when only relaxation data are used. Based on this realization, we investigate how the REDOR experiment can provide such data in a very accurate manner. We identify that with accurate rf calibration, and explicit consideration of rf field inhomogeneities, one can obtain highly accurate absolute order parameters. We then perform joint model-free analyses of 6 relaxation data sets and dipolar couplings, based on previously existing, as well as new data sets on microcrystalline ubiquitin. We show that nanosecond motion can be detected primarily in loop regions, and compare solid-state data to solution-state relaxation and RDC analyses. The protocols investigated here will serve as a useful basis towards the establishment of a routine protocol for the characterization of ps–μs motions in proteins by solid-state NMR.     

Dynamical characterization of residual and non-native structures in a partially folded protein by (15)N NMR relaxation using a model based on a distribution of correlation times

A spectral density model based on a truncated lorentzian distribution of correlation times is used to analyze the nanosecond time-scale dynamics of the partially unfolded domain 2 of annexin I from its (15)N NMR relaxation parameters measured at three magnetic field strengths. The use of a distribution of correlation times enables the characterization of the dynamical features of the NH bonds of the protein in terms of heterogeneity of dynamical states in the nanosecond range. The variation along the sequence of the two dynamical parameters introduced, namely the center and the width of the distribution, points out the different types of residual secondary structures present in the D2 domain. Moreover, it allows a physically sensible interpretation of the dynamical behavior of the different residual helices and of the non-native structures. Also, a striking correspondence is found between the parameters obtained using an extended Lipari and Szabo model and the parameters obtained using the distribution of correlation times. This result led us to propose a specific interpretation of the model-free order parameter for internal motions in the nanosecond range in the case of unfolded states.     

Dynamics of the Mrf-2 DNA-binding domain free and in complex with DNA

Mrf-2 is a member of a new class of DNA-binding proteins known as the AT-rich interaction domain family or ARID. Chemical shift indices and characteristic NOE values indicate that the three-dimensional structure of the Mrf-2 ARID in complex with DNA is nearly identical to that of the free protein. The backbone dynamics of the Mrf-2 domain free and in complex with DNA have been characterized by (15)N NMR relaxation measurements and model-free analysis. Chemical shift perturbations and dynamic studies suggest that two flexible interhelical loops, the flexible C-terminal tail, and one alpha-helix are involved in DNA recognition, indicating the importance of protein dynamics in DNA binding. Some well-structured regions, in particular the putative DNA-contacting helix, in Mrf-2 show a decrease in the order parameters (S(2)) upon complex formation. The less well-structured loops and the unstructured C-terminus show reduced flexibility upon DNA binding. In addition, the model-free analysis indicates motions on the picosecond to nanosecond and micro- to millisecond time scales at the DNA-binding surface of the bound Mrf-2 ARID, suggesting a model where interactions between the protein and DNA are highly dynamic.     

Backbone dynamics of oxidised and reduced forms of human atrial natriuretic peptide

The backbone dynamics of the 28 residue 15N-labelled human atrial natriuretic peptide have been examined by 15N NMR methods. 15N R1, R2 and [1H]-15N NOE values were determined for the oxidised and reduced forms of the peptide (ANPox and ANPrd, respectively), and analysed using reduced spectral density mapping and an extended model-free approach. The two forms possessed correlation times for overall molecular motion of 4.7 ns and were highly flexible, with substantial contributions to relaxation processes from internal motions on picosecond to nanosecond time scales. Reduction of the Cys7-Cys23 disulphide bond to form ANPrd produced a very dynamic linear peptide with a mean overall order parameter of 0.2; the intramolecular cross-link in ANPox increased this to a mean value of 0.4. A simple model for segmental backbone motion accounted for the R2 values of both species using only two variable parameters, indicating that relaxation is dominated by interactions with sites <7 residues distant in the covalent network and that changes in the conformation of the disulphide bond lead to significant chemical exchange broadening in ANPox. The contributions of backbone dynamics to configurational entropy were determined and accounted for the different receptor binding affinities of cyclised and linear natriuretic peptides.     

Prediction of methyl-side Chain Dynamics in Proteins

A simple analytical model is presented for the prediction of methyl-side chain dynamics in comparison with S(2) order parameters obtained by NMR relaxation spectroscopy. The model, which is an extension of the local contact model for backbone order parameter prediction, uses a static 3D protein structure as input. It expresses the methyl-group S(2) order parameters as a function of local contacts of the methyl carbon with respect to the neighboring atoms in combination with the number of consecutive mobile dihedral angles between the methyl group and the protein backbone. For six out of seven proteins the prediction results are good when compared with experimentally determined methyl-group S(2) values with an average correlation coefficient r = 0.65+/-0.14. For the unusually rigid cytochrome c(2) no significant correlation between prediction and experiment is found. The presented model provides independent support for the reliability of current side-chain relaxation methods along with their interpretation by the model-free formalism.     

Backbone dynamics of TEM-1 determined by NMR: evidence for a highly ordered protein

Backbone dynamics of TEM-1 beta-lactamase (263 amino acids, 28.9 kDa) were studied by 15N nuclear magnetic resonance relaxation at 11.7, 14.1, and 18.8 T. The high quality of the spectra allowed us to measure the longitudinal relaxation rate (R1), the transverse relaxation rate (R2), and the {1H}-15N NOE for up to 227 of the 250 potentially observable backbone amide groups. The model-free formalism was used to determine internal motional parameters using an axially anisotropic model. TEM-1 exhibits a small prolate axial anisotropy (D(parallel)/D(perpendicular) = 1.23 +/- 0.01) and a global correlation time (tau(m)) of 12.41 +/- 0.01 ns. The unusually high average generalized order parameter (S2) of 0.90 +/- 0.02 indicates that TEM-1 is one of the most ordered proteins studied by liquid-state NMR to date. Although the omega-loop has a high degree of order in the picosecond-to-nanosecond time scale (mean S2 value of 0.90 +/- 0.02), we observed the presence of microsecond-to-millisecond time scale motions for this loop, as for the vicinity of the active site. These motions could be relevant for the catalytic function of TEM-1. Amide exchange experiments were also performed, and several amide groups were not exchanged after 12 days, an indication that global motions in TEM-1 are also very limited. Although detailed dynamics characterization by NMR cannot be readily applied to TEM-1 in the presence of relevant substrates, the unusual picosecond-to-nanosecond dynamics behavior of TEM-1 presented here will be essential to the validation and improvement of future molecular dynamics simulations of TEM-1 in the presence of functionally relevant substrates.     

Sampling of Protein Dynamics in Nanosecond Time Scale by 15N NMR Relaxation and Self-Diffusion Measurements

Abstract

This paper presents a procedure for detection of intermediate nanosecond internal dynamics in globular proteins. The procedure uses ¹H-¹⁵N relaxation measurements at several spectrometer frequencies and hydrodynamic calculations based on experimental self-diffusion coefficients. New heteronuclear experiments, using pulse field gradients, are introduced for the measurement of translation diffusion coefficients of ¹⁵N labeled proteins. An advanced interpretation of recently published (Luginbühl et al., Biochemistry, 36, 7305–7312 (1997)) backbone amide ¹⁵N relaxation data, measured at two spectrometers (400 and 750 MHz for ¹H) for N-terminal DNA-binding domain (1–63) of 434 repressor, is presented. Non-applicability of commonly used fast (picosecond) dynamics model (FD) was justified by (i) poor fit of relaxation data by the FD model-free spectral density function both for isotropic and anisotropic models of the overall molecular tumbling; (ii) specific dependence of the overall rotation correlation times calculated from T₁/T₂ ratio on the spectrometer frequency; (iii) mismatch of the ratio of longitudinal ¹⁵N relaxation times T₁, measured at different spectrometer frequencies, in comparison with that anticipated for the IT) model; (iv) significantly underestimated overall rotation correlation time provided by the FD model (5.50±0.15 and 5.80±0.15 ns for 750 and 400 MHz spectrometer frequency respectively) in comparison with correlation time obtained from hydrodynamics. On the other hand, all relaxation and hydrodynamics data are in good correspondence with the model of intermediate (nanoseconds) dynamics. Overall rotation correlation time of 7.5±0.7 ns was calculated from experimental translation self-diffusion rate using hydrodynamics formalism (Garcia de la Torre, J. and Bloomfield, V.A. Quart. Rev. Biophys., 14, 81–139 (1981)). The statistical analysis of ¹⁵N relaxation data along with the hydrodynamic consideration clearly revealed that most of the residues in 434(1–63) repressor are involved in the nanosecond internal dynamics characterized by the the mean order parameters of 0.59±0.06 and the correlation times of ca. 5 ns.     

Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R ₁, R ₂, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a χ² function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, τ _e , τ _f , or τ _s , or the global correlation time parameter, local τ _m , heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised χ² value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.     

15N NMR relaxation studies of backbone dynamics in free and steroid-bound Delta 5-3-ketosteroid isomerase from Pseudomonas testosteroni

The backbone dynamics of Delta(5)-3-ketosteroid isomerase (KSI) from Pseudomonas testosteroni has been studied in free enzyme and its complex with a steroid ligand, 19-nortestosterone hemisuccinate (19-NTHS), by (15)N relaxation measurements. The relaxation data were analyzed using the model-free formalism to extract the model-free parameters (S(2), tau(e), and R(ex)) and the overall rotational correlation time (tau(m)). The rotational correlation times were 19.23 +/- 0.08 and 17.08 +/- 0.07 ns with the diffusion anisotropies (D( parallel)/D( perpendicular)) of 1.26 +/- 0.03 and 1.25 +/- 0.03 for the free and steroid-bound KSI, respectively. The binding of 19-NTHS to free KSI causes a slight increase in the order parameters (S(2)) for a number of residues, which are located mainly in helix A1 and strand B4. However, the majority of the residues exhibit reduced order parameters upon ligand binding. In particular, strands B3, B5, and B6, which have most of the residues involved in the dimer interaction, have the reduced order parameters in the steroid-bound KSI, indicating the increased high-frequency (pico- to nanosecond) motions in the intersubunit region of this homodimeric enzyme. Our results differ from those of previous studies on the backbone dynamics of monomeric proteins, in which high-frequency internal motions are typically restricted upon ligand binding.     

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

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

New modification of model-free approach to analysis of nuclear magnetic relaxation data in proteins

A formal approach to the analysis of 13C magnetic relaxation data in proteins has been developed. It is based on the concepts of one of the authors on the internal motions in solid polymers (Fedotov, V.D., Pulse NMR in bulk polymers, Doctoral dissertation, Kazan, USSR, 1981). According to this approach the intermolecular motions in proteins are considered as anisotropic ones and described in terms of a spectrum of correlation times. To characterize the motions a set of formal microdynamic parameters has been introduced. They are: the anisotropy parameter (a measure of spatial restriction of motion), the most probable correlation time, the parameter of the correlation time distribution width. The analysis of protonated carbon relaxation in globular proteins (bovine pancreatic trypsin inhibitor and ribonuclease S) and polymers has been carried out by the model-free approach. Microdynamic parameters of CH3-, CH2-, aromatic CH-groups have been considered within the framework of the diffusional rotation-oscillation models. To explain the backbone CH-group relaxation the model of the defect diffusion has been applied. The distinctive feature of the results obtained is the broad correlation time distribution for all groups of any type. The causes of nonexponential correlation function of local motion have been discussed. To elucidate the nature of the correlation time the carbon magnetization decays in the wide range of microdynamic parameter values imitating various experimental conditions have been calculated.     

Fast evaluation of protein dynamics from deficient <Superscript>15</Superscript>N relaxation data

Simple and convenient method of protein dynamics evaluation from the insufficient experimental ¹⁵N relaxation data is presented basing on the ratios, products, and differences of longitudinal and transverse ¹⁵N relaxation rates obtained at a single magnetic field. Firstly, the proposed approach allows evaluating overall tumbling correlation time (nanosecond time scale). Next, local parameters of the model-free approach characterizing local mobility of backbone amide N–H vectors on two different time scales, S² and R _ex , can be elucidated. The generalized order parameter, S², describes motions on the time scale faster than the overall tumbling correlation time (pico- to nanoseconds), while the chemical exchange term, R _ex , identifies processes slower than the overall tumbling correlation time (micro- to milliseconds). Advantages and disadvantages of different methods of data handling are thoroughly discussed.     

Sampling of protein dynamics in nanosecond time scale by 15N NMR relaxation and self-diffusion measurements.

This paper presents a procedure for detection of intermediate nanosecond internal dynamics in globular proteins. The procedure uses 1H-15N relaxation measurements at several spectrometer frequencies and hydrodynamic calculations based on experimental self-diffusion coefficients. New heteronuclear experiments, using pulse field gradients, are introduced for the measurement of translation diffusion coefficients of 15N labeled proteins. An advanced interpretation of recently published (Luginbühl et al., Biochemistry, 36, 7305-7312 (1997)) backbone amide 15N relaxation data, measured at two spectrometers (400 and 750 MHz for 1H) for N-terminal DNA-binding domain (1-63) of 434 repressor, is presented. Non-applicability of commonly used fast (picosecond) dynamics model (FD) was justified by (i) poor fit of relaxation data by the FD model-free spectral density function both for isotropic and anisotropic models of the overall molecular tumbling; (ii) specific dependence of the overall rotation correlation times calculated from T1/T2 ratio on the spectrometer frequency; (iii) mismatch of the ratio of longitudinal 15N relaxation times T1, measured at different spectrometer frequencies, in comparison with that anticipated for the FD model; (iv) significantly underestimated overall rotation correlation time provided by the FD model (5.50+/-0.15 and 5.80+/-0.15 ns for 750 and 400 MHz spectrometer frequency respectively) in comparison with correlation time obtained from hydrodynamics. On the other hand, all relaxation and hydrodynamics data are in good correspondence with the model of intermediate (nanoseconds) dynamics. Overall rotation correlation time of 7.5+/-0.7 ns was calculated from experimental translation self-diffusion rate using hydrodynamics formalism (Garcia de la Torre, J. and Bloomfield, V.A. Quart. Rev. Biophys., 14, 81-139 (1981)). The statistical analysis of 15N relaxation data along with the hydrodynamic consideration clearly revealed that most of the residues in 434(1-63) repressor are involved in the nanosecond internal dynamics characterized by the the mean order parameters of 0.59+/-0.06 and the correlation times of ca. 5 ns.     

Backbone dynamics of barstar: a (15)N NMR relaxation study

Backbone dynamics of uniformly (15)N-labeled barstar have been studied at 32 degrees C, pH 6.7, by using (15)N relaxation data obtained from proton-detected 2D (1)H-(15)N NMR spectroscopy. (15)N spin-lattice relaxation rate constants (R(1)), spin-spin relaxation rate constants (R(2)), and steady-state heteronuclear (1)H-(15)N NOEs have been determined for 69 of the 86 (excluding two prolines and the N-terminal residue) backbone amide (15)N at a magnetic field strength of 14.1 Tesla. The primary relaxation data have been analyzed by using the model-free formalism of molecular dynamics, using both isotropic and axially symmetric diffusion of the molecule, to determine the overall rotational correlation time (tau(m)), the generalized order parameter (S(2)), the effective correlation time for internal motions (tau(e)), and NH exchange broadening contributions (R(ex)) for each residue. As per the axially symmetric diffusion, the ratio of diffusion rates about the unique and perpendicular axes (D( parallel)/D( perpendicular)) is 0.82 +/- 0.03. The two results have only marginal differences. The relaxation data have also been used to map reduced spectral densities for the NH vectors of these residues at three frequencies: 0, omega(H), and omega(N), where omega(H),(N) are proton and nitrogen Larmor frequencies. The value of tau(m) obtained from model-free analysis of the relaxation data is 5.2 ns. The reduced spectral density analysis, however, yields a value of 5.7 ns. The tau(m) determined here is different from that calculated previously from time-resolved fluorescence data (4.1 ns). The order parameter ranges from 0.68 to 0.98, with an average value of 0.85 +/- 0.02. A comparison of the order parameters with the X-ray B-factors for the backbone nitrogens of wild-type barstar does not show any considerable correlation. Model-free analysis of the relaxation data for seven residues required the inclusion of an exchange broadening term, the magnitude of which ranges from 2 to 9.1 s(-1), indicating the presence of conformational averaging motions only for a small subset of residues.     

Comparison of (13)C(alpha)H and (15)NH backbone dynamics in protein GB1

This study presents a site-resolved experimental view of backbone C(alpha)H and NH internal motions in the 56-residue immunoglobulin-binding domain of streptococcal protein G, GB1. Using (13)C(alpha)H and (15)NH NMR relaxation data [T(1), T(2), and NOE] acquired at three resonance frequencies ((1)H frequencies of 500, 600, and 800 MHz), spectral density functions were calculated as F(omega) = 2omegaJ(omega) to provide a model-independent way to visualize and analyze internal motional correlation time distributions for backbone groups in GB1. Line broadening in F(omega) curves indicates the presence of nanosecond time scale internal motions (0.8 to 5 nsec) for all C(alpha)H and NH groups. Deconvolution of F(omega) curves effectively separates overall tumbling and internal motional correlation time distributions to yield more accurate order parameters than determined by using standard model free approaches. Compared to NH groups, C(alpha)H internal motions are more broadly distributed on the nanosecond time scale, and larger C(alpha)H order parameters are related to correlated bond rotations for C(alpha)H fluctuations. Motional parameters for NH groups are more structurally correlated, with NH order parameters, for example, being larger for residues in more structured regions of beta-sheet and helix and generally smaller for residues in the loop and turns. This is most likely related to the observation that NH order parameters are correlated to hydrogen bonding. This study contributes to the general understanding of protein dynamics and exemplifies an alternative and easier way to analyze NMR relaxation data.     

Dynamics of the metallo-beta-lactamase from Bacteroides fragilis in the presence and absence of a tight-binding inhibitor

A significant determinant for the broad substrate specificity of the metallo-beta-lactamases from Bacteroides fragilis and other similar organisms is the presence of a plastic substrate binding site that is nevertheless capable of tight substrate binding in the Michaelis complex. To achieve these two competing ends, the molecule apparently employs a flexible flap that closes over the active site in the presence of substrate. These characteristics imply that dynamic changes are an important component of the mechanism of action of these enzymes. The backbone and tryptophan side chain dynamics of the metallo-beta-lactamase from B. fragilis have been examined using (15)N NMR relaxation measurements. Two states of the protein were examined, in the presence and absence of a tight-binding inhibitor. Relaxation measurements were analyzed by the model-free method. Overall, the metallo-beta-lactamase molecule is rigid and shows little flexibility except in loops. The flexibility of the loop that covers the active site is not unusually great as compared to the other loops of the protein. Local motion on a picosecond time scale was found to be very similar throughout the protein in the presence and absence of the inhibitor, but a significant difference was observed in the motions on a nanosecond time scale (tau(e)). Large-amplitude motions with a time constant of about 1.3 ns were observed for the flexible flap region (residues 45-55) in the absence of the inhibitor. These motions were completely damped out in the presence of the inhibitor. In addition, the motion of a tryptophan side chain at the tip of the beta-hairpin of the flap shows a very significant difference in motion on the ps time scale. These results indicate that the motions of the polypeptide chain in the flap region can be invoked to explain both the wide substrate specificity (the free form has considerable amplitude of motion in this region) and the catalytic efficiency of the metallo-beta-lactamase (the motions are damped out when the inhibitor and by implication a substrate binds in the active site).