Determination of protein rotational correlation time from NMR relaxation data at various solvent viscosities

An accurate determination of the overall rotation of a protein plays a crucial role in the investigation of its internal motions by NMR. In the present work, an innovative approach to the determination of the protein rotational correlation time _R from the heteronuclear relaxation data is proposed. The approach is based on a joint fit of relaxation data acquired at several viscosities of a protein solution. The method has been tested on computer simulated relaxation data as compared to the traditional _R determination method from T₁/T₂ ratio. The approach has been applied to ribonuclease barnase from Bacillus amyloliquefaciens dissolved in an aqueous solution and deuterated glycerol as a viscous component. The resulting rotational correlation time of 5.56 ± 0.01 ns and other rotational diffusion tensor parameters are in good agreement with those determined from T₁/T₂ ratio.     

Measurement of 15N relaxation in the detergent-solubilized tetrameric KcsA potassium channel

A set of TROSY-HNCO (tHNCO)-based 3D experiments is presented for measuring ¹⁵N relaxation parameters in large, membrane-associated proteins, characterized by slow tumbling times and significant spectral overlap. Measurement of backbone ¹⁵N R ₁, R _1ρ, ¹⁵N–{¹H} NOE, and ¹⁵N CSA/dipolar cross correlation is demonstrated and applied to study the dynamic behavior of the homotetrameric KcsA potassium channel in SDS micelles under conditions where this channel is in the closed state. The micelle-encapsulated transmembrane domain, KcsA^TM, exhibits a high degree of order, tumbling as an oblate ellipsoid with a global rotational correlation time, τ_c = 38 ± 2.5 ns, at 50 °C and a diffusion anisotropy, , corresponding to an aspect ratio a/b ≥ 1.4. The N- and C-terminal intracellular segments of KcsA exhibit considerable internal dynamics (S ² values in the 0.2–0.45 range), but are distinctly more ordered than what has been observed for unstructured random coils. Relaxation behavior in these domains confirms the position of the C-terminal helix, and indicates that in SDS micelles, this amphiphilic helix does not associate into a stable homotetrameric helical bundle. The relaxation data indicate the absence of elevated backbone dynamics on the ps–ns time scale for the 5-residue selectivity filter, which selects K⁺ ions to enter the channel. Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at . An erratum to this article can be found at     

Interpretation of 15N NMR relaxation data of globular proteins using hydrodynamic calculations with HYDRONMR

HYDRONMR is an implementation of state of the art hydrodynamic modeling to calculate the spectral density functions for NH or C-H vectors in a rigid protein structure starting from an atomic level representation. Thus HYDRONMR can be used to predict NMR relaxation times from a rigid model and to compare them with the experimental results. HYDRONMR contains a single adjustable parameter, the atomic element radius. A protocol to determine the value that gives the best agreement between calculated and experimental T₁/T₂values is described. For most proteins, the value of the atomic element radius ranges between 2.8 Å and 3.8 Å with a distribution centered at 3.3 Å. Deviations from the usual range towards larger values are associated to aggregation in several proteins. Deviations to lower values may be related to large-scale motions or inappropriate model structures.If the average structure is correct, deviations between experimental T₁/T₂values and those calculated with HYDRONMR can be used to distinguish residues affected by anisotropic motion from those that are involved in chemical exchange.     

Accessibility of tobacco lipid transfer protein cavity revealed by 15N NMR relaxation studies and molecular dynamics simulations

Plant LTP1 are small helical proteins stabilized by four disulfide bridges and are characterized by the presence of an internal cavity, in which various hydrophobic ligands can be inserted. Recently, we have determined the solution structure of the recombinant tobacco LTP1_1. Unexpectedly, despite a global fold very similar to the structures already known for cereal seed LTP1, its binding properties are different: Tobacco LTP1_1 is able to bind only one monoacylated lipid, whereas cereal LTP1 can bind either one or two. The 3D structure of tobacco LTP1_1 revealed the presence of a hydrophobic cluster, not observed on cereal LTP1 structures, which may hinder one of the two entrances of the cavity defined for wheat LTP1. To better understand the mechanism of lipid entrance for tobacco LTP1_1 and to define the regions of the protein monitoring the accessibility of the cavity, we have complemented our structural data by the study of the internal dynamics of tobacco LTP1_1, using (15)N magnetic relaxation rate data and MD simulations at room and high temperatures. This work allowed us to define two regions of the protein experiencing the largest motions. These two regions delineate a portal that opens up during the simulation constituting a unique entrance of the hydrophobic cavity, in contrast with wheat LTP1 where two routes were detected. The hydrophobic interactions resulting from a few point mutations are strong enough to completely block the second portal so that the accessibility of the cavity is restricted to one entrance, explaining why this particular LTP1 binds only one lipid molecule.     

A suite of Mathematica notebooks for the analysis of protein main chain 15N NMR relaxation data

A suite of Mathematica notebooks has been designed to ease the analysis of protein main chain ¹⁵N NMR relaxation data collected at a single magnetic field strength. Individual notebooks were developed to perform the following tasks: nonlinear fitting of ¹⁵N-T ₁ and -T ₂ relaxation decays to a two parameter exponential decay, calculation of the principal components of the inertia tensor from protein structural coordinates, nonlinear optimization of the principal components and orientation of the axially symmetric rotational diffusion tensor, model-free analysis of ¹⁵N-T ₁, -T ₂, and {¹H}–¹⁵N NOE data, and reduced spectral density analysis of the relaxation data. The principle features of the notebooks include use of a minimal number of input files, integrated notebook data management, ease of use, cross-platform compatibility, automatic visualization of results and generation of high-quality graphics, and output of analyses in text format.L. Spyracopoulos is an AHFMR Medical Research Senior Scholar     

Characterization of the backbone dynamics of an anti-digoxin antibody VL domain by inverse detected 1H–15N NMR: Comparisons with X-ray data for the Fab

The dynamic behavior of the polypeptide backbone of a recombinant anti-digoxin antibody V_L domain has been characterized by measurements of ¹⁵N T₁ and T₂ relaxation times, ¹H–¹⁵N NOE values, and ¹H–²H exchange rates. These data were acquired with 2D inverse detected heteronuclear ¹H–¹⁵N NMR methods. The relaxation data are interpreted in terms of model free spectral density functions and exchange contributions to transverse relaxation rates R₂ (= 1/T₂). All characterized residues display low-amplitude picosecond timescale librational motions. Fifteen residues undergo conformational changes on the nanosecond timescale, and 24 residues have significant R₂ exchange contributions, which reflect motions on the microsecond to millisecond timescale. For several residues, microsecond to millisecond motions of nearby aromatic rings are postulated to account for some or all of their observed R₂ exchange contributions. The measured ¹H–²H exchange rates are correlated with hydrogen bonding patterns and distances from the solvent accessible surface. The degree of local flexibility indicated by the NMR measurements is compared to crystallographic B-factors derived from X-ray analyses of the native Fab and the Fab/digoxin complex. In general, both the NMR and X-ray data indicate enhanced flexibility in the turns, hypervariable loops, and portions of β-strands A, B, and G. However, on a residue-specific level, correlations among the various NMR data, and between the NMR and X-ray data, are often absent. This is attributed to the different dynamic processes and environments that influence the various observables. The combined data indicate that certain regions of the V_L domain, including the three hypervariable loops, undergo dynamic changes upon V_L:V_H association and/ or complexation with digoxin. Overall, the 26–10 V_L domain exhibits relatively low flexibility on the ps–ns timescale. The possible functional consequences of this result are considered. © 1993 Wiley-Liss, Inc.     

Measurement of 15N relaxation in deuterated amide groups in proteins using direct nitrogen detection

15N chemical shielding tensors contain useful structural information, and their knowledge is essential for accurate analysis of protein backbone dynamics. The anisotropic component (CSA) of 15N chemical shielding can be obtained from 15N relaxation measurements in solution. However, the predominant contribution to nitrogen relaxation from 15N-(1)H dipolar coupling in amide groups limits the sensitivity of these measurements to the actual CSA values. Here we present nitrogen-detected NMR experiments for measuring 15N relaxation in deuterated amide groups in proteins, where the dipolar contribution to 15N relaxation is significantly reduced by the deuteration. Under these conditions nitrogen spin relaxation becomes a sensitive probe for variations in 15N chemical shielding tensors. Using the nitrogen direct-detection experiments we measured the rates of longitudinal and transverse 15N relaxation for backbone amides in protein G in D(2)O at 11.7 T. The measured relaxation rates are validated by comparing the overall rotational diffusion tensor obtained from these data with that from the conventional 15N relaxation measurements in H(2)O. This analysis revealed a 17-24 degree angle between the NH-bond and the unique axis of the 15N chemical shielding tensor.     

Assessing potential bias in the determination of rotational correlation times of proteins by NMR relaxation

The various factors that influence the reliable and efficient determination of the correlation time describing molecular reorientation of proteins by NMR relaxation methods are examined. Nuclear Overhauser effects, spin-lattice, and spin-spin relaxation parameters of 15N NMR relaxation in ubiquitin have been determined at 17.6, 14.1, 11.7 and 9.4 Tesla. This unusually broad set of relaxation parameters has allowed the examination of the influence of chemical shift anisotropy, the functional form of the model-free spectral density, and the reliability of determined spin- spin relaxation parameters on the characterization of global tumbling of the protein. Treating the 15N chemical shift anisotropy (CSA) as an adjustable parameter, a consensus value of –170 ± 15ppm for the breadth of the chemical shift tensor and a global isotropic correlation time of 4.1ns are found when using the model-free spectral density to fit T1 and NOE data from all fields. The inclusion of T2 relaxation parameters in the determination of the global correlation time results in its increase to 4.6ns. This apparent inconsistency may explain a large portion of the discrepancy often found between NMR- and fluorescence-derived m values for proteins. The near identity of observed T2 and T1 values suggests that contributions from slow motions are not the origin of the apparent inconsistency with obtained T1 and NOE data. Various considerations suggest that the origin of this apparent discrepancy may reside in a contribution to the spectral density at zero frequency that is not represented by the simple model-free formalism in addition to the usual experimental difficulties associated with the measurement of these relaxation parameters. Finally, an axially symmetric diffusion tensor for ubiquitin is obtained using exclusively T1 and NOE data. A recommendation is reached on the types and combinations of relaxation data that can be used to reliably determine m values. It is also noted that the reliable determination of m values from 15N T1 and NOE relaxation parameters will become increasingly difficult as m increases.     

Estimating the time scale of chemical exchange of proteins from measurements of transverse relaxation rates in solution

Chemical (conformational) exchange on the ms-s time scale is reliably identified by the observation of transverse relaxation rates, R_ex, that depend upon the strength of the effective field (_1eff=B_1eff) used in spin lock or CPMG experiments. In order to determine if the exchange correlation time, _ex, is the fast or slow limit, measurements of (i) signal line shape and (ii) temperature dependence of R_ex have been commonly used in studies of stable, small molecules. However, these approaches are often not applicable to proteins, because sample stability and solubility, respectively, limit the temperature range and signal sensitivity of experiments. Herein we use a complex, but general, two-site exchange equation to show when the simple fast exchange equations for R_ex are good approximations, in the case of proteins. We then present a simple empirical equation that approximately predicts R_ex in all exchange regimes, and explains these results in a clear, straightforward manner. Finally we show how one can reliably determine whether _ex is in the fast or slow exchange limit.     

The folding transition state of the cold shock protein is strongly polarized

It has been shown recently that an 11-residue peptide fragment of transthyretin, TTR(105-115), can form amyloid fibrils in vitro by adopting an extended beta-strand conformation. We used molecular dynamics simulations on systems of TTR(105-115) peptides, for a total length of about 5 micros, to explore the process of self-assembly and the structures of the resulting aggregates. Our results suggest that an antiparallel association of the beta-strands is more probable than a parallel one and that the central residues (T106-L111) in a beta-strand have a high propensity to form inter-peptide hydrogen bonds. The study of the dynamics of self-association indicated that, for this peptide, trajectories leading to conformations with high alpha-helical content are off-pathway from those leading to aggregates with high beta-structure content. We also show that the diverse oligomeric structures that form spontaneously in the molecular dynamics simulations are, to a large extent, compatible with solid-state NMR experimental measurements, including chemical shifts, on fully formed fibrils. The strategy that we present may therefore be used in the design of new experiments to determine the structure of amyloid fibrils, such as those involving site-specific isotope labelling schemes to measure key inter-atomic distances.     

Rapid collapse precedes the fast two-state folding of the cold shock protein

The cold shock protein Bc-Csp folds very rapidly in a reaction that is well described by a kinetic two-state mechanism without intermediates. We measured the shortening of six intra-protein distances during folding by F?rster resonance energy transfer (FRET) in combination with stopped-flow experiments. Single tryptophan residues were engineered into the protein as the donors, and single 5-(((acetylamino)ethyl)amino)naphthalene-1-sulfonate (AEDANS) residues were placed as the acceptors at solvent-exposed sites of Bc-Csp. Their R0 value of about 22 A was well suited for following distance changes during the folding of this protein with a high sensitivity. The mutagenesis and the labeling did not alter the refolding kinetics. The changes in energy transfer during folding were monitored by both donor and acceptor emission and reciprocal effects were found. In two cases the donor-acceptor distances were similar in the unfolded and the folded state and, as a consequence, the kinetic changes in energy transfer upon folding were very small. For four donor/acceptor pairs we found that > or =50% of the increase in energy transfer upon folding occurred prior to the rate-limiting step of folding. This reveals that about half of the shortening of the intra-molecular distances upon folding has occurred already before the rate-limiting step and suggests that the fast two-state folding reaction of Bc-Csp is preceded by a very rapid collapse.     

Mobility of NH bonds in DNA-binding protein HU of shape Bacillus stearothermophilus from reduced spectral density mapping analysis at multiple NMR fields

The dynamics of the backbone NH bonds of protein HU from Bacillus stearothermophilus (HUBst) have been characterized using measurements of cross-relaxation, longitudinal and transverse relaxation rates at 11.7, 14.1 and 17.6 T. Linear regression of the values with the squared Larmor frequency _N ² has revealed global exchange processes, which contributed on the order of 0.5–5.0 s^-1to the transverse relaxation rate. Subsequently, the experimental values were corrected for these exchange contributions. A reduced spectral density mapping procedure has been employed with the experimental relaxation rates and seven values of the spectral density function J() have been extracted. These spectral densities have been fitted within the framework of the model-free approach. The densities agree well with an axially symmetric rotational diffusion tensor with a diffusion anisotropy D_/D_ of 1.15, indicating that the flexible arms of HUBst do not significantly contribute to the rotational diffusion. The overall correlation time is 8.9 ± 0.6 ns/rad. The fast internal motions of most of the NH bonds in the core display order parameters ranging between 0.74 and 0.83 and internal correlation times between 1 and 20 ps. For the residues in the DNA-binding -arms, an extended version of the model function has been used. The slow internal motions show correlation times of 1–2 ns. The concomitant order parameters (0.3–0.6) are lower than those observed on the fast time scale, indicating that the flexibility of the -arms is mainly determined by the slower internal motions. A substantial decrease of the generalized order parameters in the -arms starting at residues Arg⁵⁵ and Ser⁷⁴, opposite on both strands of the -ribbon arms, has been explained as a hinge motion. A comparison of the order parameters for free and DNA-bound protein has demonstrated that the slow hinge motions largely disappear when HU binds DNA.     

Backbone dynamics of free barnase and its complex with barstar determined by 15N NMR relaxation study

Backbone dynamics of uniformly ¹⁵N-labeled free barnase and its complex with unlabelled barstar have been studied at 40°C, pH 6.6, using ¹⁵N relaxation data obtained from proton-detected 2D {¹H}-¹⁵N NMR spectroscopy. ¹⁵N spin-lattice relaxation rate constants (R₁), spin-spin relaxation rate constants (R₂), and steady-state heteronuclear {¹H}-¹⁵N NOEs have been measured at a magnetic field strength of 14.1 Tesla for 91 residues of free barnase and for 90 residues out of a total of 106 in the complex (excluding three prolines and the N-terminal residue) backbone amide ¹⁵N sites of barnase. The primary relaxation data for both the cases have been analyzed in the framework of the model-free formalism using both isotropic and axially symmetric models of the rotational diffusion tensor. As per the latter, the overall rotational correlation times (_m) are 5.0 and 9.5 ns for the free and complexed barnase, respectively. The average order parameter is found to be 0.80 for free barnase and 0.86 for the complex. However, the changes are not uniform along the backbone and for about 5 residues near the binding interface there is actually a significant decrease in the order parameters on complex formation. These residues are not involved in the actual binding. For the residues where the order parameter increases, the magnitudes vary significantly. It is observed that the complex has much less internal mobility, compared to free barnase. From the changes in the order parameters, the entropic contribution of NH bond vector motion to the free energy of complex formation has been calculated. It is apparent that these motions cause significant unfavorable contributions and therefore must be compensated by many other favorable contributions to effect tight complex formation. The observed variations in the motion and their different locations with regard to the binding interface may have important implications for remote effects and regulation of the enzyme action.     

Identification of Slow Motions in the Reduced Recombinant High-potential Iron Sulfur Protein I (HiPIP I) from Ectothiorhodospira Halophila via 15N Rotating-frame NMR Relaxation Measurements

Rotating-frame 15N relaxation rate (R1) NMR experiments have been performed in order to study the dynamic behavior of the reduced recombinant high-potential iron-sulfur protein iso I (HiPIP I) from Ectothiorhodospira halophila, in the s to ms time range. Measurements of R1 were performed as a function of the effective spin-lock magnetic field amplitude by using both on and off-resonance radio frequency irradiation. The two data sets provided consistent results and were fit globally in order to identify possible exchange processes in an external loop of the reduced HiPIP I. The loop consists of residues 43-45 and the correlation time of the exchange process was determined to be 50 ± 8 s for the backbone nitrogen of Gln 44.     

Assessment of the Effects of Increased Relaxation Dispersion Data on the Extraction of 3-site Exchange Parameters Characterizing the Unfolding of an SH3 Domain

Recently a suite of six CPMG relaxation dispersion experiments has been described for quantifying millisecond time-scale exchange processes in proteins. The methodology has been applied to study the folding reaction of a G48M Fyn SH3 domain mutant that exchanges between the native state, and low populated unfolded and intermediate states. A complex non-linear global optimization protocol allows extraction of the kinetics and thermodynamics of the 3-site exchange process from the experimental data, as well as reconstruction of the amide group chemical shifts of the excited states. We show here, through a series of Monte-Carlo simulations on various synthetic data sets, that the 3-site exchange parameters extracted for this system on the basis of ¹⁵N single-quantum (SQ) dispersion profiles exclusively, recorded at a single temperature, are significantly in error. While a temperature dependent ¹⁵N study improves the robustness of extracted parameters, as does a combined analysis of ¹⁵N and ¹H SQ data sets measured at a single temperature, the best agreement is observed in cases where the full complement of six dispersion profiles per residue is analyzed.     

15N magnetic relaxation study of backbone dynamics of the ribosome-associated cold shock response protein Yfia of Escherichia coli

In the solution structure of the ribosome-associated cold shock response protein Yfia of Escherichia coli in the free state two structural segments can be distinguished: a well structured, rigid N-terminal part displaying a betaalphabetabetabetaalpha topology and a flexible C-terminal tail comprising last 20 amino-acid residues. The backbone dynamics of Yfia protein was studied by (15)N nuclear magnetic relaxation at three magnetic fields and analyzed using model-free approach. The overall diffusional tumbling of the N-terminal part is strongly anisotropic with a number of short stretches showing increased mobility either on a subnanosecond time scale, or a micro- to millisecond time scale, or both. In contrast, the unstructured polypeptide chain of the C-terminal part, which cannot be regarded as a rigid structure, shows the predominance of fast local motions over slower ones, both becoming faster closer to the C-terminus.     

Stabilization of the cold shock protein CspB from Bacillus subtilis by evolutionary optimization of Coulombic interactions

The bacterial cold shock proteins (Csp) are used by both experimentalists and theoreticians as model systems for analyzing the Coulombic contributions to protein stability. We employ Proside, a method of directed evolution, to identify stabilized variants of Bs-CspB from Bacillus subtilis. Proside links the increased protease resistance of stabilized protein variants to the infectivity of a filamentous phage. Here, three cspB libraries were used for in vitro selections to explore the stabilizing potential of charged amino acids in Bs-CspB. In the first library codons for nine selected surface residues were partially randomized, in the second one random mutations were introduced non-specifically by error-prone PCR, and in the third one the spontaneous mutation rate of the phage in Escherichia coli was used. Stabilizing mutations were found at the surface positions 1, 3, 46, 48, 65, and 66. The contributions of these mutations to stability were characterized by analyzing them individually and in combination. The best combination (M1R, E3K, K65I, and E66L) increased the midpoint of thermal unfolding of Bs-CspB from 53.8 to 85.0 degrees C. The effects of most mutations are strongly context dependent. A good example is provided by the E3R mutation. It is strongly stabilizing (DeltaDeltaGD=11.1kJ mol(-1)) in the wild-type protein, but destabilizing (DeltaDeltaGD=-4.0kJ mol(-1)) in the A46K/S48R/E66L variant. The stabilizations by charge mutations did not correlate well with the corresponding changes in the protein net charge, and they could not be ascribed to the formation of ion pairs. Previous theoretical analyses did not identify the stabilization caused by the mutations at positions 1, 46, and 48. Also, electrostatics calculations based on protein net charge or charge asymmetry did not predict well the stability changes that occur when charged residues in Bs-CspB are mutated. It remains a challenge to model the Coulombic interactions of charged residues in a protein and to determine their contributions to the Gibbs free energy of protein folding.     

Internal motion time scales of a small, highly stable and disulfide-rich protein: A 15N, 13C NMR and molecular dynamics study

Motions of the backbone CH and threonine CH bonds of toxin were investigated using natural abundance 13C NMR and molecular dynamics. Measurement of the 13C longitudinal and transverse relaxation rates employed ACCORDION techniques together with coherence selection by pulsed field gradients and sensitivity enhancement through the use of preservation of equivalent pathway, thus allowing a considerable reduction of the required spectrometer time. 13C R1, R2, 1H13C NOE were obtained, as well as the variations of R1(90° ) as a function of the rf field strength. These data were compared to those recorded by 1H and 15N NMR on a labelled sample of the toxin [Guenneugues et al. (1997) Biochemistry, 36, 16097–16108]. Both sets of data showed that picosecond to nanosecond time scale motions are well correlated to the secondary structure of the protein. This was further reinforced by the analysis of a 1 ns molecular dynamics simulation in water. Several CH and threonine CH experimentally exhibit fast motions with a correlation time longer than 500 ps, that cannot be sampled along the simulation. In addition, the backbone exhibits motions on the microsecond to millisecond time scale on more than half of its length. Thus, toxin , a highly stable protein (Tm=75°C at acidic pH) containing 61 amino acids and 4 disulfides, shows important internal motions on time scales ranging from 0.1–0.5 ps, to 10–100 ps, 1 ns, and about 30 s to 10 ms.     

The effects of ionic strength on protein stability: the cold shock protein family

Continuum electrostatic models are used to examine in detail the mechanism of protein stabilization and destabilization due to salt near physiological concentrations. Three wild-type cold shock proteins taken from mesophilic, thermophilic, and hyperthermophilic bacteria are studied using these methods. The model is validated by comparison with experimental data collected for these proteins. In addition, a number of single point mutants and three designed sequences are examined. The results from this study demonstrate that the sensitivity of protein stability toward salt is correlated with thermostability in the cold shock protein family. The calculations indicate that the mesophile is stabilized by the presence of salt while the thermophile and hyperthermophile are destabilized. A decomposition of the salt influence at a residue level permits identification of regions of the protein sequences that contribute toward the observed salt-dependent stability. This model is used to rationalize the effect of various point mutations with regard to sensitivity toward salt. Finally, it is demonstrated that designed cold shock protein variants exhibit electrostatic properties similar to the natural thermophilic and hyperthermophilic proteins.