A theory of protein dynamics to predict NMR relaxation

We present a theoretical, site-specific, approach to predict protein subunit correlation times, as measured by NMR experiments of ¹H-¹⁵N nuclear Overhauser effect, spin-lattice relaxation, and spin-spin relaxation. Molecular dynamics simulations are input to our equation of motion for protein dynamics, which is solved analytically to produce the eigenvalues and the eigenvectors that specify the NMR parameters. We directly compare our theoretical predictions to experiments and to simulation data for the signal transduction chemotaxis protein Y (CheY), which regulates the swimming response of motile bacteria. Our theoretical results are in good agreement with both simulations and experiments, without recourse to adjustable parameters. The theory is general, since it allows calculations of any dynamical property of interest. As an example, we present theoretical calculations of NMR order parameters and x-ray Debye-Waller temperature factors; both quantities show good agreement with experimental data.     

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.     

Probing protein side chain dynamics via 13C NMR relaxation

Protein side chain dynamics is associated with protein stability, folding, and intermolecular interactions. Detailed dynamics information is crucial for the understanding of protein function and biochemical and biophysical properties, which can be obtained using NMR relaxation techniques. In this review, (13)C relaxation of methine, methylene and methyl groups with and without (1)H decoupling are described briefly for a better understanding of how spin relaxation is associated with motional (dynamics) parameters. Developments in the measurement and interpretation of (13)C auto-relaxation and cross-correlated relaxation data are presented too. Finally, recent progress in the use of (13)C relaxation to probe the dynamics of protein side chains is detailed mainly for the dynamics of non-deuterated proteins on picoseconds-nanosecond timescales.     

Backbone dynamics of the Bacillus subtilis glucose permease IIA domain determined from 15N NMR relaxation measurements.

The backbone dynamics of the uniformly 15N-labeled IIA domain of the glucose permease of Bacillus subtilis have been characterized using inverse-detected two-dimensional 1H-15N NMR spectroscopy. Longitudinal (T1) and transverse (T2) 15N relaxation time constants and steady-state (1H)-15N NOEs were measured, at a spectrometer proton frequency of 500 MHz, for 137 (91%) of the 151 protonated backbone nitrogens. These data were analyzed by using a model-free dynamics formalism to determine the generalized order parameter (S2), the effective correlation time for internal motions (tau e), and 15N exchange broadening contributions (Rex) for each residue, as well as the overall molecular rotational correlation time (tau m). The T1 and T2 values for most residues were in the ranges 0.45-0.55 and 0.11-0.15 s, respectively; however, a small number of residues exhibited significantly slower relaxation. Similarly, (1H)-15N NOE values for most residues were in the range 0.72-0.80, but a few residues had much smaller positive NOEs and some exhibited negative NOEs. The molecular rotational correlation time was 6.24 +/- 0.01 ns; most residues had order parameters in the range 0.75-0.90 and tau e values of less than ca. 25 ps. Residues found to be more mobile than the average were concentrated in three areas: the N-terminal residues (1-13), which were observed to be highly disordered; the loop from P25 to D41, the apex of which is situated adjacent to the active site and may have a role in binding to other proteins; and the region from A146 to S149. All mobile residues occurred in regions close to termini, in loops, or in irregular secondary structure.     

Redox-controlled backbone dynamics of human cytochrome c revealed by N NMR relaxation measurements

Redox-controlled backbone dynamics in cytochrome c (Cyt c) were revealed by 2D ¹⁵N NMR relaxation experiments. ¹⁵N T₁ and T₂ values and ¹H-¹⁵N NOEs of uniformly ¹⁵N-labeled reduced and oxidized Cyt c were measured, and the generalized order parameters (S²), the effective correlation time for internal motion (τ_e), the ¹⁵N exchange broadening contributions (R_ex) for each residue, and the overall correlation time (τ_m) were estimated by model-free dynamics formalism. These dynamic parameters clearly showed that the backbone dynamics of Cyt c are highly restricted due to the covalently bound heme that functions as the stable hydrophobic core. Upon oxidation of the heme iron in Cyt c, the average S² value was increased from 0.88 ± 0.01 to 0.92 ± 0.01, demonstrating that the mobility of the backbone is further restricted in the oxidized form. Such increases in the S² values were more prominent in the loop regions, including amino acid residues near the thioether bonds to the heme moiety and positively charged region around Lys87. Both of the regions are supposed to form the interaction site for cytochrome c oxidase (CcO) and the electron pathway from Cyt c to CcO. The redox-dependent mobility of the backbone in the interaction site for the electron transfer to CcO suggests an electron transfer mechanism regulated by the backbone dynamics in the Cyt c-CcO system.     

Local structural plasticity of the prion protein. Analysis of NMR relaxation dynamics

A template-assisted conformational change of the cellular prion protein (PrP(C)) from a predominantly helical structure to an amyloid-type structure with a higher proportion of beta-sheet is thought to be the causative factor in prion diseases. Since flexibility of the polypeptide is likely to contribute to the ability of PrP(C) to undergo the conformational change that leads to the infective state, we have undertaken a comprehensive examination of the dynamics of two recombinant Syrian hamster PrP fragments, PrP(29-231) and PrP(90-231), using (15)N NMR relaxation measurements. The molecular motions of these PrP fragments have been studied in solution using (15)N longitudinal (T(1)) and transverse relaxation (T(2)) measurements as well as [(1)H]-(15)N nuclear Overhauser effects (NOE). These data have been analyzed using both reduced spectral density mapping and the Lipari-Szabo model free formalism. The relaxation properties of the common regions of PrP(29-231) and PrP(90-231) are very similar; both have a relatively inflexible globular domain (residues 128-227) with a highly flexible and largely unstructured N-terminal domain. Residues 29-89 of PrP(29-231), which include the copper-binding octarepeat sequences, are also highly flexible. Analysis of the spectral densities at each residue indicates that even within the structured core of PrP(C), a markedly diverse range of motions is observed, consistent with the inherent plasticity of the protein. The central portions of helices B and C form a relatively rigid core, which is stabilized by the presence of an interhelix disulfide bond. Of the remainder of the globular domain, the parts that are not in direct contact with the rigid region, including helix A, are more flexible. Most significantly, slow conformational fluctuations on a millisecond to microsecond time scale are observed for the small beta-sheet. These results are consistent with the hypothesis that the infectious, scrapie form of the protein PrP(Sc) could contain a helical core consisting of helices B and C, similar in structure to the cellular form PrP(C). Our results indicate that residues 90-140, which are required for prion infectivity, are relatively flexible in PrP(C), consistent with a lowered thermodynamic barrier to a template-assisted conformational change to the infectious beta-sheet-rich scrapie isoform.     

Solution conformation and dynamics of a tetrasaccharide related to the LewisX antigen deduced by NMR relaxation measurements

¹H-NMR cross-relaxation rates and nonselectivelongitudinal relaxation times have been obtained at two magnetic fields (7.0and 11.8 T) and at a variety of temperatures for the branchedtetrasaccharide methyl3-O--N-acetyl-galactosaminyl--galactopyranosyl-(14)[3-O--fucosyl]-glucopyranoside (1), an inhibitor of astrocyte growth. Inaddition, ¹³C-NMR relaxation data have also been recorded atboth fields. The ¹H-NMR relaxation data have been interpretedusing different motional models to obtain proton–proton correlationtimes. The results indicate that the GalNAc and Fuc rings display moreextensive local motion than the two inner Glc and Gal moieties, since thosepresent significantly shorter local correlation times. The¹³C-NMR relaxation parameters have been interpreted in termsof the Lipari–Szabo model-free approach. Thus, order parameters andinternal motion correlation times have been deduced. As obtained for the¹H-NMR relaxation data, the two outer residues possess smallerorder parameters than the two inner rings. Internal correlation times are inthe order of 100 ps. The hydroxymethyl groups have also different behaviour,with the exocyclic carbon on the glucopyranoside unit showing the highestS². Molecular dynamics simulations using a solvated systemhave also been performed and internal motion correlation functions have beendeduced from these calculations. Order parameters and interproton distanceshave been compared to those inferred from the NMR measurements. The obtainedresults are in fair agreement with the experimental data.     

A comparison of 15N NMR relaxation measurements with a molecular dynamics simulation: Backbone dynamics of the glucocorticoid receptor DNA-binding domain

The rapid motions of the backbone of the DNA-binding domain of the glucocorticoid receptor (GR DBD) have been investigated using proton-detected heteronuclear NMR experiments on ¹⁵N-labeled protein at pH 6.0 and with a 200 psec molecular dynamics simulation of hydrated GR DBD. The experimental data were interpreted in terms of a generalized order parameter (S²) and an effective correlation time (τ_e) for the internal motion of each amide bond. A back calculation, using the same model, yielded the {¹H}-¹⁵N nuclear Overhauser effects (NOEs) and the ¹⁵N spin-lattice relaxation times (T₁) from the simulated data. The rapid motions of the backbone turned out to be rather limited and uniform throughout the protein, with a somewhat reduced mobility in the two major α-helical regions and a slightly enhanced flexibility for some residues in the first zinc coordinating region. The agreement between the experimental and simulated S²-values was as good as quantitative for most of the residues, except for some residues that were subject to a more large-scale, and in the simulation thus poorly sampled, motion. Examples of such motions that were found in the simulation include jumps of the amide bond of Ile-487 between the charged oxygens of the side chain of Asp-485 and less distinct large scale motions for some of the residues in the extended regions, that were shown to give rise to noisy and/or fast decaying internal reorientational correlation functions. For these residues large differences in the simulated and experimental τ_e-values were found, indicating that motions on different time scales were dominating in the experimental and simulated values. The lower (<0.7) experimental NOEs for these residues could not be reproduced in the simulation and were shown to be a consequence of the lower τ_e-values estimated in the simulation. By combining information from the simulation and the experiment a more complete picture of the motions for these residues can be obtained as is illustrated with an estimation of the jump angle and jump frequency for the amide bond of Ile-487. © 1993 Wiley-Liss, Inc.     

Fast-time scale dynamics of outer membrane protein A by extended model-free analysis of NMR relaxation data

In order to better understand the dynamics of an integral membrane protein, backbone amide ¹⁵N NMR dynamics measurements of the β-barrel membrane protein OmpA have been performed at three magnetic fields. A total of nine relaxation data sets were globally analyzed using an extended model-free formalism. The diffusion tensor was found to be prolate axially symmetric with an axial ratio of 5.75, indicating a possible rotation of the protein within the micelle. The generalized order parameters gradually decreased from the mid-plane towards the two ends of the barrel, counteracting the dynamic gradient of the lipids in a matching bilayer, and were dramatically reduced in the extracellular loops. Large-scale internal motions on the ns time scale indicate that entire loops most likely undergo concerted (“sea anemone”-like) motions emanating from their anchoring points on the barrel. The case of OmpA in DPC micelles also illustrates inherent limitations of analyzing the data with even the most sophisticated current models of the model-free formalism. It is likely that conformational exchange processes on the ms-μs also play a role in describing the motions of some residues, but their analysis did not produce unique results that could be independently verified.     

Automated NMR determination of protein backbone dihedral angles from cross-correlated spin relaxation

The simultaneous interpretation of a suite of dipole-dipole and dipole-CSA cross-correlation rates involving the backbone nuclei ¹³C, ¹H,¹³CO, ¹⁵N and ¹H^N can be used to resolve the ambiguities associated with each individual cross-correlation rate. The method is based on the transformation of experimental cross-correlation rates via calculated values based on standard peptide plane geometry and solid-state ¹³CO CSA parameters into a dihedral angle probability surface. Triple resonance NMR experiments with improved sensitivity have been devised for the quantification of relaxation interference between ¹H(i)-¹³C(i)/¹⁵N(i)-¹H^N(i) and ¹H(i–1)-¹³C(i–1)/¹⁵N(i)-¹H^N(i) dipole-dipole mechanisms in ¹⁵N,¹³C-labeled proteins. The approach is illustrated with an application to ¹³C,¹⁵N-labeled ubiquitin.     

Molecular mechanics and dynamics calculations on (dA)10.(dT)10 incorporating distance constraints derived from NMR relaxation measurements

Structural constraints derived from proton NMR relaxation measurements on poly(dA).poly(dT) in the form of interproton separations and orientation have been combined with molecular mechanics and annealed molecular dynamics calculations to derive a model for the solution-state structure of this molecule. Three different possible starting configurations, including the standard A and B forms of Arnott and Hukins [Arnott, S., & Hukins, D. W. L. (1972) Biochem. Biophys. Res. Commun. 47, 1506-1509] and the heteronomous (H) structure [Arnott, S., Chandrasekaran, R., Hall, I. H., & Puigjaner, L. C. (1983) Nucleic Acids Res. 11, 4141-4155], were examined. Both the B- and H-DNA structures converged to the same B-like structure (approximately C2'-endo conformation on both the A and T sugars, glycosidic bond torsional angle of 63-73 degrees) with the same energies and average helical parameters that gave good fits of the NMR relaxation rates. This model also accounts for the experimental observation [Behling, R. W., & Kearns, D. R. (1986) Biochemistry 25, 3335-3346] that the AH2 proton interacts more strongly with the H1' sugar proton on the T strand than on the A strand. Although the helix repeat angle (39 degrees) is larger than that for standard B-DNA (36 degrees), this does not result in a significantly smaller minor groove, as monitored by the interstrand P-P separation. Calculations starting with the A-DNA structure lead to a very high energy structure that gave a poorer fit of the NMR data.     

Reorientational contact-weighted elastic network model for the prediction of protein dynamics: comparison with NMR relaxation

A new model for the prediction of protein backbone motions is presented. The model, termed reorientational contact-weighted elastic network model, is based on a multidimensional reorientational harmonic potential of the backbone amide bond vector orientations and it is applied to the interpretation of dynamics parameters obtained from NMR relaxation data. The individual energy terms are weighted as a function of the intervector distances and by the contact strengths of each bond vector with respect to its local environment. Correlated reorientational motional properties of the bond vectors are obtained by means of normal mode analysis. Application to a set of proteins with known three-dimensional structures yields good to excellent agreement between predicted and experimental NMR order parameters presenting an improvement over the local contact model. The reorientational eigenmodes of the reorientational contact-weighted elastic network model method provide direct information on the collective nature of protein backbone motions. The dominant eigenmodes have a notably low collectivity, which is consistent with the behavior found for reorientational eigenmodes from molecular dynamics simulations.     

Backbone dynamics of the calcium-signaling protein apo-S100B as determined by 15N NMR relaxation

Backbone dynamics of homodimeric apo-S100B were studied by (15)N nuclear magnetic resonance relaxation at 9.4 and 14.1 T. Longitudinal relaxation (T(1)), transverse relaxation (T(2)), and the (15)N-[(1)H] NOE were measured for 80 of 91 backbone amide groups. Internal motional parameters were determined from the relaxation data using the model-free formalism while accounting for diffusion anisotropy. Rotational diffusion of the symmetric homodimer has moderate but statistically significant prolate axial anisotropy (D( parallel)/D( perpendicular) = 1.15 +/- 0.02), a global correlation time of tau(m) = 7.80 +/- 0.03 ns, and a unique axis in the plane normal to the molecular symmetry axis. Of 29 residues at the dimer interface (helices 1 and 4), only one has measurable internal motion (Q71), and the order parameters of the remaining 28 were the highest in the protein (S(2) = 0.80 to 0.91). Order parameters in the typical EF hand calcium-binding loop (S(2) = 0.73 to 0.87) were slightly lower than in the pseudo-EF hand (S(2) = 0.75 to 0.89), and effective internal correlation times, tau(e), distinct from global tumbling, were detected in the calcium-binding loops. Helix 3, which undergoes a large, calcium-induced conformational change necessary for target-protein binding, does not show evidence of interchanging between the apo and Ca(2+)-bound orientations in the absence of calcium but has rapid motion in several residues throughout the helix (S(2) = 0.78 to 0.88; 10 < or = tau(e) < or = 30 ps). The lowest order parameters were found in the C-terminal tail (S(2) = 0.62 to 0.83). Large values for chemical exchange also occur in this loop and in regions nearby in space to the highly mobile C-terminal loop, consistent with exchange broadening effects observed.     

Characterization of the overall and internal dynamics of short oligonucleotides by depolarized dynamic light scattering and NMR relaxation measurements

The dynamics of three synthetic oligonucleotides d(CG)4, d(CG)6, and d(CGCGTTGTTCGCG) of different length and shape were studied in solution by depolarized dynamic light scattering (DDLS) and time-resolved nuclear Overhauser effect cross-relaxation measurements. For cylindrically symmetric molecules the DDLS spectrum is dominated by the rotation of the main symmetry axis of the cylinder. The experimental correlation times describe the rotation of the oligonucleotides under hydrodynamic stick boundary conditions. It is shown that the hydrodynamic theory of Tirado and Garcia de la Torre gives good predictions of the rotational diffusion coefficients of cylindrically symmetric molecules of the small axial ratios studied here. These relations are used to calculate the solution dimensions of the DNA fragments from measured correlation times. The hydrodynamic diameter of the octamer and dodecamer is 20.5 +/- 1.0 A, assuming a rise per base of 3.4 A. The tridecamer, d(CGCGTTGTTCGCG), adopts a hairpin structure with nearly spherical dimensions and a diameter of 23.0 +/- 2.0 A. The DDLS relaxation measurements provide a powerful method for distinguishing between different conformations of the oligonucleotides (e.g., DNA double-helix versus hairpin structure). Furthermore, the rotational correlation times are a very sensitive probe of the length of different fragments. The NMR results reflect the anisotropic motion of the molecules as well as the amount of local internal motion present. The experimental correlation time from NMR is determined by the rotation of both the short and long axes of the oligonucleotide.(ABSTRACT TRUNCATED AT 250 WORDS)     

Quantification of the MR images of hydrogels by NMR relaxation measurements

Layers of hydrogel represent a diffusional barrier that retards the process of drug release. For better prediction of drug release, a method for evaluating the polymer concentration profile was developed.