Internal bulge and tetraloop of the catalytic domain 5 of a group II intron ribozyme are flexible: implications for catalysis

RNA molecules have an inherent flexibility that enables recognition of other interacting partners through potential disorder-order transitions, yet studies to quantify such motional dynamics remain few. With an increasing database of three-dimensional structures of biologically important RNA molecules, quantifying such motions becomes important to link structural deformations with function. One such system studied intensely is domain 5 (D5) from the self-splicing group II introns, which is at the heart of its catalytic machinery. We report the dynamics of a 36 nucleotide D5 from the Pylaiella littoralis group II intron in the presence and absence of magnesium ions, and at a range of temperatures (298K-318 K). Using high-resolution NMR experiments of heteronuclear nuclear Overhauser enhancement (NOE), spin-lattice (R(1)), and spin-spin (R(2)) (13)C relaxation rates, we determined the rotational diffusion tensor of D5 using the ROTDIF program modified for RNA dynamic analysis (ROTDIF_RNA). The D5 rotational diffusion tensor has an axial symmetric ratio (D(||)/D(perpendicular)) of 1.7+/-0.3, consistent with an estimated overall rotational correlation time of tau(m)=(2D(||)+4D(perpendicular))(-1) of 6.1(+/-0.3) ns at 298 K and 4.1(+/-0.2) ns at 318 K. The measured relaxation data were analyzed with the reduced spectral density mapping formalism using assumed values of the chemical shift anisotropy of the (13)C spins. Both the relaxation data and the values of the spectral density function reveal that the functional groups in D5 implicated in magnesium ion binding and catalysis (catalytic triad, internal bulge, and tetraloop regions) exhibit thermally induced motion on a wide variety of timescales. Because these motions parallel those observed in the intramolecular stem-loop of the U6 element within the spliceosome, we hypothesize that such extensive dynamic disorder likely facilitates D5 engaging both binding and catalytic regions of the ribozyme, and these may be a conserved feature of the catalytic machinery essential for catalysis.     

Refinement of protein structure against non-redundant carbonyl <Superscript>13</Superscript>C NMR relaxation

Carbonyl ¹³C′ relaxation is dominated by the contribution from the ¹³C′ chemical shift anisotropy (CSA). The relaxation rates provide useful and non-redundant structural information in addition to dynamic parameters. It is straightforward to acquire, and offers complimentary structural information to the ¹⁵N relaxation data. Furthermore, the non-axial nature of the ¹³C′ CSA tensor results in a T₁/T₂ value that depends on an additional angular variable even when the diffusion tensor of the protein molecule is axially symmetric. This dependence on an extra degree of freedom provides new geometrical information that is not available from the NH dipolar relaxation. A protocol that incorporates such structural restraints into NMR structure calculation was developed within the program Xplor-NIH. Its application was illustrated with the yeast Fis1 NMR structure. Refinement against the ¹³C′ T₁/T₂ improved the overall quality of the structure, as evaluated by cross-validation against the residual dipolar coupling as well as the ¹⁵N relaxation data. In addition, possible variations of the CSA tensor were addressed. Electronic Supplementary Material The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Monitoring conformational dynamics with solid-state R 1ρ experiments

A new application of solid-state rotating frame (R _1ρ) relaxation experiments to observe conformational dynamics is presented. Studies on a model compound, dimethyl sulfone (DMS), show that R _1ρ relaxation due to reorientation of a chemical shift anisotropy (CSA) tensor undergoing chemical exchange can be used to monitor slow-to-intermediate timescale conformational exchange processes. Control experiments used d ₆ -DMS and alanine to confirm that the technique is monitoring reorientation of the CSA tensor rather than dipolar interactions or methyl group rotation. The application of this method to proteins could represent a new site-specific probe of conformational dynamics.     

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     

Structure and Disorder in an Unfolded State under Nondenaturing Conditions from Ensemble Models Consistent with a Large Number of Experimental Restraints

Obtaining detailed structural models of disordered states of proteins under nondenaturing conditions is important for a better understanding of both functional intrinsically disordered proteins and unfolded states of folded proteins. Extensive experimental characterization of the drk N-terminal SH3 domain unfolded state has shown that, although it appears to be highly disordered, it possesses significant nonrandom secondary and tertiary structure. In our previous attempts to generate structural models of the unfolded state using the program ENSEMBLE, we were limited by insufficient experimental restraints and conformational sampling. In this study, we have vastly expanded our experimental restraint set to include ¹H-¹⁵N residual dipolar couplings, small-angle X-ray scattering measurements, nitroxide paramagnetic relaxation enhancements, O₂-induced ¹³C paramagnetic shifts, hydrogen-exchange protection factors, and ¹⁵N R₂ data, in addition to the previously used nuclear Overhauser effects, amino terminal Cu²⁺-Ni²⁺ binding paramagnetic relaxation enhancements, J-couplings, chemical shifts, hydrodynamic radius, and solvent accessibility restraints. We have also implemented a new ensemble calculation methodology that uses iterative conformational sampling and seeks to calculate the simplest possible ensemble models. As a result, we can now generate ensembles that are consistent with much larger experimental data sets than was previously possible. Although highly heterogeneous and having broad molecular size distributions, the calculated drk N-terminal SH3 domain unfolded-state ensembles have very different properties than expected for random or statistical coils and possess significant nonnative α-helical structure and both native-like and nonnative tertiary structure.     

Determination of <Superscript>13</Superscript>C CSA Tensors: Extension of the Model-independent Approach to an RNA Kissing Complex Undergoing Anisotropic Rotational Diffusion in Solution

Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109–7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X–H two-spin systems (X = ¹³C or ¹⁵N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio κ₂=R₂^auto/R₂^cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X–H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic κ₂ depends on the anisotropy D_||/D_⊥ of rotational diffusion. In this paper, the field dependence of both κ₂ and its longitudinal counterpart κ₁=R₁^auto/R₁^cross are determined. For anisotropic rotational diffusion, our calculations show that the average κ_av = 1/2 (κ₁+κ₂), of the ratios is largely independent of the anisotropy parameter D_||/D_⊥. The field dependence of the average ratio κ_av may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor.     

Study of the rotational diffusion properties of peptides in solution

In this paper we examine the theory and method for obtaining rotational diffusion coefficients for peptides in dilute solution from ¹³C-nmr spin-lattice relaxation data. We show that even for the case of nearly equal observed relaxation times of chemically and magnetically nonequivalent alpha-carbons marked rotational anisotropy will be the usual case. We describe two interactive, minicomputer programs which are of general use in this type of work. The implications of this study on spectral density-based conformational determinations of peptides is discussed.     

Residue Specific Ribose and Nucleobase Dynamics of the cUUCGg RNA Tetraloop Motif by MNMR 13C Relaxation

The dynamics of the nucleobase and the ribose moieties in a 14-nt RNA cUUCGg hairpin-loop uniformly labeled with ¹³C and ¹⁵N were studied by ¹³C spin relaxation experiments. R₁, R_1ρ and the ¹³C-{¹H} steady-state NOE of C₆ and C_1′ in pyrimidine and C₈ and C_1′ in purine residues were obtained at 298 K. The relaxation data were analyzed by the model-free formalism to yield dynamic information on timescales of pico-, nano- and milli-seconds. An axially symmetric diffusion tensor with an overall rotational correlation time τ_c of 2.31±0.13 ns and an axial ratio of 1.35±0.02 were determined. Both findings are in agreement with hydrodynamic calculations. For the nucleobase carbons, the validity of different reported ¹³C chemical shift anisotropy values (Stueber, D. and Grant, D. M., 2002 J. Am. Chem. Soc. 124, 10539–10551; Fiala et al., 2000 J. Biomol. NMR 16, 291–302; Sitkoff, D. and Case, D. A., 1998 Prog. NMR Spectroscopy 32, 165–190) is discussed. The resulting dynamics are in agreement with the structural features of the cUUCGg motif in that all residues are mostly rigid (0.82 < S² < 0.96) in both the nucleobase and the ribose moiety except for the nucleobase of U7, which is protruding into solution (S² = 0.76). In general, ribose mobility follows nucleobase dynamics, but is less pronounced. Nucleobase dynamics resulting from the analysis of ¹³C relaxation rates were found to be in agreement with ¹⁵N relaxation data derived dynamic information (Akke et al., 1997 RNA 3, 702–709). Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Quantifying Lipari–Szabo modelfree parameters from 13CO NMR relaxation experiments

It is proposed to obtain effective Lipari–Szabo order parameters and local correlation times for relaxation vectors of protein ¹³CO nuclei by carrying out a ¹³CO-R₁ auto relaxation experiment, a transverse CSA/dipolar cross correlation and a transverse ¹³CO CSA/¹³CO–¹⁵N CSA/dipolar cross correlation experiment. Given the global rotational correlation time from ¹⁵N relaxation experiments, a new program COMFORD (CO-Modelfree Fitting Of Relaxation Data) is presented to fit the ¹³CO data to an effective order parameter , an effective local correlation time and the orientation of the CSA tensor with respect to the molecular frame. It is shown that the effective is least sensitive to rotational fluctuations about an imaginary axis and most sensitive to rotational fluctuations about an imaginary axis parallel to the NH bond direction. As such, the information is fully complementary to the ¹⁵N relaxation order parameter, which is least sensitive to fluctuations about the NH axis and most sensitive to fluctuations about the axis. The new paradigm is applied on data of Ca²⁺ saturated Calmodulin, and on available literature data for Ubiquitin. Our data indicate that the order parameters rapport on slower, and sometimes different, motions than the ¹⁵N relaxation order parameters. The CO local correlation times correlate well with the calmodulin’s secondary structure. Electronic Supplementary Material Supplementary material is available to authorized users in the online version of this article at .     

RNA phosphodiester backbone dynamics of a perdeuterated cUUCGg tetraloop RNA from phosphorus-31 NMR relaxation analysis

We have analyzed the relaxation properties of all ³¹P nuclei in an RNA cUUCGg tetraloop model hairpin at proton magnetic field strengths of 300, 600 and 900 MHz in solution. Significant H, P dipolar contributions to R ₁ and R ₂ relaxation are observed in a protonated RNA sample at 600 MHz. These contributions can be suppressed using a perdeuterated RNA sample. In order to interpret the ³¹P relaxation data (R ₁, R ₂), we measured the ³¹P chemical shift anisotropy (CSA) by solid-state NMR spectroscopy under various salt and hydration conditions. A value of 178.5 ppm for the ³¹P CSA in the static state (S ² = 1) could be determined. In order to obtain information about fast time scale dynamics we performed a modelfree analysis on the basis of our relaxation data. The results show that subnanosecond dynamics detected around the phosphodiester backbone are more pronounced than the dynamics detected for the ribofuranosyl and nucleobase moieties of the individual nucleotides (Duchardt and Schwalbe, J Biomol NMR 32:295–308, 2005; Ferner et al., Nucleic Acids Res 36:1928–1940, 2008). Furthermore, the dynamics of the individual phosphate groups seem to be correlated to the 5′ neighbouring nucleobases.     

Efficient analysis of macromolecular rotational diffusion from heteronuclear relaxation data

A novel program has been developed for the interpretation of ¹⁵N relaxation rates in terms of macromolecular anisotropic rotational diffusion. The program is based on a highly efficient simulated annealing/minimization algorithm, designed specifically to search the parametric space described by the isotropic, axially symmetric and fully anisotropic rotational diffusion tensor models. The high efficiency of this algorithm allows extensive noise-based Monte Carlo error analysis. Relevant statistical tests are systematically applied to provide confidence limits for the proposed tensorial models. The program is illustrated here using the example of the cytochrome c from Rhodobacter capsulatus, a four-helix bundle heme protein, for which data at three different field strengths were independently analysed and compared.     

Analysis of Sub-τc and Supra-τc Motions in Protein Gβ1 Using Molecular Dynamics Simulations

The functions of proteins depend on the dynamical behavior of their native states on a wide range of timescales. To investigate these dynamics in the case of the small protein Gβ1, we analyzed molecular dynamics simulations with the model-free approach of nuclear magnetic relaxation. We found amplitudes of fast timescale motions (sub-τ_c, where τ_c is the rotational correlation time) consistent with S² obtained from spin relaxation measurements as well as amplitudes of slow timescale motions (supra-τ_c) in quantitative agreement with S² order parameters derived from residual dipolar coupling measurements. The slow timescale motions are associated with the large variations of the ³J couplings that follow transitions between different conformational substates. These results provide further characterization of the large structural fluctuations in the native states of proteins that occur on timescales longer than the rotational correlation time.     

Anisotropic rotational diffusion in model-free analysis for a ternary DHFR complex

Model-free analysis has been extensively used to extract information on motions in proteins over a wide range of timescales from NMR relaxation data. We present a detailed analysis of the effects of rotational anisotropy on the model-free analysis of a ternary complex for dihydrofolate reductase (DHFR). Our findings show that the small degree of anisotropy exhibited by DHFR (D_||/D=1.18) introduces erroneous motional models, mostly exchange terms, to over 50% of the NH spins analyzed when isotropic tumbling is assumed. Moreover, there is a systematic change in S², as large as 0.08 for some residues. The significant effects of anisotropic rotational diffusion on model-free motional parameters are in marked contrast to previous studies and are accentuated by lowering of the effective correlation time using isotropic tumbling methods. This is caused by the preponderance of NH vectors aligned perpendicular to the principal diffusion tensor axis and is readily detected because of the high quality of the relaxation data. A novel procedure, COPED (COmparison of Predicted and Experimental Diffusion tensors) is presented for distinguishing genuine motions from the effects of anisotropy by comparing experimental relaxation data and data predicted from hydrodynamic analyses. The procedure shows excellent agreement with the slow motions detected from the axially symmetric model-free analysis and represents an independent procedure for determining rotational diffusion and slow motions that can confirm or refute established procedures that rely on relaxation data. Our findings show that neglect of even small degrees of rotational diffusion anisotropy can introduce significant errors in model-free analysis when the data is of high quality. These errors can hinder our understanding of the role of internal motions in protein function.     

Characterization of the overall and local dynamics of a protein with intermediate rotational anisotropy: Differentiating between conformational exchange and anisotropic diffusion in the B3 domain of protein G

Because the overall tumbling provides a major contribution to protein spectral densities measured in solution, the choice of a proper model for this motion is critical for accurate analysis of protein dynamics. Here we study the overall and backbone dynamics of the B3 domain of protein G using ¹⁵N relaxation measurements and show that the picture of local motions is markedly dependent on the model of overall tumbling. The main difference is in the interpretation of the elevated R ₂ values in the -helix: the isotropic model results in conformational exchange throughout the entire helix, whereas no exchange is predicted by anisotropic models that place the longitudinal axis of diffusion tensor almost parallel to the helix axis. Due to small size (fast tumbling) of the protein, the T ₁ values have low sensitivity to NH bond orientation. The diffusion tensor derived from orientation dependence of R ₂/R ₁ is anisotropic (D _par/D _perp=1.4), with a small rhombic component. In order to distinguish the correct picture of motion, we apply model-independent methods that are sensitive to conformational exchange and do not require knowledge of protein structure or assumptions about its dynamics. A comparison of the CSA/dipolar cross-correlation rate constants with ¹⁵N relaxation rates and the estimation of R _ex terms from relaxation data at 9.4 and 14.1 T indicate no conformational exchange in the helix, in support of the anisotropic models. The experimentally derived diffusion tensor is in excellent agreement with theoretical predictions from hydrodynamic calculations; a detailed comparison with various hydrodynamic models revealed optimal parameters for hydrodynamic calculations.     

13C spin relaxation measurements in RNA: Sensitivity and resolution improvement using spin-state selective correlation experiments

A set of new NMR pulse sequences has been designed for the measurement of ¹³C relaxation rate constants in RNA and DNA bases: the spin-lattice relaxation rate constant R(C_z), the spin-spin relaxation rate constant R(C₊), and the CSA-dipolar cross-correlated relaxation rate constant . The use of spin-state selective correlation techniques provides increased sensitivity and spectral resolution. Sensitivity optimised C-C filters are included in the pulse schemes for the suppression of signals originating from undesired carbon isotopomers. The experiments are applied to a 15% ¹³C-labelled 33-mer RNA–theophylline complex. The measured ratios indicate that ¹³C CSA tensors do not vary significantly for the same type of carbon (C₂, C₆, C₈), but that they differ from one type to another. In addition, conformational exchange effects in the RNA bases are detected as a change in the relaxation decay of the narrow ¹³C doublet component when varying the spacing of a CPMG pulse train. This new approach allows the detection of small exchange effects with a higher precision compared to conventional techniques.     

Redor in IS1S2 systems

An approach to the determination of the 2-¹³C chemical shift (CS) tensor orientation in pyrimidine bases via heteronuclear MAS NMR spectroscopy is presented. Considering a dipolar coupled spin 1/2 network of the type S₁-I-S₂ consisting of directly bonded heteronuclear spins, we have carried out numerical simulations to assess the sensitivity of I-S REDOR spinning sidebands to the Euler angles defining the orientation of the I-S₁ and I-S₂ dipolar vectors in the I spin CS tensor principal axes system. Our investigations clearly demonstrate the potential of I-S REDOR studies in IS₁S₂ systems for obtaining with high reliability and accuracy the I spin chemical shift tensor orientation in the molecular frame spanned by the two internuclear vectors I-S₁ and I-S₂. The significant contribution to the observed REDOR sideband intensities from anti-phase operator terms which are present at the start of the data acquisition is illustrated. The procedure for the recording and analysis of the I-S REDOR spectra in IS₁S₂ systems is presented and the measurement of the 2-¹³C CS tensor orientation in a polycrystalline sample of [1,3-¹⁵N₂, 2-¹³C] uracil, which is one of the four bases in RNA, is experimentally demonstrated.     

Model-free analysis for large proteins at high magnetic field strengths

Protein backbone dynamics is often characterized using model-free analysis of three sets of ¹⁵N relaxation data: longitudinal relaxation rate (R ₁), transverse relaxation rate (R ₂), and ¹⁵N–{H} NOE values. Since the experimental data is limited, a simplified model-free spectral density function is often used that contains one Lorentzian describing overall rotational correlation but not one describing internal motion. The simplified spectral density function may be also used in estimating the overall rotational correlation time, by making the R ₂/R ₁ largely insensitive to internal motions, as well as used as one of the choices in the model selection protocol. However, such approximation may not be valid for analysis of relaxation data of large proteins recorded at high magnetic field strengths since the contribution to longitudinal relaxation from the Lorentzian describing the overall rotational diffusion of the molecule is comparably small relative to that describing internal motion. Here, we quantitatively estimate the errors introduced by the use of the simplified spectral density in model-free analysis for large proteins at high magnetic field strength.     

Conformation of the common purine (β) ribosides in solution: further evidence for a correlation between N-S state of the ribose moiety and syn-anti equilibrium

The solution conformations of adenosine, guanosine and inosine in liquid ND₃ have been determined by NMR. Comparison of the Karplus analysis of the proton HR spectra of the ribose moiety obtained in this solvent with the data from aqueous solutions of A and I proves that the conformations of the nucleosides are very similar in both liquids. From the analysis of the vicinal coupling constants of the ring protons it has been deduced that the S state C(2′)-endo is slightly preferred. The mole fraction in S approximates 0.6 for all three nucleosides. C-13 relaxation measurements have been applied in the determination of the correlation times for rotational diffusion. Only at temperatures below −40‡ C is the pseudorotation of the furanoside ring slowed down sufficiently for it not to contribute to the measured relaxation rates. From NOE studies and T¹ measurements on the individual protons it is derived that the N, C(3′)-endo, form of the ribose is correlated with an anti conformation of the base (Y≈210‡ to 220‡) and the S, C(2′)-endo, form of the ribose with a syn conformation of the base (Y≈30‡ to 50‡). The glycosyl torsion angles derived for the two conformations of A, G, and I are equal within the limits of accuracy.     

Protein conformational exchange measured by 1H R1ρ relaxation dispersion of methyl groups

Activated dynamics plays a central role in protein function, where transitions between distinct conformations often underlie the switching between active and inactive states. The characteristic time scales of these transitions typically fall in the microsecond to millisecond range, which is amenable to investigations by NMR relaxation dispersion experiments. Processes at the faster end of this range are more challenging to study, because higher RF field strengths are required to achieve refocusing of the exchanging magnetization. Here we describe a rotating-frame relaxation dispersion experiment for ¹H spins in methyl ¹³CHD₂ groups, which improves the characterization of fast exchange processes. The influence of ¹H–¹H rotating-frame nuclear Overhauser effects (ROE) is shown to be negligible, based on a comparison of R _1ρ relaxation data acquired with tilt angles of 90° and 35°, in which the ROE is maximal and minimal, respectively, and on samples containing different ¹H densities surrounding the monitored methyl groups. The method was applied to ubiquitin and the apo form of calmodulin. We find that ubiquitin does not exhibit any ¹H relaxation dispersion of its methyl groups at 10 or 25 °C. By contrast, calmodulin shows significant conformational exchange of the methionine methyl groups in its C-terminal domain, as previously demonstrated by ¹H and ¹³C CPMG experiments. The present R _1ρ experiment extends the relaxation dispersion profile towards higher refocusing frequencies, which improves the definition of the exchange correlation time, compared to previous results.