Estimates of methyl 13C and 1H CSA values (Δσ) in proteins from cross-correlated spin relaxation

Simple pulse schemes are presented for the measurement of methyl ¹³C and ¹H CSA values from ¹H–¹³C dipole/¹³C CSA and ¹H–¹³C dipole/¹H CSA cross-correlated relaxation. The methodology is applied to protein L and malate synthase G. Average ¹³C CSA values are considerably smaller for Ile than Leu/Val (17 vs 25 ppm) and are in good agreement with previous solid state NMR studies of powders of amino acids and dipeptides and in reasonable agreement with quantum-chemical DFT calculations of methyl carbon CSA values in peptide fragments. Small averaged ¹H CSA values on the order of 1 ppm are measured, consistent with a solid state NMR determination of the methyl group ¹H CSA in dimethylmalonic acid.     

Spin-state selection for increased confidence in cross-correlation rates measurements

A new approach is described for measuring chemical shift anisotropy (CSA)/dipolar cross-correlated relaxation (CCR) rates based on the selection of the individual ¹⁵N doublet components prior to the relaxation period. The method uses the spin-state-selective element (S³E) of Sørensen and co-authors [Meissner et al. (1997) J. Mag. Reson., 128, 92–97]. The main advantage of the new method compared to other J-resolved experiments is that it does not create problems of additional signal overlap encountered in coupled spectra. At the same time, this approach allows a simpler control of magnetization pathways than the indirect methods. The method is demonstrated for the B3 domain of protein G.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s10858-004-7562-8     

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.     

Cross-correlated spin relaxation effects in methyl <Superscript>1</Superscript>H CPMG-based relaxation dispersion experiments: Complications and a simple solution

Artifacts associated with the measurement of methyl ¹H single quantum CPMG-based relaxation dispersion profiles are described. These artifacts arise due to the combination of cross-correlated spin relaxation effects involving intra-methyl ¹H–¹H dipolar interactions and imperfections in ¹H refocusing pulses that are applied during CPMG intervals that quantify the effects of chemical exchange on measured transverse relaxation rates. As a result substantial errors in extracted exchange parameters can be obtained. A simple work-around is presented where the ¹H chemical shift difference between the exchanging states is extracted from a combination of ¹³C single quantum and ¹³C–¹H multiple quantum dispersion profiles. The approach is demonstrated with an application to a folding/unfolding reaction involving a G48M mutant Fyn SH3 domain.     

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.     

Transverse relaxation optimized triple-resonance NMR experiments for nucleic acids

Triple resonance HCN and HCNCH experiments are reliable methods of establishing sugar-to-base connectivity in the NMR spectra of isotopicaly labeled oligonucleotides. However, with larger molecules the sensitivity of the experiments is drastically reduced due to relaxation processes. Since the polarization transfer between ¹³C and ¹⁵N nuclei relies on rather small heteronuclear coupling constants (11–12 Hz), the long evolution periods (up to 30–40 ms) in the pulse sequences cannot be avoided. Therefore any effort to enhance sensitivity has to concentrate on manipulating the spin system in such a way that the spin–spin relaxation rates would be minimized. In the present paper we analyze the efficiency of the two known approaches of relaxation rate control, namely the use of multiple-quantum coherence (MQ) and of the relaxation interference between chemical shift anisotropy and dipolar relaxation – TROSY. Both theoretical calculations and experimental results suggest that for the sugar moiety (H1-C1-N1/9) the MQ approach is clearly preferable. For the base moiety (H6/8-C6/8-N1/9), however, the TROSY shows results superior to the MQ suppression of the dipole–dipole relaxation at moderate magnetic fields (500 MHz) and the sensitivity improvement becomes dramatically more pronounced at very high fields (800 MHz). The pulse schemes of the triple-resonance HCN experiments with sensitivity optimized performance for unambiguous assignments of intra-residual sugar-to-base connectivities combining both approaches are presented.     

31P NMR relaxation measurements of the phosphate backbone of a double stranded hexadeoxynucleotide in solution: determination of the chemical shift anisotropy

The five phosphates of the deoxynucleotide d(CpGpTpApCpG)₂ have been assigned by two-dimensional heteronuclear NMR spectroscopy. The chemical shift anisotropy and correlation time of each phosphate group has been determined from measurements of the spin-lattice, spin-spin relaxation rate constants and the ³¹P-{¹H} nuclear Overhauser enhancement (NOE) at three magnetic field strengths (4.7 T, 9.4 T, and 11.75 T) and two temperatures (288 K and 298 K). As expected, the relaxation data require two mechanisms to account for the observed rate constants, i.e. dipole-dipole and chemical shift anisotropy. At 9.4 T and 11.75 T, the latter mechanism dominates the relaxation, leading to insignificant NOE intensities. The correlation time, chemical shift anisotropy and effective P-H distance were obtained from least-squares fitting to the data. Comparison of the fitted value for the correlation time with that obtained from ¹H measurements shows that the molecule behaves essentially as rigid rotor on the nanosecond timescale. Large amplitude motions observed in long segments of DNA are due to bending motions that do not contribute significantly to relaxation in short oligonucleotides.Abbreviations CSA chemical shift anisotropy - NOE nuclear Overhauser enhancement Offprint requests to: A. N. Lane     

Sensitivity enhancement in NMR of macromolecules by application of optimal control theory

NMR of macromolecules is limited by large transverse relaxation rates. In practice, this results in low efficiency of coherence transfer steps in multidimensional NMR experiments, leading to poor sensitivity and long acquisition times. The efficiency of coherence transfer can be maximized by design of relaxation optimized pulse sequences using tools from optimal control theory. In this paper, we demonstrate that this approach can be adopted for studies of large biological systems, such as the 800 kDa chaperone GroEL. For this system, the ¹H–¹⁵N coherence transfer module presented here yields an average sensitivity enhancement of 20–25% for cross-correlated relaxation induced polarization transfer (CRIPT) experiments.Supplementary material to this paper is available in electronic form at http://dx.doi.org/10.1007/s10858-005-3592-0     

C, N CP MAS and high resolution multinuclear NMR study of methyl

Temperature-dependence of protein dynamics can provide information on details of the free energy landscape by probing the characteristics of the potential responsible for the fluctuations. We have investigated the temperature-dependence of picosecond to nanosecond backbone dynamics at carbonyl carbon sites in chicken villin headpiece subdomain protein using a combination of three NMR relaxation rates: ¹³C′ longitudinal rate, and two cross-correlated rates involving dipolar and chemical shift anisotropy (CSA) relaxation mechanisms, ¹³C′/¹³C′-¹³C^α CSA/dipolar and ¹³C′/¹³C′–¹⁵N CSA/dipolar. Order parameters have been extracted using the Lipari-Szabo model-free approach assuming a separation of the time scales of internal and molecular motions in the 2–16°C temperature range. There is a gradual deviation from this assumption from lower to higher temperatures, such that above 16°C the separation of the time scales is inconsistent with the experimental data and, thus, the Lipari-Szabo formalism can not be applied. While there are variations among the residues, on the average the order parameters indicate a markedly steeper temperature dependence at backbone carbonyl carbons compared to that probed at amide nitrogens in an earlier study. This strongly advocates for probing sites other than amide nitrogen for accurate characterization of the potential and other thermodynamics characteristics of protein backbone.     

Temperature dependence of fast carbonyl backbone dynamics in chicken villin headpiece subdomain

Temperature-dependence of protein dynamics can provide information on details of the free energy landscape by probing the characteristics of the potential responsible for the fluctuations. We have investigated the temperature-dependence of picosecond to nanosecond backbone dynamics at carbonyl carbon sites in chicken villin headpiece subdomain protein using a combination of three NMR relaxation rates: ¹³C′ longitudinal rate, and two cross-correlated rates involving dipolar and chemical shift anisotropy (CSA) relaxation mechanisms, ¹³C′/¹³C′-¹³C^α CSA/dipolar and ¹³C′/¹³C′–¹⁵N CSA/dipolar. Order parameters have been extracted using the Lipari-Szabo model-free approach assuming a separation of the time scales of internal and molecular motions in the 2–16°C temperature range. There is a gradual deviation from this assumption from lower to higher temperatures, such that above 16°C the separation of the time scales is inconsistent with the experimental data and, thus, the Lipari-Szabo formalism can not be applied. While there are variations among the residues, on the average the order parameters indicate a markedly steeper temperature dependence at backbone carbonyl carbons compared to that probed at amide nitrogens in an earlier study. This strongly advocates for probing sites other than amide nitrogen for accurate characterization of the potential and other thermodynamics characteristics of protein backbone.     

Measurement of 13Cα-13CO cross-relaxation rates in 15N-/13C-labelled proteins

Summary Internal motions play an important role in the biological function of proteins and NMR relaxation studies may characterize them over a wide range of frequencies. An experimental pulse scheme is proposed for the measurement of the ¹³CO-¹³C cross-relaxation rate. For sensitivity reasons, this measurement is performed in an indirect manner through several coherence transfer steps, which should thus be calibrated independently. Contributions of other relaxation pathways can be eliminated by the determination of the initial slope of the buildup curve. The cross-relaxation rates have been determined on a ¹⁵N-/¹³C-labelled 116-residue protein and the significant variations along the sequence have been interpreted as evidence of an increased amount of fast local motion.     

Comparison of fast backbone dynamics at amide nitrogen and carbonyl sites in dematin headpiece C-terminal domain and its S74E mutant

We perform a detailed comparison of fast backbone dynamics probed at amide nitrogen versus carbonyl carbon sites for dematin headpiece C-terminal domain (DHP) and its S74E mutant (DHPS74E). Carbonyl dynamics is probed via auto-correlated longitudinal rates and transverse C′/C′-C^α CSA/dipolar and C′/C′–N CSA/dipolar cross-correlated rates, while ¹⁵N data are taken from a previous study. Resulting values of effective order parameters and internal correlation times support the conclusion that C′ relaxation reports on a different subset of fast motions compared to those probed at N–H bond vectors in the same peptide planes. ¹³C′ order parameters are on the average 0.08 lower than ¹⁵N order parameters with the exception of the flexible loop region in DHP. The reduction of mobility in the loop region upon the S74E mutation can be seen from the ¹⁵N order parameters but not from the ¹³C order parameters. Internal correlation times at ¹³C′ sites are on the average an order of magnitude longer than those at ¹⁵N sites for the well-structured C-terminal subdomains, while the more flexible N-terminal subdomains have more comparable average internal correlation times.     

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.     

Improved accuracy of <Superscript>15</Superscript>N–<Superscript>1</Superscript>H scalar and residual dipolar couplings from gradient-enhanced IPAP-HSQC experiments on protonated proteins

The presence of dipole-dipole cross-correlated relaxation as well as unresolved E.COSY effects adversely impacts the accuracy of ¹ J _NH splittings measured from gradient-enhanced IPAP-HSQC spectra. For isotropic samples, the size of the systematic errors caused by these effects depends on the values of ² J _NHα , ³ J _NHβ and ³ J _HNHα . Insertion of band-selective ¹H decoupling pulses in the IPAP-HSQC experiment eliminates these systematic errors and for the protein GB3 yields ¹ J _NH splittings that agree to within a root-mean-square difference of 0.04 Hz with values measured for perdeuterated GB3. Accuracy of the method is also highlighted by a good fit to the GB3 structure of the ¹H-¹⁵N RDCs extracted from the minute differences in ¹J_NH splitting measured at 500 and 750 MHz ¹H frequencies, resulting from magnetic susceptibility anisotropy. A nearly complete set of ² J _NHα couplings was measured in GB3 in order to evaluate whether the impact of cross-correlated relaxation is dominated by the ¹⁵N–¹H ^α or ¹⁵N–¹H ^β dipolar interaction. As expected, we find that ² J _NHα  ≤ 2 Hz, with values in the α-helix (0.86 ± 0.52 Hz) slightly larger than in β-sheet (0.66 ± 0.26 Hz). Results indicate that under isotropic conditions, N–H^N/N–H ^β cross-correlated relaxation often dominates. Unresolved E.COSY effects under isotropic conditions involve ³ J _HNHα and J _NHα , but when weakly aligned any aliphatic proton proximate to both N and H^N can contribute. Electronic supplementary material  The online version of this article (doi:) contains supplementary material, which is available to authorized users.     

Model selection for the interpretation of protein side chain methyl dynamics

A number of different dynamics models are considered for fitting ¹³C and ²H side chain methyl relaxation rates. It is shown that in cases where nanosecond time scale dynamics are present the extended Lipari–Szabo model which is explicitly parameterized to include the effects of slow motions can produce wide distributions of fitting parameters even in cases where the errors are relatively small and large numbers of relaxation rates are considered. In contrast, fits of ¹⁵N backbone dynamics using this model are far more robust. The origin of this difference is analyzed and can be explained by the different functional forms of the spectral density in these two cases. The utility of a number of models for the analysis of methyl side chain dynamics is presented.     

Mapping of the spectral density function of a Cα−Hα bond vector from NMR relaxation rates of a 13C-labelled α-carbon in motilin

Summary The peptide hormone motilin was synthesised with a ¹³C-enriched -carbon in the leucine at position 10. In aqueous solution, six different relaxation rates were measured for the ¹³C–H fragment as a function of temperature and with and without the addition of 30% (v/v) of the cosolvent d ₂-1,1,1,3,3,3-hexafluoro-2-propanol (HFP). The relaxation rates were analysed employing the spectral density mapping technique introduced by Peng and Wagner [(1992) J. Magn. Reson., 98, 308–322] and using the model-free approach by Lipari and Szabo [(1982) J. Am. Chem. Soc., 104, 4546–4570]. The fit to various models of dynamics was also considered. Different procedures to evaluate the overall rotational correlation time were compared. A single exponential time correlation function was found to give a good fit to the measured spectral densities only for motilin in 30% (v/v) HFP at low temperatures, whereas at high temperatures in this solvent, and in D₂O at all temperatures, none of the considered models gave an acceptable fit. A new empirical spectral density function was tested and found to accurately fit the experimental spectral density mapping points. The application of spectral density mapping based on NMR relaxation data for specific ¹³C–¹H vector is shown to be a highly useful method to study biomolecular dynamics. Advantages are high sensitivity, high precision and uniform sampling of the spectral density function over the frequency range.Abbreviations CD circular dichroism - NOE nuclear Overhauser enhancement - NOESY two-dimensional NOE spectroscopy - INEPT insensitive nuclei enhanced by polarisation transfer - DANTE delays alternating with nutations for tailored excitation - WALTZ-16 wideband, alternating phase, low-power technique for zero residual splitting - FID Free induction decay - ppm parts per million - TSPA 3-trimethylsilyl-(3,3,2,2-d)-propionic acid - HFP d ₂-1,1,1,3,3,3-hexafluoro-2-propanol - CPMG Carr-Purcell-Meiboom-Gill - TFD time-resolved fluorescence depolarisation - CSA chemical shift anisotropy Partly presented at the symposium Dynamics and Function of Biomolecules, Szeged, Hungary, July 31–August 2, 1993.     

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.     

Selectively 13C-enriched DNA: Dynamics of the C1′-H1′ vector in d(CGCAAATTTGCG)2

Summary In order to examine the internal dynamic processes of the dodecamer d(CGCAAATTTGCG)₂, the ¹³C-enriched oligonucleotide has been synthesized. The three central thymines were selectively ¹³C-labeled at the C1′ position and their spin-lattice relaxation parameters R(C_Z), R(C_X,Y), R(H_Z→C_Z), R(2H_ZC_Z), R(2H_ZC_X,Y) and R(H _infZ ^supC ) were measured. Density functions were computed for two models of internal motions. Comparisons of the experimental data were made with the spin-lattice relaxation rates rather than with the density functions, whose values were altered by accumulation of the uncertainties of each relaxation rate measurement. The spin-lattice relaxation rates were computed with respect to the motions of the sugar around the C1′-N1 bond. A two-state jump model between the anti- and syn-conformations with P(anti)/P(syn)=91/9 or a restricted rotation model with Δχ=28° and an internal diffusion coefficient of 30×10⁷ s^-1 gave a good fit with the experimental data. Twist, tilt or roll base motions have little effect on ¹³C1′ NMR relaxation. Simulation of spin-relaxation rates with the data obtained at several temperatures between 7 and 32 °C, where the dodecamer is double stranded, shows that the internal motion amplitude is independent of the temperature within this range, as expected for internal motion. Using the strong correlation which exists in a B-DNA structure between the χ and δ angle, we suggest that the change in the glycosidic angle value should be indicative of a sugar puckering between the C1′-exo and C2′-endo conformations.     

An NMR investigation of putative interresidue H-bonding in methyl α-cellobioside in solution

Methyl α-cellobioside (methyl β-d-glucopyranosyl-(1→4)-α-d-glucopyranoside) was labeled with ¹³C at C4′ for use in NMR studies in DMSO-d₆ solvent to attempt the detection of a trans-H-bond J-coupling (^3hJ_CCOH) between C4′ and OH3. Analysis of the OH3 signal at 600 MHz revealed only the presence of two homonuclear J-couplings: ³J_H3,OH3 and a smaller, longer range J_HH. No evidence for ^3hJ_C4′,OH3 was found. The longer range J_HH was traced to ⁴J_H4,OH3 based on 2D ¹H–¹H COSY data and inspection of the H2 and H4 signal lineshapes. A limited set of DFT calculations was performed on a methyl cellobioside mimic to evaluate the structural dependencies of ⁴J_H2,O3H and ⁴J_H4,O3H on the H3–C3–O3–H torsion angle. Computed couplings range from about −0.7 to about +1.1 Hz, with maximal values observed when the C–H and O–H bonds are roughly diaxial.     

Interference between Cross-correlated Relaxation and the Measurement of Scalar and Dipolar Couplings by Quantitative J

The effects of cross-correlated relaxation in Quantitative J methods are analyzed. One-bond ¹H–¹³C scalar and dipolar couplings of protein methine and methylene sites are obtained by monitoring proton and carbon magnetization in Quantitative J experiments. We find that scalar and dipolar couplings of the same pair of nuclei vary depending on the type of magnetization involved. These discrepancies can be as large as several Hz for methylene moieties. The contribution of dynamic frequency shifts, which are known to affect J couplings, is too small to explain the observed differences. We show that processes of magnetization transfer originated by cross-correlated relaxation are largely responsible for these discrepancies. We estimate the error transferred to methylene J values by cross-correlation interference, and show that is close to the experimentally observed one. Furthermore, this analysis indicates that cross-correlated relaxation effects under isotropic and anisotropic media differ, indicating that errors are not cancelled in residual dipolar coupling measurements.