Direct measurement of the 15N CSA/dipolar relaxation interference from coupled HSQC spectra

Here we propose a method for the measurement of the ¹⁵N CSA/dipolar relaxation interference based on direct comparison of the ¹⁵N doublet components observed in a ¹H-coupled ¹H-¹⁵N HSQC-type spectrum. This allows the determination of the cross-correlation rates with no need for correction factors associated with other methods. The signal overlap problem of coupled HSQC spectra is addressed here by using the IPAP scheme (Ottiger et al., 1998). The approach is applied to the B3 domain of protein G to show that the method provides accurate measurements of the ¹⁵N CSA/dipolar cross-correlation rates.     

A Sensitive Pulse Scheme for Measuring the Backbone Dihedral Angle ψ Based on Cross-correlation Between 13Cα-1Hα Dipolar and Carbonyl Chemical Shift Anisotropy Relaxation Interactions

A pulse scheme for measuring cross-correlation between 13C-1H dipolar and carbonyl chemical shift anisotropy relaxation mechanisms is presented from which the protein backbone dihedral angle is measured. The method offers significant sensitivity gains relative to our recently published scheme for measuring based on this cross-correlation effect [Yang et al. (1997) J. Am. Chem. Soc., 119, 11938-11940]. The utility of the method is demonstrated with an application to a 42 kDa complex of 15N,13C-labeled maltose binding protein and -cyclodextrin.     

Local mobility of 15N labeled biomolecules characterized through cross-correlation rates: Applications to paramagnetic proteins*

The mobility of 15N labeled proteins can be characterized by measuring the cross-correlation rates N,NI that govern the conversion of Zeeman order Nz of an amide 15N nucleus into longitudinal two-spin order 2NzIz involving the amide 15N and 1H nuclei. This represents an alternative to the measurement of 15N self-relaxation rates 1/T1 and 1/T2 or 1/T1. The rate of interconversion between Nz and 2NzIz is due to cross-correlation between fluctuations of different interactions and is not affected by a variety of relaxation mechanisms that contribute to the self-relaxation rates 1/T1, 1/T2 and 1/T1. Spin diffusion among protons, which affects the measurements, can be quenched by various means that are evaluated by experiments and simulations. By applying an off-resonance radio-frequency (RF) field in the vicinity of the nitrogen resonance, the spectral density function J() can be determined at the frequency origin and at the nitrogen Larmor frequency. The methods are applied to the paramagnetic High-Potential Iron-Sulfur Protein iso I (HiPIP I) from E. halophila in its reduced state.     

Measurement of 15N csa/dipolar cross-correlation rates by means of Spin State Selective experiments

We propose a method for the determination of (15)N csa/dipolar cross-correlation rates based on the measurement of the two apparent transverse (or longitudinal) relaxation rates associated with each component of the nitrogen doublet (N(alpha) and N(beta)). This is achieved by inserting a spin state selective scheme in conventional inverse Carr-Purcell-Meiboom-Gill (or inversion-recovery) pulse sequence which allows for the edition of a HSQC-type spectrum for each of the spin states. Transverse cross-correlation rates necessitate two independent sets of measurements (for N(alpha) and N(beta), respectively), whereas for longitudinal cross correlation rates, besides N(alpha) and N(beta) measurements, the method requires the knowledge of both the (15)N longitudinal auto-relaxation rate and the longitudinal two-spin order (2NzHz) auto-relaxation rate. These additional parameters are mandatory because of the non-exponential behavior of the N(alpha) and N(beta) longitudinal decays. Conversely, the present method does not require any complex manipulation of 2D spectra, the cross-correlation rates being obtained from the difference of the two (N(alpha) and N(beta)) apparent relaxation rates. This approach is applied to (15)N-labelled ubiquitin at two different magnetic fields (9.4 T and 14.1 T).     

Measurement of the protein backbone dihedral angle φ based on quantification of remote CSA/DD interference in inter-residue 13C′(i − 1)-13Cα(i) multiple-quantum coherences

A novel triple-resonance NMR method is presented for the measurement of the protein backbone dihedral angle based on differential multiple-quantum relaxation induced by relaxation interference between ¹H(i)-¹³C(i) dipolar and ¹³C(i–1) (carbonyl) chemical shift anisotropy mechanisms. The method employs a simultaneous transfer of ¹⁵N magnetization to the inter- and intra-residue ¹³C carbons as well as the directly attached carbonyl carbon ¹³C. Results obtained on ¹³C,¹⁵N-labeled ubiquitin demonstrate the potential of the method.     

The use of TROSY for detection and suppression of conformational exchange NMR line broadening in biological macromolecules

The interference between conformational exchange-induced time-dependent variations of chemical shifts in a pair of scalar coupled ¹H and ¹⁵N spins is used to construct novel TROSY-type NMR experiments to suppress NMR signal loss in [¹⁵N,¹H]-correlation spectra of a 14-mer DNA duplex free in solution and complexed with the Antp homeodomain. An analysis of double- and zero-quantum relaxation rates of base ¹H–¹⁵N moieties showed that for certain residues the contribution of conformational exchange-induced transverse relaxation might represent a dominant relaxation mechanism, which, in turn, can be effectively suppressed by TROSY. The use of the new TROSY method for exchange-induced transverse relaxation optimization is illustrated with two new experiments, 2D ^h1 J _HN,^h2 J _NN-quantitative [¹⁵N,¹H]-TROSY to measure ^h1 J _HN and ^h2 J _NN scalar coupling constants across hydrogen bonds in nucleic acids, and 2D (^h2 J _NN+^h1 J _NH)-correlation-[¹⁵N,¹H]-TROSY to correlate ¹H^N chemical shifts of bases with the chemical shifts of the tertiary ¹⁵N spins across hydrogen bonds using the sum of the trans-hydrogen bond coupling constants in nucleic acids.     

Similarities between intra- and intermolecular hydrogen bonds in RNA kissing complexes found by means of cross-correlated relaxation

The bond lengths and dynamics of intra- and intermolecular hydrogen bonds in an RNA kissing complex have been characterized by determining the NMR relaxation rates of various double- and triple-quantum coherences that involve an imino proton and two neighboring nitrogen-15 nuclei belonging to opposite bases. New experiments allow one to determine the chemical shift anisotropy of the imino protons. The bond lengths derived from dipolar relaxation and the lack of modulations of the nitrogen chemical shifts indicate that the intermolecular hydrogen bonds which hold the kissing complex together are very similar to the intramolecular hydrogen bonds in the double-stranded stem of the RNA.     

Pressure effect on the dynamics of an isolated α-helix studied by 15N-1H NMR relaxation

Dynamics and structure of (1–36)bacteriorhodopsin solubilized in chloroform/methanol mixture (1:1) were investigated by ¹H-¹⁵N NMR spectroscopy under a hydrostatic pressure of 2000 bar. It was shown that the peptide retains its spatial structure at high pressure. ¹⁵N transverse and longitudinal relaxation times, ¹⁵N{¹H} nuclear Overhauser effects, chemical shifts and the translation diffusion rate of the peptide at 2000 bar were compared with the respective data at ambient pressure [Orekhov et al. (1999) J. Biomol. NMR, 14, 345–356]. The model free analysis of the relaxation data for the helical 9–31 fragment revealed that the high pressure decreases the overall rotation and translation diffusion, as well as apparent order parameters of fast picosecond internal motions (S² _f) but has no effect on internal nanosecond motions (S² _s and _s) of the peptide. The decrease of translation and overall rotation diffusion was attributed to the increase in solvent viscosity and the decrease of apparent order parameters S² _f to a compression of hydrogen bonds. It is suggested that this compression causes an elongation of H-N bonds and a decrease of absolute values of chemical shift anisotropy (CSA). In particular, the observed decrease of S² _f at 2000 bar can be explained by 0.001 nm increase of N-H bond lengths and 10 ppm decrease of ¹⁵N CSA values.     

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.     

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.     

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 effect of noncollinearity of 15N-1H dipolar and 15N CSA tensors and rotational anisotropy on 15N relaxation, CSA/dipolar cross correlation, and TROSY

Current approaches to 15N relaxation in proteins assume that the 15N-1H dipolar and 15N CSA tensors are collinear. We show theoretically that, when there is significant anisotropy of molecular rotation, different orientations of the two tensors, experimentally observed in proteins, nucleic acids, and small peptides, will result in differences in site- specific correlation functions and spectral densities. The standard treatments of the rates of longitudinal and transverse relaxation of amide 15N nuclei, of the 15N CSA/15N-1H dipolar cross correlation, and of the TROSY experiment are extended to account for the effect of noncollinearity of the 15N-1H dipolar and 15N CSA (chemical shift anisotropy) tensors. This effect, proportional to the degree of anisotropy of the overall motion, (D/D–1), is sensitive to the relative orientation of the two tensors and to the orientation of the peptide plane with respect to the diffusion coordinate frame. The effect is negligible at small degrees of anisotropy, but is predicted to become significant for D/D1.5, and at high magnetic fields. The effect of noncollinearity of 15N CSA and 15N-1H dipolar interaction is sensitive to both gross (hydrodynamic) properties and atomic-level details of protein structure. Incorporation of this effect into relaxation data analysis is likely to improve both precision and accuracy of the derived characteristics of protein dynamics, especially at high magnetic fields and for molecules with a high degree of anisotropy of the overall motion. The effect will also make TROSY efficiency dependent on local orientation in moderately anisotropic systems.     

Cross-correlation between a carbonyl C' chemical shift anisotropy and a long-range dipolar C'HA coupling in proteins using symmetrical reconversion

A new sequence is described to measure the cross-correlation rates between the chemical shift anisotropy of the carbonyl carbon-13 nucleus and the dipole-dipole interaction between this carbonyl and the alpha-proton in proteins. The sequence is based on the symmetrical reconversion principle and is insensitive to experimental errors and to violations of the secular approximation. The cross-correlation rate depends on the backbone angle . The advantages and limitations of the sequence are discussed.     

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.     

Cross correlations between 13C-1H dipolar interactions and 15N chemical shift anisotropy in nucleic acids

Two sets of cross-correlated relaxation rates involving chemical shift anisotropy and dipolar interactions have been measured in an RNA kissing complex. In one case, both the CSA and dipolar interaction tensors are located on the same nucleotide base and are rigidly fixed with respect to each other. In the other case, the CSA tensor is located on the nucleotide base whereas the dipolar interaction is located on the adjoining ribose unit. Analysis of the measured rates in terms of isotropic or anisotropic rotational diffusion has been carried out for both cases. A marked difference between the two models is observed for the cross-correlation rates involving rigidly fixed spin interactions. The influence of internal motions about the glycosidic linkage between the nucleotide base and the ribose unit on cross-correlated relaxation rates has been estimated by applying a model of restricted rotational diffusion. Local motions seem to have a more pronounced effect on cross-correlated relaxation rates when the two spin interactions are not rigidly fixed with respect to each other.     

Effects of Protein–pheromone Complexation on Correlated Chemical Shift Modulations

Major urinary protein (MUP) is a pheromone-carrying protein of the lipocalin family. Previous studies by isothermal titration calorimetry (ITC) show that the affinity of MUP for the pheromone 2-methoxy-3-isobutylpyrazine (IBMP) is mainly driven by enthalpy, with a small unfavourable entropic contribution. Entropic terms can be attributed in part to changes in internal motions of the protein upon binding. Slow internal motions can lead to correlated or anti-correlated modulations of the isotropic chemical shifts of carbonyl C′ and amide N nuclei. Correlated chemical shift modulations (CSM/CSM) in MUP have been determined by measuring differences of the transverse relaxation rates of zero- and double-quantum coherences ZQC{C′N} and DQC{C′N}, and by accounting for the effects of correlated fluctuations of dipole–dipole couplings (DD/DD) and chemical shift anisotropies (CSA/CSA). The latter can be predicted from tensor parameters of C′ and N nuclei that have been determined in earlier work. The effects of complexation on slow time-scale protein dynamics can be determined by comparing the temperature dependence of the relaxation rates of APO-MUP (i.e., without ligand) and HOLO-MUP (i.e., with IBMP as a ligand). Electronic supplementary material Electronic supplementary material is available for this article at and accessible for authorised users.     

Structural properties of polyubiquitin chains in solution

Because polyubiquitin chain structure modulates Ub-mediated signaling, knowledge of the physiological conformations of chain signals should provide insights into specific recognition. Here, we characterized the solution conformations of K48-linked Ub(2) and Ub(4) using a combination of NMR techniques, including chemical shift mapping of the interdomain interface, domain orientation measurements on the basis of 15N relaxation and residual dipolar couplings, and the solvent accessibility studies. Our data indicate a switch in the conformation of Ub(2), from open to closed, with increasing pH. The closed conformation features a well-defined interface that is related to, but distinguishable from, that observed in the Ub(2) crystal structure. This interface is dynamic in solution, such that important hydrophobic residues (L8, I44, V70) that are sequestered at the interface in the closed conformation may be accessible for direct interactions with recognition factors. Our results suggest that the distal two units of Ub(4), which is the minimum signal for efficient proteasomal degradation, may adopt the closed Ub(2) conformation.     

A method to construct confidence interval for expected response to multi-trait selection

Summary Confidence intervals are constructed for the expected responses to three types of multi-trait selection. The influence of numbers of replicates and genotypes used in a progeny test experiment on the precision of response of multi-trait selection is discussed based on the structure of the established intervals. Special attention is paid to the characteristics of the intervals constructed for the conventional least square selection indices.     

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.