Errors in the measurement of cross-correlated relaxation rates and how to avoid them

Accurate measurement of dipole/dipole transverse cross-correlated relaxation [Formula: see text] in methylenes and primary amines of uniformly [Formula: see text]-labeled proteins

Side chains possess a broader conformational space (compared to the backbone) and are directly affected by intra- and intermolecular interactions, hence their dynamics and the corresponding NMR relaxation data are more sensitive and informative. Nevertheless, transverse relaxation in [Formula: see text] ([Formula: see text] or [Formula: see text]) spin systems is predominantly non-measurable in uniformly [Formula: see text]-labeled proteins due to cross-correlation effects. In the present publication, we propose a number of pulse sequences for accurate and precise measurement of the dipole-dipole transverse cross-correlated relaxation rate [Formula: see text], which, similarly to [Formula: see text] measurements, provides information about the amplitudes of intramolecular dynamics. The suggested approach has allowed us to circumvent a number of obstacles that were limiting earlier applications of [Formula: see text]: (1) impossibility of transmission of the central component of the triplet of [Formula: see text] group to [Formula: see text]-acquisition via INEPT has been solved by transmission of the averaged signal of "inner" and "outer" components of the triplet; (2) direct recording of the entire triplets resulting in substantial overlap of side chain signals has been replaced by recording of individual singlets with the use of [Formula: see text]-modulated approach and constant-time evolution; (3) low sensitivity has been enhanced via proton acquisition which required special attention to a zero-quantum coherence evolution. The proposed method expands the set of "dynamics sensors" covering protein side chains and substantially improves the quality and the level of detail of experimental data describing dynamic processes in proteins and protein complexes.

Distance-independent Cross-correlated Relaxation and Isotropic Chemical Shift Modulation in Protein Dynamics Studies

Cross-correlated relaxation (CCR) in multiple-quantum coherences differs from other relaxation phenomena in its theoretical ability to be mediated across an infinite distance. The two interfering relaxation mechanisms may be dipolar interactions, chemical shift anisotropies, chemical shift modulations or quadrupolar interactions. These properties make multiple-quantum CCR an attractive probe for structure and dynamics of biomacromolecules not accessible from other measurements. Here, we review the use of multiple-quantum CCR measurements in dynamics studies of proteins. We compile a list of all experiments proposed for CCR rate measurements, provide an overview of the theory with a focus on protein dynamics, and present applications to various protein systems.

NMR relaxation parameters of methyl groups as a tool to map the interfaces of helix-helix interactions in membrane proteins

In the case of soluble proteins, chemical shift mapping is used to identify the intermolecular interfaces when the NOE-based calculations of spatial structure of the molecular assembly are impossible or impracticable. However, the reliability of the membrane protein interface mapping based on chemical shifts or other relevant parameters was never assessed. In the present work, we investigate the predictive power of various NMR parameters that can be used for mapping of helix-helix interfaces in dimeric TM domains. These parameters are studied on a dataset containing three structures of helical dimers obtained for two different proteins in various membrane mimetics. We conclude that the amide chemical shifts have very little predictive value, while the methyl chemical shifts could be used to predict interfaces, though with great care. We suggest an approach based on conversion of the carbon NMR relaxation parameters of methyl groups into parameters of motion, and one of such values, the characteristic time of methyl rotation, appears to be a reliable sensor of interhelix contacts in transmembrane domains. The carbon NMR relaxation parameters of methyl groups can be measured accurately and with high sensitivity and resolution, making the proposed parameter a useful tool for investigation of protein-protein interfaces even in large membrane proteins. An approach to build the models of transmembrane dimers based on perturbations of methyl parameters and TMDOCK software is suggested.

How uniform is the peptide plane geometry? A high-accuracy NMR study of dipolar Cα-C'/H N-N cross-correlated relaxation

Highly precise and accurate measurements of very small NMR cross-correlated relaxation rates, namely those between protein H (i) (N) -N(i) and C (i-1) (α) -C(i-1)' dipoles, are demonstrated with an error of 0.03 s(-1) for GB3. Because the projection angles between the two dipole vectors are very close to the magic angle the rates range only from -0.2 to +0.2 s(-1). Small changes of the average vector orientations have a dramatic impact on the relative values. The rates suggest deviation from idealized peptide plane geometry caused by twists around the C'-N bonds and/or pyramidalization of the nitrogen atoms. A clear alternating pattern along the sequence is observed in β strands 1, 3 and 4 of GB3, where the side chains of almost all residues with large positive rates are solvent exposed. In the α helix all rates are relatively large and positive. Some of the currently most accurate structures of GB3 determined by both high resolution X-ray crystallography and NMR are in satisfactory agreement with the experimental rates in the helix and β strand 3, but not in the loops and the two central strands of the sheet for which no alternating pattern is predicted.

Quantitative 2D and 3D Gamma-HCP experiments for the determination of the angles alpha and zeta in the phosphodiester backbone of oligonucleotides

The quantitative Gamma-(HCP) experiment, a novel heteronuclear NMR pulse sequence for the determination of the RNA backbone angles alpha(O3'(i-1)-P(i)-O5'(i)-C5'(i)) and zeta(C3'(i)-O3'(i)-P(i+1)-O5'(i+1)) in (13)C-labeled RNA, is introduced. The experiment relies on the interaction between the CH bond vector dipole and the (31)P chemical shift anisotropy (CSA), which affects the relaxation of the (13)C,(31)P double- and zero-quantum coherence and thus the intensity of the detectable magnetization. With the new pulse sequence, five different cross-correlated relaxation rates along the phosphodiester backbone can be measured in a quantitative manner, allowing projection-angle and torsion-angle restraints for the two backbone angles alpha and zeta to be extracted. Two versions of the pulse sequence optimized for the CH and CH(2) groups are introduced and demonstrated for a 14-mer cUUCGg tetraloop RNA model system and for a 27-mer RNA with a previously unknown structure. The restraints were incorporated into the calculation of a very high resolution structure of the RNA model system (Nozinovic, S.; et al. Nucleic Acids Res. 2010, 38, 683). Comparison with the X-ray structure of the cUUCGg tetraloop confirmed the high quality of the data, suggesting that the method can significantly improve the quality of RNA structure determination.

Precise structural determination of weakly binding peptides by utilizing dihedral angle constraints

Structural determination of target-bound conformations of peptides is of primary importance for the optimization of peptide ligands and peptide-mimetic design. In the structural determination of weakly binding ligands, transferred nuclear Overhauser effect (TrNOE) methods have been widely used. However, not many distance constraints can be obtained from small peptide ligands by TrNOE, especially for peptides bound to a target molecule in an extended conformation. Therefore, for precise structural determination of weakly binding peptides, additional structural constraints are required. Here, we present a strategy to systematically introduce dihedral angle constraints obtained from multiple transferred cross-correlated relaxation experiments and demonstrate precise structures of weakly binding peptides. As a result, we could determine the bioactive conformations of phage-derived peptide ligands and define their core binding motifs.

Pairwise NMR experiments for the determination of protein backbone dihedral angle Phi based on cross-correlated spin relaxation

Novel cross-correlated spin relaxation (CCR) experiments are described, which measure pairwise CCR rates for obtaining peptide dihedral angles Phi. The experiments utilize intra-HNCA type coherence transfer to refocus 2-bond JNCalpha coupling evolution and generate the N(i)-Calpha(i) or C'(i-1)-Calpha(i) multiple quantum coherences which are required for measuring the desired CCR rates. The contribution from other coherences is also discussed and an appropriate setting of the evolution delays is presented. These CCR experiments were applied to 15N- and 13C-labeled human ubiquitin. The relevant CCR rates showed a high degree of correlation with the Phi angles observed in the X-ray structure. By utilizing these CCR experiments in combination with those previously established for obtaining dihedral angle Psi, we can determine high resolution structures of peptides that bind weakly to large target molecules.

Bloch-Redfield-Wangsness theory engine implementation using symbolic processing software

We describe a general method for the automated symbolic processing of Bloch-Redfield-Wangsness relaxation theory equations for liquid-phase spin dynamics in the algebraically challenging case of rotationally modulated interactions. The processing typically takes no more than a few seconds (on a contemporary single-processor workstation) and yields relaxation rate expressions that are completely general with respect to the spectral density functions, relative orientations, and magnitudes of the interaction tensors, with all cross-correlations accounted for. The algorithm easily deals with fully rhombic interaction tensors, and is able, with little if any modification, to treat a large variety of the relaxation mechanisms encountered in NMR, EPR, and spin dynamics in general.

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.

Site-Specific Variations of Carbonyl Chemical Shift Anisotropies in Proteins

By combining molecular dynamics (MD) simulation with a novel extended density functional theory method, we calculate site-specific carbonyl chemical shift tensors in the SMN Tudor domain. We formulate a simple model for the C' chemical shift anisotropy (CSA) based solely on the isotropic chemical shift. Using this simple chemical shift tensor model and the MD simulation, an accurate prediction of transverse C'/N-H cross-correlated relaxation rates can be obtained.

Symmetrical reconversion: measuring cross-correlation rates with enhanced accuracy

A new strategy has been developed to measure cross-correlation rates with much enhanced accuracy. The method relies on the use of four complementary experiments. Errors due to pulse miscalibration and to uncontrolled attenuation factors associated with relaxation are cancelled out. Problems due to violations of the secular approximation are greatly alleviated. The method has been applied to the measurement of N/NH (CSA/DD) cross-correlated relaxation rates in human ubiquitin.