Cross-correlated Relaxation Rates Research Articles

Studies of proline conformational dynamics in IDPs by 13C-detected cross-correlated NMR relaxation

Intrinsically disordered proteins (IDPs) are significantly enriched in proline residues, which can populate specific local secondary structural elements called PPII helices, characterized by small packing densities. Proline is often thought to promote disorder, but it can participate in specific π·CH interactions with aromatic side chains resulting in reduced conformational flexibilities of the polypeptide. Differential local motional dynamics are relevant for the stabilization of preformed structural elements and can serve as nucleation sites for the establishment of long-range interactions. NMR experiments to probe the dynamics of proline ring systems would thus be highly desirable. Here we present a pulse scheme based on 13C detection to quantify dipole–dipole cross-correlated relaxation (CCR) rates at methylene CH2 groups in proline residues. Applying 13C-CON detection strategy provides exquisite spectral resolution allowing applications also to high molecular weight IDPs even in conditions approaching the physiological ones. The pulse scheme is illustrated with an application to the 220 amino acids long protein Osteopontin, an extracellular cytokine involved in inflammation and cancer progression, and a construct in which three proline-aromatic sequence patches have been mutated.

Proton TOCSY NMR relaxation rates quantitate protein side chain mobility in the Pin1 WW domain

Protein side chain dynamics play a vital role in many biological processes, but differentiating mobile from rigid side chains remains a technical challenge in structural biology. Solution NMR spectroscopy is ideally suited for this but suffers from limited signal-to-noise, signal overlap, and a need for fractional 13C or 2H labeling. Here we introduce a simple strategy measuring initial 1H relaxation rates during a 1H TOCSY sequence like DIPSI-2, which can be appended to the beginning of any multi-dimensional NMR sequence that begins on 1H. The TOCSY RF field compels all 1H atoms to behave similarly under the influence of strong coupling and rotating frame cross-relaxation, so that differences in relaxation rates are due primarily to side chain mobility. We apply the scheme to a thermostable mutant Pin1 WW domain and demonstrate that the observed 1H relaxation rates correlate well with two independent NMR measures of side-chain dynamics, cross-correlated 13C relaxation rates in 13CβH2 methylene groups and maximum observable 3J couplings sensitive to the χ1 side chain dihedral angle (3JHα,Hβ, 3JN,Hβ, and 3JCO,Hβ). The most restricted side chains belong to Trp26 and Asn40, which are closely packed to constitute the folding center of the WW domain. None of the other conserved aromatic residues is as immobile as the first tryptophan side chain of the WW domain. The proposed 1H relaxation methodology should make it relatively easy to measure side chain dynamics on uniformly 15N- or 13C-labeled proteins, so long as chemical shift assignments are obtainable.

Cross-correlated relaxation rates provide facile exchange signature in selectively labeled RNA

Gerhard Wagner has made numerous contributions to NMR spectroscopy, particularly his developments in the field of spin-relaxation stand out in directly mapping the spectral density functions of proteins. He and his group developed experimental techniques to reveal the importance of dynamics to protein biological function and drug discovery. On his 75th birthday, we take this opportunity to highlight how some of those seminal ideas developed for proteins are being extended to RNAs.The role of dynamics in the structure and function of RNA has been a major interest in drug design and therapeutics. Here we present the use of cross-correlated relaxation rates (ηxy) from anti-TROSY (R2α) and TROSY (R2β) to rapidly obtain qualitative information about the chemical exchange taking place within the bacterial and human A-site RNA system while reducing the sets of relaxation experiments required to map dynamics. We show that ηxy correlates with the order parameter which gives information on how flexible or rigid a residue is. We further show R2β/ηxy can rapidly be used to probe chemical exchange as seen from its agreement with Rex. In addition, we report the ability of R2β/ηxy to determine chemical exchange taking place within the bacterial A-site RNA during structural transitions at pH 6.2 and 6.5. Finally, comparison of the R2β/ηxy ratios indicates bacterial A-site has greater R2β/ηxy values for G19 (1.34 s−1), A20 (1.38 s−1), U23 (1.63 s−1) and C24 (1.51 s−1) than human A-site [A19 (0.76 s−1), A20 (1.01 s−1), U23 (0.74 s−1) and C24 (0.71 s−1)]. Taken together, we have shown that the chemical exchange can quickly be analyzed for RNA systems from cross-correlated relaxation rates.

Correlated dipolar and dihedral fluctuations in a protein

Dihedral fluctuations are not directly amenable due to the limitation of the experimental probe. NMR experiments probe dipolar fluctuations given in terms of cross-correlated relaxation (CCR) rates, given by the zero frequency spectral density function of the fluctuations. Here, we calculate the zero frequency spectral function from molecular dynamics trajectories for dipolar and dihedral angle fluctuations and show that they are correlated. Thus, the CCR can be a marker of dihedral fluctuations.

TRACT revisited: an algebraic solution for determining overall rotational correlation times from cross-correlated relaxation rates.

Accurate rotational correlation times (τc) are critical for quantitative analysis of fast timescale NMR dynamics. As molecular weights increase, the classic derivation of τc using transverse and longitudinal relaxation rates becomes increasingly unsuitable due to the non-trivial contribution of remote dipole-dipole interactions to longitudinal relaxation. Derivations using cross-correlated relaxation experiments, such as TRACT, overcome these limitations but are erroneously calculated in 65% of the citing literature. Herein, we developed an algebraic solutions to the Goldman relationship that facilitate rapid, point-by-point calculations for straightforward identification of appropriate spectral regions where global tumbling is likely to be dominant. The rigid-body approximation of the Goldman relationship has been previously shown to underestimate TRACT-based rotational correlation time estimates. This motivated us to develop a second algebraic solution that employs a simplified model-free spectral density function including an order parameter term that could, in principle, be set to an average backbone S2 ≈ 0.9 to further improve the accuracy of τc estimation. These solutions enabled us to explore the boundaries of the Goldman relationship as a function of the H-N internuclear distance ( r ), difference of the two principal components of the axially-symmetric 15N CSA tensor (ΔδN), and angle of the CSA tensor relative to the N-H bond vector (θ). We hope our algebraic solutions and analytical strategies will increase the accuracy and application of the TRACT experiment.

Early Divergence in Misfolding Pathways of Amyloid-Beta Peptides.

The amyloid cascade hypothesis proposes that amyloid‐beta (Aβ) aggregation is the initial triggering event in Alzheimer's disease. Here, we utilize NMR spectroscopy and monitor the structural dynamics of two variants of Aβ, Aβ40 and Aβ42, as a function of temperature. Despite having identical amino acid sequence except for the two additional C‐terminal residues, Aβ42 has higher aggregation propensity than Aβ40. As revealed by the NMR data on dynamics, including backbone chemical shifts, intra‐methyl cross‐correlated relaxation rates and glycine‐based singlet‐states, the C‐terminal region of Aβ, especially the G33‐L34‐M35 segment, plays a particular role in the early steps of temperature‐induced Aβ aggregation. In Aβ42, the distinct dynamical behaviour of C‐terminal residues at higher temperatures is accompanied with marked changes in the backbone dynamics of residues V24‐K28. The distinctive role of the C‐terminal region of Aβ42 in the initiation of aggregation defines a target for the rational design of Aβ42 aggregation inhibitors.

The measurement of relaxation rates of degenerate 1H transitions in methyl groups of proteins using acute angle radiofrequency pulses

A simple NMR experiment for the measurement of transverse relaxation rates of degenerate 1H spins in 13CH3 methyl groups of deuterated proteins, is described. The experiment relies on the use of acute-angle 1H radio-frequency pulses, whereby a series of methyl 1H R2 decays is acquired with different values of the 1H pulse flip-angle, which modulates the relative contributions of the slow- and fast-relaxing components of 1H magnetization during the relaxation delay. These are subsequently analyzed simultaneously to extract the transverse relaxation rates of both components (RS and RF), along with the rate of cross-relaxation between these components, δ. The dipolar 1H–1H cross-correlated relaxation rate η = (RF – RS)/2 and the cross-relaxation rate δ, extracted from such acute-angle-pulse R2 decay series are compared with those derived from well-established methodology that uses relaxation-violated methyl 1H coherence transfer (so-called ‘forbidden’ experiments). Good agreement is achieved for the rates η derived from the two techniques, while slightly more accurate values of δ are obtained from analysis of acute-angle-pulse R2 series. Recording of acute-angle-pulse R2 series represents an attractive alternative to existing methodologies for quantifying methyl 1H relaxation and dynamics of the methyl three-fold symmetry axis in selectively [13CH3]-methyl-labeled, deuterated proteins – particularly so for very high-molecular-weight proteins, where the measurements of RF rates or the build-up of methyl 1H magnetization in relaxation-violated coherence transfer experiments, are problematic due to low sensitivity.

Using Cross-Correlated Spin Relaxation to Characterize Backbone Dihedral Angle Distributions of Flexible Protein Segments.

Crucial to the function of proteins is their existence as conformational ensembles sampling numerous and structurally diverse substates. Despite this widely accepted notion there is still a high demand for meaningful and reliable approaches to characterize protein ensembles in solution. As it is usually conducted in solution, NMR spectroscopy offers unique possibilities to address this challenge. Particularly, cross‐correlated relaxation (CCR) effects have long been established to encode both protein structure and dynamics in a compelling manner. However, this wealth of information often limits their use in practice as structure and dynamics might prove difficult to disentangle. Using a modern Maximum Entropy (MaxEnt) reweighting approach to interpret CCR rates of Ubiquitin, we demonstrate that these uncertainties do not necessarily impair resolving CCR‐encoded structural information. Instead, a suitable balance between complementary CCR experiments and prior information is found to be the most crucial factor in mapping backbone dihedral angle distributions. Experimental and systematic deviations such as oversimplified dynamics appear to be of minor importance. Using Ubiquitin as an example, we demonstrate that CCR rates are capable of characterizing rigid and flexible residues alike, indicating their unharnessed potential in studying disordered proteins.

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.

Utilizing dipole-dipole cross-correlated relaxation for the measurement of angles between pairs of opposing CαHα-CαHα bonds in anti-parallel β-sheets

Dipole-dipole cross-correlated relaxation (CCR) between two spin pairs is rich with macromolecular structural and dynamic information on inter-nuclear bond vectors. Measurement of short range dipolar CCR rates has been demonstrated for a variety of inter-nuclear vector spin pairs in proteins and nucleic acids, where the multiple quantum coherence necessary for observing the CCR rate is created by through-bond scalar coupling. In principle, CCR rates can be measured for any pair of inter-nuclear vectors where coherence can be generated between one spin of each spin pair, regardless of both the distance between the two spin pairs and the distance of the two spins forming the multiple quantum coherence. In practice, however, long range CCR (lrCCR) rates are challenging to measure due to difficulties in linking spatially distant spin pairs. By utilizing through-space relaxation allowed coherence transfer (RACT), we have developed a new method for the measurement of lrCCR rates involving CαHα bonds on opposing anti-parallel β-strands. The resulting lrCCR rates are straightforward to interpret since only the angle between the two vectors modulates the strength of the interference effect. We applied our lrCCR measurement to the third immunoglobulin-binding domain of the streptococcal protein G (GB3) and utilize published NMR ensembles and static NMR/X-ray structures to highlight the relationship between the lrCCR rates and the CαHα-CαHα inter-bond angle and bond mobility. Furthermore, we employ the lrCCR rates to guide the selection of sub-ensembles from the published NMR ensembles for enhancing the structural and dynamic interpretation of the data. We foresee this methodology for measuring lrCCR rates as improving the generation of structural ensembles by providing highly accurate details concerning the orientation of CαHα bonds on opposing anti-parallel β-strands.

Triple resonance ¹⁵Ν NMR relaxation experiments for studies of intrinsically disordered proteins.

Description of protein dynamics is known to be essential in understanding their function. Studies based on a well established [Formula: see text] NMR relaxation methodology have been applied to a large number of systems. However, the low dispersion of [Formula: see text] chemical shifts very often observed within intrinsically disordered proteins complicates utilization of standard 2D HN correlated spectra because a limited number of amino acids can be characterized. Here we present a suite of triple resonance HNCO-type NMR experiments for measurements of five [Formula: see text] relaxation parameters ([Formula: see text], [Formula: see text], NOE, cross-correlated relaxation rates [Formula: see text] and [Formula: see text]) in doubly [Formula: see text],[Formula: see text]-labeled proteins. We show that the third spectral dimension combined with non-uniform sampling provides relaxation rates for almost all residues of a protein with extremely poor chemical shift dispersion, the C terminal domain of [Formula: see text]-subunit of RNA polymerase from Bacillus subtilis. Comparison with data obtained using a sample labeled by [Formula: see text] only showed that the presence of [Formula: see text] has a negligible effect on [Formula: see text], [Formula: see text], and on the cross-relaxation rate (calculated from NOE and [Formula: see text]), and that these relaxation rates can be used to calculate accurate spectral density values. Partially [Formula: see text]-labeled sample was used to test if the observed increase of [Formula: see text] [Formula: see text] in the presence of [Formula: see text] corresponds to the [Formula: see text] dipole-dipole interactions in the [Formula: see text],[Formula: see text]-labeled sample.

Cross-correlated relaxation rates between protein backbone H-X dipolar interactions.

The relaxation interference between dipole-dipole interactions of two separate spin pairs carries structural and dynamics information. In particular, when compared to individual dynamic behavior of those spin pairs, such cross-correlated relaxation (CCR) rates report on the correlation between the spin pairs. We have recently mapped out correlated motion along the backbone of the protein GB3, using CCR rates among and between consecutive HN-N and Hα-Cα dipole-dipole interactions. Here, we provide a detailed account of the measurement of the four types of CCR rates. All rates were obtained from at least two different pulse sequences, of which the yet unpublished ones are presented. Detailed comparisons between the different methods and corrections for unwanted pathways demonstrate that the averaged CCR rates are highly accurate and precise with errors of 1.5-3% of the entire value ranges.

Direct Investigation of Slow Correlated Dynamics in Proteins via Dipolar Interactions.

The synchronization of native state motions as they transition between microstates influences catalysis kinetics, mediates allosteric interactions, and reduces the conformational entropy of proteins. However, it has proven difficult to describe native microstates because they are usually minimally frustrated and may interconvert on the micro- to millisecond time scale. Direct observation of concerted equilibrium fluctuations would therefore be an important tool for describing protein native states. Here we propose a strategy that relates NMR cross-correlated relaxation (CCR) rates between dipolar interactions to residual dipolar couplings (RDCs) of individual consecutive H(N)-N and H(α)-C(α) bonds, which act as a proxy for the peptide planes and the side chains, respectively. Using Xplor-NIH ensemble structure calculations restrained with the RDC and CCR data, we observe collective motions on time scales slower than nanoseconds in the backbone for GB3. To directly access the correlations from CCR, we develop a structure-free data analysis. The resulting dynamic correlation map is consistent with the ensemble-restrained simulations and reveals a complex network. In general, we find that the bond motions are on average slightly correlated and that the local environment dominates many observations. Despite this, some patterns are typical over entire secondary structure elements. In the β-sheet, nearly all bonds are weakly correlated, and there is an approximately binary alternation in correlation intensity corresponding to the solvent exposure/shielding alternation of the side chains. For α-helices, there is also a weak correlation in the H(N)-N bonds. The degree of correlation involving H(α)-C(α) bonds is directly affected by side-chain fluctuations, whereas loops show complex and nonuniform behavior.

Identification of Dynamic Modes in an Intrinsically Disordered Protein Using Temperature-Dependent NMR Relaxation.

The dynamic modes and time scales sampled by intrinsically disordered proteins (IDPs) define their function. Nuclear magnetic resonance (NMR) spin relaxation is probably the most powerful tool for investigating these motions delivering site-specific descriptions of conformational fluctuations from throughout the molecule. Despite the abundance of experimental measurement of relaxation in IDPs, the physical origin of the measured relaxation rates remains poorly understood. Here we measure an extensive range of auto- and cross-correlated spin relaxation rates at multiple magnetic field strengths on the C-terminal domain of the nucleoprotein of Sendai virus, over a large range of temperatures (268-298 K), and combine these data to describe the dynamic behavior of this archetypal IDP. An Arrhenius-type relationship is used to simultaneously analyze up to 61 relaxation rates per amino acid over the entire temperature range, allowing the measurement of local activation energies along the chain, and the assignment of physically distinct dynamic modes. Fast (τ ≤ 50 ps) components report on librational motions, a dominant mode occurs on time scales around 1 ns, apparently reporting on backbone sampling within Ramachandran substates, while a slower component (5-25 ns) reports on segmental dynamics dominated by the chain-like nature of the protein. Extending the study to three protein constructs of different lengths (59, 81, and 124 amino acids) substantiates the assignment of these contributions. The analysis is shown to be remarkably robust, accurately predicting a broad range of relaxation data measured at different magnetic field strengths and temperatures. The ability to delineate intrinsic modes and time scales from NMR spin relaxation will improve our understanding of the behavior and function of IDPs, adding a new and essential dimension to the description of this biologically important and ubiquitous class of proteins.

Spectral density mapping at multiple magnetic fields suitable for [formula omitted] NMR relaxation studies

Standard spectral density mapping protocols, well suited for the analysis of 15N relaxation rates, introduce significant systematic errors when applied to 13C relaxation data, especially if the dynamics is dominated by motions with short correlation times (small molecules, dynamic residues of macromolecules). A possibility to improve the accuracy by employing cross-correlated relaxation rates and on measurements taken at several magnetic fields has been examined. A suite of protocols for analyzing such data has been developed and their performance tested. Applicability of the proposed protocols is documented in two case studies, spectral density mapping of a uniformly labeled RNA hairpin and of a selectively labeled disaccharide exhibiting highly anisotropic tumbling. Combination of auto- and cross-correlated relaxation data acquired at three magnetic fields was applied in the former case in order to separate effects of fast motions and conformational or chemical exchange. An approach using auto-correlated relaxation rates acquired at five magnetic fields, applicable to anisotropically moving molecules, was used in the latter case. The results were compared with a more advanced analysis of data obtained by interpolation of auto-correlated relaxation rates measured at seven magnetic fields, and with the spectral density mapping of cross-correlated relaxation rates. The results showed that sufficiently accurate values of auto- and cross-correlated spectral density functions at zero and 13C frequencies can be obtained from data acquired at three magnetic fields for uniformly 13C-labeled molecules with a moderate anisotropy of the rotational diffusion tensor. Analysis of auto-correlated relaxation rates at five magnetic fields represents an alternative for molecules undergoing highly anisotropic motions.

Chemical Shielding Anisotropies for Chloroform Exchanging between a Free Site and a Complex with Cryptophane-D: A Cross-Correlated NMR Relaxation Study.

The case of (13)C-labeled chloroform exchanging between a free site in solution and the encaged site within the cryptophane-D cavity is investigated using the measurements of longitudinal cross-correlated relaxation rates, involving the interference of the dipole-dipole and chemical shielding anisotropy interactions. A compact theoretical expression is provided, along with an experimental protocol, based on INEPT (insensitive nuclei enhanced by polarization)-enhanced double-quantum-filtered inversion recovery measurements. The analysis of the build-up curves results in a set of cross-correlated relaxation rates for both the (13)C and (1)H spins at the two sites. It is demonstrated that the results can be given a consistent interpretation in terms of molecular-level properties, such as rotational correlation times, the Lipari-Szabo order parameter, and interaction strength constants. The analysis yields the bound-site carbon-13 chemical shielding anisotropy, ΔσC = -58 ± 8 ppm, in good agreement with most recent liquid-crystal measurements and the corresponding proton shielding anisotropy, ΔσH = 14 ± 2 ppm.

Spectral density mapping protocols for analysis of molecular motions in disordered proteins

Spectral density mapping represents the method of choice for investigations of molecular motions of intrinsically disordered proteins (IDPs). However, the current methodology has been developed for well-folded proteins. In order to find conditions for a reliable analysis of relaxation of IDPs, accuracy of the current reduced spectral density mapping protocols applied to IDPs was examined and new spectral density mapping methods employing cross-correlated relaxation rates have been designed. Various sources of possible systematic errors were analyzed theoretically and the presented approaches were tested on a partially disordered protein, delta subunit of bacterial RNA polymerase. Results showed that the proposed protocols provide unbiased description of molecular motions of IDPs and allow to separate slow exchange from fast dynamics.

High‐Dimensional NMR Spectra for Structural Studies of Biomolecules

Recent developments in the acquisition and processing of NMR data sets facilitate the recording of ultra-high-resolution NMR spectra in a reasonable time. The new experiments allow easy resonance assignment for folded and unfolded proteins, as well as the precise determination of spectral parameters, for example, chemical shifts, NOE contacts, coupling constants or cross-correlated relaxation rates. Owing to exceptional resolution of 4D-6D spectroscopy, detailed studies of biomolecules of unprecedented complexity are now possible. Herein, the principles of acquisition and processing methods are presented. The main applications of high-dimensional NMR experiments, including backbone and side-chain resonance assignment in proteins, as well as heteronuclear edited NOE techniques are reviewed.

Probing Local Backbone Geometries in Intrinsically Disordered Proteins by Cross-Correlated NMR Relaxation.

Probing Local Backbone Geometries in Intrinsically Disordered Proteins by Cross-Correlated NMR Relaxation.