Cross-correlated Relaxation Research Articles

Insights into Ligand-Mediated Activation of an Oligomeric Ring-Shaped Gene-Regulatory Protein from Solution- and Solid-State NMR

The 91 kDa oligomeric ring-shaped ligand binding protein TRAP (trp RNA binding attenuation protein) regulates the expression of a series of genes involved in tryptophan (Trp) biosynthesis in bacilli. When cellular Trp levels rise, the free amino acid binds to sites buried in the interfaces between each of the 11 (or 12, depending on the species) protomers in the ring. Crystal structures of Trp-bound TRAP show the Trp ligands are sequestered from solvent by a pair of loops from adjacent protomers that bury the bound ligand via polar contacts to several threonine residues. Binding of the Trp ligands occurs cooperatively, such that successive binding events occur with higher apparent affinity but the structural basis for this cooperativity is poorly understood. We used solution methyl-TROSY NMR relaxation experiments focused on threonine and isoleucine sidechains, as well as magic angle spinning solid-state NMR 13C–13C and 15N-13C chemical shift correlation spectra on uniformly labeled samples recorded at 800 and 1200 MHz, to characterize the structure and dynamics of the protein. Methyl 13C relaxation dispersion experiments on ligand-free apo TRAP revealed concerted exchange dynamics on the µs-ms time scale, consistent with transient sampling of conformations that could allow ligand binding. Cross-correlated relaxation experiments revealed widespread disorder on fast timescales. Chemical shifts for methyl-bearing side chains in apo- and Trp-bound TRAP revealed subtle changes in the distribution of sampled sidechain rotameric states. These observations reveal a pathway and mechanism for induced conformational changes to generate homotropic Trp-Trp binding cooperativity.

Cross-correlated relaxation in the NMR of near-equivalent spin pairs: Longitudinal relaxation and long-lived singlet order.

The evolution of nuclear spin state populations is investigated for the case of a 13C2-labeled triyne in solution, for which the near-equivalent coupled pairs of 13C nuclei experience cross-correlated relaxation mechanisms. Inversion-recovery experiments reveal different recovery curves for the main peak amplitudes, especially when the conversion of population imbalances to observable coherences is induced by a radio frequency pulse with a small flip angle. Measurements are performed over a range of magnetic fields by using a sample shuttle apparatus. In some cases, the time constant TS for decay of nuclear singlet order is more than 100 times larger than the time constant T1 for the equilibration of longitudinal magnetization. The results are interpreted by a theoretical model incorporating cross-correlated relaxation mechanisms, anisotropic rotational diffusion, and an external random magnetic field. A Lindbladian formalism is used to describe the dissipative dynamics of the spin system in an environment of finite temperature. Good agreement is achieved between theory and experiment.

A set of cross-correlated relaxation experiments to probe the correlation time of two different and complementary spin pairs

Intrinsically disordered proteins (IDPs) defy the conventional structure-function paradigm by lacking a well-defined tertiary structure and exhibiting inherent flexibility. This flexibility leads to distinctive spin relaxation modes, reflecting isolated and specific motions within individual peptide planes. In this work, we propose a new pulse sequence to measure the longitudinal 13C′ CSA-13C′-13Cα DD CCR rate ΓzC′/C′Cα and present a novel 3D version of the transverse ΓxyC′/C′Cα CCR rate, adopting the symmetrical reconversion approach. We combined these rates with the analogous ΓxyN/NH and ΓzN/NH CCR rates to derive residue-specific correlation times for both spin-pairs within the same peptide plane. The presented approach offers a straightforward and intuitive way to compare the correlation times of two different and complementary spin vectors, anticipated to be a valuable aid to determine IDPs backbone dihedral angles distributions. We performed the proposed experiments on two systems: a folded protein ubiquitin and Coturnix japonica osteopontin, a prototypical IDP. Comparative analyses of the results show that the correlation times of different residues vary more for IDPs than globular proteins, indicating that the dynamics of IDPs is largely heterogeneous and dominated by local fluctuations.

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.

NMR relaxation and diffusion studies to probe the motional dynamics of risperidone within PLGA microsphere

The present study aims to investigate the motional dynamics of risperidone within polylactic co-glycolic acid (PLGA) microsphere by employing solution state 1H and 19F nuclear magnetic resonance (NMR) measurements. Risperidone, a second-generation fluorinated antipsychotic drug used for the treatment of schizophrenia is commercially marketed as PLGA microsphere formulation resulting in prolonged release of the drug in solution. Although the current trend in the pharmaceutical market is to develop drug formulation with long-acting release (LAR) products, complete physicochemical characterization of such formulations are scarce. Especially the effects of microsphere encapsulation on the motional properties and diffusion behavior of the drugs are not discussed adequately in any of the earlier reports. We therefore, have employed NMR relaxation and diffusion measurements to decipher the interaction of PLGA cavity water with risperidone. A detailed analysis of NMR relaxation rates confirmed the event of encapsulation and the presence of local motion in the non-fluorinated end of risperidone. Further, the relaxation data indicated a significant alteration in 19F chemical shift anisotropy (CSA) and CSA/dipole-dipole (DD) cross-correlated relaxation mechanism and decreased effect of solvent relaxation pointing out reduced water concentration within the microsphere cavity. 1H and 19F diffusion coefficients of risperidone led to the information about hydrodynamic radius of risperidone in free and encapsulated states. Measurement of hydrodynamic radius supported the presence of limited water in PLGA cavity allowing higher translational mobility of risperidone after the encapsulation.

Sometimes pulses just have to be perfect – An example based on the measurement of amide proton transverse relaxation rates in proteins

The measurement of spin relaxation rates provides a unique avenue for quantifying dynamic processes in biomolecules. In order to simplify analysis of the measurements so that a few key intuitive parameters can be extracted, it is often the case that experiments are designed to eliminate interference effects between different classes of spin relaxation. One example emerges in the measurement of amide proton (1HN) transverse relaxation rates in 15N labeled proteins, where 15N inversion pulses are applied during a relaxation element to eliminate cross-correlated spin relaxation between 1HN-15N dipole-1HN CSA interactions. We show that unless these pulses are essentially perfect, significant oscillations in magnetization decay profiles can be obtained, due to the excitation of multiple-quantum coherences, leading potentially to errors in measured R2 rates. With the recent development of experiments for quantifying electrostatic potentials via amide proton relaxation rates, the need for highly accurate measurement schemes becomes critical. Straightforward modifications to existing pulse sequences are suggested to achieve this goal.

Slow methyl axes motions in perdeuterated villin headpiece subdomain probed by cross-correlated NMR relaxation measurements.

Protein methyl groups can participate in multiple motional modes on different time scales. Sub-nanosecond to nano-second time scale motions of methyl axes are particularly challenging to detect for small proteins in solutions. In this work we employ NMR relaxation interference between the methyl H-H/H-C dipole-dipole interactions [Sun&Tugarinov, J. Magn. Reason. 2012] to characterize methyl axes motions as a function of temperature in a small model protein villin headpiece subdomain (HP36), in which all non-exchangeable protons are deuterated with the exception of methyl groups of leucine and valine residues. The data points to the existence of slow motional modes of methyl axes on sub-nanosecond to nanosecond time scales. Further, at high temperatures for which the overall tumbling of the protein is on the order of 2 ns, we observe a coupling between the slow internal motion and the overall molecular tumbling, based on the anomalous order parameters and their temperature-dependent trends. The addition of 28%(w/w) glycerol-d8 increases the viscosity of the solvent and separates the timescales of internal and overall tumbling, thus permitting for another view of the necessity of the coupling assumption for these sites at high temperatures.

Probing Methyl Group Dynamics in Proteins by NMR Cross-Correlated Dipolar Relaxation and Molecular Dynamics Simulations.

Nuclear magnetic resonance (NMR) spin relaxation is the most informative approach to experimentally probe the internal dynamics of proteins on the picosecond to nanosecond time scale. At the same time, molecular dynamics (MD) simulations of biological macromolecules are steadily improving through better physical models, enhanced sampling methods, and increased computational power, and they provide exquisite information about flexibility and its role in protein stability and molecular interactions. Many examples have shown that MD is now adept in probing protein backbone motion, but improvements are still required toward a quantitative description of the dynamics of side chains, for example, probed by the dynamics of methyl groups. Thus far, the comparison of computation with experiment for side chain dynamics has primarily focused on the relaxation of 13C and 2H nuclei induced by autocorrelated variation of spin interactions. However, the cross-correlation of 13C-1H dipolar interactions in methyl groups offers an attractive alternative. Here, we establish a computational framework to extract cross-correlation relaxation parameters of methyl groups in proteins from all-atom MD simulations. To demonstrate the utility of the approach, cross-correlation relaxation rates of ubiquitin are computed from MD simulations performed with the AMBER99SB*-ILDN and CHARMM36 force fields. Simulation results were found to agree well with those obtained by experiment. Moreover, the data obtained with the two force fields are highly consistent.

Cross-correlation effects in the solution NMR spectra of near-equivalent spin-1/2 pairs.

The nuclear magnetic resonance (NMR) spectra of spin-1/2 pairs contain four peaks, with two inner peaks much stronger than the outer peaks in the near-equivalence regime. We have observed that the strong inner peaks have significantly different linewidths when measurements were performed on a 13C2-labelled triyne derivative. This linewidth difference may be attributed to strong cross-correlation effects. We develop the theory of cross-correlated relaxation in the case of near-equivalent homonuclear spin-1/2 pairs, in the case of a molecule exhibiting strongly anisotropic rotational diffusion. Good agreement is found with the experimental NMR lineshapes.

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.

Multispin Cross-Correlated Transverse Dipolar NMR Relaxation in Solution

In this paper, we want to consider what would be involved in calculating the R2 relaxation of amide protons in a protein caused by dipolar interactions with nearby protons, for which there are many. NMR textbooks give analytical equations and sometimes derivations for solution NMR relaxation due to dipolar interactions between two spins. There are also closed equations for dipolar interactions between three spins, which include relaxation interference, also known as cross-correlated cross-relaxation. We here derive an expression for interference between four spins. For larger systems, such as amide protons in a protein, we develop a local-field methodology, from which solution relaxation interference can be computed for a basically limitless number of interacting spins.

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.

Richard Ernst beyond Fourier transforms: A legacy of multiple reincarnations

This piece highlights the rich scientific legacy of Richard Ernst in the field of magnetic resonance, which encompasses studies of chemical exchange, Overhauser effects, cross-correlated relaxation, quantum computing, and phase encoding in magnetic resonance imaging.

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.

Observation of Sub-Microsecond Protein Methyl-Side Chain Dynamics by Nanoparticle-Assisted NMR Spin Relaxation.

Amino-acid side-chain properties in proteins are key determinants of protein function. NMR spin relaxation of side chains is an important source of information about local protein dynamics and flexibility. However, traditional solution NMR relaxation methods are most sensitive to sub-nanosecond dynamics lacking information on slower ns-μs time-scale motions. Nanoparticle-assisted NMR spin relaxation (NASR) of methyl-side chains is introduced here as a window into these ns-μs dynamics. NASR utilizes the transient and nonspecific interactions between folded proteins and slowly tumbling spherical nanoparticles (NPs), whereby the increase of the relaxation rates reflects motions on time scales from ps all the way to the overall tumbling correlation time of the NPs ranging from hundreds of ns to μs. The observed motional amplitude of each methyl group can then be expressed by a model-free NASR S2 order parameter. The method is demonstrated for 2H-relaxation of CH2D methyl moieties and cross-correlated relaxation of CH3 groups for proteins Im7 and ubiquitin in the presence of anionic silica-nanoparticles. Both types of relaxation experiments, dominated by either quadrupolar or dipolar interactions, yield highly consistent results. Im7 shows additional dynamics on the intermediate time scales taking place in a functionally important loop, whereas ubiquitin visits the majority of its conformational substates on the sub-ns time scale. These experimental observations are in good agreement with 4-10 μs all-atom molecular dynamics trajectories. NASR probes side-chain dynamics on a much wider range of motional time scales than previously possible, thereby providing new insights into the interplay between protein structure, dynamics, and molecular interactions that govern protein function.

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.

Detecting anisotropic segmental dynamics in disordered proteins by cross-correlated spin relaxation.

Among the numerous contributions of Geoffrey Bodenhausen to NMR spectroscopy, his developments in the field of spin-relaxation methodology and theory will definitely have a long lasting impact. Starting with his seminal contributions to the excitation of multiple-quantum coherences, he and his group thoroughly investigated the intricate relaxation properties of these "forbidden fruits" and developed experimental techniques to reveal the relevance of previously largely ignored cross-correlated relaxation (CCR) effects, as "the essential is invisible to the eyes". Here we consider CCR within the challenging context of intrinsically disordered proteins (IDPs) and emphasize its potential and relevance for the studies of structural dynamics of IDPs in the future years to come. Conventionally, dynamics of globularly folded proteins are modeled and understood as deviations from otherwise rigid structures tumbling in solution. However, with increasing protein flexibility, as observed for IDPs, this apparent dichotomy between structure and dynamics becomes blurred. Although complex dynamics and ensemble averaging might impair the extraction of mechanistic details even further, spin relaxation uniquely encodes a protein's structural memory. Due to significant methodological developments, such as high-dimensional non-uniform sampling techniques, spin relaxation in IDPs can now be monitored in unprecedented resolution. Not embedded within a rigid globular fold, conventional spin probes might not suffice to capture the inherently local nature of IDP dynamics. To better describe and understand possible segmental motions of IDPs, we propose an experimental approach to detect the signature of anisotropic segmental dynamics by quantifying cross-correlated spin relaxation of individual and spin pairs. By adapting Geoffrey Bodenhausen's symmetrical reconversion principle to obtain zero frequency spectral density values, we can define and demonstrate more sensitive means to characterize anisotropic dynamics in IDPs.

High-field solution state DNP using cross-correlations

At the magnetic fields of common NMR instruments, electron Zeeman frequencies are too high for efficient electron-nuclear dipolar cross-relaxation to occur in solution. The rate of that process fades with the electron Zeeman frequency as ω-2 – in the absence of isotropic hyperfine couplings, liquid state dynamic nuclear polarisation (DNP) in high-field magnets is therefore impractical. However, contact coupling and dipolar cross-relaxation are not the only mechanisms that can move electron magnetisation to nuclei in liquids: multiple cross-correlated (CC) relaxation processes also exist, involving various combinations of interaction tensor anisotropies. The rates of some of those processes have more favourable high-field behaviour than dipolar cross-relaxation, but due to the difficulty of their numerical – and particularly analytical – treatment, they remain largely uncharted. In this communication, we report analytical evaluation of every rotationally driven relaxation process in liquid state for 1e1n and 2e1n spin systems, as well as numerical optimisations of the steady-state DNP with respect to spin Hamiltonian parameters. A previously unreported cross-correlated DNP (CCDNP) mechanism was identified for the 2e1n system, involving multiple relaxation interference effects and inter-electron exchange coupling. Using simulations, we found realistic spin Hamiltonian parameters that yield stronger nuclear polarisation at high magnetic fields than dipolar cross-relaxation.