Comprehensive description of NMR cross-correlated relaxation under anisotropic molecular tumbling and correlated local dynamics on all time scales

Uncovering allostery and regulation in SORCIN through molecular dynamics simulations

Soluble resistance-related calcium-binding protein or Sorcin is an allosteric, calcium-binding Penta-EF hand (PEF) family protein implicated in multi-drug resistant cancers. Sorcin is known to bind chemotherapeutic molecules such as Doxorubicin. This study uses in-silico molecular dynamics simulations to explore the dynamics and allosteric behavior of Sorcin in the context of Ca2+ uptake and Doxorubicin binding. The results show that Ca2+ binding induces large, but reversible conformational changes in the Sorcin structure which manifest as rigid body reorientations that preserve the local secondary structure. A reciprocal allosteric handshake centered around the EF5 hand is found to be key in Sorcin dimer formation and stabilization. Binding of Doxorubicin results in rearrangement of allosteric communities which disrupts long-range allosteric information transfer from the N-terminal domain to the middle lobe. However, this binding does not result in secondary structure destabilization. Sorcin does not appear to have a distinct Ca2+ activated mode of Doxorubicin binding.Communicated by Ramaswamy H. Sarma.

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.

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 15 N 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 15 N 1 H N and 13 C ' 13 C α 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.

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.

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.

Detection of Correlated Protein Backbone and Side-Chain Angle Fluctuations

NMR methods for the characterization of local protein motions have attained a high level of sophistication. Measurement of the synchronization between those motions, however, poses a serious challenge. Such correlated motions are one of the underlying mechanisms for the propagation of local changes to remote sites and as such for information transfer. Here, we demonstrate the experimental detection of the synchronization of motion over an intermediate range. To that purpose, we designed pulse sequences for the measurement of cross-correlated relaxation between the backbone H^N -N and side-chain H^β -C^β dipoles in Ile, Thr, and Val in the protein GB3. These bonds are related through two and three intervening dihedral angles. We show that the correlated motions inherent in a structural ensemble obtained from a large and diverse array of NMR probes are in excellent agreement with our measurements.

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 H^N-N and H^α-C^α 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.

Spatio-temporal coordination among functional residues in protein

The microscopic basis of communication among the functional sites in bio-macromolecules is a fundamental challenge in uncovering their functions. We study the communication through temporal cross-correlation among the binding sites. We illustrate via Molecular Dynamics simulations the properties of the temporal cross-correlation between the dihedrals of a small protein, ubiquitin which participates in protein degradation in eukaryotes. We show that the dihedral angles of the residues possess non-trivial temporal cross-correlations with asymmetry with respect to exchange of the dihedrals, having peaks at low frequencies with time scales in nano-seconds and an algebraic tail with a universal exponent for large frequencies. We show the existence of path for temporally correlated degrees of freedom among the functional residues. We explain the qualitative features of the cross-correlations through a general mathematical model. The generality of our analysis suggests that temporal cross-correlation functions may provide convenient theoretical framework to understand bio-molecular functions on microscopic basis.

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.

Correlated motions are a fundamental property of β-sheets

Correlated motions in proteins can mediate fundamental biochemical processes such as signal transduction and allostery. The mechanisms that underlie these processes remain largely unknown due mainly to limitations in their direct detection. Here, based on a detailed analysis of protein structures deposited in the protein data bank, as well as on state-of-the art molecular simulations, we provide general evidence for the transfer of structural information by correlated backbone motions, mediated by hydrogen bonds, across β-sheets. We also show that the observed local and long-range correlated motions are mediated by the collective motions of β-sheets and investigate their role in large-scale conformational changes. Correlated motions represent a fundamental property of β-sheets that contributes to protein function.

The nuclear Overhauser effect from a quantitative perspective

The nuclear Overhauser enhancement or effect (NOE) is the most important measure in liquid-state NMR with macromolecules. Thus, the NOE is the subject of numerous reviews and books. Here, the NOE is revisited in light of our recently introduced measurements of exact nuclear Overhauser enhancements (eNOEs), which enabled the determination of multiple-state 3D protein structures. This review encompasses all relevant facets from the theoretical considerations to the use of eNOEs in multiple-state structure calculation. Important aspects include a detailed presentation of the relaxation theory relevant for the nuclear Overhauser effect, the estimation of the correction for spin diffusion, the experimental determination of the eNOEs, the conversion of eNOE rates into distances and validation of their quality, the distance-restraint classification and the protocols for calculation of structures and ensembles.

Liquid-liquid transition in a strong bulk metallic glass-forming liquid

Polymorphic phase transitions are common in crystalline solids. Recent studies suggest that phase transitions may also exist between two liquid forms with different entropy and structure. Such a liquid-liquid transition has been investigated in various substances including water, Al2O3-Y2O3 and network glass formers. However, the nature of liquid-liquid transition is debated due to experimental difficulties in avoiding crystallization and/or measuring at high temperatures/pressures. Here we report the thermodynamic and structural evidence of a temperature-induced weak first-order liquid-liquid transition in a bulk metallic glass-forming system Zr(41.2)Ti(13.8)Cu(12.5)Ni10Be(22.5) characterized by non- (or weak) directional bonds. Our experimental results suggest that the local structural changes during the transition induce the drastic viscosity changes without a detectable density anomaly. These changes are correlated with a heat capacity maximum in the liquid. Our findings support the hypothesis that the 'strong' kinetics (low fragility) of a liquid may arise from an underlying lambda transition above its glass transition.

Measuring dynamic and kinetic information in the previously inaccessible supra-τ(c) window of nanoseconds to microseconds by solution NMR spectroscopy

Nuclear Magnetic Resonance (NMR) spectroscopy is a powerful tool that has enabled experimentalists to characterize molecular dynamics and kinetics spanning a wide range of time-scales from picoseconds to days. This review focuses on addressing the previously inaccessible supra-tc window (defined as τ(c) < supra-τ(c) < 40 μs; in which tc is the overall tumbling time of a molecule) from the perspective of local inter-nuclear vector dynamics extracted from residual dipolar couplings (RDCs) and from the perspective of conformational exchange captured by relaxation dispersion measurements (RD). The goal of the first section is to present a detailed analysis of how to extract protein dynamics encoded in RDCs and how to relate this information to protein functionality within the previously inaccessible supra-τ(c) window. In the second section, the current state of the art for RD is analyzed, as well as the considerable progress toward pushing the sensitivity of RD further into the supra-τ(c) scale by up to a factor of two (motion up to 25 μs). From the data obtained with these techniques and methodology, the importance of the supra-τ(c) scale for protein function and molecular recognition is becoming increasingly clearer as the connection between motion on the supra-τ(c) scale and protein functionality from the experimental side is further strengthened with results from molecular dynamics simulations.

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.

Weak long-range correlated motions in a surface patch of ubiquitin involved in molecular recognition

Long-range correlated motions in proteins are candidate mechanisms for processes that require information transfer across protein structures, such as allostery and signal transduction. However, the observation of backbone correlations between distant residues has remained elusive, and only local correlations have been revealed using residual dipolar couplings measured by NMR spectroscopy. In this work, we experimentally identified and characterized collective motions spanning four β-strands separated by up to 15 Å in ubiquitin. The observed correlations link molecular recognition sites and result from concerted conformational changes that are in part mediated by the hydrogen-bonding network.