Quantifying Lipari-Szabo modelfree parameters from 13CO NMR relaxation experiments

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 [Formula: see text] and present a novel 3D version of the transverse [Formula: see text] 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.

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.

NMR studies of dynamic biomolecular conformational ensembles

Multidimensional heteronuclear NMR approaches can provide nearly complete sequential signal assignments of isotopically enriched biomolecules. The availability of assignments together with measurements of spin relaxation rates, residual spin interactions, J-couplings and chemical shifts provides information at atomic resolution about internal dynamics on timescales ranging from ps to ms, both in solution and in the solid state. However, due to the complexity of biomolecules, it is not possible to extract a unique atomic-resolution description of biomolecular motions even from extensive NMR data when many conformations are sampled on multiple timescales. For this reason, powerful computational approaches are increasingly applied to large NMR data sets to elucidate conformational ensembles sampled by biomolecules. In the past decade, considerable attention has been directed at an important class of biomolecules that function by binding to a wide variety of target molecules. Questions of current interest are: "Does the free biomolecule sample a conformational ensemble that encompasses the conformations found when it binds to various targets; and if so, on what time scale is the ensemble sampled?" This article reviews recent efforts to answer these questions, with a focus on comparing ensembles obtained for the same biomolecules by different investigators. A detailed comparison of results obtained is provided for three biomolecules: ubiquitin, calmodulin and the HIV-1 trans-activation response RNA.

NMR Spectroscopic Studies of the Conformational Ensembles of Intrinsically Disordered Proteins

Intrinsically disordered proteins (IDPs) are characterized by substantial conformational flexibility and thus not amenable to conventional structural biology techniques. Given their inherent structural flexibility NMR spectroscopy offers unique opportunities for structural and dynamic studies of IDPs. The past two decades have witnessed significant development of NMR spectroscopy that couples advances in spin physics and chemistry with a broad range of applications. This chapter will summarize key advances in NMR methodology. Despite the availability of efficient (multi-dimensional) NMR experiments for signal assignment of IDPs it is discussed that NMR of larger and more complex IDPs demands spectral simplification strategies capitalizing on specific isotope-labeling strategies. Prototypical applications of isotope labeling-strategies are described. Since IDP-ligand association and dissociation processes frequently occur on time scales that are amenable to NMR spectroscopy we describe in detail the application of CPMG relaxation dispersion techniques to studies of IDP protein binding. Finally, we demonstrate that the complementary usage of NMR and EPR data provide a more comprehensive picture about the conformational states of IDPs and can be employed to analyze the conformational ensembles of IDPs.

Loss of conformational entropy in protein folding calculated using realistic ensembles and its implications for NMR-based calculations

The loss of conformational entropy is a major contribution in the thermodynamics of protein folding. However, accurate determination of the quantity has proven challenging. We calculate this loss using molecular dynamic simulations of both the native protein and a realistic denatured state ensemble. For ubiquitin, the total change in entropy is TΔSTotal = 1.4 kcal⋅mol(-1) per residue at 300 K with only 20% from the loss of side-chain entropy. Our analysis exhibits mixed agreement with prior studies because of the use of more accurate ensembles and contributions from correlated motions. Buried side chains lose only a factor of 1.4 in the number of conformations available per rotamer upon folding (ΩU/ΩN). The entropy loss for helical and sheet residues differs due to the smaller motions of helical residues (TΔShelix-sheet = 0.5 kcal⋅mol(-1)), a property not fully reflected in the amide N-H and carbonyl C=O bond NMR order parameters. The results have implications for the thermodynamics of folding and binding, including estimates of solvent ordering and microscopic entropies obtained from NMR.

Analysis of 15N-1H NMR relaxation in proteins by a combined experimental and molecular dynamics simulation approach: picosecond-nanosecond dynamics of the Rho GTPase binding domain of plexin-B1 in the dimeric state indicates allosteric pathways

We investigate picosecond–nanosecond dynamics of the Rho-GTPase Binding Domain (RBD) of plexin-B1, which plays a key role in plexin-mediated cell signaling. Backbone 15N relaxation data of the dimeric RBD are analyzed with the model-free (MF) method, and with the slowly relaxing local structure/molecular dynamics (SRLS-MD) approach. Independent analysis of the MD trajectories, based on the MF paradigm, is also carried out. MF is a widely popular and simple method, SRLS is a general approach, and SRLS-MD is an integrated approach we developed recently. Corresponding parameters from the RBD dimer, a previously studied RBD monomer mutant, and the previously studied complex of the latter with the GTPase Rac1, are compared. The L2, L3, and L4 loops of the plexin-B1 RBD are involved in interactions with other plexin domains, GTPase binding, and RBD dimerization, respectively. Peptide groups in the loops of both the monomeric and dimeric RBD are found to experience weak and moderately asymmetric local ordering centered approximately at the C(i–1)(α)–C(i)(α) axes, and nanosecond backbone motion. Peptide groups in the α-helices and the β-strands of the dimer (the β-strands of the monomer) experience strong and highly asymmetric local ordering centered approximately at the C(i–1)(α)–C(i)(α) axes (N–H bonds). N–H fluctuations occur on the picosecond time scale. An allosteric pathway for GTPase binding, providing new insights into plexin function, is delineated.

Temperature dependence of fast carbonyl backbone dynamics in chicken villin headpiece subdomain

Temperature-dependence of protein dynamics can provide information on details of the free energy landscape by probing the characteristics of the potential responsible for the fluctuations. We have investigated the temperature-dependence of picosecond to nanosecond backbone dynamics at carbonyl carbon sites in chicken villin headpiece subdomain protein using a combination of three NMR relaxation rates: (13)C' longitudinal rate, and two cross-correlated rates involving dipolar and chemical shift anisotropy (CSA) relaxation mechanisms, (13)C'/(13)C'-(13)C(α) CSA/dipolar and (13)C'/(13)C'-(15)N CSA/dipolar. Order parameters have been extracted using the Lipari-Szabo model-free approach assuming a separation of the time scales of internal and molecular motions in the 2-16°C temperature range. There is a gradual deviation from this assumption from lower to higher temperatures, such that above 16°C the separation of the time scales is inconsistent with the experimental data and, thus, the Lipari-Szabo formalism can not be applied. While there are variations among the residues, on the average the order parameters indicate a markedly steeper temperature dependence at backbone carbonyl carbons compared to that probed at amide nitrogens in an earlier study. This strongly advocates for probing sites other than amide nitrogen for accurate characterization of the potential and other thermodynamics characteristics of protein backbone.

Integrated computational approach to the analysis of NMR relaxation in proteins: application to ps-ns main chain 15N-1H and global dynamics of the Rho GTPase binding domain of plexin-B1

An integrated computational methodology for interpreting NMR spin relaxation in proteins has been developed. It combines a two-body coupled-rotator stochastic model with a hydrodynamics-based approach for protein diffusion, together with molecular dynamics based calculations for the evaluation of the coupling potential of mean force. The method is applied to ¹⁵N relaxation of N-H bonds in the Rho GTPase binding (RBD) domain of plexin-B1, which exhibits intricate internal mobility. Bond vector dynamics are characterized by a rhombic local ordering tensor, S, with principal values S₀² and S₂², and an axial local diffusion tensor, D₂, with principal values D(2,||) and D(2,⊥). For α-helices and β-sheets we find that S₀² ~ -0.5 (strong local ordering), -1.2 < S₂² < -0.8 (large S tensor anisotropy), D(2,⊥) ~ D₁ = 1.93 × 10⁷ s⁻¹ (D₁ is the global diffusion rate), and log(D(2,||)/D₁) ~ 4. For α-helices the z-axis of the local ordering frame is parallel to the C(α)-C(α) axis. For β-sheets the z-axes of the S and D₂ tensors are parallel to the N-H bond. For loops and terminal chain segments the local ordering is generally weaker and more isotropic. On average, D(2,⊥) ~ D₁ also, but log(D(2,||)/D₁) is on the order of 1-2. The tensor orientations are diversified. This study sets forth an integrated computational approach for treating NMR relaxation in proteins by combining stochastic modeling and molecular dynamics. The approach developed provides new insights by its application to a protein that experiences complex dynamics.

Combining methods for speeding up multi-dimensional acquisition. Sparse sampling and fast pulsing methods for unfolded proteins

Resonance assignment of intrinsically disordered proteins is made difficult by the extensive spectral overlaps. High-resolution 3D and 4D spectra are thus essential for this purpose. We have adapted the series of 3D BEST-experiments proposed by Lescop et al. [E. Lescop, P. Schanda, B. Brutscher, A set of BEST triple-resonance experiments for time-optimized protein resonance assignment, J. Magn. Reson. 187 (2007) 163-169] to the case of unfolded proteins. Longer acquisitions in the indirect dimensions are obtained by implementing semi-constant time evolution and sparse sampling. Using maximum entropy reconstruction for the indirect dimensions, the artifact intensity due to sparse sampling can be reduced to a level similar to the other sources of noise. The reduction of the sampled increments and the shorter duration of individual transients makes it possible to record a 4D experiment with reasonable resolution in less than 60 h.

Comparison of fast backbone dynamics at amide nitrogen and carbonyl sites in dematin headpiece C-terminal domain and its S74E mutant

We perform a detailed comparison of fast backbone dynamics probed at amide nitrogen versus carbonyl carbon sites for dematin headpiece C-terminal domain (DHP) and its S74E mutant (DHPS74E). Carbonyl dynamics is probed via auto-correlated longitudinal rates and transverse C'/C'-C(alpha) CSA/dipolar and C'/C'-N CSA/dipolar cross-correlated rates, while (15)N data are taken from a previous study. Resulting values of effective order parameters and internal correlation times support the conclusion that C' relaxation reports on a different subset of fast motions compared to those probed at N-H bond vectors in the same peptide planes. (13)C' order parameters are on the average 0.08 lower than (15)N order parameters with the exception of the flexible loop region in DHP. The reduction of mobility in the loop region upon the S74E mutation can be seen from the (15)N order parameters but not from the (13)C order parameters. Internal correlation times at (13)C' sites are on the average an order of magnitude longer than those at (15)N sites for the well-structured C-terminal subdomains, while the more flexible N-terminal subdomains have more comparable average internal correlation times.

Phosphorylation-induced changes in backbone dynamics of the dematin headpiece C-terminal domain

Dematin is an actin-binding protein abundant in red blood cells and other tissues. It contains a villin-type 'headpiece' F-actin-binding domain at its extreme C-terminus. The isolated dematin headpiece domain (DHP) undergoes a significant conformational change upon phosphorylation. The mutation of Ser74 to Glu closely mimics the phosphorylation of DHP. We investigated motions in the backbone of DHP and its mutant DHPS74E using several complementary NMR relaxation techniques: laboratory frame (15)N NMR relaxation, which is sensitive primarily to the ps-ns time scale, cross-correlated chemical shift modulation NMR relaxation detecting correlated mus-ms time scale motions of neighboring (13)C' and (15)N nuclei, and cross-correlated relaxation of two (15)N-(1)H dipole-dipole interactions detecting slow motions of backbone NH vectors in successive amino acid residues. The results indicate a reduction in mobility upon the mutation in several regions of the protein. The additional salt bridge formed in DHPS74E that links the N- and C-terminal subdomains is likely to be responsible for these changes.

Direct 13C-detection for carbonyl relaxation studies of protein dynamics

We describe a method that uses direct 13C-detection for measuring rotating-frame carbonyl (13CO) relaxation rates to describe protein functional dynamics. Key advantages of method include the following: (i) unique access to 13CO groups that lack a scalar-coupled 15N-1H group; (ii) insensitivity to 15N/1H exchange-broadening that can derail 1H-detected 15N and HNCO methods; (iii) avoidance of artifacts caused by incomplete water suppression. We demonstrate the approach for both backbone and side-chain 13CO groups. Accuracy of the 13C-detected results is supported by their agreement with those obtained from established HNCO-based approaches. Critically, we show that the 13C-detection approach provides access to the 13CO groups of functionally important residues that are invisible via 1H-detected HNCO methods because of exchange-broadening. Hence, the 13C-based method fills gaps inherent in canonical 1H-detected relaxation experiments, and thus provides a novel complementary tool for NMR studies of biomolecular flexibility.

Parameterization of peptide 13C carbonyl chemical shielding anisotropy in molecular dynamics simulations

NMR chemical shielding anisotropy (CSA) relaxation is an important tool in the study of dynamical processes in proteins and nucleic acids in solution. Herein, we investigate how dynamical variations in local geometry affect the chemical shielding anisotropy relaxation of the carbonyl carbon nucleus, using the following protocol: 1) Using density functional theory, the carbonyl (13)C' CSA is computed for 103 conformations of the model peptide group N-methylacetamide (NMA). 2) The variations in computed (13)C' CSA parameters are fitted against quadratic hypersurfaces containing cross terms between the variables. 3) The predictive quality of the CSA hypersurfaces is validated by comparing the predicted and de novo calculated (13)C' CSAs for 20 molecular dynamics snapshots. 4) The CSA fluctuations and their autocorrelation and cross correlation functions due to bond-length and bond-angle distortions are predicted for a chemistry Harvard molecular mechanics (CHARMM) molecular dynamics trajectory of Ca(2+)-saturated calmodulin and GB3 from the hypersurfaces, as well as for a molecular dynamics (MD) simulation of an NMA trimer using a quantum mechanically correct forcefield. We find that the fluctuations can be represented by a 0.93 scaling factor of the CSA tensor for both R(1) and R(2) relaxations for residues in helix, coil, and sheet alike. This result is important, as it establishes that (13)C' relaxation is a valid tool for measurement of interesting dynamical events in proteins.