A structural mode-coupling approach to 15N NMR relaxation in proteins

SRLS analysis of 15N spin relaxation from E. coli ribonuclease HI: the tensorial perspective

15N–H relaxation parameters from ribonuclease HI (RNase H), acquired in previous work at magnetic fields of 14.1 and 18.8 T, and at 300 K, are analyzed with the mode-coupling slowly relaxing local structure (SRLS) approach. In accordance with standard theoretical treatments of restricted motions, SRLS approaches N-H bond dynamics from a tensorial perspective. As shown previously, a physically adequate description of this phenomenon has to account for the asymmetry of the local spatial restrictions. So far, we used rhombic local ordering tensors; this is straightforward but computationally demanding. Here, we propose substantiating the asymmetry of the local spatial restrictions in terms of tilted axial local ordering (S) and local diffusion (D2) tensors. Although less straightforward, this description provides physically sound structural and dynamic information and is efficient computationally. We find that the local order parameter, S(0)2, is on average 0.89 (0.84, and may be as small as 0.6) for the secondary structure elements (loops). The main local ordering axis deviates from the C(i-1)α-C(i)α axis by less than 6°. At 300 K, D(2,perpendicular) is virtually the same as the global diffusion rate, D1 = 1.8 × 10(7) s(-1). The correlation time 1/6D(2,parallel) ranges from 3-125 (208-344) ps for the secondary structure elements (loops) and is on average 125 ps for the C-terminal segment. The main local diffusion axis deviates from the N-H bond by less than 2° (10°) for the secondary structure elements (loops). An effective data-fitting protocol, which leads in most cases to unambiguous results with limited uncertainty, has been devised. A physically sound and computationally effective methodology for analyzing 15N relaxation in proteins, that provides a new picture of N–H bond structural dynamics in proteins, has been set forth.

Theory of nonrigid rotational motion applied to NMR relaxation in RNA

Solution NMR spectroscopy can elucidate many features of the structure and dynamics of macromolecules, yet relaxation measurements, the most common source of experimental information on dynamics, can sample only certain ranges of dynamic rates. A complete characterization of motion of a macromolecule thus requires the introduction of complementary experimental approaches. Solid-state NMR spectroscopy successfully probes the time scale of nanoseconds to microseconds, a dynamic window where solution NMR results have been deficient, and probes conditions where the averaging effects of rotational diffusion of the molecule are absent. Combining the results of the two distinct techniques within a single framework provides greater insight into dynamics, but this task requires the common interpretation of results recorded under very different experimental conditions. Herein, we provide a unified description of dynamics that is robust to the presence of large-scale conformational exchange, where the diffusion tensor of the molecule varies on a time scale comparable to rotational diffusion in solution. We apply this methodology to the HIV-1 TAR RNA molecule, where conformational rearrangements are both substantial and functionally important. The formalism described herein is of greater generality than earlier combined solid-state/solution NMR interpretations, if detailed molecular structures are available, and can offer a more complete description of RNA dynamics than either solution or solid-state NMR spectroscopy alone.

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.

Methyl dynamics of a Ca2+-calmodulin-peptide complex from NMR/SRLS

We developed the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS accounts for dynamical coupling between the tumbling of the protein and the local motion of the probe and for general tensorial properties. It is the generalization of the traditional model-free (MF) method, which does not account for mode-coupling and treats only simple tensorial properties. SRLS is applied herein to ²H relaxation of ¹³CDH₂ groups in the complex of Ca(2+)-calmodulin with the peptide smMLCKp. Literature data comprising ²H T₁ and T₂ acquired at 14.1 and 17.6 T, and 288, 295, 308, and 320 K, are used. We find that mode-coupling is a small effect for methyl dynamics. On the other hand, general tensorial properties are important. In particular, it is important to allow for the asymmetry of the local spatial restrictions, which can be represented in SRLS by a rhombic local ordering tensor with components S(0)(2) and S(2)(2). The principal axes frame of this tensor is obviously different from the axial frames of the magnetic tensors. Here, we find that -0.2 ≤ S(0)(2) ≤ 0.5 and -0.4 ≤ S(2)(2) ≤ 0. MF features a single "generalized" order parameter, S, confined to the 0-0.316 range; the local geometry is inherently simple. The parameter S is inaccurate, having absorbed unaccounted for effects, notably S(2)(2) ≠ 0. We find that the methionine methyls (the other methyl types) reorient with rates of 8.6 × 10⁹ to 21.4 × 10⁹ (0.67 × 10⁹ to 6.5 × 10⁹) 1/s. The corresponding activation energies are 10 (10-27) kJ/mol. By contrast, MF yields inaccurate effective local motional correlation times, τ(e), with nonphysical temperature dependence. Thus, the problematic S- and τ(e)-based MF picture of methyl dynamics has been replaced with an insightful physical picture based on a local ordering tensor related to structural features, and a local diffusion tensor that yields accurate activation energies.

Backbone dynamics of deoxy and carbonmonoxy hemoglobin by NMR/SRLS

The slowly relaxing local structure (SRLS) approach, developed for NMR spin relaxation analysis in proteins, is applied herein to amide ¹⁵N relaxation in deoxy and carbonmonoxy hemoglobin. Experimental data including ¹⁵N T₁, T₂ and ¹⁵N-{¹H} NOE, acquired at 11.7 and 14.1 T, and 29 and 34 °C, are analyzed. The restricted local motion of the N-H bond is described in terms of the principal value (S(0)(2)) and orientation (β(D)) of an axial local ordering tensor, S, and the principal values (R(||)(L) and R(⊥)(L)) and orientation (β(O)) of an axial local diffusion tensor, R(L). The parameters c₀² (the potential coefficient in terms of which S(0)(2) is defined), R(||)(L), β(D), and β(O) are determined by data fitting; R(⊥)(L) is set equal to the global motional rate, R(C), found previously to be (5.2-5.8) × 10⁶ 1/s in the temperature range investigated. The principal axis of S is (nearly) parallel to the C(i-1)(α)-C(i)(α) axis; when the two axes are parallel, β(D) = -101.3° (in the frame used). The principal axis of R(L) is (nearly) parallel to the N-H bond; when the two axes are parallel, β(O) = -101.3°. For "rigid" N-H bonds located in secondary structure elements the best-fit parameters are S(0)(2) = 0.88-0.95 (corresponding to local potentials of 8.6-19.9 k(B)T), R(||)(L) = 10⁹-10¹⁰ 1/s, β(D) = -101.3° ± 2.0°, and β(O) = -101.3° ± 4°. For flexible N-H bonds located in loops the best-fit values are S(0)(2) = 0.75-0.80 (corresponding to local potentials of 4.5-5.5 k(B)T), R(||)(L) = (1.0-6.3) × 10⁸ 1/s, β(D) = -101.3° ± 4.0°, and β(O) = -101.3° ± 10°. These results are important in view of their physical clarity, inherent potential for further interpretation, consistency, and new qualitative insights provided (vide infra).

Slow exchange model of nonrigid rotational motion in RNA for combined solid-state and solution NMR studies

Functional RNA molecules are conformationally dynamic and sample a multitude of dynamic modes over a wide range of frequencies. Thus, a comprehensive description of RNA dynamics requires the inclusion of a broad range of motions across multiple dynamic rates which must be derived from multiple spectroscopies. Here we describe a slow conformational exchange theoretical approach to combining the description of local motions in RNA that occur in the nanosecond to microsecond window and are detected by solid-state NMR with nonrigid rotational motion of the HIV-1 transactivation response element (TAR) RNA in solution as observed by solution NMR. This theoretical model unifies the experimental results generated by solution and solid-state NMR and provides a comprehensive view of the dynamics of HIV-1 TAR RNA, a well-known paradigm of an RNA where function requires extensive conformational rearrangements. This methodology provides a quantitative atomic level view of the amplitudes and rates of the local and collective displacements of the TAR RNA molecule and provides directly motional parameters for the conformational capture hypothesis of this classical RNA-ligand interaction.

On the measurement of ¹⁵N-{¹H} nuclear Overhauser effects. 2. Effects of the saturation scheme and water signal suppression

Measurement of steady-state (15)N-{(1)H} nuclear Overhauser effects forms a cornerstone of most methods to determine protein backbone dynamics from spin-relaxation data, since it is the most reliable probe of very fast motions on the ps-ns timescale. We have, in two previous publications (J. Magn. Reson. 192 (2008) 302-313; J. Am. Chem. Soc. 131 (2009) 6048-6049) reevaluated spin-dynamics during steady-state (or "saturated") and reference experiments, both of which are required to determine the NOE ratio. Here we assess the performance of several windowed and windowless sequences to achieve effective saturation of protons in steady-state experiments. We also evaluate the influence of the residual water signal due to radiation damping on the NOE ratio. We suggest a recipe that allows one to determine steady-state (15)N-{(1)H} NOE's without artifacts and with the highest possible accuracy.

Electron-nuclear interactions as probes of domain motion in proteins

Long range interactions between nuclear spins and paramagnetic ions can serve as a sensitive monitor of internal motion of various parts of proteins, including functional loops and separate domains. In the case of interdomain motion, the interactions between the ion and NMR-observable nuclei are modulated in direction and magnitude mainly by a combination of overall and interdomain motions. The effects on observable parameters such as paramagnetic relaxation enhancement (PRE) and pseudocontact shift (PCS) can, in principle, be used to characterize motion. These parameters are frequently used for the purpose of structural refinements. However, their use to probe actual domain motions is less common and is lacking a proper theoretical treatment from a motional perspective. In this work, a suitable spin Hamiltonian is incorporated in a two body diffusion model to produce the time correlation function for the nuclear spin-paramagnetic ion interactions. Simulated observables for nuclei in different positions with respect to the paramagnetic ion are produced. Based on these simulations, it demonstrated that both the PRE and the PCS can be very sensitive probes of domain motion. Results for different nuclei within the protein sense different aspects of the motions. Some are more sensitive to the amplitude of the internal motion, others are more sensitive to overall diffusion rates, allowing separation of these contributions. Experimentally, the interaction strength can also be tuned by substitution of different paramagnetic ions or by varying magnetic field strength (in the case of lanthanides) to allow the use of more detailed diffusion models without reducing the reliability of data fitting.

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.

The physical basis of model-free analysis of NMR relaxation data from proteins and complex fluids

NMR relaxation experiments have provided a wealth of information about molecular motions in macromolecules and ordered fluids. Even though a rigorous theory of spin relaxation is available, the complexity of the investigated systems often makes the interpretation of limited datasets challenging and ambiguous. To allow physically meaningful information to be extracted from the data without commitment to detailed dynamical models, several versions of a model-free (MF) approach to data analysis have been developed. During the past 2 decades, the MF approach has been used in the vast majority of all NMR relaxation studies of internal motions in proteins and other macromolecules, and it has also played an important role in studies of colloidal systems. Although the MF approach has been almost universally adopted, substantial disagreement remains about its physical foundations and range of validity. It is our aim here to clarify these issues. To this end, we first present rigorous derivations of the three well-known MF formulas for the time correlation function relevant for isotropic solutions. These derivations are more general than the original ones, thereby substantially extending the range of validity of the MF approach. We point out several common misconceptions and explain the physical significance of the approximations involved. In particular, we discuss symmetry requirements and the dynamical decoupling approximation that plays a key role in the MF approach. We also derive a new MF formula, applicable to anisotropic fluids and solids, including microcrystalline protein samples. The so-called slowly relaxing local structure (SRLS) model has been advanced as an alternative to the MF approach that does not require dynamical decoupling of internal and global motions. To resolve the existing controversy about the relative merits of the SRLS model and the MF approach, we formulate and solve a planar version of the SRLS model. The analytical solution of this model reveals the unphysical consequences of the symmetrical two-body Smoluchowski equation as applied to protein dynamics, thus refuting the widely held belief that the SRLS model is more accurate than the MF approach. The different results obtained by analyzing data with these two approaches therefore do not indicate the importance of dynamical coupling between internal and global motions. Finally, we explore the two principal mechanisms of dynamical coupling in proteins: torque-mediated and friction-mediated coupling. We argue by way of specific analytically solvable models that torque-mediated coupling (which the SRLS model attempts to capture) is unimportant because the relatively slow internal motions that might couple to the global motion tend to be intermittent (jumplike) in character, whereas friction-mediated coupling (which neither the SRLS model nor the MF approach incorporates) may be important for proteins with unstructured parts or flexibly connected domains.

General theoretical/computational tool for interpreting NMR spin relaxation in proteins

We developed in recent years the slowly relaxing local structure (SRLS) approach for analyzing NMR spin relaxation in proteins. SRLS is a two-body coupled rotator model which accounts rigorously for mode-coupling between the global motion of the protein and the local motion of the spin-bearing probe and allows for general properties of the second rank tensors involved. We showed that a general tool of data analysis requires both capabilities. Several important functionalities were missing in our previous implementations of SRLS in data fitting schemes, and in some important cases, the calculations were tedious. Here we present a general implementation which allows for asymmetric local and global diffusion tensors, distinct local ordering and local diffusion frames, and features a rhombic local potential which includes Wigner matrix element terms of ranks 2 and 4. A recently developed hydrodynamics-based approach for calculating global diffusion tensors has been incorporated into the data-fitting scheme. The computational efficiency of the latter has been increased significantly through object-oriented programming within the scope of the C++ programming language, and code parallelization. A convenient graphical user interface is provided. Currently autocorrelated (15)N spin relaxation data can be analyzed effectively. Adaptation to any autocorrelated and cross-correlated relaxation analysis is straightforward. New physical insight is gleaned on largely preserved local structure in solution, even in chain segments which experience slow local motion. Prospects associated with improved dynamic models, and new applications made possible by the current implementation of SRLS, are delineated.

Evidence for domain motion in proteins affecting global diffusion properties: a nuclear magnetic resonance study

The rotational diffusion of proteins is an important hydrodynamic property. Compact protein structures were found previously to exhibit hydration layer viscosity, etaloc, higher than the viscosity of bulk water, eta. This implies an apparent activation energy for rotational diffusion higher than the activation energy of water viscosity, Eeta=15.4+/-0.3 kJ/mol. In this study we examine etaloc of internally mobile proteins using 15N spin relaxation methods. We also examine the activation enthalpy, DeltaH#, and activation entropy, DeltaS#, for rotational diffusion. Of particular relevance are internally mobile ligand-free forms and compact ligand-bound forms of multidomain proteins. Adenylate kinase (AKeco) and Ca2+-calmodulin (Ca2+-CaM) are typical examples. For AKeco (Ca2+-CaM) we find that DeltaH# is 14.5+/-0.5 (15.7+/-0.4) kJ/mol. For the complex of AKeco with the inhibitor AP5A (the complex of Ca2+-CaM with the peptide smMLCKp), we find that DeltaH# is 18.1+/-0.7 (18.2+/-0.5) kJ/mol. The internally mobile outer surface protein A has DeltaH#=12.6+/-0.8 kJ/mol, and the compact protein Staphylococcal nuclease has DeltaH#=18.8+/-0.6 kJ/mol. For the internally mobile and compact proteins studied, <|DeltaS(|> equals 62+/-7 J/(mol K) and 44+/-5 J/(mol K), respectively. The fact is that etaloc>eta (DeltaH#>Eeta) for compact proteins was ascribed previously to electrostatic interactions between surface sites and water rigidifying the hydration layer. We find herein that obliteration of these interactions by domain motion leads to etaloc approximately eta, DeltaH# approximately Eeta, and large activation entropy for internally mobile protein structures.

Accurate sampling of high-frequency motions in proteins by steady-state (15)N-{(1)H} nuclear Overhauser effect measurements in the presence of cross-correlated relaxation

The steady-state {(1)H}-(15)N NOE experiment is used in most common NMR analyses of backbone dynamics to accurately ascertain the effects of the fast dynamic modes. We demonstrate here that, in its most common implementation, this experiment generates an incorrect steady state in the presence of CSA/dipole cross-correlated relaxation leading to large errors in the characterization of these high-frequency modes. This affects both the quantitative and qualitative interpretation of (15)N backbone relaxation in dynamic terms. We demonstrate further that minor changes in the experimental implementation effectively remove these errors and allow a more accurate interpretation of protein backbone dynamics.

Structural biology by NMR: structure, dynamics, and interactions

The function of bio-macromolecules is determined by both their 3D structure and conformational dynamics. These molecules are inherently flexible systems displaying a broad range of dynamics on time-scales from picoseconds to seconds. Nuclear Magnetic Resonance (NMR) spectroscopy has emerged as the method of choice for studying both protein structure and dynamics in solution. Typically, NMR experiments are sensitive both to structural features and to dynamics, and hence the measured data contain information on both. Despite major progress in both experimental approaches and computational methods, obtaining a consistent view of structure and dynamics from experimental NMR data remains a challenge. Molecular dynamics simulations have emerged as an indispensable tool in the analysis of NMR data.

Extended model free approach to analyze correlation functions of multidomain proteins in the presence of motional coupling

Interdomain motion in proteins plays an important role in biomolecular interaction. Its presence also complicates interpretation of many spectroscopy measurements. Nuclear magnetic resonance (NMR) study of domain dynamics relies on knowledge of its rotational correlation function. The extended model free (EMF) approach has been implemented to analyze coupled domain and overall motions for calmodulin, a dual-domain protein; however, the validity of EMF treatment in coupled motion has not been tested. We performed stochastic simulations on a dual-vector system employing two simple restraints to drive hydrodynamics and domain coupling: (1) both unitary vectors diffuse randomly on the surface of a sphere and (2) vectors are correlated through user-defined intervector potential. The resulting correlation curve can be adequately fit with either a single- or double-exponential decay function. The latter is consistent with the EMF treatment. The derived order parameters S (2) range from about 0.4 to 1, while the motion separation, the ratio of overall and domain motion time scales (tau m/tau s), ranges from 1 to 4. A complete overlap between time scales occurs when S (2) is less than 0.4, and the correlation function effectively behaves as a single-exponential. The S (2) values are consistent with theoretical predictions from the given potential function, differing by no more than 0.03, suggesting EMF to be a generally valid approach. In addition, from the dependence of S (2) on tau m/tau s obtained from simulation, we found a cosine potential, favoring extended conformers, as opposed to the normally assumed cone potential, reached a better agreement to experimental data.

Re-evaluation of the model-free analysis of fast internal motion in proteins using NMR relaxation

NMR spin relaxation retains a central role in the characterization of the fast internal motion of proteins and their complexes. Knowledge of the distribution and amplitude of the motion of amino acid side chains is critical for the interpretation of the dynamical proxy for the residual conformational entropy of proteins, which can potentially significantly contribute to the entropy of protein function. A popular treatment of NMR relaxation phenomena in macromolecules dissolved in liquids is the so-called model-free approach of Lipari and Szabo. The robustness of the mode-free approach has recently been strongly criticized and the remarkable range and structural context of the internal motion of proteins, characterized by such NMR relaxation techniques, attributed to artifacts arising from the model-free treatment, particularly with respect to the symmetry of the underlying motion. We develop an objective quantification of both spatial and temporal asymmetry of motion and re-examine the foundation of the model-free treatment. Concerns regarding the robustness of the model-free approach to asymmetric motion appear to be generally unwarranted. The generalized order parameter is robustly recovered. The sensitivity of the model-free treatment to asymmetric motion is restricted to the effective correlation time, which is by definition a normalized quantity and not a true time constant and therefore of much less interest in this context. With renewed confidence in the model-free approach, we then examine the microscopic distribution of side chain motion in the complex between calcium-saturated calmodulin and the calmodulin-binding domain of the endothelial nitric oxide synthase. Deuterium relaxation is used to characterize the motion of methyl groups in the complex. A remarkable range of Lipari-Szabo model-free generalized order parameters are seen with little correlation with basic structural parameters such as the depth of burial. These results are contrasted with the homologous complex with the neuronal nitric oxide synthase calmodulin-binding domain, which has distinctly different thermodynamic origins for high affinity binding.

Pressure effects on the ensemble dynamics of ubiquitin inspected with molecular dynamics simulations and isotropic reorientational eigenmode dynamics

According to NMR chemical shift data, the ensemble of ubiquitin is a mixture of "open" and "closed" conformations at rapid equilibrium. Pressure perturbations provide the means to study the transition between the two conformers by imposing an additional constraint on the system's partial molar volume. Here we use nanosecond-timescale molecular dynamics simulations to characterize the network of correlated motions accessible to the conformers at low- and high-pressure conditions. Using the isotropic reorientational eigenmode dynamics formalism to analyze our simulation trajectories, we reproduce NMR relaxation data without fitting any parameters of our model. Comparative analysis of our results suggests that the two conformations behave very differently. The dynamics of the "closed" conformation are almost unaffected by pressure and are dominated by large-amplitude correlated motions of residues 23-34 in the extended alpha-helix. The "open" conformation under conditions of normal pressure displays increased mobility, focused on the loop residues 17-20, 46-55, and 58-59 at the bottom of the core of the structure, as well as the C-terminal residues 69-76, that directly participate in key protein-protein interactions. For the same conformation, a pressure increase induces a loss of separability between molecular tumbling and internal dynamics, while motions between different backbone sites become uncorrelated.

Protein dynamics from a NMR perspective: networks of coupled rotators and fractional Brownian dynamics

Nuclear magnetic resonance (NMR) has proven to be the most valuable tool for investigating internal dynamics of proteins. In this perspective, the interpretation of NMR relaxation data eventually relies on a model of the motions. In this article, we propose to compare two radically different approaches that aim at describing internal dynamics in proteins. It is shown that the correlation functions predicted by a network of coupled rotators can be interpreted in terms of a heuristic approach based on fractional Brownian dynamics for each of the vectors in the network. Our results are interpreted in terms of the probability distributions of relaxation modes in both processes, the median of which turns out to be the relevant quantity for the comparison of both models.

An improved picture of methyl dynamics in proteins from slowly relaxing local structure analysis of 2H spin relaxation

Protein dynamics is intimately related to biological function. Core dynamics is usually studied with 2H spin relaxation of the 13CDH2 group, analyzed traditionally with the model-free (MF) approach. We showed recently that MF is oversimplified in several respects. This includes the assumption that the local motion of the dynamic probe and the global motion of the protein are decoupled, the local geometry is simple, and the local ordering is axially symmetric. Because of these simplifications MF has yielded a puzzling picture where the methyl rotation axis is moving rapidly with amplitudes ranging from nearly complete disorder to nearly complete order in tightly packed protein cores. Our conclusions emerged from applying to methyl dynamics in proteins the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Polimeno, A.; Freed, J. H. J. Phys. Chem. 1995, 99, 10995-11006.), which can be considered the generalization of MF, with all the simplifications mentioned above removed. The SRLS picture derived here for the B1 immunoglobulin binding domain of peptostreptococcal protein L, studied over the temperature range of 15-45 degrees C, is fundamentally different from the MF picture. Thus, methyl dynamics is characterized structurally by rhombic local potentials with varying symmetries and dynamically by tenfold slower rates of local motion. On average, potential rhombicity decreases, mode-coupling increases, and the rate of local motion increases with increasing temperature. The average activation energy for local motion is 2.0 +/- 0.2 kcal/mol. Mode-coupling affects the analysis even at 15 degrees C. The accuracy of the results is improved by including in the experimental data set relaxation rates associated with rank 2 coherences.

Protein dynamics from NMR: the slowly relaxing local structure analysis compared with model-free analysis

(15)N-(1)H spin relaxation is a powerful method for deriving information on protein dynamics. The traditional method of data analysis is model-free (MF), where the global and local N-H motions are independent and the local geometry is simplified. The common MF analysis consists of fitting single-field data. The results are typically field-dependent, and multifield data cannot be fit with standard fitting schemes. Cases where known functional dynamics has not been detected by MF were identified by us and others. Recently we applied to spin relaxation in proteins the slowly relaxing local structure (SRLS) approach, which accounts rigorously for mode mixing and general features of local geometry. SRLS was shown to yield MF in appropriate asymptotic limits. We found that the experimental spectral density corresponds quite well to the SRLS spectral density. The MF formulas are often used outside of their validity ranges, allowing small data sets to be force-fitted with good statistics but inaccurate best-fit parameters. This paper focuses on the mechanism of force-fitting and its implications. It is shown that MF analysis force-fits the experimental data because mode mixing, the rhombic symmetry of the local ordering and general features of local geometry are not accounted for. Combined multifield multitemperature data analyzed with the MF approach may lead to the detection of incorrect phenomena, and conformational entropy derived from MF order parameters may be highly inaccurate. On the other hand, fitting to more appropriate models can yield consistent physically insightful information. This requires that the complexity of the theoretical spectral densities matches the integrity of the experimental data. As shown herein, the SRLS spectral densities comply with this requirement.

Predicting internal protein dynamics from structures using coupled networks of hindered rotators

Internal motions in proteins, such as oscillations of internuclear vectors u(N(i)H(i) (N)) of amide bonds about their equilibrium position, can be characterized by a local order parameter. This dynamic parameter can be determined experimentally by measuring the longitudinal and transverse relaxation rates of (15)N(i) nuclei by suitable NMR methods. In this paper, it is shown that local variations of order parameters S(ii) (2) can be predicted from the knowledge of the structure. To this effect, the diffusive motion of the internuclear vector u(N(i)H(i) (N)) is described in a potential that takes into account the deviations of the angles theta(ij) between u(N(i)H(i) (N)) and neighboring vectors u(N(j)H(j) (N)) from their average value and similarly of deviations of the angles subtended between u(N(i)H(i) (N)) and u(X(j)Y(j)), where X(j) and Y(j) are heavy atoms in the vicinity of the u(N(i)H(i) (N)) vector under investigation. It is shown how the concept of vicinity can be defined by a simple cutoff threshold, i.e., by neglecting vectors u(X(j)Y(j)) with distances d(N(i),X(j))>7.5 A. The local order parameters S(ii) (2) can be predicted from the structure using a limited set of coordinates of heavy atoms. The inclusion of a larger number of heavy atoms does not improve the predictions. Applications to calmodulin, calbindin, and interleukin 4 illustrate the success and limitations of the predictions.

An overview of recent developments in the interpretation and prediction of fast internal protein dynamics

During the past decades, NMR spectroscopy has emerged as a unique tool for the study of protein dynamics. Indeed, relaxation studies on isotopically labeled proteins can provide information on the overall motions as well as the internal fast, sub-nanosecond, dynamics. Therefore, the interpretation and the prediction of spin relaxation rates in proteins are important issues that have motivated numerous theoretical and methodological developments, including the description of overall dynamics and its possible coupling to internal mobility, the introduction of models of internal dynamics, the determination of correlation functions from experimental data, and the relationship between relaxation and thermodynamical quantities. A brief account of recent developments that have proven useful in this domain are presented.

Site-specific dynamics of strands in ss- and dsDNA as revealed by time-domain fluorescence of 2-aminopurine

It is well recognized that structure and dynamics of DNA strands guide proteins toward their cognate sites in DNA. While the dynamics is controlled primarily by the nucleotide sequence, the context of a particular sequence in relation to an open end could also play a significant role. In this work we have used the fluorescent analogue of adenine, 2-aminopurine (2-AP), to extract information on site-specific dynamics of DNA strands associated with 30-70 nucleotides length. Measurement of fluorescence lifetime and anisotropy decay kinetics in various types of DNA strands in which 2-AP was located in specific positions revealed novel insights into the dynamics of strands. We find that in single-stranded (ss) DNA, the extent of motional dynamics of the bases falls off sharply from the very end toward the middle of the strand. In contrast, the flexibility of the backbone decreases more gradually in the same direction. In double-stranded (ds) DNA, the level of base-pair fraying increases toward the ends in a graded manner. Surprisingly, the same is countered by the presence of ss-overhangs emanating from dsDNA ends. Moreover, the extent of concerted motion of bases in duplex DNA increased from the end to the middle of the duplex, a result which is both striking and counterintuitive. Most surprisingly, the two complementary strands of a duplex that were unequal in length exhibited differential dynamics: the longer one with overhangs showed a distinctly higher level of flexibility than the recessed shorter strand in the same duplex. All these results, taken together, provoke newer insights in our understanding of how different bases in DNA strands are endowed with specific dynamic properties as a function of their positions. These properties are likely to be used in facilitating specific recognitions of DNA bases by proteins during various DNA-protein interaction systems.

A model of interdomain mobility in a multidomain protein

Domain mobility plays an essential role in the biological function of multidomain systems. The characteristic times of domain motions fall into the interval from nano- to milliseconds, amenable to NMR studies. Proper analysis of NMR relaxation data for these systems in solution has to account for interdomain motions, in addition to the overall tumbling and local intradomain dynamics. Here we propose a model of interdomain mobility in a multidomain protein, which considers domain reorientations as exchange/interconversion between two distinct conformational states of the molecule, combined with fully anisotropic overall tumbling. Analysis of 15N-relaxation data for Lys48-linked diubiquitin at pH 4.5 and 6.8 showed that this model adequately fits the experimental data and allows characterization of both structural and motional properties of diubiquitin, thus providing information about the relative orientation of ubiquitin domains in both interconverting states. The analysis revealed that the two domains reorient on a time scale of 9-30 ns, with the amplitudes sufficient for allowing a protein ligand access to the binding sites sequestered at the interface in the closed conformation. The analysis of a possible mechanism controlling the equilibrium between the interconverting states in diubiquitin points toward protonation of His68, which results in three different charged states of the molecule, with zero, +e, and +2e net charge. Only two of the three states are noticeably populated at pH 4.5 or 6.8, which assures applicability of the two-state model to diubiquitin at these conditions. We also compare our model with the "extended model-free" approach and discuss possible future developments of the model.

Methyl Dynamics in Proteins from NMR Slowly Relaxing Local Structure Spin Relaxation Analysis: A New Perspective

NMR spin relaxation of (2)H nuclei in (13)CH(2)D groups is a powerful method for studying side-chain motion in proteins. The analysis is typically carried out with the original model-free (MF) approach adapted to methyl dynamics. The latter is described in terms of axial local motions around, and of, the methyl averaging axis, mutually decoupled and independent of the global motion of the protein. Methyl motion is characterized primarily by the axial squared order parameter, S(axis)2, associated with fluctuations of the methyl averaging axis. This view is shown to be oversimplified by applying to typical experimental data the slowly relaxing local structure (SRLS) approach of Polimeno and Freed (Adv. Chem. Phys. 1993, 83, 89) which can be considered the generalization of the MF approach. Neglecting mode coupling and the asymmetry of the local ordering and treating approximately features of local geometry imply inaccurate values of S(axis)2, hence of the residual configurational entropy derived from it. S(axis)2, interpreted as amplitude of motion, was found to range from near disorder to almost complete order. Contrary to this picture, we find with the SRLS approach a moderate distribution in the magnitude of asymmetric local ordering and significant variation in its symmetry. The latter important property can be associated implicitly with the contribution of side-chain rotamer jumps. This is consistent with experimental residual dipolar coupling studies and theoretical work based on molecular dynamics simulations and molecular mechanics considerations. Configurational entropy is obtained in the SRLS approach directly from experimentally determined asymmetric potentials. Inconsistency between order parameters from 2H relaxation and from eta(HC-HH) cross-correlation and increase in order parameters with increasing temperature were observed with the MF approach. These discrepancies are reconciled, and physically tenable temperature dependence is obtained with the SRLS approach.

Activation Energy of Catalysis-Related Domain Motion in E. coli Adenylate Kinase

Adenylate kinase from E. coli (AKeco), folded into domains CORE, AMPbd, and LID, catalyzes the reaction AMP + ATP <--> 2ADP. Previous X-ray crystallography and optical solution methods showed that the domains AMPbd and LID, and the conserved P-loop, execute large-amplitude catalysis-related motions. We used (15)N NMR spin relaxation methods to find that the simplified model-free (MF) analysis does not, whereas our general Slowly Relaxing Local Structure analysis does, detect catalytic domain motion. SRLS set for the first time the correlation time for domain motion at tau(L)perpendicular = 8.2 ns, to be compared with tau(m) = 15.1 ns for global tumbling. These results were obtained at 303 K. Herein we conduct a temperature-dependent investigation of tau(L)perpendicular and tau(m) in the range of 288-310 K. We found that the activation energy for global tumbling is Ea = 16.9 +/- 0.5 kJ/mol, the hydrodynamic volume of hydrated AKeco is 65.6 +/- 2.1 nm3, its radius is 2.50 +/- 0.03 nm, and the number of hydration layers is 1.77. The average tau(L)perpendicular value decreases from 11 ns at 288 K to 4 ns at 310 K, with activation energies of 29.7 +/- 3.3, 32.1 +/- 4.3, and 30.4 +/- 4.3 kJ/mol for the domains AMPbd and LID, and the catalytic P-loop, respectively. These values are two-to-three times smaller than typical activation energies of enzymatic reactions. Hence kinase catalysis appears not to be controlled by domain motion in the ligand-free enzyme. However, the latter process clearly facilitates important mechanical aspects such as steric recognition and capturing of the AMP and ATP substrates, their proper positioning for phosphorylation, and the release of the ADP product.

Interdomain mobility in di-ubiquitin revealed by NMR

Domain orientation and dynamics can play an essential role in the function of multidomain proteins. Lys48-linked polyubiquitin chains, the principal signal for proteasomal protein degradation, adopt a closed conformation at physiological conditions, in which the functionally important residues Leu8, Ile44, and Val70 are sequestered at the interdomain interface. This interface must open in order for these groups to become available for interactions with various chain-recognition factors. Knowledge of the mechanism of domain motion leading to the opening of the interdomain interface in polyubiqutin is, therefore, essential for the understanding of the processes controlling molecular recognition events in polyubiquitin signaling. Here we use NMR to characterize the interdomain dynamics that open the interface in a di-ubiquitin chain. This process occurs via domain reorientations on a 10-ns time scale and with the amplitudes that are sufficient for making functionally important hydrophobic residues in polyubiquitin available for direct interactions with various ubiquitin-binding factors. The analysis revealed the structures of the interconverting conformational states of di-ubiquitin and the rates and amplitudes of this process at near-physiological and acidic pH. The proposed mechanism of domain reorientation is quite general and could serve as a paradigm of interdomain mobility in other multidomain systems.

Resolving the motional modes that code for RNA adaptation

Using a domain elongation strategy, we decoupled internal motions in RNA from overall rotational diffusion. This allowed us to site-specifically resolve a manifold of motional modes in two regulatory RNAs from HIV-1 with the use of nuclear magnetic resonance spin relaxation methods. Base and sugar librations vary on a picosecond time scale and occur within helical domains that move collectively at diffusion-limited nanosecond time scales. Pivot points are short, functionally important, and highly mobile internal loops. These spontaneous changes in RNA conformation correlate quantitatively with those that follow adaptive recognition of diverse targets. Thus, ligands may stabilize existing RNA conformations rather than inducing new ones.

Toward an integrated computational approach to CW-ESR spectra of free radicals

Interpretation of structural properties and dynamic behaviour of molecules in solution is of fundamental importance to understand their stability, chemical reactivity and catalytic action. Information can be gained, in principle, by a variety of spectroscopic techniques, magnetic as well as optical. In particular, continuous wave electron spin resonance (CW-ESR) measurements are highly informative. However, the wealth of structural and dynamic information which can be extracted from ESR spectroscopy is, at present, limited by the necessity of employing computationally efficient models, which are increasingly complex as they need to take into account diverse relaxation processes affecting the spectrum. In this paper, we address the basic theoretical tools needed to predict, essentially ab initio, CW-ESR spectra observables according to the stochastic Liouville equation (SLE) approach, combined with quantum mechanical and hybrid methods for the accurate and efficient computation of structural, spectroscopic and magnetic properties of molecular systems. We shall discuss, on one hand, the quantum mechanical calculation of magnetic observables, via density functional theory (DFT), time-dependent DFT (TD-DFT) and application of the polarizable continuum model (PCM) for the description of environmental effects, including anisotropic environments and systems where different regions are characterized by different dielectric constants. One the other hand, the explicit evaluation of dynamical effects will be discussed based on the numerically exact treatment of the SLE in the presence of several relaxation processes, which has been proven to be a challenging task.

PhosphoThr peptide binding globally rigidifies much of the FHA domain from Arabidopsis receptor kinase-associated protein phosphatase

A net increase in the backbone rigidity of the kinase-interacting FHA domain (KI-FHA) from the Arabidopsis receptor kinase-associated protein phosphatase (KAPP) accompanies the binding of a phosphoThr peptide from its CLV1 receptor-like kinase partner, according to (15)N NMR relaxation at 11.7 and 14.1 T. All of the loops of free KI-FHA display evidence of nanosecond-scale motions. Many of these same residues have residual dipolar couplings that deviate from structural predictions. Binding of the CLV1 pT868 peptide seems to reduce nanosecond-scale fluctuations of all loops, including half of the residues of recognition loops. Residues important for affinity are found to be rigid, i.e., conserved residues and residues of the subsite for the key pT+3 peptide position. This behavior parallels SH2 and PTB domain recognition of pTyr peptides. PhosphoThr peptide binding increases KI-FHA backbone rigidity (S(2)) of three recognition loops, a loop nearby, seven strands from the beta-sandwich, and a distal loop. Compensating the trend of increased rigidity, binding enhances fast mobility at a few sites in four loops on the periphery of the recognition surface and in two loops on the far side of the beta-sandwich. Line broadening evidence of microsecond- to millisecond-scale fluctuations occurs across the six-stranded beta-sheet and nearby edges of the beta-sandwich; this forms a network connected by packing of interior side chains and H-bonding. A patch of the slowly fluctuating residues coincides with the site of segment-swapped dimerization in crystals of the FHA domain of human Chfr. Phosphopeptide binding introduces microsecond- to millisecond-scale fluctuations to more residues of the long 8/9 recognition loop of KI-FHA. The rigidity of this FHA domain appears to couple as a whole to pThr peptide binding.

Escherichia coli adenylate kinase dynamics: comparison of elastic network model modes with mode-coupling (15)N-NMR relaxation data

The dynamics of adenylate kinase of Escherichia coli (AKeco) and its complex with the inhibitor AP(5)A, are characterized by correlating the theoretical results obtained with the Gaussian Network Model (GNM) and the anisotropic network model (ANM) with the order parameters and correlation times obtained with Slowly Relaxing Local Structure (SRLS) analysis of (15)N-NMR relaxation data. The AMPbd and LID domains of AKeco execute in solution large amplitude motions associated with the catalytic reaction Mg(+2)*ATP + AMP --> Mg(+2)*ADP + ADP. Two sets of correlation times and order parameters were determined by NMR/SRLS for AKeco, attributed to slow (nanoseconds) motions with correlation time tau( perpendicular) and low order parameters, and fast (picoseconds) motions with correlation time tau( parallel) and high order parameters. The structural connotation of these patterns is examined herein by subjecting AKeco and AKeco*AP(5)A to GNM analysis, which yields the dynamic spectrum in terms of slow and fast modes. The low/high NMR order parameters correlate with the slow/fast modes of the backbone elucidated with GNM. Likewise, tau( parallel) and tau( perpendicular) are associated with fast and slow GNM modes, respectively. Catalysis-related domain motion of AMPbd and LID in AKeco, occurring per NMR with correlation time tau( perpendicular), is associated with the first and second collective slow (global) GNM modes. The ANM-predicted deformations of the unliganded enzyme conform to the functional reconfiguration induced by ligand-binding, indicating the structural disposition (or potential) of the enzyme to bind its substrates. It is shown that NMR/SRLS and GNM/ANM analyses can be advantageously synthesized to provide insights into the molecular mechanisms that control biological function.

Main Chain and Side Chain Dynamics of the Ubiquitin Conjugating Enzyme Variant Human Mms2 in the Free and Ubiquitin-Bound States†

Protein ubiquitination involves a cascade of enzymatic steps where ubiquitin (Ub) is sequentially transferred as a thiolester intermediate from an E1 enzyme to an E2 enzyme and finally to the protein target with the help of a Ub-protein ligase. Protein ubiquitination brought about by the Ubc13-Mms2 (E2-E2) complex has a unique role in the cell, unrelated to protein degradation. The Mms2-Ubc13 heterodimer links Ub molecules to one another through an isopeptide bond between its own C-terminus and Lys-63 on another Ub. The role of Mms2 is to orient a target-bound Ub molecule such that its Lys-63 is proximal to the C-terminus of the Ub molecule that is covalently linked to the active site of Ubc13. To gain insight into the influence of protein dynamics on the affinity of Ub for Mms2, we have determined pico- to nanosecond time scale fluctuations of the main chain and methyl side chains of human Mms2 in the free and Ub-bound states using solution state (15)N and (2)H nuclear magnetic resonance relaxation measurements. Analysis of the relaxation data allows for a semiquantitative estimation of the conformational entropy change (TDeltaS(NMR)) for the main chain and side chain methyl groups of Mms2 upon binding Ub. The value of TDeltaS(NMR) for the main chain and side chain methyl groups of Mms2 is -8 +/- 2 and -2 +/- 2 kcal mol(-)(1), respectively. The experimental DeltaG(binding) for the Mms2.Ub complex is -6 kcal mol(-)(1). Estimation of DeltaG(binding) using an empirical structure-based approach that does not account for changes in main chain entropy yields a value of -17 +/- 2 kcal mol(-)(1). However, inclusion of TDeltaS(NMR) for the main chain of Mms2 increases the estimated DeltaG(binding) to -9 +/- 3 kcal mol(-)(1). Assuming that changes in Ub main chain dynamics contribute to TDeltaS(NMR) to the same extent as Mms2, the estimated DeltaG(binding) is further reduced to -1 +/- 4 kcal mol(-)(1), a value close to the experimental DeltaG(binding).

Hyaluronan chain conformation and dynamics

An overview of the present state of research in the field of hyaluronan chain conformational aspects is presented. The relationship between structure and dynamics are illustrated for a series of hyaluronan oligomers. Conformational characteristics of hyaluronan chains are discussed, together with the dynamic chain patterns, evaluated by using a theoretical approach to diffusive polymer dynamics. The dependence of correlation times and NMR relaxation parameters from the chain dimension are investigated. Topological features and dimensional properties are related to the structural determinants by using classical computational methods of molecular mechanics and Monte Carlo simulation.

Isotropic Reorientational Eigenmode Dynamics Complements NMR Relaxation Measurements for RNA

(13)C NMR relaxation measurements alone are often not sufficient to describe the motions of small RNA molecules in solution. In the case where the global tumbling time of the RNA is on the same time scale as its internal motions, standard Lipari-Szabo analysis becomes inadequate, and other methods must be used to describe the dynamics. Here, molecular dynamics simulations of the iron-responsive element (IRE) RNA hairpin are analyzed using isotropic reorientational eigenmode dynamics (iRED) to provide a picture of the motions of the RNA. The results show that indeed there is no separability of global and internal motions, and thus the order parameters determined from experimental data cannot be quantitatively accurate. iRED analysis also identifies correlated motions, providing a new picture of the dynamics of the IRE loop.

Determination of protein rotational correlation time from NMR relaxation data at various solvent viscosities

An accurate determination of the overall rotation of a protein plays a crucial role in the investigation of its internal motions by NMR. In the present work, an innovative approach to the determination of the protein rotational correlation time tau(R) from the heteronuclear relaxation data is proposed. The approach is based on a joint fit of relaxation data acquired at several viscosities of a protein solution. The method has been tested on computer simulated relaxation data as compared to the traditional tau(R) determination method from T(1)/T(2) ratio. The approach has been applied to ribonuclease barnase from Bacillus amyloliquefaciens dissolved in an aqueous solution and deuterated glycerol as a viscous component. The resulting rotational correlation time of 5.56 +/- 0.01 ns and other rotational diffusion tensor parameters are in good agreement with those determined from T(1)/T(2) ratio.

A phase cycle scheme that significantly suppresses offset-dependent artifacts in the R2-CPMG 15N relaxation experiment

R2-CPMG 15N relaxation experiments form the basis of NMR dynamics measurements, both for analysis of nano-pico second dynamics and milli-micro second dynamics (kinetics). It has been known for some time that in the practical limit of finite pulse widths, which becomes acute when using cryogenic probes, systematic errors in the apparent R2 relaxation behavior occur for spins far off-resonance from the RF carrier. Inaccurate measurement of R2 rates propagates into quantitative models such as model-free relaxation analysis, rotational diffusion tensor analysis, and relaxation dispersion. The root of the problem stems from evolution of the magnetization vectors out of the XY-plane, both during the pulses as well as between the pulses. These deviations vary as a function of pulse length, number of applied CPMG pulses, and CPMG inter-pulse delay. Herein, we analyze these effects in detail with experimentation, numerical simulations, and analytical equations. Our work suggests a surprisingly simple change in the phase progression of the CPMG pulses, which leads to a remarkable improvement in performance. First, the applicability range of the CPMG experiment is increased by a factor of two in spectral width; second, the dynamical/kinetic processes that can be assessed are significantly extended towards the slower time scale; finally, the robustness of the relaxation dispersion experiments is greatly improved.

Gated electron transfers and electron pathways in azurin: a NMR dynamic study at multiple fields and temperatures

Dynamic properties of electron transfer pathways in a small blue copper cupredoxin are explored using an extensive 15N NMR relaxation study of reduced Pseudomonas aeruginosa azurin at four magnetic fields (500-900 MHz) and at two temperatures chosen well below the melting point of the protein. Following a careful model-free analysis, several protein regions with different dynamic regimes are identified. Nanosecond time-scale mobility characterizes various residues of the hydrophobic surface patch believed to mark the natural entry point for electrons, notably the surface-exposed copper-ligand His117. These findings are consistent with a gated electron transfer process according to the "dynamic docking" model. Residues 47-49 along intramolecular pathways of electrons show rigidity that is remarkably conserved when increasing the temperature. Three different conformational exchange processes were observed in the millisecond range, one near the only disulfide bridge in the molecule and two near the copper ion. The latter two processes are consistent with previous data such as crystal structures at various pH values and NMR relaxation dispersion experiments; they may indicate an additional gated electron transfer mechanism at slower time-scales.

High frequency dynamics in hemoglobin measured by magnetic relaxation dispersion

The magnetic relaxation dispersion profiles for formate, acetate, and water protons are reported for aqueous solutions of hemoglobin singly and doubly labeled with a nitroxide and mercury(II) ion at cysteines at beta-93. Using two spin labels, one nuclear and one electron spin, a long intramolecular vector is defined between the two beta-93 positions in the protein. The paramagnetic contributions to the observed 1H spin-lattice relaxation rate constant are isolated from the magnetic relaxation dispersion profiles obtained on a dual-magnet apparatus that provides spectral density functions characterizing fluctuations sensed by intermoment dipolar interactions in the time range from the tens of microseconds to approximately 1 ps. Both formate and acetate ions are found to bind specifically within 5 angstroms of the beta-93 spin-label position and the relaxation dispersion has inflection points corresponding to correlation times of 30 ps and 4 ns for both ions. The 4-ns motion is identified with exchange of the anions from the site, whereas the 30-ps correlation time is identified with relative motions of the spin label and the bound anion in the protein environment close to beta-93. The magnetic field dependence of the paramagnetic contributions in both cases is well described by a simple Lorentzian spectral density function; no peaks in the spectral density function are observed. Therefore, the high frequency motions of the protein monitored by the intramolecular vector defined by the electron and nuclear spin are well characterized by a stationary random function of time. Attempts to examine long vector fluctuations by employing electron spin and nuclear spin double-labeling techniques did not yield unambiguous characterization of the high frequency motions of the vector between beta-93 positions on different chains.

NMR backbone dynamics of the human type I interferon binding subunit, a representative cytokine receptor

The antiviral and antiproliferative activities of type I interferons (IFNs) are mediated by a common receptor, and its second subunit (IFNAR2) exhibits nanomolar affinity to both IFNalpha and IFNbeta subtypes. We have previously determined the structure of the IFN-binding extracellular domain of IFNAR2 (IFNAR2-EC) using multidimensional NMR [Chill, J. H., Quadt, S. R., Levy, R., Schreiber, G. E., and Anglister, J. (2003) Structure 11, 791-802], showing it to comprise two fibronectin domains linked by a hinge. As the first cytokine receptor structure determined in the unliganded state and in solution, IFNAR2-EC offers an opportunity to characterize the dynamics of the cytokine receptor family and their correlation to biological function. Backbone dynamics of IFNAR2-EC were investigated using 15N relaxation at 11.74 and 18.79 T, and measurements of residual dipolar couplings (RDCs). Dynamics of the binding site distinguish between rigid structural domains, which stabilize the binding site conformation, and a more flexible binding interface which interacts with the ligand. Measurements of diffusional anisotropy and RDCs and model-free analysis all show that the backbone of the hinge interdomain region of IFNAR2-EC is rigid on the picosecond to nanosecond time scale. Signal transduction in cytokines receptors is initiated by ligand-induced juxtaposition of the two receptor subunits, triggering the mutual phosphorylation of kinases associated to their cytoplasmic domains. The rigidity of the hinge ensures correct positioning of the receptor subunits in the ternary signaling complex and modulates the interaction between kinases in the cytoplasm, thereby controlling the rate and efficiency of phosphorylation.