Anisotropic rotational diffusion in model-free analysis for a ternary DHFR complex

Model-free analysis has been extensively used to extract information on motions in proteins over a wide range of timescales from NMR relaxation data. We present a detailed analysis of the effects of rotational anisotropy on the model-free analysis of a ternary complex for dihydrofolate reductase (DHFR). Our findings show that the small degree of anisotropy exhibited by DHFR (D_||/D=1.18) introduces erroneous motional models, mostly exchange terms, to over 50% of the NH spins analyzed when isotropic tumbling is assumed. Moreover, there is a systematic change in S², as large as 0.08 for some residues. The significant effects of anisotropic rotational diffusion on model-free motional parameters are in marked contrast to previous studies and are accentuated by lowering of the effective correlation time using isotropic tumbling methods. This is caused by the preponderance of NH vectors aligned perpendicular to the principal diffusion tensor axis and is readily detected because of the high quality of the relaxation data. A novel procedure, COPED (COmparison of Predicted and Experimental Diffusion tensors) is presented for distinguishing genuine motions from the effects of anisotropy by comparing experimental relaxation data and data predicted from hydrodynamic analyses. The procedure shows excellent agreement with the slow motions detected from the axially symmetric model-free analysis and represents an independent procedure for determining rotational diffusion and slow motions that can confirm or refute established procedures that rely on relaxation data. Our findings show that neglect of even small degrees of rotational diffusion anisotropy can introduce significant errors in model-free analysis when the data is of high quality. These errors can hinder our understanding of the role of internal motions in protein function.     

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 _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 _R determination method from T₁/T₂ 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 T₁/T₂ ratio.     

Fast evaluation of protein dynamics from deficient <Superscript>15</Superscript>N relaxation data

Simple and convenient method of protein dynamics evaluation from the insufficient experimental ¹⁵N relaxation data is presented basing on the ratios, products, and differences of longitudinal and transverse ¹⁵N relaxation rates obtained at a single magnetic field. Firstly, the proposed approach allows evaluating overall tumbling correlation time (nanosecond time scale). Next, local parameters of the model-free approach characterizing local mobility of backbone amide N–H vectors on two different time scales, S² and R _ex , can be elucidated. The generalized order parameter, S², describes motions on the time scale faster than the overall tumbling correlation time (pico- to nanoseconds), while the chemical exchange term, R _ex , identifies processes slower than the overall tumbling correlation time (micro- to milliseconds). Advantages and disadvantages of different methods of data handling are thoroughly discussed.     

Measurement of 15N relaxation in the detergent-solubilized tetrameric KcsA potassium channel

A set of TROSY-HNCO (tHNCO)-based 3D experiments is presented for measuring ¹⁵N relaxation parameters in large, membrane-associated proteins, characterized by slow tumbling times and significant spectral overlap. Measurement of backbone ¹⁵N R ₁, R _1ρ, ¹⁵N–{¹H} NOE, and ¹⁵N CSA/dipolar cross correlation is demonstrated and applied to study the dynamic behavior of the homotetrameric KcsA potassium channel in SDS micelles under conditions where this channel is in the closed state. The micelle-encapsulated transmembrane domain, KcsA^TM, exhibits a high degree of order, tumbling as an oblate ellipsoid with a global rotational correlation time, τ_c = 38 ± 2.5 ns, at 50 °C and a diffusion anisotropy, , corresponding to an aspect ratio a/b ≥ 1.4. The N- and C-terminal intracellular segments of KcsA exhibit considerable internal dynamics (S ² values in the 0.2–0.45 range), but are distinctly more ordered than what has been observed for unstructured random coils. Relaxation behavior in these domains confirms the position of the C-terminal helix, and indicates that in SDS micelles, this amphiphilic helix does not associate into a stable homotetrameric helical bundle. The relaxation data indicate the absence of elevated backbone dynamics on the ps–ns time scale for the 5-residue selectivity filter, which selects K⁺ ions to enter the channel. Electronic Supplementary Material Supplementary material is available to authorised users in the online version of this article at . An erratum to this article can be found at     

Sampling of Protein Dynamics in Nanosecond Time Scale by 15N NMR Relaxation and Self-Diffusion Measurements

Abstract

This paper presents a procedure for detection of intermediate nanosecond internal dynamics in globular proteins. The procedure uses ¹H-¹⁵N relaxation measurements at several spectrometer frequencies and hydrodynamic calculations based on experimental self-diffusion coefficients. New heteronuclear experiments, using pulse field gradients, are introduced for the measurement of translation diffusion coefficients of ¹⁵N labeled proteins. An advanced interpretation of recently published (Luginbühl et al., Biochemistry, 36, 7305–7312 (1997)) backbone amide ¹⁵N relaxation data, measured at two spectrometers (400 and 750 MHz for ¹H) for N-terminal DNA-binding domain (1–63) of 434 repressor, is presented. Non-applicability of commonly used fast (picosecond) dynamics model (FD) was justified by (i) poor fit of relaxation data by the FD model-free spectral density function both for isotropic and anisotropic models of the overall molecular tumbling; (ii) specific dependence of the overall rotation correlation times calculated from T₁/T₂ ratio on the spectrometer frequency; (iii) mismatch of the ratio of longitudinal ¹⁵N relaxation times T₁, measured at different spectrometer frequencies, in comparison with that anticipated for the IT) model; (iv) significantly underestimated overall rotation correlation time provided by the FD model (5.50±0.15 and 5.80±0.15 ns for 750 and 400 MHz spectrometer frequency respectively) in comparison with correlation time obtained from hydrodynamics. On the other hand, all relaxation and hydrodynamics data are in good correspondence with the model of intermediate (nanoseconds) dynamics. Overall rotation correlation time of 7.5±0.7 ns was calculated from experimental translation self-diffusion rate using hydrodynamics formalism (Garcia de la Torre, J. and Bloomfield, V.A. Quart. Rev. Biophys., 14, 81–139 (1981)). The statistical analysis of ¹⁵N relaxation data along with the hydrodynamic consideration clearly revealed that most of the residues in 434(1–63) repressor are involved in the nanosecond internal dynamics characterized by the the mean order parameters of 0.59±0.06 and the correlation times of ca. 5 ns.     

Determination of <Superscript>13</Superscript>C CSA Tensors: Extension of the Model-independent Approach to an RNA Kissing Complex Undergoing Anisotropic Rotational Diffusion in Solution

Chemical shift anisotropy (CSA) tensor parameters have been determined for the protonated carbons of the purine bases in an RNA kissing complex in solution by extending the model-independent approach [Fushman, D., Cowburn, D. (1998) J. Am. Chem. Soc. 120, 7109–7110]. A strategy for determining CSA tensor parameters of heteronuclei in isolated X–H two-spin systems (X = ¹³C or ¹⁵N) in molecules undergoing anisotropic rotational diffusion is presented. The original method relies on the fact that the ratio κ₂=R₂^auto/R₂^cross of the transverse auto- and cross-correlated relaxation rates involving the X CSA and the X–H dipolar interaction is independent of parameters related to molecular motion, provided rotational diffusion is isotropic. However, if the overall motion is anisotropic κ₂ depends on the anisotropy D_||/D_⊥ of rotational diffusion. In this paper, the field dependence of both κ₂ and its longitudinal counterpart κ₁=R₁^auto/R₁^cross are determined. For anisotropic rotational diffusion, our calculations show that the average κ_av = 1/2 (κ₁+κ₂), of the ratios is largely independent of the anisotropy parameter D_||/D_⊥. The field dependence of the average ratio κ_av may thus be utilized to determine CSA tensor parameters by a generalized model-independent approach in the case of molecules with an overall motion described by an axially symmetric rotational diffusion tensor.     

Unraveling protein dynamics through fast spectral density mapping

Spectral density mapping at multiple NMR field strengths is probably the best method to describe the dynamical behavior of a protein in solution through the analysis of ¹⁵N heteronuclear relaxation parameters. Nevertheless, such analyses are scarcely reported in the literature, probably because this method is excessively demanding in spectrometer measuring time. Indeed, when using n different magnetic fields and assuming the validity of the high frequency approximation, the discrete sampling of the spectral density function with 2n + 1 points needs the measurement of 3n ¹⁵N heteronuclear relaxation measurements (n R ₁, n R ₂, and n¹⁵N{¹H}NOEs). Based on further approximations, we proposed a new strategy that allows us to describe the spectral density with n + 2 points, with the measurement of a total of n + 2 heteronuclear relaxation parameters. Applied to the dynamics analysis of the protein p13 ^MTCP1 at three different NMR fields, this approach allowed us to divide by nearly a factor of two the total measuring time, without altering further results obtained by the “model free” analysis of the resulting spectral densities. Furthermore, simulations have shown that this strategy remains applicable to any low isotropically tumbling protein ( ns), and is valid for the types of motion generally envisaged for proteins.     

Fluctuations, exchange processes, and water diffusion in aqueous protein systems: A study of bovine serum albumin by diverse NMR techniques

Experimental frequency, concentration, and temperature dependences of the deuteron relaxation times T₁ and T₂ of D₂O solutions of bovine serum albumin are reported and theoretically described in a closed form without formal parameters. Crucial processes of the theoretical concept are material exchange, translational diffusion of water molecules on the rugged surfaces of proteins, and tumbling of the macromolecules. It is also concluded that, apart from averaging of the relaxation rates in the diverse deuteron phases, material exchange contributes to transverse relaxation by exchange modulation of the Larmor frequency. The rate limiting factor of macromolecular tumbling is determined by the free water content. In a certain analogy to the classical free-volume theory, a “free-water-volume theory” is presented. There are two characteristic water mass fractions indicating the saturation of the hydration shells (C_s ≈ 0.3) and the onset of protein tumbling (C₀ ≈ 0.6). The existence of the translational degrees of freedom of water molecules in the hydration shells has been verified by direct measurement of the diffusion coefficient using an NMR field-gradient technique. The concentration and temperature dependences show phenomena indicating a percolation transition of clusters of free water. The threshold water content was found to be C_c^w ≈ 0.43.     

NMR exchange broadening arising from specific low affinity protein self-association: Analysis of nitrogen-15 nuclear relaxation for rat CD2 domain 1

Nuclear spin relaxation monitored by heteronuclear NMR provides a useful method to probe the overall and internal molecular motion for biological macromolecules over a variety of time scales. Nitrogen-15 NMR relaxation parameters have been recorded for the N-terminal domain of the rat T-cell antigen CD2 (CD2d1) in a dilution series from 1.20 mM to 40 M (pH 6.0, 25 °C). The data have been analysed within the framework of the model- free formalism of Lipari and Szabo to understand the molecular origin of severely enhanced transverse relaxation rates found for certain residues. These data revealed a strong dependence of the derived molecular correlation time _c upon the CD2d1 protein concentration. Moreover, a number of amide NH resonances exhibited exchange broadening and chemical shifts both strongly dependent on protein concentration. These amide groups cluster on the major -sheet surface of CD2d1 that coincides with a major lattice contact in the X-ray structure of the intact ectodomain of rat CD2. The complete set of relaxation data fit well to an equilibrium monomer–dimer exchange model, yielding estimates of exchange rate constants (k_ON=5000 M^-1 s^-1; k_OFF=7 s^-1) and a dissociation constant (K_D 3–6 mM) that is consistent with the difficulty in detecting the weak interactions for this molecule by alternative biophysical methods. The self-association of CD2d1 is essentially invariant to changes in buffer composition and ionic strength and the associated relaxation phenomena cannot be explained as a result of neglecting anisotropic rotational diffusion in the analysis. These observations highlight the necessity to consider low affinity protein self-association interactions as a source of residue specific exchange phenomena in NMR spectra of macromolecular biomolecules, before the assignment of more elaborate intramolecular conformational mechanisms.     

Backbone dynamics of the human CC-chemokine eotaxin

Eotaxin is a CC chemokine with potent chemoattractant activity towards eosinophils. ¹⁵N NMR relaxation data have been used to characterize the backbone dynamics of recombinant human eotaxin. ¹⁵N longitudinal (R₁) and transverse (R₂) auto relaxation rates, heteronuclear ¹H-¹⁵N steady-state NOEs, and transverse cross-relaxation rates (_xy) were obtained at 30 °C for all resolved backbone secondary amide groups using ¹ H-detected two-dimensional NMR experiments. Ratios of transverse auto and cross relaxation rates were used to identify NH groups influenced by slow conformational rearrangement. Relaxation data were fit to the extended model free dynamics formalism, yielding parameters describing axially symmetric molecular rotational diffusion and the internal dynamics of each NH group. The molecular rotational correlation time (_m) is 5.09±0.02 ns, indicating that eotaxin exists predominantly as a monomer under the conditions of the NMR study. The ratio of diffusion rates about unique and perpendicular axes (D/D) is 0.81±0.02. Residues with large amplitudes of subnanosecond motion are clustered in the N-terminal region (residues 1–19), the C-terminus (residues 68–73) and the loop connecting the first two -strands (residues 30–37). N-terminal flexibility appears to be conserved throughout the chemokine family and may have implications for the mechanism of chemokine receptor activation. Residues exhibiting significant dynamics on the microsecond–millisecond time scale are located close to the two conserved disulfide bonds, suggesting that these motions may be coupled to disulfide bond isomerization.     

Monitoring conformational dynamics with solid-state R 1ρ experiments

A new application of solid-state rotating frame (R _1ρ) relaxation experiments to observe conformational dynamics is presented. Studies on a model compound, dimethyl sulfone (DMS), show that R _1ρ relaxation due to reorientation of a chemical shift anisotropy (CSA) tensor undergoing chemical exchange can be used to monitor slow-to-intermediate timescale conformational exchange processes. Control experiments used d ₆ -DMS and alanine to confirm that the technique is monitoring reorientation of the CSA tensor rather than dipolar interactions or methyl group rotation. The application of this method to proteins could represent a new site-specific probe of conformational dynamics.     

Deriving quantitative dynamics information for proteins and RNAs using ROTDIF with a graphical user interface

To facilitate rigorous analysis of molecular motions in proteins, DNA, and RNA, we present a new version of ROTDIF, a program for determining the overall rotational diffusion tensor from single- or multiple-field nuclear magnetic resonance relaxation data. We introduce four major features that expand the program’s versatility and usability. The first feature is the ability to analyze, separately or together, ¹³C and/or ¹⁵N relaxation data collected at a single or multiple fields. A significant improvement in the accuracy compared to direct analysis of R ₂/R ₁ ratios, especially critical for analysis of ¹³C relaxation data, is achieved by subtracting high-frequency contributions to relaxation rates. The second new feature is an improved method for computing the rotational diffusion tensor in the presence of biased errors, such as large conformational exchange contributions, that significantly enhances the accuracy of the computation. The third new feature is the integration of the domain alignment and docking module for relaxation-based structure determination of multi-domain systems. Finally, to improve accessibility to all the program features, we introduced a graphical user interface that simplifies and speeds up the analysis of the data. Written in Java, the new ROTDIF can run on virtually any computer platform. In addition, the new ROTDIF achieves an order of magnitude speedup over the previous version by implementing a more efficient deterministic minimization algorithm. We not only demonstrate the improvement in accuracy and speed of the new algorithm for synthetic and experimental ¹³C and ¹⁵N relaxation data for several proteins and nucleic acids, but also show that careful analysis required especially for characterizing RNA dynamics allowed us to uncover subtle conformational changes in RNA as a function of temperature that were opaque to previous analysis.     

Off-resonance R1rho relaxation outside of the fast exchange limit: an experimental study of a cavity mutant of T4 lysozyme

An ¹⁵N off-resonance R ₁ spin relaxation study of an L99A point mutant of T4 lysozyme is presented. Previous CPMG-based relaxation dispersion studies of exchange in this protein have established that the molecule interconverts between a populated ground state and an excited state (3.4%) with an exchange rate constant of 1450 s^–1 at 25°C. It is shown that for the majority of residues in this protein the offset dependence of the R ₁ relaxation rates cannot be well fit using models which are only valid in the fast exchange regime. In contrast, a recently derived expression by Trott and Palmer (J. Magn. Reson., 154, 157–160, 2002) which is valid over a wider window of exchange than other relations, is shown to fit the data well. Values of (signed) chemical shift differences between exchanging sites have been extracted and are in reasonable agreement with shift differences measured using CPMG methods. A set of simulations is presented which help establish the exchange regimes that are best suited to analysis by off-resonance R ₁ techniques.     

Backbone dynamics of the channel-forming antibiotic zervamicin IIB studied by 15N NMR relaxation

The backbone dynamics of the channel-forming peptide antibiotic zervamicin IIB (Zrv-IIB) in methanol were studied by 15N nuclear magnetic resonance relaxation measurements at 11.7, 14.1 and 18.8 T magnetic fields. The anisotropic overall rotation of the peptide was characterized based on 15N relaxation data and by hydrodynamic calculations. 'Model-free' analysis of the relaxation data showed that the peptide is fairly rigid on a sub-nanosecond time-scale. The residues from the polar side of Zrv-IIB helix are involved in micro-millisecond time-scale conformational exchange. The conformational exchange observed might indicate intramolecular processes or specific intermolecular interactions of potential relevance to Zrv-IIB ion channel formation.     

Dynamics in the cyclic Enterobacterial common antigen as studied by <Superscript>13</Superscript>C NMR relaxation

The motional properties of the cyclic enterobacterial common antigen (cECA), consisting of four trisaccharide repeat units, have been investigated by carbon-13 spin relaxation. R₁, R₂ and NOE relaxation parameters have been determined at three magnetic field strengths. The data were interpreted within the model-free framework to include the possibility of motional anisotropy, and overall as well as local dynamical parameters were fitted separately for each ring carbon. The motional anisotropy was addressed by assuming an axially symmetric diffusion tensor, which was fitted from the overall correlation times for each site in the sugar residues using the previously determined crystal structure. The data were found to be in agreement with an oblate shape of the molecule, and the values for D_iso and were in good agreement with translational diffusion data and an estimate based on calculation of the moment of inertia tensor, respectively. The local dynamics in cECA were found to be residue-dependent. Somewhat lower values for the order parameters, as well as longer local correlation times, were observed for the -linked ManNAcA residue compared to the two -linked residues in the trisaccharide repeat unit.     

<Superscript>15</Superscript>N transverse relaxation measurements for the characterization of µs–ms dynamics are deteriorated by the deuterium isotope effect on <Superscript>15</Superscript>N resulting from solvent exchange

¹⁵N R₂ relaxation measurements are key for the elucidation of the dynamics of both folded and intrinsically disordered proteins (IDPs). Here we show, on the example of the intrinsically disordered protein α-synuclein and the folded domain PDZ2, that at physiological pH and near physiological temperatures amide—water exchange can severely skew Hahn-echo based ¹⁵N R₂ relaxation measurements as well as low frequency data points in CPMG relaxation dispersion experiments. The nature thereof is the solvent exchange with deuterium in the sample buffer, which modulates the ¹⁵N chemical shift tensor via the deuterium isotope effect, adding to the apparent relaxation decay which leads to systematic errors in the relaxation data. This results in an artificial increase of the measured apparent ¹⁵N R₂ rate constants—which should not be mistaken with protein inherent chemical exchange contributions, R_ex, to ¹⁵N R₂. For measurements of ¹⁵N R₂ rate constants of IDPs and folded proteins at physiological temperatures and pH, we recommend therefore the use of a very low D₂O molar fraction in the sample buffer, as low as 1%, or the use of an external D₂O reference along with a modified ¹⁵N R₂ Hahn-echo based experiment. This combination allows for the measurement of R_ex contributions to ¹⁵N R₂ originating from conformational exchange in a time window from µs to ms.     

Anisotropic rotational motions of poly(L-glutamic acid) in the alpha-helix conformation

The anisotropic rotational motion of the backbone and the side chains of poly(L -glutamic acid) in the α-helical structure was investigated using the ¹³C-T₁ and T₂ relaxation times of all carbon atoms with directly attached protons, obtained at a ¹³C-Larmor frequency of 67.89 MHz. The evaluation of the nmr data was carried out according to the previously derived anisotropic diffusion model, in which the macromolecule is considered a rigid rod. The rotation of the backbone is characterized by two diffusion constants, D₁ and D₃, describing the rotation perpendicular to and around the symmetry axis. The additional internal motion of the C^β-methylene group is described as a jump process with a jump rate, k₁, between two allowed rotametric states. Steric considerations indicate that the occupation of the third rotameric position is forbidden. The rotation of the C^γ-methylene group is decribed as a one-dimensional diffusion process around the C^β–C^γ bond. Investigation of the temperature dependence of the relaxation parameters led to the temperature dependence of the dynamic parameters. Activation energies were determined from these data. The dynamic parameters obtained for poly(L -glutamic acid) at 291 K are compared with the corresponding results of a previous study of poly(L -lysine). The development of an anisotropic diffusion model for the motions of the rod-shaped poly(L -lysine) α-helix and its application to the interpretation of the ¹³C-relaxation data of this molecule have already been published previously. In this model, both the overall molecular tumbling and the various internal motions have been characterized by diffusion constants or jump rates typical for each process. These dynamic parameters can be calculated from the spin–lattice relaxation times, the spin–spin relaxation times and the NOE factors of the C^α, C^β, and C^γ nuclei of the polypetide. In the present paper, we describe the application of the above-mentioned dynamic model to the interpretation of ¹³C-relaxation studies of a further homopolypeptide, poly(L -glutamic acid), in the α-helical structure. Furthermore, we studied the temperature dependence of the relaxation times of this polymer and determined the anisotropic diffusion parameters at each temperature. From their temperature dependence and from comparison of our present results with the data of our previous study of poly(L -lysine), we were able to derive new insights into the intramolecular diffusion processes and the excitation of various motions.     

Two dimensional diffusion of small molecules on protein surfaces: an EPR study of the restricted translational diffusion of protein-bound spin labels

Heisenberg spin exchange rates and dipole-dipole spin lattice relaxation rates for deuterated ¹⁴N- and ¹⁵N-spin labels bound selectively to the histidine His15 and to the lysines Lys13, 96, 97 of the lysozyme molecule have been determined with the aid of electron spin resonance spectroscopy. The results can be interpreted in terms of a two dimensional translational diffusion of the nitroxide tips of the spin labels along the protein surface within restricted surface areas. The spin labels are regarded as models for long amino acid side chains and as probes for the dynamics of protein and water in the vicinity of the protein surface. The translational diffusion coefficient DP_II is reduced by a factor of between six and thirty compared to the value of D found for the spin labels in bulk water, its value for T = 295 K is given by (1.3±0.6)·10^–10m²s^–1 D (2.4±0.3) 10^–11 m²s^–1. Offprint requests to: H.-J. Steinhoff