Model-free analysis for large proteins at high magnetic field strengths

Protein backbone dynamics is often characterized using model-free analysis of three sets of ¹⁵N relaxation data: longitudinal relaxation rate (R ₁), transverse relaxation rate (R ₂), and ¹⁵N–{H} NOE values. Since the experimental data is limited, a simplified model-free spectral density function is often used that contains one Lorentzian describing overall rotational correlation but not one describing internal motion. The simplified spectral density function may be also used in estimating the overall rotational correlation time, by making the R ₂/R ₁ largely insensitive to internal motions, as well as used as one of the choices in the model selection protocol. However, such approximation may not be valid for analysis of relaxation data of large proteins recorded at high magnetic field strengths since the contribution to longitudinal relaxation from the Lorentzian describing the overall rotational diffusion of the molecule is comparably small relative to that describing internal motion. Here, we quantitatively estimate the errors introduced by the use of the simplified spectral density in model-free analysis for large proteins at high magnetic field strength.     

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.     

Simple tests for the validation of multiple field spin relaxation data

¹⁵N spin relaxation data is widely used to extract detailed dynamic information regarding bond vectors such as the amide N–H bond of the protein backbone. Analysis is typically carried using the Lipari–Szabo model-free approach. Even though the original model-free equation can be determined from single field R ₁, R ₂ and NOE, over-determination of more complex motional models is dependent on the recording of multiple field datasets. This is especially important for the characterization of conformational exchange which affects R ₂ in a field dependent manner. However, severe artifacts can be introduced if inconsistencies arise between experimental setups with different magnets (or samples). Here, we propose the use of simple tests as validation tools for the assessment of consistency between different datasets recorded at multiple magnetic fields. Synthetic data are used to show the effects of inconsistencies on the proposed tests. Moreover, an analysis of data currently deposited in the BMRB is performed. Finally, two cases from our laboratory are presented. These tests are implemented in the open-source program relax, and we propose their use as a routine check-up for assessment of multiple field dataset consistency prior to any analysis such as model-free calculations. We believe this will aid in the extraction of higher quality dynamics information from ¹⁵N spin relaxation data.     

Quantitative analysis of backbone motion in proteins using MAS solid-state NMR spectroscopy

We present a comprehensive analysis of protein dynamics for a micro-crystallin protein in the solid-state. Experimental data include ¹⁵N T ₁ relaxation times measured at two different magnetic fields as well as ¹H–¹⁵N dipole, ¹⁵N CSA cross correlated relaxation rates which are sensitive to the spectral density function J(0) and are thus a measure of T ₂ in the solid-state. In addition, global order parameters are included from a ¹H,¹⁵N dipolar recoupling experiment. The data are analyzed within the framework of the extended model-free Clore–Lipari–Szabo theory. We find slow motional correlation times in the range of 5 and 150 ns. Assuming a wobbling in a cone motion, the amplitude of motion of the respective amide moiety is on the order of 10° for the half-opening angle of the cone in most of the cases. The experiments are demonstrated using a perdeuterated sample of the chicken α-spectrin SH3 domain.     

Model-free model elimination: A new step in the model-free dynamic analysis of NMR relaxation data

Model-free analysis is a technique commonly used within the field of NMR spectroscopy to extract atomic resolution, interpretable dynamic information on multiple timescales from the R ₁, R ₂, and steady state NOE. Model-free approaches employ two disparate areas of data analysis, the discipline of mathematical optimisation, specifically the minimisation of a χ² function, and the statistical field of model selection. By searching through a large number of model-free minimisations, which were setup using synthetic relaxation data whereby the true underlying dynamics is known, certain model-free models have been identified to, at times, fail. This has been characterised as either the internal correlation times, τ _e , τ _f , or τ _s , or the global correlation time parameter, local τ _m , heading towards infinity, the result being that the final parameter values are far from the true values. In a number of cases the minimised χ² value of the failed model is significantly lower than that of all other models and, hence, will be the model which is chosen by model selection techniques. If these models are not removed prior to model selection the final model-free results could be far from the truth. By implementing a series of empirical rules involving inequalities these models can be specifically isolated and removed. Model-free analysis should therefore consist of three distinct steps: model-free minimisation, model-free model elimination, and finally model-free model selection. Failure has also been identified to affect the individual Monte Carlo simulations used within error analysis. Each simulation involves an independent randomised relaxation data set and model-free minimisation, thus simulations suffer from exactly the same types of failure as model-free models. Therefore, to prevent these outliers from causing a significant overestimation of the errors the failed Monte Carlo simulations need to be culled prior to calculating the parameter standard deviations.     

Mapping of the spectral density function of a Cα−Hα bond vector from NMR relaxation rates of a 13C-labelled α-carbon in motilin

Summary The peptide hormone motilin was synthesised with a ¹³C-enriched -carbon in the leucine at position 10. In aqueous solution, six different relaxation rates were measured for the ¹³C–H fragment as a function of temperature and with and without the addition of 30% (v/v) of the cosolvent d ₂-1,1,1,3,3,3-hexafluoro-2-propanol (HFP). The relaxation rates were analysed employing the spectral density mapping technique introduced by Peng and Wagner [(1992) J. Magn. Reson., 98, 308–322] and using the model-free approach by Lipari and Szabo [(1982) J. Am. Chem. Soc., 104, 4546–4570]. The fit to various models of dynamics was also considered. Different procedures to evaluate the overall rotational correlation time were compared. A single exponential time correlation function was found to give a good fit to the measured spectral densities only for motilin in 30% (v/v) HFP at low temperatures, whereas at high temperatures in this solvent, and in D₂O at all temperatures, none of the considered models gave an acceptable fit. A new empirical spectral density function was tested and found to accurately fit the experimental spectral density mapping points. The application of spectral density mapping based on NMR relaxation data for specific ¹³C–¹H vector is shown to be a highly useful method to study biomolecular dynamics. Advantages are high sensitivity, high precision and uniform sampling of the spectral density function over the frequency range.Abbreviations CD circular dichroism - NOE nuclear Overhauser enhancement - NOESY two-dimensional NOE spectroscopy - INEPT insensitive nuclei enhanced by polarisation transfer - DANTE delays alternating with nutations for tailored excitation - WALTZ-16 wideband, alternating phase, low-power technique for zero residual splitting - FID Free induction decay - ppm parts per million - TSPA 3-trimethylsilyl-(3,3,2,2-d)-propionic acid - HFP d ₂-1,1,1,3,3,3-hexafluoro-2-propanol - CPMG Carr-Purcell-Meiboom-Gill - TFD time-resolved fluorescence depolarisation - CSA chemical shift anisotropy Partly presented at the symposium Dynamics and Function of Biomolecules, Szeged, Hungary, July 31–August 2, 1993.     

Interpretation of H-NMR Experiments on the Orientation of the Transmembrane Helix WALP23 by Computer Simulations

Orientation, dynamics, and packing of transmembrane helical peptides are important determinants of membrane protein structure, dynamics, and function. Because it is difficult to investigate these aspects by studying real membrane proteins, model transmembrane helical peptides are widely used. NMR experiments provide information on both orientation and dynamics of peptides, but they require that motional models be interpreted. Different motional models yield different interpretations of quadrupolar splittings (QS) in terms of helix orientation and dynamics. Here, we use coarse-grained (CG) molecular dynamics (MD) simulations to investigate the behavior of a well-known model transmembrane peptide, WALP23, under different hydrophobic matching/mismatching conditions. We compare experimental ²H-NMR QS (directly measured in experiments), as well as helix tilt angle and azimuthal rotation (not directly measured), with CG MD simulation results. For QS, the agreement is significantly better than previously obtained with atomistic simulations, indicating that equilibrium sampling is more important than atomistic details for reproducing experimental QS. Calculations of helix orientation confirm that the interpretation of QS depends on the motional model used. Our simulations suggest that WALP23 can form dimers, which are more stable in an antiparallel arrangement. The origin of the preference for the antiparallel orientation lies not only in electrostatic interactions but also in better surface complementarity. In most cases, a mixture of monomers and antiparallel dimers provides better agreement with NMR data compared to the monomer and the parallel dimer. CG MD simulations allow predictions of helix orientation and dynamics and interpretation of QS data without requiring any assumption about the motional model.     

Three-dimensional structure of echistatin and dynamics of the active site

Summary The snake venom protein echistatin contains the cell recognition sequence Arg-Gly-Asp and is a potent inhibitor of platelet aggregation. The three-dimensional structure of echistatin and the dynamics of the active RGD site are presented. A set of structures was determined using the Distance Geometry method and subsequently refined by Molecular Dynamics and energy minimization. Disulfide pairings are suggested, based on violations of experimental constraints. The structures satisfy 230 interresidue distance constraints, derived from nuclear Overhauser effect measurements, five hydrogen-bonding constraints, and 21 torsional constraints from vicinal spin-spin coupling constants. The segment from Gly⁵ to Cys²⁰ and from Asp³⁰ to Asn⁴² has a well-defined conformation and the Arg-Gly-Asp sequence, which adopts a turn-like structure, is located at the apex of a nine-residue loop connecting the two strands of a distorted -sheet. The mobility of the Arg-Gly-Asp site has been quantitatively characterized by ¹⁵N relaxation measurements. The overall correlation time of echistatin was determined from fluorescence measurements, and was used in a model-free analysis to determine internal motional parameters. The active site has order parameters of 0.3–0.5, i.e., among the smallest values ever observed at the active site of a protein. Correlation of the flexible region of the protein as characterized by relaxation experiments and the NMR solution structures was made by calculating generalized order parameters from the ensemble of three-dimensional structures. The motion of the RGD site detected experimentally is more extensive than a simple RGD loop wagging motional model, suggested by an examination of superposed solution structures.     

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.     

Diffusion and dynamics of penetratin in different membrane mimicking media

The interaction between the cell-penetrating peptide (CPP) penetratin and different membrane mimetic environments has been investigated by two different NMR methods: ¹⁵N spin relaxation and translational diffusion. Diffusion coefficients were measured for penetratin in neutral and in negatively charged bicelles of different size, in sodium dodecyl sulfate micelles (SDS), and in aqueous solution. The diffusion coefficients were used to estimate the amount of free and bicelle/micelle-bound penetratin and the results revealed that penetratin binds almost fully to all studied membrane mimetics. ¹⁵N relaxation data for three sites in penetratin were interpreted with the model-free approach to obtain overall and local dynamics. Overall correlation times for penetratin were in agreement with findings for other peptides of similar size in the same solvents. Large differences in order parameters were observed for penetratin in the different membrane mimetics. Negatively charged surfaces were seen to restrict motional flexibility, while a more neutral membrane mimetic did not. This indicates that although the peptide binds to both bicelles and SDS micelles, the interaction between penetratin and the various membrane mimetics is different.     

Solution conformation and dynamics of a tetrasaccharide related to the LewisX antigen deduced by NMR relaxation measurements

¹H-NMR cross-relaxation rates and nonselectivelongitudinal relaxation times have been obtained at two magnetic fields (7.0and 11.8 T) and at a variety of temperatures for the branchedtetrasaccharide methyl3-O--N-acetyl-galactosaminyl--galactopyranosyl-(14)[3-O--fucosyl]-glucopyranoside (1), an inhibitor of astrocyte growth. Inaddition, ¹³C-NMR relaxation data have also been recorded atboth fields. The ¹H-NMR relaxation data have been interpretedusing different motional models to obtain proton–proton correlationtimes. The results indicate that the GalNAc and Fuc rings display moreextensive local motion than the two inner Glc and Gal moieties, since thosepresent significantly shorter local correlation times. The¹³C-NMR relaxation parameters have been interpreted in termsof the Lipari–Szabo model-free approach. Thus, order parameters andinternal motion correlation times have been deduced. As obtained for the¹H-NMR relaxation data, the two outer residues possess smallerorder parameters than the two inner rings. Internal correlation times are inthe order of 100 ps. The hydroxymethyl groups have also different behaviour,with the exocyclic carbon on the glucopyranoside unit showing the highestS². Molecular dynamics simulations using a solvated systemhave also been performed and internal motion correlation functions have beendeduced from these calculations. Order parameters and interproton distanceshave been compared to those inferred from the NMR measurements. The obtainedresults are in fair agreement with the experimental data.     

A suite of Mathematica notebooks for the analysis of protein main chain 15N NMR relaxation data

A suite of Mathematica notebooks has been designed to ease the analysis of protein main chain ¹⁵N NMR relaxation data collected at a single magnetic field strength. Individual notebooks were developed to perform the following tasks: nonlinear fitting of ¹⁵N-T ₁ and -T ₂ relaxation decays to a two parameter exponential decay, calculation of the principal components of the inertia tensor from protein structural coordinates, nonlinear optimization of the principal components and orientation of the axially symmetric rotational diffusion tensor, model-free analysis of ¹⁵N-T ₁, -T ₂, and {¹H}–¹⁵N NOE data, and reduced spectral density analysis of the relaxation data. The principle features of the notebooks include use of a minimal number of input files, integrated notebook data management, ease of use, cross-platform compatibility, automatic visualization of results and generation of high-quality graphics, and output of analyses in text format.L. Spyracopoulos is an AHFMR Medical Research Senior Scholar     

The role of parametric linkage methods in complex trait analyses using microsatellites

Many investigators of complexly inherited familial traits bypass classical segregation analysis to perform model-free genome-wide linkage scans. Because model-based or parametric linkage analysis may be the most powerful means to localize genes when a model can be approximated, model-free statistics may result in a loss of power to detect linkage. We performed limited segregation analyses on the electrophysiological measurements that have been collected for the Collaborative Study on the Genetics of Alcoholism. The resulting models are used in whole-genome scans. Four genomic regions provided a model-based LOD > 2 and only 3 of these were detected (p < 0.05) by a model-free approach. We conclude that parametric methods, using even over-simplified models of complex phenotypes, may complement nonparametric methods and decrease false positives.     

Direct observation of the properties of cholesterol in membranes by deuterium NMR

The properties of cholesterol in bilayers of egg phosphatidylcholine (PC) were investigated directly by means of ²H-NMR of specifically-deuterated species (C3, C7, C26, C27). Quadrupole splittings were a measure of molecular ordering, and relaxation times T₁ and T_2e were indicators of rates of motion. The importance of the use of echoes for spectral acquisition is emphasised, particularly to obtain accurate values of the quadrupole splitting. In the case of overlapping powder patterns from two labelled positions, the use of the absolute value mode of spectral presentation is shown to yield reasonable estimates of the individual quadrupole splittings. Spectral properties were monitored as a function of cholesterol concentration and temperature. Increasing cholesterol concentration led to a high degree of ordering for the rigid ring system of cholesterol, approaching a molecular order parameter of 0.8 at 50 mol% cholesterol. The isopropyl methyl groups were in all cases less ordered anmore mobile than the ring system, but responded in a similar fashion to variable cholesterol concentration and temperature. The observation of a minimum in the temperature dependence of T₁ for cholesterol-7,7-d₂ led to a direct estimate of its correlation time for molecular motion, 3.5 × 10^?9 s rad^?1. This indicates that the overall rate of motion of cholesterol is considerably slower than that of the lipids in which it is located. The short T_2e values suggest that the motional spectrum of cholesterol is rich in low frequencies. The parallel temperature and cholesterol dependences of quadrupole splittings for different positions on the rigid ring system of cholesterol indicate that the position of the axis of motional averaging of the molecule is not changing, and is the same as that determined in an earlier study. It is emphasised that the steep temperature dependence and small quadrupole splittings for the chain isopropyl methyl groups of cholesterol do not necessarily indicate a high degree of disorder, but may be due to their axes of motional averaging lying at angles close to 54° with respect to the director of the ordered lipids.     

Singular value decomposition of 3-D DNA melting curves reveals complexity in the melting process

The thermal denaturation of synthetic deoxypolynucleotides of defined sequence was studied by a three dimensional melting technique in which complete UV absorbance spectra were recorded as a function of temperature. The results of such an experiment defined a surface bounded by absorbance, wavelength, and temperature. A matrix of the experimental data was built, and analyzed by the method of singular value decomposition (SVD). SVD provides a rigorous, model-free analytical tool for evaluating the number of significant spectral species required to account for the changes in UV absorbance accompany-ing the duplex – to – single strand transition. For all of the polynucleotides studied (Poly dA – Poly dT; [Poly (dAdT)]₂; Poly dG – Poly dC; [Poly(dGdC)]₂), SVD indicated the existence of at least 4 – 5 significant spectral species. The DNA melting transition for even these simple repeating sequences cannot, therefore, be a simple two-state process. The basis spectra obtained by SVD analysis were found to be unique for each polynucleotide studied. Differential scanning calorimetry was used to obtain model free estimates for the enthalpy of melting for the polynucleotides studied, with results in good agreement with previously published values. Received: 16 April 1997 / Accepted: 9 July 1997     

Computationally efficient gradients for relaxation matrix-based structure refinement including the accommodation of internal motions

Summary A general method for deriving analytical gradients based on NOESY cross-peak intensities is presented. This method allows for very rapid calculation of exact gradients of cross-peak intensities with respect to parameters directly related to the pairwise dipole-dipole interaction giving rise to the cross peak. In the simplest case, gradients with respect to internuclear separation can be calculated, which allows for the rational modification of distance constraints used in structural refinement. In the general case, any arbitrary level of knowledge of the internal dynamics of the molecule can be introduced, thereby providing a pathway for the experimental determination of motional parameters. The motional characteristics of the internuclear vectors defining dipole-dipole interactions are cast in model-free terms. The form of the gradient circumvents many of the limitations of gradients expressed in terms of Cartesian or dihedral variables. The gradients presented are simple, direct, and exact and require little computational effort to calculate.