Optimization of resolution and sensitivity of 4D NOESY using multi-dimensional decomposition

Highly resolved multi-dimensional NOE data are essential for rapid and accurate determination of spatial protein structures such as in structural genomics projects. Four-dimensional spectra contain almost no spectral overlap inherently present in lower dimensionality spectra and are highly amenable to application of automated routines for spectral resonance location and assignment. However, a high resolution 4D data set using conventional uniform sampling usually requires unacceptably long measurement time. Recently we have reported that the use of non-uniform sampling and multi-dimensional decomposition (MDD) can remedy this problem. Here we validate accuracy and robustness of the method, and demonstrate its usefulness for fully protonated protein samples. The method was applied to 11 kDa protein PA1123 from structural genomics pipeline. A systematic evaluation of spectral reconstructions obtained using 15-100% subsets of the complete reference 4D 1H-13C-13C-1H NOESY spectrum has been performed. With the experimental time saving of up to six times, the resolution and the sensitivity per unit time is shown to be similar to that of the fully recorded spectrum. For the 30% data subset we demonstrate that the intensities in the reconstructed and reference 4D spectra correspond with a correlation coefficient of 0.997 in the full range of spectral amplitudes. Intensities of the strong, middle and weak cross-peaks correlate with coefficients 0.9997, 0.9965, and 0.83. The method does not produce false peaks. 2% of weak peaks lost in the 30% reconstruction is in line with theoretically expected noise increase for the shorter measurement time. Together with good accuracy in the relative line-widths these translate to reliable distance constrains derived from sparsely sampled, high resolution 4D NOESY data.

MUNIN: application of three-way decomposition to the analysis of heteronuclear NMR relaxation data

MUNIN (Multidimensional NMR Spectra Interpretation), a recently introduced approach exploiting the mathematical concept of three-way decomposition, is proposed for separation and quantitative relaxation measurements of strongly overlapped resonances in sets of heteronuclear two-dimensional spectra that result from typical relaxation experiments. The approach is general and may also be applied to sets of two-dimensional spectra with arbitrary modulation along the third dimension (e.g., J-coupling, diffusion). Here, the method is applied for the analysis of 15N rotating frame relaxation data.

MUNIN: a new approach to multi-dimensional NMR spectra interpretation

A new method, MUNIN (Multi-dimensional NMR spectra interpretation), is introduced for the automated interpretation of three-dimensional NMR spectra. It is based on a mathematical concept referred to as three-way decomposition. An NMR spectrum is decomposed into a sum of components, with each component corresponding to one or a group of peaks. Each component is defined as the direct product of three one-dimensional shapes. A consequence is reduction in dimensionality of the spectral data used in further analysis. The decomposition may be applied to frequency-domain or time-domain data, or to a mixture of these. Features of MUNIN include good resolution in crowded regions and the absence of assumptions about line shapes. Uniform sampling of time-domain data, a prerequisite for discrete Fourier transform, is not required. This opens an avenue for the processing of NMR data that do not follow oscillating behaviour, e.g. from relaxation measurements. The application of MUNIN is illustrated for a 1H-15N-NOESY-HSQC, where each component is defined as the set of all NOE peaks formed by a given amide group. As a result, the extraction of structural information simply consists of one-dimensional peak picking of the shape along the NOE-axis obtained for each amide group.

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.

Pressure effect on the dynamics of an isolated alpha-helix studied by 15N-1H NMR relaxation

Dynamics and structure of (1-36)bacteriorhodopsin solubilized in chloroform/methanol mixture (1:1) were investigated by 1H-15N NMR spectroscopy under a hydrostatic pressure of 2000 bar. It was shown that the peptide retains its spatial structure at high pressure. 15N transverse and longitudinal relaxation times, 15N[1H] nuclear Overhauser effects, chemical shifts and the translation diffusion rate of the peptide at 2000 bar were compared with the respective data at ambient pressure [Orekhov et al. (1999) J. Biomol. NMR, 14, 345-356]. The model free analysis of the relaxation data for the helical 9-31 fragment revealed that the high pressure decreases the overall rotation and translation diffusion, as well as apparent order parameters of fast picosecond internal motions (S2) but has no effect on internal nanosecond motions (S2 and taus) of the peptide. The decrease of translation and overall rotation diffusion was attributed to the increase in solvent viscosity and the decrease of apparent order parameters S2f to a compression of hydrogen bonds. It is suggested that this compression causes an elongation of H-N bonds and a decrease of absolute values of chemical shift anisotropy (CSA). In particular, the observed decrease of S2f at 2000 bar can be explained by 0.001 nm increase of N-H bond lengths and 10 ppm decrease of 15N CSA values.

Sampling of protein dynamics in nanosecond time scale by 15N NMR relaxation and self-diffusion measurements

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 FD 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.

Effect of Coupling between Rotational and Translational Brownian Motions on NMR Spin Relaxation: Consideration Using Green Function of Rigid Body Diffusion

Using the Green function of arbitrary rigid Brownian diffusion (Goldstein, Biopolymers 33, 409-436, 1993), it was analytically shown that coupling between translation and rotation diffusion degrees of freedom does not affect the correlation functions relevant to the NMR intramolecular relaxation. It follows that spectral densities usually used for the anisotropic rotation diffusion (Woessner, J. Chem. Phys. 37, 647-654, 1962) can be regarded as exact in respect to the rotation-translation coupling for the spin system connected with a rigid body. Copyright 1998 Academic Press.

Model-free approach beyond the borders of its applicability

Model calculations presented in this article show that commonly used methodology of 15N relaxation data analysis completely fails in detecting nanosecond time scale motions if the major part of the molecule is involved in these motions. New criteria are introduced for the detection of such cases, based on the dependence of the apparent overall correlation time, derived from the T1/T2 ratio, on the spectrometer frequency. Correctly estimating the overall rotation correlation time tauR was shown to play the key role in model-free data analysis. It is found, however, that in cases of slow internal motions with characteristic times of more than 3-4 ns, the effective tauR provided by the T1/T2 ratio for individual amide nitrogens can be used for the characterization of the fast picosecond internal dynamics.

Backbone dynamics of (1-71)- and (1-36)bacterioopsin studied by two-dimensional (1)H- (15)N NMR spectroscopy

The backbone dynamics of uniformly (15)N-labelled fragments (residues 1-71 and 1-36) of bacterioopsin, solubilized in two media (methanol-chloroform (1:1), 0.1 M (2)HCO(2)NH(4), or SDS micelles) have been investigated using 2D proton-detected heteronuclear (1)H-(15)N NMR spectroscopy at two spectrometer frequencies, 600 and 400 MHz. Contributions of the conformational exchange to the transverse relaxation rates of individual nitrogens were elucidated using a set of different rates of the CPMG spin-lock pulse train and were essentially suppressed by the high-frequency CPMG spin-lock. We found that most of the backbone amide groups of (1-71)bacterioopsin in SDS micelles are involved in the conformational exchange process over a rate range of 10(3) to 10(4) s(-1). This conformational exchange is supposed to be due to an interaction between two α-helixes of (1-71)bacterioopsin, since the hydrolysis of the peptide bond in the loop region results in the disappearance of exchange line broadening. (15)N relaxation rates and (1)H-(15)N NOE values were interpreted using the model-free approach of Lipari and Szabo [Lipari, G. and Szabo, A. (1982) J. Am. Chem. Soc., 104, 4546-4559]. In addition to overall rotation of the molecule, the backbone N-H vectors of the peptides are involved in two types of internal motions: fast, on a time scale <20 ps, and intermediate, on a time scale close to 1 ns. The intermediate dynamics in the α-helical stretches was mostly attributed to bending motions. A decrease in the order parameter of intermediate motions was also observed for residues next to Pro(50), indicating an anisotropy of the overall rotational diffusion of the molecule. Distinctly mobile regions are identified by a large decrease in the order parameter of intermediate motions and correspond to the N- and C-termini, and to a loop connecting the α-helixes of (1-71)bacterioopsin. The internal dynamics of the α-helixes on the millisecond and nanosecond time scales should be taken into account in the development of a model of the functioning bacteriorhodopsin.

Manifestation of intramolecular motions on pico- and nanosecond time scales in (1)H- (15)N NMR relaxation: Analysis of dynamic models of one- and two-helical subunits of bacterioopsin

The influence of the internal dynamics of two polypeptides comprising transmembrane α-helix A or two α-helices A and B of bacterioopsin on experimentally accessible (15)N NMR relaxation rates was investigated by molecular dynamics (MD) simulations, combined with more simple mechanic considerations. 'Model-free' order parameters and correlation times of internal motions [Lipari, G. and Szabo, A. (1982) J. Am. Chem. Soc., 104, 4546-4559] were calculated for these models. It was found that both peptides exhibit two types of internal motions of the amide bonds, on the pico- and nanosecond time scales, affecting (15)N NMR relaxation. The fast fluctuations are local and correspond to the librational motions of the individual N-H vectors in an effective potential of atoms of the surrounding matrix. In contrast, the motions on the nanosecond time scale imply concerted collective vibrations of a large number of atoms and could be represented as bending oscillation of α-helices, strongly overdamped by the ambient solvent. A few other molecular mechanisms of slow internal motion were found, such as local distortions of the α-helices (e.g., α-aneurysm), delocalized distortions of the α-helical backbone, as well as oscillations of the tilt angle between the axes of the α-helices A and B. The results are compared with (15)N NMR relaxation data measured for the (1-36)bacterioopsin and (1-71)bacterioopsin polypeptides in chloroform-methanol (1:1) and in SDS micelles [Orekhov, V.Yu., Pervushin, K.V. and Arseniev, A.S. (1994) Eur. J. Biochem., 219, 887-896].

An estimate of spin diffusion in a spin subset: Application to iterative distance calculation from 3D (15)N NOESY-HMQC

A method for quantification of distances between amide hydrogens using only the 3D NOESY-HMQC experiment recorded on a (15)N-labelled protein is presented. This method is based on an approximate expression of the NOE intensities between amide hydrogens obtained from continuum modelling of the non-amide spins; this expression is used in a distance calculation algorithm. The algorithm has been named CROWD, standing for Continuum approximation of Relaxati On path Ways between Dilute spins. This approximation as well as the CROWD algorithm are tested on a simulated case; the CROWD algorithm is then applied to experimental data, measured on a fragment of bacteriorhodopsin.