Rafael Brüschweiler

Covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy is introduced, which is a new scheme for establishing nuclear spin correlations from NMR experiments. In this method correlated spin dynamics is directly displayed in terms of a covariance matrix of a series of one-dimensional (1D) spectra. In contrast to two-dimensional (2D) Fourier transform NMR, in a covariance spectrum the spectral resolution along the indirect dimension is determined by the favorable spectral resolution obtainable along the detection dimension, thereby reducing the time-consuming sampling requirement along the indirect dimension. The covariance method neither involves a second Fourier transformation nor does it require separate phase correction or apodization along the indirect dimension. The new scheme is demonstrated for cross-relaxation (NOESY) and J-coupling based magnetization transfer (TOCSY) experiments.

Validation of Molecular Dynamics Simulations of Biomolecules Using NMR Spin Relaxation as Benchmarks: Application to the AMBER99SB Force Field

Biological function of biomolecules is accompanied by a wide range of motional behavior. Accurate modeling of dynamics by molecular dynamics (MD) computer simulations is therefore a useful approach toward the understanding of biomolecular function. NMR spin relaxation measurements provide rigorous benchmarks for assessing important aspects of MD simulations, such as the amount and time scales of conformational space sampling, which are intimately related to the underlying molecular mechanics force field. Until recently, most simulations produced trajectories that exhibited too much dynamics particularly in flexible loop regions. Recent modifications made to the backbone φ and ψ torsion angle potentials of the AMBER and CHARMM force fields indicate that these changes produce more realistic molecular dynamics behavior. To assess the consequences of these changes, we performed a series of 5-20 ns molecular dynamics trajectories of human ubiquitin using the AMBER99 and AMBER99SB force fields for different conditions and water models and compare the results with NMR experimental backbone N-H S(2) order parameters. A quantitative analysis of the trajectories shows significantly improved agreement with experimental NMR data for the AMBER99SB force field as compared to AMBER99. Because NMR spin relaxation data (T1, T2, NOE) reflect the combined effects of spatial and temporal fluctuations of bond vectors, it is found that comparison of experimental and back-calculated NMR spin-relaxation data provides a more objective way of assessing the quality of the trajectory than order parameters alone. Analysis of a key mobile β-hairpin in ubiquitin demonstrates that the dynamics of mobile sites are not only reduced by the modified force field, but the extent of motional correlations between amino acids is also markedly diminished.

Two-dimensional NMR spectroscopy with soft pulses

Two-dimensional spectroscopy is today routinely used in order to facilitate the assignment of resonance lines in NMR spectra and to determine molecular structure (1, 2). Homonuclear correlation spectroscopy (COSY) and NOE spectroscopy (NOESY), for example, are the two pivotal methods in the structural analysis of biological macromolecules in solution (3). Whenever a detailed analysis of the cross-peak multiplet structure is desired, e.g., for the quantitative determination of coupling constants, high-resolution 2D spectra are required. High resolution may also favor sensitivity in cases where the cross peaks are antiphase as in COSY spectra. High-resolution 2D spectroscopy is, however, often faced with practical limitations of data storage and excessive measurement time caused by the large number of required t, experiments. We propose in this communication to employ frequency-selective soft radiofrequency pulses in order to circumvent the mentioned limitations. When excitation and detection are focused to a small area of the 2D spectrum, high resolution can be achieved by concentrating all available data points to this area. O ther selective experiments derived from 2D spectroscopy have recently been proposed by Kessler et al. (4). These experiments result, however, in one-dimensional spectra corresponding to cross sections through 2D spectra. The experiment described in this communication, on the other hand, delivers true 2D spectra of restricted frequency ranges. Two types of frequency selectivity in 2D spectra are illustrated in Fig. 1. In Fig. 1 a a restricted frequency range A& is excited in o1 by selective preparation pulses resulting in a band parallel to the w2 axis. If it is desirable to restrict also the frequency range in w2, selective pulses can be. incorporated into the mixing sequence in order to allow coherence transfer only between the ranges AQ, and Aa2 (Fig. lb). Alternatively, w2 selectivity can be achieved by means of audiofrequency filters; however, in some cases it is achieved at the expense of sensitivity as will become clear in the following. Frequency selection with soft pulses throughout the entire pulse sequence offers in addition the possibility to interleave experiments for selection of different nonoverlapping spectral regions thus avoiding relaxation delays between experiments. It is evident that the principles above are applicable to all types of 2D experiments.

The future of NMR-based metabolomics

The two leading analytical approaches to metabolomics are mass spectrometry (MS) and nuclear magnetic resonance (NMR) spectroscopy. Although currently overshadowed by MS in terms of numbers of compounds resolved, NMR spectroscopy offers advantages both on its own and coupled with MS. NMR data are highly reproducible and quantitative over a wide dynamic range and are unmatched for determining structures of unknowns. NMR is adept at tracing metabolic pathways and fluxes using isotope labels. Moreover, NMR is non-destructive and can be utilized in vivo. NMR results have a proven track record of translating in vitro findings to in vivo clinical applications.

NMR in metabolomics and natural products research: two sides of the same coin.

Small molecules are central to biology, mediating critical phenomena such as metabolism, signal transduction, mating attraction, and chemical defense. The traditional categories that define small molecules, such as metabolite, secondary metabolite, pheromone, hormone, and so forth, often overlap, and a single compound can appear under more than one functional heading. Therefore, we favor a unifying term, biogenic small molecules (BSMs), to describe any small molecule from a biological source. In a similar vein, two major fields of chemical research,natural products chemistry and metabolomics, have as their goal the identification of BSMs, either as a purified active compound (natural products chemistry) or as a biomarker of a particular biological state (metabolomics). Natural products chemistry has a long tradition of sophisticated techniques that allow identification of complex BSMs, but it often fails when dealing with complex mixtures. Metabolomics thrives with mixtures and uses the power of statistical analysis to isolate the proverbial “needle from a haystack”, but it is often limited in the identification of active BSMs. We argue that the two fields of natural products chemistry and metabolomics have largely overlapping objectives: the identification of structures and functions of BSMs, which in nature almost inevitably occur as complex mixtures. Nuclear magnetic resonance (NMR) spectroscopy is a central analytical technique common to most areas of BSM research. In this Account, we highlight several different NMR approaches to mixture analysis that illustrate the commonalities between traditional natural products chemistry and metabolomics. The primary focus here is two-dimensional (2D) NMR; because of space limitations, we do not discuss several other important techniques, including hyphenated methods that combine NMR with mass spectrometry and chromatography. We first describe the simplest approach of analyzing 2D NMR spectra of unfractionated mixtures to identify BSMs that are unstable to chemical isolation. We then show how the statistical method of covariance can be used to enhance the resolution of 2D NMR spectra and facilitate the semi-automated identification of individual components in a complex mixture. Comparative studies can be used with two or more samples, such as active vs inactive, diseased vs healthy, treated vs untreated, wild type vs mutant, and so on. We present two overall approaches to comparative studies: a simple but powerful method for comparing two 2D NMR spectra and a full statistical approach using multiple samples. The major bottleneck in all of these techniques is the rapid and reliable identification of unknown BSMs; the solution will require all the traditional approaches of both natural products chemistry and metabolomics as well as improved analytical methods, databases, and statistical tools.

New approaches to the dynamic interpretation and prediction of NMR relaxation data from proteins.

NMR relaxation experiments of isotopically labeled proteins provide a wealth of information on reorientational global and local dynamics on nanosecond and subnanosecond timescales for folded and nonfolded proteins in solution. Recent methodological advances in the interpretation of relaxation data have led to a better understanding of the overall tumbling behavior, the separability of internal and overall motions, and the presence of correlated dynamics between different nuclear sites, as well as to new insights into the relationship between reorientational dynamics and primary and tertiary protein structure. Some of the new methods are particularly useful when dealing with nonfolded protein states.

Theory of covariance nuclear magnetic resonance spectroscopy

Covariance nuclear magnetic resonance (NMR) spectroscopy provides an effective way for establishing nuclear spin connectivities in molecular systems. The method, which identifies correlated spin dynamics in terms of covariances between 1D spectra, benefits from a high spectral resolution along the indirect dimension without requiring apodization and Fourier transformation along this dimension. The theoretical treatment of covariance NMR spectroscopy is given for NOESY and TOCSY experiments. It is shown that for a large class of 2D NMR experiments the covariance spectrum and the 2D Fourier transform spectrum can be related to each other by means of Parsevals theorem. A general procedure is presented for the construction of a symmetric spectrum with improved resolution along the indirect frequency domain as compared to the 2D FT spectrum.

Collective protein dynamics and nuclear spin relaxation

Theoretical methods are developed and applied to the protein crambin as a model system to characterize collective normal mode dynamics and their effects on correlations between torsion angle fluctuations and heteronuclear NMR relaxation parameters. Backbone N–H NMR S2 order parameters are found to be predominantly determined by local φ and ψ torsion angle fluctuations induced by collective protein modes. The ratio between Cβ–Hβ and Cα–Hα order parameters directly yields fluctuation amplitudes of the sidechain χ1 torsion angles. The results allow a more direct interpretation of motional effects monitored by nuclear spin relaxation.

Protein Conformational Flexibility from Structure-Free Analysis of NMR Dipolar Couplings: Quantitative and Absolute Determination of Backbone Motion in Ubiquitin†

A robust procedure for the determination of protein-backbone motions on time scales of pico- to milliseconds directly from residual dipolar couplings has been developed that requires no additional scaling relative to external references. The results for ubiquitin (blue in graph: experimental N-HN order parameters) correspond closely to the amplitude, nature, and distribution of motion found in a 400 ns molecular-dynamics trajectory of ubiquitin (red).

Self-consistent residual dipolar coupling based model-free analysis for the robust determination of nanosecond to microsecond protein dynamics

Residual dipolar couplings (RDCs) provide information about the dynamic average orientation of inter-nuclear vectors and amplitudes of motion up to milliseconds. They complement relaxation methods, especially on a time-scale window that we have called supra-