Constraints from Nuclear Overhauser Effects

Distance Constraints from Nuclear Overhauser Effects 

The principle source of experimental conformational data in an NMR structure determination is constraints on short interatomic distances between hydrogen atoms obtained from NMR measurements of the nuclear Overhauser effect (NOE). NOEs result from cross-relaxation mediated by the dipole-dipole interaction between spatially proximate nu- 

The intensity of an NOE, given by the volume V of the corresponding cross peak in a NOESY spectrum [11, 13, 14] is related to the distance r between the two interacting spins by 

The quantification of an NOE amounts to determining the volume of the corresponding cross peak in the NOESY spectrum. Since the linewidths can vary appreciably for different resonances, cross-peak volumes should in principle be determined by integration over the peak area rather than by measuring peak heights. However, one should also keep in mind that, according to Eq. (1), the relative error of the distance estimate is only one sixth of the relative error of the volume determination. Furthermore, Eq. (1) involves factors that have their origin in the complex internal dynamics of the macromolecule and are beyond practical reach such that even a very accurate measurement of peak volumes will not yield equally accurate conformational constraints. 

On the basis of Eq. (1), NOEs are usually treated as upper bounds on interatomic distances rather than as precise distance constraints, because the presence of internal motions and, possibly, chemical exchange may diminish the strength of an NOE [23]. In fact, much of the robustness of the NMR structure determination method is due to the use of upper distance bounds instead of exact distance constraints in conjunction with the observation that internal motions and exchange effects usually reduce rather than increase the NOEs [5]. For the same reason, the absence of an NOE is in general not interpreted as a lower bound on the distance between the two interacting spins. 

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Distance Constraints from Nuclear Overhauser Effects... 

In de novo three-dimensional structure determinations of proteins in solution by NMR spectroscopy, the key conformational data are upper distance limits derived from nuclear Overhauser effects (NOEs) [11, 14]. In order to extract distance constraints from a NOESY spectrum, its cross peaks have to be assigned, i.e. the pairs of hydrogen atoms that give rise to cross peaks have to be identified. The basis for the NOESY assignment... 

Many other intermolecular and intramolecular contacts are described by distances (hydrogen bond lengths, van der Waals contact, experimentally determined distances from nuclear Overhauser effect (NOE) spectra, fluorescence energy transfer, etc.) so that the distance matrix representation can be used to specify all the known information about a molecular structure. These bounds are entered into a distance geometry program, as are other bounds that specify constraints on modeling problems, such as constraints to superimpose atoms in different molecules. Hypotheses about intra- or intermolecular conformations and interactions are easily specified with distance constraints models can be built quickly to test different hypotheses simply by changing the distance constraints. 

The basis for the determination of solution conformation from NMR data lies in the determination of cross relaxation rates between pairs of protons from cross peak intensities in two-dimensional nuclear Overhauser effect (NOE) experiments. In the event that pairs of protons may be assumed to be rigidly fixed in an isotopically tumbling sphere, a simple inverse sixth power relationship between interproton distances and cross relaxation rates permits the accurate determination of distances. Determination of a sufficient number of interproton distance constraints can lead to the unambiguous determination of solution conformation, as illustrated in the early work of Kuntz, et al. (25). While distance geometry algorithms remain the basis of much structural work done today (1-4), other approaches exist. For instance, those we intend to apply here represent NMR constraints as pseudoenergies for use in molecular dynamics or molecular mechanics programs (5-9). 

The most important structural probe is the nuclear Overhauser effect (NOE), which provides valuable information on the structure of linear peptides. Briefly, the observation of a direct NOE between a pair of protons indicates the presence of a significant population of conformers in which the distance between these two proteins is relatively short. The overall pattern of connectivity therefore corresponds to a particular conformation. Constraints on both backbone and side chain dihedral angles are obtained from coupling contacts. An example of a two-dimensional NMR spectrum for a synthetic peptide related to residues 6-13 of human growth hormone is shown in Figure 8. 

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