Interproton distances intensities

Usually, simplified representations of the data are used to obtain preliminary structures. Thus, lower and upper bounds on the interproton distances are estimated from the NOE intensity [10], using appropriate reference distances for calibration. The bounds should include the estimates of the cumulative error due to all sources such as peak integration errors, spin diffusion, and internal dynamics. 

A combined approach is to use interproton distances determined by simulation and experimental NOE intensities to calculate the dynamic behavior of specific linkages in an oligosaccharide. The MM force field was employed for the computer simulation of calonyctin Ai (40) where interglycosidic NOEs served as experimental distance restraints for the molecular dynamics 104). 

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). 

In the modified ISPA approach,166 16 the distances are calculated from the NOE intensities using special calibration curves, which take into account that short distances are typically overestimated and long distances underestimated in the classical ISPA due to the spin diffusion, but ignores individual differences between specific pairs of protons. The curves are calibrated based on NOE data for interproton distances with fixed values. Model calculations for a short DNA duplex showed that this approach produces good results,166 however, it is expected that the errors should increase for larger molecules with more prominent spin diffusion. 

In addition to the arbitrary model, distance calculations with MARDIGRAS require isotropic rotational correlation time rc as input parameter. Effective rotational correlation time can be estimated by a number of experimental approaches.1 6 An approach that usually produces self-consistent results is to estimate rc based on the same NOESY data that are used for distance calculations. MARDIGRAS can be run at a series of correlation times, and a rc range can be selected that reproduces best fixed interproton distances and distances with limited variation, see, for example, Ulyanov et al 20 For that purpose, the experimental NOE intensities (which are integrated in arbitrary units) must be normalized based on the total sum of all observed intensities if possible, intensities of diagonal peaks must also be integrated and included to make the dependence of calculated distances on rc more apparent, see a discussion in Tonelli.176 Fixed interproton distances and distances with limited variation in nucleic acids are listed in Table 2. 

Finally, it is important to add pseudoatom corrections121 for pairs of methylene protons and Leu/Val methyl groups that have not been stereospecifically assigned. This can be done automatically by programs such as CYANA114 during the process of converting NOE intensities into interproton distance restraints. 

These investigators employed the CHARMm force field with the carbohydrate parameters of Ha et al. jn j s MD simulations in vacuo. They note particularly, as have others, >135 that the use of the isolated spin pair approximation (ISPA), which is often used to convert NOE intensities into interproton distances, can be extremely inaccurate. Within ISPA, the assumption is made that the NOE intensity NOEfj) between two protons arises only from spin relaxation between the two protons. This approximation neglects the effects of spin diffusion and internal motion. Taking for calibration a known interproton distance (r f) and its associated NOE (NO f), the ISPA distance two protons i and j) may be derived from Eq. [14].i35... 

Intensity of NMR signal at time "P Coupling constant for nuclei i and j Distance between protons i and y Distance of closest approach of two spins Interproton distance... 

If quantitative information on interproton distance is required, then it is necessary to plot the NOESY off-diagonal peak intensity against the mixing time after which mutual proton spin flips are monitored. The slope of this plot, (T, is given by [39]... 

Cross-relaxation rates and the ensuing interproton distances are determined by Eq.[2], which requires full relaxation. However, with Eq. [4] it is possible to extrapolate from partially relaxed NOE intensities to the fully relaxed quantities (32, 34). This approach, however, requires that accurate Ti values are available for individual protons, which might be an obstacle in the case of macromolecules. Another possibility to correct for partial relaxation effects utilizes the ratio between above- and below-diagonal crosspeak intensities which in the case of a partially relaxed NOESY spectrum deviate significantly from 1. The details of this approach are beyond the scope of this chapter and have been described elsewhere (35). Both correction procedures have been implemented in our program SYMM (35), which we have used for the correction of the SRP 28mer NOESY data, which had been acquired with a typical, short repetition delay of 2.5 sec. 

Several methods have been described for using 3D NOESY-NOESY cross-peak intensities for structural refinement such as the two-spin approximation (4,5), Taylor series expansion of the NOE-rate equation (6), and direct gradient refinement method (7). The two-spin approximation requires that the NOESY derived distances be obtained from vanishingly short experimental mixing times where the build-up of NOE intensity is linear with respect to interproton distance and the effect of spin diffusion (NOE intensity mediated by multiple relaxation pathways) are minimal. 

Calculating Interproton Distances from Experimental NOE Intensities. It... 

Basic data obtained from NMR studies consist of distance and torsion angle restraints. Once resonances have been assigned, nuclear Overhauser effect (NOE) contacts are selected and their intensities are used to calculate interproton distances. Information on torsion angles are based on the measurement of coupling constants and analysis of proton chemical shifts. Together, this information is used to formulate a nonlinear optimization problem, the solution of which should provide the correct protein structure. Typically, a hybrid energy function of the following form is employed ... 

Owing to the fact that absolute values of correlation times are usually not available, interproton distances cannot be directly calculated. Distances are instead obtained by calibration of the cross peak intensities against an internal distance standard, usually the distance between diastereotopic geminal protons (178 pm) or aromatic protons of Tyr (242 pm). Assuming isotropic tumbling and rigid-body model for all parts of the molecule. Equation [9] is then used to calculate all interproton distances ... 

There are several potentially serious problems involved in the interpretation of NMR data in terms of distance constraints. First, a phenomenon called spin diffusion may result in spurious NOESY cross-peaks between protons that share a common neighboring proton, but which themselves are greater than 5 A apart. Second, biological macromolecules are always flexible to at least some degree, and NOESY cross-peak intensities are expected to reflect the inverse average sixth root of the interproton distances. As a result, it is entirely possible for a proton to appear to be adjacent to two other protons simultaneously, when the other two protons are nevertheless always greater than 10 A apart. Finally, NOESY cross-peak intensities are affected by numerous spectral artefacts and well as by other sources of relaxation, which may cause many cross-peaks to be missing. 

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