Simulating the effect of the two-spin approximation on the generation of protein structures from NOE data

Abstract

The use of structural information derived from NMR data, when combined with computer modeling techniques, has enabled the structures of many proteins to be determined ( 1-6). Among the most useful structural information is interproton distances which can be derived from nuclear Overhauser enhancement experiments. For small rigid molecules, the intensity of the NOE between protons i andj is proportional to the inverse sixth power of the distance between the two protons. In macromolecules, indirect magnetization transfer (spin diffusion) from nearby protons and intramolecular dynamics affect the magnitude of the NOE between protons i andj and contribute to errors in estimating interproton distances from NOE cross peaks ( 7-9). Several methods have been proposed for dealing with the spin-diffusion problem. These methods make use of the relaxation matrix to incorporate multispin effects (10-14). The simplest but least systematic approach is to calculate a theoretical spectrum from the relaxation matrix using a trial structure, and to adjust distances by trial and error between pairs of protons whose calculated cross peaks have the largest deviations from the experimental values ( 15-18). In another approach theoretical cross peaks from a trial structure are merged with experimental NOES ( I2,19,20), and after the solution of the Bloch equations is inverted to obtain the relaxation matrix, the resulting distances can be added as constraints in a molecular-dynamics or distance geometry refinement. The most rigorous and computationally intensive procedures involve the direct refinement of calculated against experimental NOE spectra, either by analytically evaluating the gradients of the calculated NOES with respect to coordinates (21-23) or by using a Monte-Carlo procedure (24). Despite the recent focus on incorporating spin-diffusion effects in the refinement of macromolecular structures, it is unclear how much error is introduced by spin diffusion. This is of interest because, although the direct refinement of calculated against experimental NOE intensities is in principle the more “correct” procedure, it is much more computationally intensive than re-