Complete relaxation matrix refinement of NMR structures of proteins using analytically calculated dihedral angle derivatives of NOE intensities.

A new method for refining three-dimensional (3D) NMR structures of proteins is described, which takes account of the complete relaxation pathways. Derivatives of the NOE intensities with respect to the dihedral angles are analytically calculated, and efficiently evaluated with the use of a filter technique for identifying the dominant terms of these derivatives. This new method was implemented in the distance geometry program DIANA. As an initial test, we refined 30 rigid distorted helical structures, using a simulated data set of NOE distance constraints for a rigid standard alpha-helix. The final root-mean-square deviations of the refined structures relative to the standard helix were less than 0.1 A, and the R-factors dropped from values between 7% and 32% to values of less than 0.5% in all cases, which compares favorably with the results from distance geometry calculations. In particular, because spin diffusion was not explicitly considered in the evaluation of 'exact' 1H-1H distances corresponding to the simulated NOE intensities, a group of nearly identical distance geometry structures was obtained which had about 0.5 A root-mean-square deviation from the standard alpha-helix. Further test calculations using an experimental NOE data set recorded for the protein trypsin inhibitor K showed that the complete relaxation matrix refinement procedure in the DIANA program is functional also with systems of practical interest.