Defining the precision with which a protein structure is determined by NMR. Application to motilin

A simple procedure is introduced for accurately defining the precision with which the Cartesian coordinates of any macromolecular structure are determined by nuclear Overhauser data. The method utilizes an ensemble of structures obtained from an array of independent simulated data sets derived from a final structure. Using the noise-free, back-calculated NOE spectrum as the "true" NOE spectrum, simulated Monte Carlo data sets are created by superimposing onto the "true" spectrum Gaussian distributed noise with a standard deviation equal to that of the residuals. Full relaxation matrix refinements of the simulated data sets provide probability distributions of the Cartesian coordinates for each atom in the model. Molecular dynamics simulations are included to estimate the effect of sparse information on the precision. The procedure is applied here to the 22-residue peptide hormone motilin, and the results are compared to those obtained using the conventional method of analyzing multiple refinements using a single distance constraint set. The average root mean square deviation for alpha-carbon atoms in the central portion (Arg12-Arg18) of the single helix of motilin was determined to be 0.72 A by the Monte Carlo method, compared to 1.3 A determined by an analysis of the 10 best DIANA structures using the same number of constraints between the same atoms. The origin of the bias of the conventional method is discussed.