Protein structure calculation with data imputation: the use of substitute restraints.

The amount of experimental restraints e.g., NOEs is often too small for calculating high quality three-dimensional structures by restrained molecular dynamics. Considering this as a typical missing value problem we propose here a model based data imputation technique that should lead to an improved estimation of the correct structure. The novel automated method implemented in AUREMOL makes a more efficient use of the experimental information to obtain NMR structures with higher accuracy. It creates a large set of substitute restraints that are used either alone or together with the experimental restraints. The new approach was successfully tested on three examples: firstly, the Ras-binding domain of Byr2 from Schizosaccharomyces pombe, the mutant HPr (H15A) from Staphylococcus aureus, and a X-ray structure of human ubiquitin. In all three examples, the quality of the resulting final bundles was improved considerably by the use of additional substitute restraints, as assessed quantitatively by the calculation of RMSD values to the "true" structure and NMR R-factors directly calculated from the original NOESY spectra or the published diffraction data.