Computing Protein Structures from Electron Density Maps: The Missing Fragment Problem
Rapid protein structure determination relies greatly on the availability of software that can automatically generate a protein model from an experimental electron density map. Tremendous advances in this area have been achieved recently. In favorable cases, available software can build over 90% of the final model. However, in less favorable circumstances, particularly at medium-low resolution, only about 2/3 completeness is attained. Manual completion of these partial models is usually feasible but time-consuming. The electron density in areas of missing fragments is often of poorer quality, especially for flexible loops, making manual interpretation particularly difficult. Except for the beginning and end of the protein chain, the end points of each missing fragment are known from the partial model. Due to the kinematic chain structure of the protein backbone, loop completion can be approached as an inverse kinematics problem. A fast, two-stage inverse kinematics algorithm is presented that fits a protein chain of known sequence to the electron density map between two anchor points. Our approach first samples a large set of candidates that meet the closure constraint and then refines the most promising candidates to improve the fit. The algorithm has been tested and used to aid protein model completion in areas of poor density, closing loops of up to 12 residues to within 0.3 of the final refined structure. It has also been used to close missing loops of the same length in partial models built at medium-low resolution to within 0.6 Å.