title: Fast determination of the optimal rotational matrix for macromolecular superpositions.
abstract: Finding the rotational matrix that minimizes the sum of squared deviations between two vectors is an important problem in bioinformatics and crystallography. Traditional algorithms involve the inversion or decomposition of a 3 x 3 or 4 x 4 matrix, which can be computationally expensive and numerically unstable in certain cases. Here, we present a simple and robust algorithm to rapidly determine the optimal rotation using a Newton-Raphson quaternion-based method and an adjoint matrix. Our method is at least an order of magnitude more efficient than conventional inversion/decomposition methods, and it should be particularly useful for high-throughput analyses of molecular conformations.
authors.affiliation: Johnson & Johnson Pharmaceutical Research and Development, L.L.C., 665 Stockton Drive, Exton, Pennsylvania 19341, USA. pliu24@its.jnj.com
authors.forename: Pu
authors.initials: P
authors.lastname: Liu
authors.forename: Dimitris K
authors.initials: DK
authors.lastname: Agrafiotis
authors.forename: Douglas L
authors.initials: DL
authors.lastname: Theobald
mesh_terms: D000465:Algorithms; D019295:Computational Biology / Q000379:methods*; D003461:Crystallography; D057166:High-Throughput Screening Assays / Q000379:methods*; D011487:Protein Conformation; D011506:Proteins / Q000737:chemistry*; D012399:Rotation; D013997:Time Factors
chemical_list: D011506:Proteins