Fast determination of the optimal rotational matrix for macromolecular superpositions.
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.
Liu
Pu
P
Johnson & Johnson Pharmaceutical Research and Development, L.L.C., 665 Stockton Drive, Exton, Pennsylvania 19341, USA. pliu24@its.jnj.com
Agrafiotis
Dimitris K
DK
Theobald
Douglas L
DL
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
D011506:Proteins