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 3 3 or 4 3 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. q 2009 Wiley Periodicals, Inc. J Comput Chem 00: 000–000, 2010 Key words: rotational matrix; superposition; RMSD; quaternion; adjoint matrix; root mean squared deviation; protein structure alignment; fragment-assembly; conformational sampling

• Type: Journal
• Year: 2010
• Where: JCC
• Authors: Pu Liu, Dimitris K. Agrafiotis, Douglas L. Theobald
• Keywords: Adjoint Matrix, JCC 2010, Matrix, Rotational Matrix