Fast determination of the optimal rotational matrix for macromolecular superpositions

2009-theobald-rmsd

Pu Liu; Dimitris K. Agrafiotis; Douglas L. Theobald

2009-01-01 (print)

Journal of Computational Chemistry (J. Comput. Chem.). n/a-n/a. doi:10.1002/jcc.21439

Description

This one computes the optimal rotation in addition to (specifically: after) just computing the minimal RMSD value. It uses 2005-theobald-rmsd (ref. 14) for finding the optimal RMSD (ie leading eigenvalue of key matrix).

Rapid calculation of RMSDs using a quaternion-based characteristic polynomial

2005-theobald-rmsd

Douglas L. Theobald

2005-06-23 (online) – 2005-07-01 (print)

Acta Crystallographica Section A Foundations of Crystallography (Acta Crystallogr., Sect. A: Found. Crystallogr.). 61, 4, 478-480. doi:10.1107/S0108767305015266

Description

Instead of doing matrix diagonalization or inversion, use netwon-raphson root-finding on a characteristic polynomial.

Mainly builds off of 1987-horn-rmsd (ref. 5).

Using quaternions to calculate RMSD

2004-dill-rmsd

Evangelos A. Coutsias; Chaok Seok; Ken A. Dill

2004-01-01 (online) – 2004-11-30 (print)

Journal of Computational Chemistry (J. Comput. Chem.). 25, 15, 1849-1857. doi:10.1002/jcc.20110

Description

Similar to 2005-theobald-rmsd, builds off of 1987-horn-rmsd (ref. 5). Proves identity with normal 3x3 methods.

Derives the derivative of RMSD wrt coordinates, although "it is well known"

On the orthogonal transformation used for structural comparisons

1989-kearsley-rmsd

S. K. Kearsley

1989-02-01 (print)

Acta Crystallographica Section A Foundations of Crystallography (Acta Crystallogr., Sect. A: Found. Crystallogr.). 45, 2, 208-210. doi:10.1107/S0108767388010128

Description

2005-theobald-rmsd cites for quaternion RMSD

A note on the rotational superposition problem

1988-diamond-rmsd

R. Diamond

1988-03-01 (print)

Acta Crystallographica Section A Foundations of Crystallography (Acta Crystallogr., Sect. A: Found. Crystallogr.). 44, 2, 211-216. doi:10.1107/S0108767387010535

Description

2005-theobald-rmsd cites for quaternion RMSD

Closed-form solution of absolute orientation using unit quaternions

1987-horn-rmsd

Berthold K. P. Horn

1987-04-01 (online) – 1987-04-01 (print)

Journal of the Optical Society of America A (J. Opt. Soc. Amer. A). 4, 4, 629. doi:10.1364/JOSAA.4.000629

Description

2005-theobald-rmsd cites for quaternion RMSD

A solution for the best rotation to relate two sets of vectors

1978-kabsch-rmsd

W. Kabsch

1976-09-01 (print)

Acta Crystallographica Section A (Acta Crystallogr. A). 32, 5, 922-923. doi:10.1107/S0567739476001873

Description

2005-theobald-rmsd says this suffers from rotoinversions because it uses 3x3 rotations instead of 4x4 quaternions.

A Fast 3 x N Matrix Multiply Routine for Calculation of Protein RMSD

2014-haque-fast-rmsd

Imran S Haque; Kyle A Beauchamp; Vijay S Pande

bioRxiv (bioRxiv).