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The Kabsch algorithm, also known as the Kabsch-Umeyama algorithm, [1] named after Wolfgang Kabsch and Shinji Umeyama, is a method for calculating the optimal rotation matrix that minimizes the RMSD (root mean squared deviation) between two paired sets of points.
Coutsias, et al. presented a simple derivation, based on quaternions, for the optimal solid body transformation (rotation-translation) that minimizes the RMSD between two sets of vectors. [2] They proved that the quaternion method is equivalent to the well-known Kabsch algorithm . [ 3 ]
RMSD is a measure of accuracy, to compare forecasting errors of different models for a particular dataset and not between datasets, as it is scale-dependent. [1] RMSD is always non-negative, and a value of 0 (almost never achieved in practice) would indicate a perfect fit to the data. In general, a lower RMSD is better than a higher one.
The RMSD of two aligned structures indicates their divergence from one another. Structural alignment can be complicated by the existence of multiple protein domains within one or more of the input structures, because changes in relative orientation of the domains between two structures to be aligned can artificially inflate the RMSD.
[2] The application of secondary chemical shifts to characterize protein flexibility is based on an assumption that the proximity of chemical shifts to random coil values is a manifestation of increased protein mobility, while significant differences from random coil values are an indication of a relatively rigid structure.
The artificial landscapes presented herein for single-objective optimization problems are taken from Bäck, [1] Haupt et al. [2] and from Rody Oldenhuis software. [3] Given the number of problems (55 in total), just a few are presented here. The test functions used to evaluate the algorithms for MOP were taken from Deb, [4] Binh et al. [5] and ...
The Lanczos algorithm is most often brought up in the context of finding the eigenvalues and eigenvectors of a matrix, but whereas an ordinary diagonalization of a matrix would make eigenvectors and eigenvalues apparent from inspection, the same is not true for the tridiagonalization performed by the Lanczos algorithm; nontrivial additional steps are needed to compute even a single eigenvalue ...
Generally scores below 0.20 corresponds to randomly chosen unrelated proteins whereas structures with a score higher than 0.5 assume roughly the same fold. [2] A quantitative study [ 3 ] shows that proteins of TM-score = 0.5 have a posterior probability of 37% in the same CATH topology family and of 13% in the same SCOP fold family.