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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 ]
Let P and Q be two sets, each containing N points in .We want to find the transformation from Q to P.For simplicity, we will consider the three-dimensional case (=).The sets P and Q can each be represented by N × 3 matrices with the first row containing the coordinates of the first point, the second row containing the coordinates of the second point, and so on, as shown in this matrix:
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.
Examples of correlation between RCI and other methods of measuring motional amplitudes in proteins. NMR RMSD - root mean square fluctuations of atomic coordinates in NMR ensembles, MD RMSD - root mean square fluctuations of atomic coordinates in MD ensembles, S2 - model-free order parameter, RCI - random coil index, B-factor - temperature factor of X-ray structures; RCI->NMR RMSD - root mean ...
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 ...
MATLAB is a widely used proprietary software for performing numerical computations. [1] [2] [3] It comes with its own programming language, in which numerical algorithms can be implemented. GNU MCSim a simulation and numerical integration package, with fast Monte Carlo and Markov chain Monte Carlo capabilities.
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.