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The most basic possible comparison between protein structures makes no attempt to align the input structures and requires a precalculated alignment as input to determine which of the residues in the sequence are intended to be considered in the RMSD calculation. Structural superposition is commonly used to compare multiple conformations of the same protein (in which case no alignment is necessary, since the sequences are the same) and to evaluate the quality of alignments produced using only sequence information between two or more sequences whose structures are known. This method traditionally uses a simple least-squares fitting algorithm, in which the optimal rotations and translations are found by minimizing the sum of the squared distances among all structures in the superposition.<ref name="martin"/> More recently, maximum likelihood and Bayesian methods have greatly increased the accuracy of the estimated rotations, translations, and covariance matrices for the superposition.<ref name="theobald"/><ref name="theobald2"/>
Algorithms based on multidimensional rotations and modified [[quaternion]]s have been developed to identify topological relationships between protein structures without the need for a predetermined alignment. Such algorithms have successfully identified canonical folds such as the [[helix bundle|four-helix bundle]].<ref name="Diederichs"/> The [http://wishart.biology.ualberta.ca/SuperPose/ SuperPose] {{Webarchive|url=https://web.archive.org/web/20151031151001/http://wishart.biology.ualberta.ca/SuperPose/ |date=2015-10-31 }} method is sufficiently extensible to correct for relative ___domain rotations and other structural pitfalls.<ref name="Maiti"/>
===Evaluating similarity===
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