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Bias‐free separation of internal and overall motion of biomolecules
Author(s) -
Schieborr Ulrich,
Rüterjans Heinz
Publication year - 2001
Publication title -
proteins: structure, function, and bioinformatics
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 1.699
H-Index - 191
eISSN - 1097-0134
pISSN - 0887-3585
DOI - 10.1002/prot.1141
Subject(s) - residual , translation (biology) , covariance , rotation (mathematics) , motion (physics) , principal component analysis , covariance matrix , cartesian coordinate system , algorithm , rotation around a fixed axis , statistical physics , biological system , computer science , mathematics , physics , chemistry , artificial intelligence , classical mechanics , statistics , geometry , biology , messenger rna , gene , biochemistry
Collective internal motions are known to be important for the function of biological macromolecules. It has been discussed in the past whether the application of superimposing algorithms to remove the overall motion from a structural ensemble introduces artificial correlations between distant atoms. Here we present a new method to eliminate residual rotation and translation from cartesian modes derived from a normal mode analysis or from a principal component analysis. Bias‐free separation is based on the idea that the addition of modes of pure rotation/translation can compensate the residual overall motion. Removal of overall motion must reduce the “total amount of motion” (TAM) in the mode. Our algorithm allows to back‐calculate revised covariance matrices. The approach was applied to two model systems that show residual overall motion, when analyzed using all atoms as reference for the superimposing algorithm. In both cases, our algorithm was capable of eliminating residual covariances caused by the overall motion, while retaining internal covariances even for very distant atoms. A structural ensemble obtained for a 13‐ns molecular dynamics simulation of the protein Ribonuclease T1 showed a covariance matrix of the corrected modes with significantly sharper contours after applying the bias‐free separation. Proteins 2001;45:207–218. © 2001 Wiley‐Liss, Inc.