Collective internal motions are known to be important for the function of b
iological macromolecules. It has been discussed in the past whether the app
lication of superimposing algorithms to remove the overall motion from a st
ructural ensemble introduces artificial correlations between distant atoms.
Here we present a new method to eliminate residual rotation and translatio
n from cartesian modes derived from a normal mode analysis or from a princi
pal 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 c
ovariance matrices. The approach was applied to two model systems that show
residual overall motion, when analyzed using all atoms as reference for th
e superimposing algorithm. In both cases, our algorithm was capable of elim
inating residual covariances caused by the overall motion, while retaining
internal covariances even for very distant atoms. A structural ensemble obt
ained for a 13-ns molecular dynamics simulation of the protein Ribonuclease
T1 showed a covariance matrix of the corrected modes with significantly sh
arper contours after applying the bias-free separation. (C) 2001 Wiley-Liss
, Inc.