Essential dynamics of proteins.

Analysis of extended molecular dynamics (MD) simulations of lysozyme in vacuo and in aqueous solution reveals that it is possible to separate the configurational space into two subspaces: (1) an "essential" subspace containing only a few degrees of freedom in which anharmonic motion occurs that comprises most of the positional fluctuations; and (2) the remaining space in which the motion has a narrow Gaussian distribution and which can be considered as "physically constrained." If overall translation and rotation are eliminated, the two spaces can be constructed by a simple linear transformation in Cartesian coordinate space, which remains valid over several hundred picoseconds. The transformation follows from the covariance matrix of the positional deviations. The essential degrees of freedom seem to describe motions which are relevant for the function of the protein, while the physically constrained subspace merely describes irrelevant local fluctuations. The near-constraint behavior of the latter subspace allows the separation of equations of motion and promises the possibility of investigating independently the essential space and performing dynamic simulations only in this reduced space.