Simulations of biomolecular dynamics are commonly interpreted in terms of harmonic or quasi-harmonic models for the dynamics of the system. Harmonic models assume that the molecule exhibit oscillations around one energy minimum. However, experimental data suggest that the protein samples multiple minima and that transitions among minima shows a broad distribution of energy barriers.

To elucidate the nature of the dynamics of a protein we have studied the molecular dynamics trajectories of various proteins in aqueous solution. These trajectories show that proteins sample multiple local energy minima. Transitions among minima involve collective motions of amino acids over long distances. We show that nonlinear motions are responsible for most of the atomic fluctuations of the protein. These atomic fluctuations are not well described by large motions of individual atoms or a small group of atoms, but rather by concerted motions of many atoms. These motions are nonlinear in the sense that they describe transitions among different basins of attraction. The signature of these nonlinear motions can be seen in local and global structural variables.

A method for extracting molecule optimal dynamic coordinates (MODC) is presented. A generalization of this method to identify small (1-3) dimensional subspaces of the configurational space is used to describe the dynamics of proteins within the context of, nonlinear, multi-basin dynamics.

1996-1997 Mathematics in High Performance Computing