Fluctuation and Cross-correlation Analysis of Protein Motions Observed in Nanosecond Molecular Dynamics Simulations

Nanosecond molecular dynamics simulations of bovine pancreatic trypsin inhibitor and lysozyme in water are analyzed in terms of backbone atomic positional fluctuations and dynamical cross-correlations. It is found that although the molecular systems are stable, B-factors calculated over a time period as long as 500 ps are not representative for the motions within the proteins. This is especially true for the most mobile residues. On a nanosecond time-scale, the B-factors calculated from the simulations of the proteins in solution are considerably larger than those obtained by structure refinement of the proteins in crystals, based on X-ray data. The time evolution of the atomic fluctuations shows that for large portions of the proteins under study, atomic positional fluctuations are not yet converged after a nanosecond. Cross-correlations do not converge faster than the fluctuations themselves. Most display very erratic behavior if the sampling covers less than about 200 ps. It is also shown that inclusion of mobile atoms into the procedure used to remove rigid-body motion from the simulation can lead to spurious correlations between the motions of the atoms at the surface of the protein.