Hierarchical structure of the energy landscape of proteins revisited by time series analysis. II. Investigation of explicit solvent effects.

Time series analysis tools are employed on the principal modes obtained from the C(alpha) trajectories from two independent molecular-dynamics simulations of alpha-amylase inhibitor (tendamistat). Fluctuations inside an energy minimum (intraminimum motions), transitions between minima (interminimum motions), and relaxations in different hierarchical energy levels are investigated and compared with those encountered in vacuum by using different sampling window sizes and intervals. The low-frequency low-indexed mode relationship, established in vacuum, is also encountered in water, which shows the reliability of the important dynamics information offered by principal components analysis in water. It has been shown that examining a short data collection period (100 ps) may result in a high population of overdamped modes, while some of the low-frequency oscillations (<10 cm(-1)) can be captured in water by using a longer data collection period (1200 ps). Simultaneous analysis of short and long sampling window sizes gives the following picture of the effect of water on protein dynamics. Water makes the protein lose its memory: future conformations are less dependent on previous conformations due to the lowering of energy barriers in hierarchical levels of the energy landscape. In short-time dynamics (<10 ps), damping factors extracted from time series model parameters are lowered. For tendamistat, the friction coefficient in the Langevin equation is found to be around 40-60 cm(-1) for the low-indexed modes, compatible with literature. The fact that water has increased the friction and that on the other hand has lubrication effect at first sight contradicts. However, this comes about because water enhances the transitions between minima and forces the protein to reduce its already inherent inability to maintain oscillations observed in vacuum. Some of the frequencies lower than 10 cm(-1) are found to be overdamped, while those higher than 20 cm(-1) are slightly increased. As for the long-time dynamics in water, it is found that random-walk motion is maintained for approximately 200 ps (about five times of that in vacuum) in the low-indexed modes, showing the lowering of energy barriers between the higher-level minima.