Determination of protein surface hydration shell free energy of water motion: theoretical study and molecular dynamics simulation.

Water on protein surface plays a crucial role in the mechanistic aspects of biological processes; principally, this is characterized into two kinds of water molecules, biological water and bulk water. As compared to pure water, many aspects of the dynamics and structure of the surrounding water near the protein surface are much less understood. Evidence shows that those properties of the surrounding water induced by the presence of the biological systems differ from those of bulk water and that water has low mobility in the hydration shell. An intriguing question remains as to how to make a quantitative estimate of the hydration shell free energy when there is interaction between the protein and the hydration water. To explore this problem, we perform molecular dynamics simulation of the water motion in the hydration shell with respect to bulk water. A fractional Brownian motion theory combined with numerical simulation and a molecular dynamics simulation was developed. This theory was used to directly establish the connection between the dynamics of the protein surface water motion and the interaction between water and protein; this offers the possibility of determining the hydration shell free energy. In this study, we focused on water motion at the protein surface that is within a 4.4 Å layer, which is referred to as the hydration shell. We demonstrate that it actually follows a fractional Brownian motion. In this regime, a developed fractional Fokker-Planck equation, which is used to describe the dynamics of protein surface water motion, permits us to solve the mean first passage time of water molecules through the hydration shell. We then estimate the protein surface hydration shell free energy (HSFE), which depends on the barrier height of the hydration shell. For myoglobin, its HSFE is about 1.73 kcal/mol, and the accompanying activation entropy is 1.40R, where R is the gas constant. Corresponding reduced water mobility is observed for water surrounding myoglobin. In accord with the analysis of the radial distribution function, it is revealed that the effect of temperature on the HSFE is weak. The results show that the protein surface is wrapped by a shell of low mobility water motion and this hydration shell is dynamic rather than static.