Water Sites, Networks, And Free Energies with Grand Canonical Monte Carlo

Water molecules play integral roles in the formation of many protein-ligand complexes, and recent computational efforts have been focused on predicting the thermodynamic properties of individual waters and how they may be exploited in rational drug design. However, when water molecules form highly coupled hydrogen-bonding networks, there is, as yet, no method that can rigorously calculate the free energy to bind the entire network or assess the degree of cooperativity between waters. In this work, we report theoretical and methodological developments to the grand canonical Monte Carlo simulation technique. Central to our results is a rigorous equation that can be used to calculate efficiently the binding free energies of water networks of arbitrary size and complexity. Using a single set of simulations, our methods can locate waters, estimate their binding affinities, capture the cooperativity of the water network, and evaluate the hydration free energy of entire protein binding sites. Our techniques have been applied to multiple test systems and compare favorably to thermodynamic integration simulations and experimental data. The implications of these methods in drug design are discussed.