On the calculation of solvation free energy from Kirkwood-Buff integrals: A large scale molecular dynamics study

Solvation of (bio)molecules in water is severely affected by the presence of co-solvent within the hydration shell of the solute structure. Furthermore, since solute molecules can range from small molecules, such as methane, to large protein structures, it is imperative to understand the detailed structure-function relationship on the microscopic level. Although such an understanding can be obtained through molecular dynamic simulations, excessively large system sizes and simulation times are required in order to obtain meaningful results. In this context, Kirkwood-Buff (KB) theory, which connects the microscopic pair-wise molecular distributions to global thermodynamic properties, together with the recently developed technique called finite size scaling, may provide a method to reduce computational times. In this paper, we present a molecular dynamics test simulation to calculate and compare the KB integrals, for the solvation of methane in methanol in water, calculated via two different methods: via the radial distribution functions and via the fluctuation method. In the results reported here we demonstrate that the latter method can produce equivalent results by using a relatively small system size. In future work we thus intend using the fluctuation method and finite size scaling to study the conformational transitions of large (bio)macromolecules.