Efficient Combination of Environment Change and Alchemical Perturbation within the Enveloping Distribution Sampling (EDS) Scheme: Twin-System EDS and Application to the Determination of Octanol-Water Partition Coefficients

The methodology of Enveloping Distribution Sampling (EDS) is extended to probe a single-simulation alternative to the thermodynamic cycle that is standardly used for measuring the effect of a modification of a chemical compound, e.g. from a given species to a chemical derivative for a ligand or solute molecule, on the free-enthalpy change associated with a change in environment, e.g. from the unbound state to the bound state for a protein-ligand system or from one solvent to another one for a solute molecule. This alternative approach relies on the coupled simulation of two systems (computational boxes) 1 and 2, and the method is therefore referred to as twin-system EDS. Systems 1 and 2 account for the two choices of environment. The end states of the alchemical perturbation for the twin-system associate the two alternative forms X and Y of the molecule to systems 1 and 2 or 2 and 1, respectively. In this way, the processes of transforming one molecule into the other are carried out simultaneously in opposite directions in the two environments, leading to a change in free enthalpy that is smaller than for the two individual processes and to an energy-difference distribution that is more symmetric As an illustration, the method is applied to the calculation of octanol-water partition coefficients for C-4 to C-8 alkanes, 1-hexanol and 1,2-dimethoxyethane. It is shown in particular that the consideration of the residual hydration of octanol leads to calculated partition coefficients that are in better agreement with reported experimental numbers.