Retaining the Self Interactions in Alchemical Free Energy Calculations

Abstract

Alchemical transformations of chemical species into others provide a common numerical method to compute free energy differences. This method is particularly well suited to compute relative free energy differences formulated as thermodynamic cycles. Moreover, it allows us to compute experimentally measurable quantities, such as the relative binding free energy of small molecules to proteins.The drawback of the alchemical methods is that the annihilation/creation processes of mutated particles present sampling issues and singularities that reduce the accuracy of the calculation. It is therefore important to understand whether the process of annihilation can be simplified and perhaps even avoided.We report a rigorous proof that it is possible to find an alchemical pathway from the native to the mutant system, in which “self interactions” (bonded and non-bonded) are retained without affecting the relative free energy difference. We also provide a molecular dynamics illustrating of this proof in which a cycles of solvated side chains is considered.