On the Path to Optimal Alchemistry

Alchemical free energy calculations have become a standard and widely used tool, in particular for calculating and comparing binding affinities of drugs. Although methods to compute such free energies have improved significantly over the last decades, the choice of path between the end states of interest is usually still the same as two decades ago. We will show that there is a fundamentally arbitrary, implicit choice of parametrization of this path. To address this, the notion of the length of a path or a metric is required. A metric recently introduced in the context of the accelerated weight histogram method also proves to be very useful here. We demonstrate that this metric can not only improve the efficiency of sampling along a given path, but that it can also be used to improve the actual choice of path. For a set of relevant use cases, the combination of these improvements can increase the efficiency of alchemical free energy calculations by up to a factor 16.