Correction Schemes for Absolute Binding Free Energies Involving Lipid Bilayers

Absolute binding free-energy (ABFE) calculations are playing an increasing role in drug design, especially as they can be performed on a range of disparate compounds and direct comparisons between them can be made. It is, however, especially important to ensure that they are as accurate as possible, as unlike relative binding free-energy (RBFE) calculations, one does not benefit as much from a cancellation of errors during the calculations. In most modern implementations of ABFE calculations, a particle mesh Ewald scheme is typically used to treat the electrostatic contribution to the free energy. A central requirement of such schemes is that the box preserves neutrality throughout the calculation. There are many ways to deal with this problem that have been discussed over the years ranging from a neutralizing plasma with a post hoc correction term through to a simple co-alchemical ion within the same box. The post hoc correction approach is the most widespread. However, the vast majority of these studies have been applied to a soluble protein in a homogeneous solvent (water or salt solution). In this work, we explore which of the more common approaches would be the most suitable for a simulation box with a lipid bilayer within it. We further develop the idea of the so-called Rocklin correction for lipid-bilayer systems and show how such a correction could work. However, we also show that it will be difficult to make this generalizable in a practical way and thus we conclude that the use of a "co-alchemical ion" is the most useful approach for simulations involving lipid membrane systems.