A streamlined, general approach for computing ligand binding free energies and its application to GPCR-bound cholesterol

Persistent, direct interactions between proteins in complex phases and small molecules acting as ligands, including processes taking place in lamellar environments like the membrane or in crowded, non-dilute environments, are critical to action of numerous drugs. Few computational approaches have been developed for making quantitative predictions of binding probabilities in environments other than dilute isotropic solution. Available techniques, ranging from simple automated docking procedures to sophisticated thermodynamics-based methods, have been developed almost exclusively for use in soluble proteins. Here we extend the asymptotically exact Alchemical Free Energy 1 ar X iv :1 80 1. 04 90 1v 1 [ qbi o. Q M ] 1 5 Ja n 20 18 Perturbation technique to quantifying occupancies of sites on proteins in a complex bulk, including phase-separated, anisotropic, or non-dilute solutions, using a thermodynamically consistent and easily generalized approach that resolves several previous ambiguities. To incorporate the complex bulk without overcomplicating the overall thermodynamic cycle, we simplify the common approach for ligand restraints by using a single distance-from-bound-configuration (DBC) ligand restraint during AFEP decoupling from protein. DBC restraints should be generalizable to binding modes of most small molecules, even those with strong orientational dependence. We apply this approach to calculate the likelihood that cholesterol binds to widely-studied crystallographic sites on 3 GPCRs (β2-adrenergic, 5HT-2B, and μ-opioid) at a range of concentrations. Non-ideality of cholesterol in a binary cholesterol:phosphatidylcholine (POPC) bilayer is characterized and consistently incorporated into the interpretation.