Before revision:  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 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 .
After revision:  Available techniques, ranging from simple automated docking procedures to sophisticated thermodynamics-based methods, have been developed with soluble proteins in mind. Biologically and pharmacologically relevant protein-ligand interactions often occur in complex environments, including lamellar phases like membranes and crowded, non-dilute solutions. Here we revisit the theoretical bases of ligand binding equilibria, avoiding overly specific assumptions that are nearly always made when describing receptor-ligand binding. Building on this formalism, we extend the asymptotically exact Alchemical Free Energy 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 .