Title: A streamlined, general approach for computing ligand binding free energies and its application to GPCR-bound cholesterol,
Abstract: The theory of receptor-ligand binding equilibria has long been
well-established in biochemistry, and was primarily constructed to describe
dilute aqueous solutions. Accordingly, few computational approaches have been
developed for making quantitative predictions of binding probabilities in
environments other than dilute isotropic solution. Existing 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 ambiguities of current frameworks. 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 compute the likelihood that membrane cholesterol binds to known
crystallographic sites on 3 GPCRs at a range of concentrations. Non-ideality of
cholesterol in a binary cholesterol:POPC bilayer is characterized and
consistently incorporated into the interpretation.