Binding Free Energies of Host-Guest Systems by Nonequilibrium Alchemical Simulations with Constrained Dynamics: Theoretical Framework

The fast-switching decoupling method is a powerful nonequilibrium technique to compute absolute binding free energies of ligand-receptor complexes (Sandberg et al., J. Chem. Theory Comput. 2014, 11, 423-435). Inspired by the theory of noncovalent binding association of Gilson and co-workers (Biophys. J. 1997, 72, 1047-100), we develop two approaches, termed binded-domain and single-point alchemical-path schemes (BiD-AP and SiP-AP), based on the possibility of performing alchemical trajectories during which the ligand is constrained to fixed positions relative to the receptor. The BiD-AP scheme exploits a recent generalization of nonequilibrium work theorems to estimate the free energy difference between the coupled and uncoupled states of the ligand receptor complex. With respect to the fast-switching decoupling method without constraints, BiD-AP prevents the ligand from leaving the binding site, but still requires an estimate of the positional binding-site volume, which may not be a simple task. On the other side, the SiP-AP scheme allows avoidance of the calculation of the binding-site volume by introducing an additional equilibrium simulation of ligand and receptor in the bound state. In the companion article (DOI: 10.1021/acs.jctc.7b00595), we show that the extra computational effort required by SiP-AP leads to a significant improvement of accuracy in the free energy estimates.