Comparison of enveloping distribution sampling and thermodynamic integration to calculate binding free energies of phenylethanolamine N-methyltransferase inhibitors

The relative binding free energy between two ligands to a specific protein can be obtained using various computational methods. The more accurate and also computationally more demanding techniques are the so-called free energy methods which use conformational sampling from molecular dynamics or Monte Carlo simulations to generate thermodynamic averages. Two such widely applied methods are the thermodynamic integration (TI) and the recently introduced enveloping distribution sampling (EDS) methods. In both cases relative binding free energies are obtained through the alchemical perturbations of one ligand into another in water and inside the binding pocket of the protein. TI requires many separate simulations and the specification of a pathway along which the system is perturbed from one ligand to another. Using the EDS approach, only a single automatically derived reference state enveloping both end states needs to be sampled. In addition, the choice of an optimal pathway in TI calculations is not trivial and a poor choice may lead to poor convergence along the pathway. Given this, EDS is expected to be a valuable and computationally efficient alternative to TI. In this study, the performances of these two methods are compared using the binding of ten tetrahydroisoquinoline derivatives to phenylethanolamine N-transferase as an example. The ligands involve a diverse set of functional groups leading to a wide range of free energy differences. In addition, two different schemes to determine automatically the EDS reference state parameters and two different topology approaches are compared.