Accelerating and Automating the Free Energy Perturbation Absolute Binding Free Energy Calculation with the RED-E Function

The accurate prediction of the binding affinities between small molecules and biological macromolecules plays a fundamental role in structure-based drug design, which is still challenging. The free energy perturbation-based absolute binding free energy (FEP-ABFE) approach has shown potential in its reliability. To correctly calculate the energy related to the ligand being restrained by the receptor, additional restraints between the ligand and the receptor are needed. However, determining the restraint parameters for individual ligands empirically is too trivial to be automated, and usually gives rise to numerical instabilities, which set back the applications of FEP-ABFE. To address these issues, we derived the analytical expression for the probability distribution of energy differences, P(Delta U), during the process of restraint addition, which is called the RED-E (restraint energy distribution at equilibrium position) function. Simulations indicated that the RED-E function can accurately describe P(Delta U) when restraints are added at the equilibrium position. Based on the RED-E function, an automatic restraint selection method was proposed to select the best restraint. With this method, there is a high phase-space overlap between the free and restrained states, such that using a 2-lambda perturbation can accurately calculate the free energy of the restraint addition, which is a nearly 6 times acceleration compared with current widely used 12-lambda perturbation method. The RED-E function gives insight into the non-Gaussian behavior of the sampled P(Delta U) in certain FEP processes in an analytical way. The highly automated and accelerated restraint selection also makes it possible for the large-scale application of FEP-ABFE in real drug discovery practices.