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(ΔU), 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(ΔU) 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-λ perturbation can accurately calculate the free energy of
the restraint addition, which is a nearly 6 times acceleration compared
with current widely used 12-λ perturbation method. The RED-E
function gives insight into the non-Gaussian behavior of the sampled P(ΔU) 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.