SSFEP: Single Step Free Energy Perturbation

Background

Free energy perturbation (FEP) has long been considered the gold standard in calculating relative ligand-binding free energies. However, FEP is often impractical for evaluating a large number of changes to a parent ligand due to the large computational cost. Single Step Free Energy Perturbation (SSFEP) is an alternative that can be orders of magnitude faster than conventional FEP when evaluating a large number of changes to a parent ligand, while maintaining useful accuracy for small functional group modifications [5].

The SSFEP method involves post-processing of MD simulation data of a ligand in a given environment in the canonical ensemble to estimate the alchemical free energy change of chemically modifying the ligand. The following FEP formula is used,

(1)\[\Delta G_\mathrm{L1 \rightarrow L2}^\mathrm{env} = -k_\mathrm{B}T \ln \left< e^{-\beta \Delta E}\right>_\mathrm{L1}\]

where \(k_\mathrm{B}\) is the Boltzmann constant and \(T\) is the temperature. The angular brackets indicate an average of the exponential factor over the MD trajectory of ligand \(L1\) in the given environment, env, which can be either the solvated protein or water. \(\Delta E\) is the energy difference between the two systems involving L1 and L2, which in practice is computed as the difference in the interaction energies of the two ligands in the corresponding environment:

\[\Delta E = E_{L2}^{\mathrm{env}} - E_{L1}^{\mathrm{env}}\]

The environment env in each system is defined as all non-ligand atoms. Once \(\Delta G_{L1\rightarrow L2}^\mathrm{protein}\) and \(\Delta G_{L1\rightarrow L2}^\mathrm{water}\) are computed according to Eq. (1), the relative binding free energy is given by

\[\Delta \Delta G_{L1\rightarrow L2}^\mathrm{bind} = \Delta G_{L1\rightarrow L2}^\mathrm{protein} - \Delta G_{L1\rightarrow L2}^\mathrm{water}\]

The SSFEP approach allows the data from simulation of a single protein–ligand complex to be rapidly post-processed to evaluate tens to hundreds of potential modifications involving multiple sites on the parent ligand. Given this, the best results are achieved when SSFEP is used to evaluate small modifications to the parent ligand.

The ability of standard FEP and SSFEP to reproduce the experimental relative binding affinities of known ligands for two proteins, ACK1 and p38 MAP kinase, was tested [6]; SSFEP was able to produce comparable results to full FEP while requiring a small fraction of the computational resources [6].