Single Step Free Energy Perturbation (SSFEP)
============================================
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 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 large number of changes to a parent ligand,
while maintaining useful accuracy for small functional group modifications
:cite:`Raman:2012`.
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. Zwanzig's FEP formula is
used,
.. math::
:label: zwanzigformula
\Delta G_\mathrm{L1 \rightarrow L2}^\mathrm{env} = -k_\mathrm{B}T \ln \left< e^{-\beta \Delta E}\right>_\mathrm{L1}
where :math:`k_\mathrm{B}` is the Boltzmann constant and :math:`T` is the
temperature. The angular brackets indicate an average of the exponential factor
over the MD trajectory of ligand :math:`L1` in the given environment, ``env``,
which can be either the solvated protein or water. :math:`\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:
.. math::
\Delta E = E_{L2 - \mathrm{env}} - E_{L1 - \mathrm{env}}
The environment ``env`` in each system is defined as all atoms with the
exception of ligand atoms. As the environment is constant between the two
ligands, the internal environmental energy cancels exactly during the
computation of :math:`\Delta E`. In addition, as the difference between L1 and
L2 involves a very small number of heavy atom modifications, we expect any
differential intra-ligand energy terms to also cancel exactly between the
solution and protein environments. Therefore, once :math:`\Delta
G_{L1\rightarrow L2}^\mathrm{protein}` and :math:`\Delta G_{L1\rightarrow
L2}^\mathrm{water}` are computed according to Eq. :eq:`zwanzigformula`,
the relative binding free energy is given by
.. math::
\Delta \Delta G_{L1\rightarrow L2}^\mathrm{bind} = G_{L1\rightarrow L2}^\mathrm{protein} - 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.
In a recent study :cite:`Raman:2016`, 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. SSFEP was able to produce
comparable results to ful FEP while requiring a small
fraction of the computational resources.
.. include:: usage.rst
..
.. include:: interface.rst