In this section, we provided a brief overview of how to analyze
alchemical free energy results while also mentioning some recom-
mended procedures to check for possible issues affecting the reli-
ability of the estimate. For a more detailed explanation of the best
practices and tools available for the analysis of equilibrium free
energy calculations, we highly recommend reading the article by
Klimovich et al. [30].4.7 Sampling and
Modeling Challenges
As in all MD simulations, issues may arise as a consequence of
limited sampling and model inaccuracies. Inadequate sampling
might manifest itself as poorly converged free energy estimates,
which can be identified through convergence plots and the size of
the uncertainty in estimates. Repeating the calculations, possibly
using different starting structures, is a simple yet appropriate way to
assess the precision of the calculations and highlight possible con-
vergence problems, confirming that the results are reproducible. It
is important to assess whether converged results can be obtained
within the timescale of the planned calculations for the specific
system of interest. Alchemical free energy calculations are expected
to be more accurate than implicit solvent end-point methods and
scoring functions, [6, 8, 9]. However, they are also sensitive to
sampling issues [86] such that they can become unreliable if the
phase space explored by the simulations is inadequate for capturing
the conformational ensembles that largely determine the binding
free energy. Moreover, severe sampling issues due to very slow
degrees of freedom that cannot be sampled during the timescale
of the simulations can result in apparently converged calculations
despite affecting the predicted affinities. This can be the case when
the ligand induces conformational changes in the protein. If these
changes are known, the problem may be tackled by separately
calculating the potential of mean force (PMF) for the conforma-
tional change with methods such as umbrella sampling. Mobley
et al. [87] used such an approach to take into account the free
energy contribution of a valine side chain rearrangement that was
not sampled during the alchemical calculations. Lin et al. [88] have
used umbrella sampling to calculate the free energy change
involved in the large loop rearrangement that is associated with
the binding of type-II kinase inhibitors. In many instances, how-
ever, similar slow degrees of freedom might be unknown, and left
unsampled. The position of structural water molecules can be
important as well. If these water molecules are not present in the
starting structure for the calculations, but are important for bind-
ing, and if diffusion to their most stable location is kinetically
hindered, this too can result in convergence issues and biased
results. Sampling schemes that try to tackle these issues have been
developed or are subject of active research [89–92], but are outside
the scope of this discussion.222 Matteo Aldeghi et al.