Affinity Calculations of Cyclodextrin Host–Guest Complexes: Assessment of Strengths and Weaknesses of End-Point Free Energy Methods

The
end-point methods like MM/PBSA or MM/GBSA estimate the free
energy of a biomolecule by combining its molecular mechanics energy
with solvation free energy and entropy terms. On the one hand, their
performance largely depends on the particular system of interest,
and despite numerous attempts to improve their reliability that have
resulted in many variants, there is still no clear alternative to
improve their accuracy. On the other hand, the relatively small cyclodextrin
host–guest complexes, for which high-quality binding calorimetric
data are usually available, are becoming reference models for testing
the accuracy of free energy methods. In this work, we further assess
the performance of various MM/PBSA-like approaches as applied to cyclodextrin
complexes. To this end, we select a set of complexes between β-cyclodextrin
and 57 small organic molecules that has been previously studied with
the binding energy distribution analysis method in combination with
an implicit solvent model (Wickstrom,
L.; He, P.; Gallicchio, E.; Levy, R. M. J. Chem. Theory Comput. 2013, 9, 3136−3150). For each complex, a conventional 1.0 μs
molecular dynamics simulation in explicit solvent is performed. Then
we employ semiempirical quantum chemical calculations, several variants
of the MM-PB­(GB)­SA methods, entropy estimations, etc., to assess the
reliability of the end-point affinity calculations. The best end-point
protocol in this study, which combines DFTB3 energies with entropy
corrections, yields estimations of the binding free energies that
still have substantial errors (RMSE = 2.2 kcal/mol), but it exhibits
a good prediction capacity in terms of ligand ranking (R2 = 0.66) that is close to or even better than that of
rigorous free energy methodologies. Our results can be helpful to
discriminate between the intrinsic limitations of the end-point methods
and other sources of error, such as the underlying energy and continuum
solvation methods.