Computational Calorimetry: High-Precision Calculation of Host–Guest Binding Thermodynamics

We
present a strategy for carrying out high-precision calculations
of binding free energy and binding enthalpy values from molecular
dynamics simulations with explicit solvent. The approach is used to
calculate the thermodynamic profiles for binding of nine small molecule
guests to either the cucurbit[7]­uril (CB7) or β-cyclodextrin
(βCD) host. For these systems, calculations using commodity
hardware can yield binding free energy and binding enthalpy values
with a precision of ∼0.5 kcal/mol (95% CI) in a matter of days.
Crucially, the self-consistency of the approach is established by
calculating the binding enthalpy directly, via end point potential
energy calculations, and indirectly, via the temperature dependence
of the binding free energy, i.e., by the van’t Hoff equation.
Excellent agreement between the direct and van’t Hoff methods
is demonstrated for both host–guest systems and an ion-pair
model system for which particularly well-converged results are attainable.
Additionally, we find that hydrogen mass repartitioning allows marked
acceleration of the calculations with no discernible cost in precision
or accuracy. Finally, we provide guidance for accurately assessing
numerical uncertainty of the results in settings where complex correlations
in the time series can pose challenges to statistical analysis. The
routine nature and high precision of these binding calculations opens
the possibility of including measured binding thermodynamics as target
data in force field optimization so that simulations may be used to
reliably interpret experimental data and guide molecular design.