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

Abstract

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.

HYDROPHOBE Challenge: A Joint Experimental and Computational Study on the Host–Guest Binding of Hydrocarbons to Cucurbiturils, Allowing Explicit Evaluation of Guest Hydration Free-Energy Contributions

“…The MD1 and MD2 submissions were absolute binding free energy calculations generated using molecular dynamics simulations and referenced to the standard concentration of 1 M. The free energy difference between the bound and unbound state was computed using the attach-pull-release (APR) method described in detail by Henriksen et al 27 Briefly, this approach involves attaching a set of restraints to control the position and orientation of the guest relative to the host, followed by removal of the guest from the host into bulk solvent. The work of moving the guest along this free energy path can be computed from the mean restraint coordinate values using thermodynamic integration (or other similar approaches, such as multi-state Bennet acceptance ratio (MBAR)).…”

“…The orientation of the CB7 host portal openings was aligned with the long box axis via six restraints to three non-interacting anchor particles at fixed positions in the laboratory frame. These restraints (one distance, two angle, and three dihedral) were present in all phases of the APR approach and were chosen in such a way as to not perturb the internal degrees of freedom of the host (see Henriksen et al 27 for complete description). In contrast, restraints between the anchor particles and the guest molecule, as well as conformational restraints which forced apart the CB7 portal openings, were attached by increasing the force constant over a series of 15 simulations.…”

“…18–21 Computational methods are therefore particularly valuable in order to rationalize experimental trends and to understand the interplay between the two main contributors. 22–27 …”

Fast and Flexible GPU Accelerated Binding Free Energy Calculations within the AMBER Molecular Dynamics Package

“…30, 37 Overall, we have achieved a greater than 360X performance enhancement for RFEB protein-ligand complex systems over a single CPU core, or greater than 30X performance improvement over a CPU node. With our code, these calculations can now be carried out on the order of hours on a single cost-efficient GeForce GPU, instead of weeks on a single node or having to utilize large number of CPU nodes with expensive interconnects.…”

How Does Solvation Affect the Binding of Hydrophilic Amino Saccharides to Cucurbit[7]uril with Exceptional Anomeric Selectivity?

“…[56] Thus, a further elaborate study for enthalpy/entropy calculations along with free-energy considerations will be needed to confirm this assessment. [57] …”