Comprehensive Evaluation of End-Point Free Energy Techniques in Carboxylated-Pillar[6]arene Host-Guest Binding: IV. The QM Treatment, GB Models and the Multi-Trajectory Extension

Abstract

Due to the similarity of host–guest complexes and protein–ligand and protein–protein assemblies, computational tools for protein–drug complexes are commonly applied in host–guest binding. One of the methods with the highest popularity is the end-point free energy technique, which estimates the binding affinity with gas-phase and solvation contributions extracted from simplified end-point sampling. Our series papers on a set of carboxylated-pillararene host–guest complexes have proven with solid numerical evidence that standard end-point techniques are practically useless in host–guest binding, but alterations, such as slightly increasing interior dielectric constant in post-processing calculation and shifting to the multi-trajectory realization in conformational sampling, could better the situation and pull the end-point method back to the pool of usable tools. Also, the force-field selection plays a critical role, as it determines the sampled region in the conformational space. In the current work, we continue the efforts to explore potentially promising end-point modifications in host–guest binding and further extend the sampling time to an unprecedent length. Specifically, we comprehensively benchmarked the shift from the original MM description to QM Hamiltonians in post-processing the popular single-trajectory sampling. Two critical settings in the multi-scale QM/GBSA regime are the selections of the QM Hamiltonian and the implicit-solvent model, and a scan of combinations of popular semi-empirical QM Hamiltonians and GB models is performed. The multi-scale QM/GBSA treatment is further combined with the three-trajectory sampling protocol, introducing a further advanced modification. The sampling lengths in the host–guest complex, solvated guest and solvated host ensembles are extended to 500 ns, 500 ns and 12,000 ns. As a result, the sampling quality in end-point calculations is unprecedently high, enabling us to draw conclusive pictures of investigated forms of modified end-point free energy methods. Numerical results suggest that the shift to the QM Hamiltonian does not better the situation in the popular single-trajectory regime, but noticeable improvements are observed in the three-trajectory sampling regime, especially for the DFTB/GBSA parameter combination (either DFTB2 or its third-order extension), the quality metrics of which reach an unprecedently high level and surpass existing predictions (including costly alchemical transformations) on this dataset, hinting on the applicability of the advanced three-trajectory QM/GBSA end-point modification for host–guest complexes.