Host–Guest Relative Binding Affinities at Density-Functional Theory Level from Semiempirical Molecular Dynamics Simulations

Abstract

Relative free energies for the binding of nine cyclic carboxylate ligands to the octaacid deep-cavity host were calculated at the combined density-functional theory and molecular mechanics (DFT/MM) level of theory. The DFT calculations employed the BLYP functional and the 6-31G* basis set for the ligand. We employed free-energy perturbations (FEP) with the reference-potential approach and used molecular dynamics (MD) simulations with the semiempirical quantum mechanical (SQM) PM6-DH+ method for the ligand as an intermediate level between MM and DFT/MM to improve the convergence. Thus, the relative binding free energy of two ligands was first calculated at the MM level by an alchemical transformation from one ligand to another in both the bound and unbound states. Then, for each ligand the free-energy correction for going from the MM to the SQM/MM potentials was calculated using explicit SQM/MM MD simulations. Finally, the free-energy correction for going from the SQM/MM to the DFT/MM potentials was estimated with FEP without running any DFT/MM simulations. Instead, the free energy was calculated by single-step exponential averaging (ssEA) or employing the cumulant approximation to the second order (CA). The results show that CA converges much better than ssEA and with 500-4500 DFT/MM single-point energy calculations, converged free energies with a precision of 0.3 kJ/mol can be obtained. These free energies reproduce the experimental binding free energy differences with a mean absolute deviation of 3.4 kJ/mol, a correlation (R 2) of 0.97 and correct signs for all of the eight free-energy differences. This is appreciably better than the results obtained at the SQM/MM level of theory and also slightly better than those obtained with MM. We show that the convergence of the SQM/MM→DFT/MM perturbations can be monitored by the use of Wu and Kofke's bias metric Π and by the standard deviation of the difference between the SQM/MM and DFT/MM energies. Finally, we show that the use of the intermediate SQM/MM MD simulations improves the convergence of the free energies by a factor of at least two, compared to doing direct MM→DFT/MM perturbations.

Development of a Robust Indirect Approach for MM → QM Free Energy Calculations That Combines Force-Matched Reference Potential and Bennett’s Acceptance Ratio Methods

“…These include the use of frozen density functional approximations, 27,28 orthogonal space random walk strategies, 29 integrated Hamiltonian sampling, 30 paradynamics, 31,32 and trajectory reweighting. 25,33-36 Others have noted the importance of choosing the most compatible reference potential 37-40 or have sought to improve the reference potential to increase the distribution overlap between reference and QM/MM potential energy surfaces. 32,38,41,42 Of particular note are those methods that perform ad hoc parametrization of the MM reference potential via “force matching” to the QM/MM potential 19,39,43-50 to enhance the conformational overlap between the levels of theory.…”

Robust, Efficient and Automated Methods for Accurate Prediction of Protein-Ligand Binding Affinities in AMBER Drug Discovery Boost

“…Free energy simulations have a number of applications, including the calculation of relative ligand binding free energies (RBFEs). 61,[93][94][95][96][97] In this type of application, a drug (ligand) has been found to bind to a protein target, and one seeks to find similar drugs that are potentially more efficacious. A set of ligands is proposed that differ from the lead ligand by adding or removing functional groups, and the computational chemist is tasked with predicting their RBFEs.…”

Targeted Free Energy Perturbation Revisited: Accurate Free Energies from Mapped Reference Potentials

“…While much progress has been made in developing empirical potentials capable of accurate predictions, − a full or partial quantum mechanical (QM) representation of the system was often found to be desirable. For instance, hybrid molecular mechanics/quantum mechanics potential energy surfaces based on post-Hartree–Fock, density functional theory (DFT), or quantum machine learning potentials − have been used to overcome some of the shortcomings of empirical and semiempirical calculations to study ligand binding − and chemical reactions. − However, the use of accurate quantum chemical methods severely limits the size of the system that can be studied.…”