Analytical Model of the Free Energy of Alchemical Molecular Binding

Potential distribution theory of alchemical transfer

We present an analytical description of the Alchemical Transfer Method (ATM) for molecular binding using the Potential Distribution Theory (PDT) formalism. ATM models the binding free energy by mapping the bound and unbound states of the complex by translating the ligand coordinates. PDT relates the free energy and the probability densities of the perturbation energy along the alchemical path to the probability density at the initial state, which is the unbound state of the complex in the case of a binding process. Hence, the ATM probability density of the transfer energy at the unbound state is first related by a convolution operation of the probability densities for coupling the ligand to the solvent and coupling it to the solvated receptor-for which analytical descriptions are available-with parameters obtained from maximum likelihood analysis of data from double-decoupling alchemical calculations. PDT is then used to extend this analytical description along the alchemical transfer pathway. We tested the theory on the alchemical binding of five guests to the tetramethyl octa-acid host from the SAMPL8 benchmark set. In each case, the probability densities of the perturbation energy for transfer along the alchemical transfer pathway obtained from numerical calculations match those predicted from the theory and double-decoupling simulations. The work provides a solid theoretical foundation for alchemical transfer, offers physical insights on the form of the probability densities observed in alchemical transfer calculations, and confirms the conceptual and numerical equivalence between the alchemical transfer and double-decoupling processes.

Relative Binding Free Energy Calculations for Ligands with Diverse Scaffolds with the Alchemical Transfer Method

We present an extension of the alchemical transfer method (ATM) for the estimation of relative binding free energies of molecular complexes applicable to conventional, as well as scaffold-hopping, alchemical transformations. Named ATM-RBFE, the method is implemented in the free and open-source OpenMM molecular simulation package and aims to provide a simpler and more generally applicable route to the calculation of relative binding free energies than what is currently available. ATM-RBFE is based on sound statistical mechanics theory and a novel coordinate perturbation scheme designed to swap the positions of a pair of ligands such that one is transferred from the bulk solvent to the receptor binding site while the other moves simultaneously in the opposite direction. The calculation is conducted directly in a single solvent box with a system prepared with conventional setup tools, without splitting of electrostatic and nonelectrostatic transformations, and without pairwise soft-core potentials. ATM-RBFE is validated here against the absolute binding free energies of the SAMPL8 GDCC host-guest benchmark set and against protein-ligand benchmark sets that include complexes of the estrogen receptor ERα and those of the methyltransferase EZH2. In each case the method yields self-consistent and converged relative binding free energy estimates in agreement with absolute binding free energies and reference literature values, as well as experimental measurements.

Alchemical Transfer Approach to Absolute Binding Free Energy Estimation

The alchemical transfer method (ATM) for the calculation of standard binding free energies of noncovalent molecular complexes is presented. The method is based on a coordinate displacement perturbation of the ligand between the receptor binding site and the explicit solvent bulk and a thermodynamic cycle connected by a symmetric intermediate in which the ligand interacts with the receptor and solvent environments with equal strength. While the approach is alchemical, the implementation of the ATM is as straightforward as that for physical pathway methods of binding. The method is applicable, in principle, with any force field, as it does not require splitting the alchemical transformations into electrostatic and nonelectrostatic steps, and it does not require soft-core pair potentials. We have implemented the ATM as a freely available and open-source plugin of the OpenMM molecular dynamics library. The method and its implementation are validated on the SAMPL6 SAMPLing host-guest benchmark set. The work paves the way to streamlined alchemical relative and absolute binding free energy implementations on many molecular simulation packages and with arbitrary energy functions including polarizable, quantum-mechanical, and artificial neural network potentials.

Combining Alchemical Transformation with a Physical Pathway to Accelerate Absolute Binding Free Energy Calculations of Charged Ligands to Enclosed Binding Sites

We present a new approach to more accurately and efficiently compute the absolute binding free energy for receptor-ligand complexes. Currently, the double decoupling method (DDM) and the potential of mean force method (PMF) are widely used to compute the absolute binding free energy of biomolecular complexes. DDM relies on alchemically decoupling the ligand from its environments, which can be computationally challenging for large ligands and charged ligands because of the large magnitude of the decoupling free energies involved. In contrast, the PMF method uses a physical pathway to directly transfer the ligand from solution to the receptor binding pocket and thus avoids some of the aforementioned problems in DDM. However, the PMF method has its own drawbacks: because of its reliance on a ligand binding/unbinding pathway that is free of steric obstructions from the receptor atoms, the method has difficulty treating ligands with buried atoms. To overcome the limitation in the standard PMF approach and enable buried ligands to be treated, here we develop a new method called AlchemPMF in which steric obstructions along the physical pathway for binding are alchemically removed. We have tested the new approach on two important drug targets involving charged ligands. One is HIV-1 integrase bound to an allosteric inhibitor; the other is the human telomeric DNA G-quadruplex in complex with a natural product protoberberine buried in the binding pocket. For both systems, the new approach leads to more reliable estimates of absolute binding free energies with smaller error bars and closer agreements with experiments compared with those obtained from the existing methods, demonstrating the effectiveness of the new method in overcoming the hysteresis often encountered in PMF binding free energy calculations of such systems. The new approach could also be used to improve the sampling of water equilibration and resolvation of the binding pocket as the ligand is extracted.