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

Abstract

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.

Relative Binding Free Energy between Chemically Distant Compounds Using a Bidirectional Nonequilibrium Approach

“…Both techniques have been either applied to strictly congeneric compounds 31 or tested on structurally similar compounds imposing an appropriate restraining potential that maintains the ligand alignment in order to enhance the convergence of the calculations. 32 …”

“…It may also involve orientational ω coordinates as well, as long as u r remains symmetrical, with respect to the exchange of the label. 32 Using eq 8 , we find that, for the restrained system, the free-energy change is given by where the integration domain of the ζ AB coordinates is the volume of the system and entire solid angle: The two identical integrals, depending on the ζ AB coordinates on the denominator and numerator of eq 10 , simplify, recovering eq 7 hence showing that Δ G bound ′ = Δ G bound , QED. We stress once more that the free energy estimate ( eq 10 ) is independent of the COM–COM restraint potential if and only if the latter is symmetrical, with respect to the exchange of the guest labels.…”

“…I (ζ) is equal to one if the host–guest relative coordinates ζ correspond to a bound configuration, and zero otherwise. 32 , 69 − 71 Note that, in the second equality of eq 7 , we have integrated away the decoupled ζ B and ζ A coordinates in the numerator and denominator, respectively, obtaining, in both cases, an 8π 2 V term, which simplifies.…”

Application of the Alchemical Transfer and Potential of Mean Force Methods to the SAMPL8 Host-Guest Blinded Challenge

“…[12] ATM, implemented on top of the versatile OpenMM molecular dynamics engine, [26] promises to provide an accurate and streamlined route to absolute [12] and relative binding free calculations. [30] While alchemical, ATM, similar to the PMF pathway method, [13] makes use of a single simulation system, and it avoids problematic vacuum intermediates and the splitting of the alchemical path into electrostatic and non-electrostatic transformations. ATM also does not require soft-core pair potentials and modifications of energy routines, and can be easily implemented as a controlling routine on top of existing force routines of MD engines.…”

A New Formulation for the Concerted Alchemical Calculation of van der Waals and Coulomb Components of Solvation Free Energies

“…Concerted alchemical transformations are suitable for advanced sampling schemes such as λ dynamics , and adaptive biasing. , Furthermore, they are more convenient than sequential evaluation approaches, where each step is associated with different sampling requirements and statistical errors . Other authors evaluated transformations with simultaneous changes in the LJ and Coulomb potentials, applying either a modified soft-core model or a capping function that acts directly on the total alchemical potential energy rather than on each alchemically affected pair interaction. − In contrast, our proposal relies on the LBF approach, thus bringing about all of the benefits mentioned earlier.…”