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

Abstract

In the context of advanced hit-to-lead drug design based on atomistic molecular dynamics simulations, we propose a dual topology alchemical approach for calculating the relative binding free energy (RBFE) between two chemically distant compounds. The method (termed NE-RBFE) relies on the enhanced sampling of the end-states in bulk and in the bound state via Hamiltonian Replica Exchange, alchemically connected by a series of independent and fast nonequilibrium (NE) simulations. The technique has been implemented in a bidirectional fashion, applying the Crooks theorem to the NE work distributions for RBFE predictions. The dissipation of the NE process, negatively affecting accuracy, has been minimized by introducing a smooth regularization based on shifted electrostatic and Lennard-Jones non bonded potentials. As a challenging testbed, we have applied our method to the calculation of the RBFEs in the recent host–guest SAMPL international contest, featuring a macrocyclic host with guests varying in the net charge, volume, and chemical fingerprints. Closure validation has been successfully verified in cycles involving compounds with disparate Tanimoto coefficients, volume, and net charge. NE-RBFE is specifically tailored for massively parallel facilities and can be used with little or no code modification on most of the popular software packages supporting nonequilibrium alchemical simulations, such as Gromacs, Amber, NAMD, or OpenMM. The proposed methodology bypasses most of the entanglements and limitations of the standard single topology RBFE approach for strictly congeneric series based on free-energy perturbation, such as slowly relaxing cavity water, sampling issues along the alchemical stratification, and the need for highly overlapping molecular fingerprints.

NE‐RDFE: A protocol and toolkit for computing relative dissociation free energies with GROMACS between dissimilar molecules using bidirectional nonequilibrium dual topology schemes

“…The RDFE is recovered from the forward and reverse work distribution exploiting the Crooks theorem 32 and the Bennett acceptance ratio 4,33 . The dissipation (defined as the difference between the mean NE work and the underlying free energy, and affecting accuracy and precision in NE‐RDFE calculations) is significantly tamed as the ghost molecule (or most of it) is let grow (i.e., its interaction with the environment is alchemically switched on) in the cavity that is occupied by decoupling partner, using a weak harmonic restraint between the centers of mass of the two ligands, with no effects on the resulting RDFE as rigorously proved in Reference 31.…”

“…The theory of bidirectional NE‐RDFE is described in full detail in Reference 31. Here, we provide a brief summary of how the method works.…”

“…Also note that k of the order of a few kcal/molÅ 2 is sufficient to set the distance between the ligands COM of order of the fraction of the Angstrom at standard temperature. While the free energy of the transmutation is independent on k, 31 the dissipation and hence accuracy and precision in a real calculation (few hundreds of NE trajectories) are not. An excessively loose restraint may let the initially ghost ligand grow far from the binding site with a high probability, whereas a too tight COM‐COM restraint can hinder the readjustment of the growing ligand in the binding pocket.…”

“…Recently, we have devised a bidirectional nonequilibrium (NE) alchemical technique affording the calculation of the RDFE between non‐congeneric chemical compounds differing in volume, chemical connectivity and net charge (NE‐RDFE) 31 . The method relies on a preliminary HREM sampling of the end‐states where the fully coupled ligand, say A, coexists with the decoupled partner, say (B), with the definition of the hot‐region involving both ligands and the host binding site.…”

“…The NE‐RDFE methodology was implemented in the ORAC code 34 and successfully applied to the SAMPL9 35 host–guest systems 31 . In this note, we describe in detail how this inherently massively parallel technique can be straightforwardly adapted to the GROMACS code 36 with no intervention on the source code.…”