Symmetry-Adapted Restraints for Binding Free Energy Calculations br

Binding free energy calculations rely critically on aprecise definition of the bound state and well-designed ligandrestraints to ensure that binding free energy calculations convergerapidly and yield estimates of well-defined thermodynamicquantities. The distance-to-bound-configuration (DBC) is a singlevariable that can precisely delineate the bound state of a ligandincluding translational, rotational and conformational degrees offreedom and has been successfully used to capture binding modeswith complex geometries. DBC is defined as the root-mean-squaredeviation (RMSD) of ligand coordinates in the frame of reference ofthe binding site. In the special case where the ligand featuressymmetry-equivalent atoms, a standard RMSD arbitrarily distin-guishes equivalent poses, mixing equivalent and nonequivalentdegrees of freedom, and preventing the precise delineation of the bound state ensemble, which negates the benefits of defining aflat-bottom binding restraint. To remedy this, we introduce a symmetry-adapted DBC coordinate where the RMSD is minimized overpermutations of equivalent ligand atoms. This coordinate is implemented in a portable software library, the Collective VariablesModule. We tested the approach by computing the absolute binding free energy of benzene to the engineered site of a mutantlysozyme (L99A/M102H) using alchemical free energy perturbation. We found that the symmetry-adapted restraint leads to well-behaved convergence of both the decoupling free energy in the binding site and the restrained free energy in the gas phase,recovering the affinity computed using a classic center-of-mass restraint. Thus, symmetry-adapted DBC seamlessly generalizes thebenefits of DBC restraints to the case of symmetric ligands. The underlying symmetric RMSD coordinate can also be used foranalyzing or biasing simulations in other contexts than affinity predictions.