Implicit ligand theory for relative binding free energies: II. An estimator based on control variates

Implicit ligand theory describes the relationship between the noncovalent binding free energy and the binding free energy between a ligand and multiple rigid receptor conformations. We have previously shown that if the receptor conformations are sampled from or reweighed to a holo ensemble, the binding free energy relative to the ligand that defines the ensemble can be calculated. Here, we apply a variance reduction technique known as control variates to derive a new statistical estimator for the relative binding free energy. In applications to a data set of 6 reference ligands and 18 test ligands, statistically significant differences between the estimators are not observed for most systems. However, in cases where such differences are observed, the new estimator is more accurate, precise, and converges more quickly. Performance improvements are most consistent where there is a clear correlation, with a correlation coefficient greater than 0.3, between the control variate and the statistic being averaged.