"Gibbs Sampler Based λ-dynamics utilizing a Rao-Blackwell Estimator for Alchemical Free Energy Calculation"
Free energy calculations are fundamental for understanding many important chemical and biophysical processes, such as protein conformational changes, protein-protein interactions and protein-ligand binding. Calculating protein-ligand binding free energy is of particular interest as it has important applications in drug discovery. With decades of theoretical methodology development and computational hardware improvement, protein-ligand binding free energy calculations have started to play an essential role in accelerating modern drug discovery.
One of the methodologies for calculating protein-ligand binding free energy is called λ-dynamics, which is a generalized ensemble method and has the ability to calculate relative binding free energies for multiple ligands simultaneously in a single simulation. In λ-dynamics, a cutoff based empirical estimator was originally used to estimate the free energies. In our recent work, we developed a novel formulation of λ-dynamics called Gibbs Sampler based λ-dynamics (GSLD) and a new free energy estimator called Rao-Blackwell estimator (RBE) for use in conjunction with GSLD. Compared with the original λ-dynamics, GSLD is more flexible and easier to implement, and retains the capacity to calculate free energies for multiple ligands simultaneously in a single simulation. Compared with the empirical estimator, RBE has two advantages: (1) RBE is an unbiased estimator that does not depend on ad hoc cutoff values that are used in the empirical estimators; (2) RBE usually has smaller variance than the empirical estimators. In addition, we show that RBE is a continuous generalization of the multistage Bennett acceptance ratio (MBAR) method or the unbinned weighted histogram analysis method (UWHAM), which are widely used free energy estimation methods. Thus, our recent work both improves the computational framework for free energy calculations in drug discovery, and elsewhere, and provides a formal link between currents method of processing the data from such calculations and the general formalism of the Rao-Blackwell Estimator.