Comparison of thermodynamic integration and Bennett's acceptance ratio for calculating relative protein-ligand binding free energies

The performances of Bennett's acceptance ratio method and thermodynamic integration (TI) for the calculation of free energy differences in protein simulations are compared. For the latter, the standard trapezoidal rule, Simpson's rule, and Clenshaw-Curtis integration are used as numerical integration methods. We evaluate the influence of the number and definition of intermediate states on the precision, accuracy, and efficiency of the free energy calculations. Our results show that non-equidistantly spaced intermediate states are in some cases beneficial for the TI methods. Using several combinations of softness parameters and the power dependence, it is shown that these benefits are strongly dependent on the shape of the integrand. Although TI is more user-friendly due to its simplicity, it was found that Bennett's acceptance ratio method is the more efficient method. It is also the least dependent on the choice of the intermediate states, making it more robust than TI.