Enhancing MM/P(G)BSA Methods: Integration of Formulaic Entropy for Improved Binding Free Energy Calculations

Balancing computational efficiency and precision, MM/P(G)BSA methods have been widely employed in the estimation of binding free energies within biological systems. However, the entropy contribution to the binding free energy is often neglected in MM/P(G)BSA calculations, due to the computational cost of conventional methods such as normal mode analysis (NMA). In this work, the entropy effect using a formulaic entropy can be computed from one single structure according to variations in the polar and non-polar solvents accessible surface areas and the count of rotatable bonds in ligands. It was incorporated into MM/P(G)BSA methods to enhance their performance. Extensive benchmarking reveals that the integration of formulaic entropy systematically elevates the performance of both MM/PBSA and MM/GBSA without incurring additional computational expenses. In addition, we found the inclusion of dispersion can deteriorate the correlation performance (R_p) but reduce the root mean square error (RMSE) of both MM/PBSA and MM/GBSA. Notably, MM/PBSA_S, including the formulaic entropy but excluding the dispersion, surpasses all other MM/P(G)BSA methods across a spectrum of datasets. Our investigation furnishes a valuable and practical MM/P(G)BSA method, optimizing binding free energy calculations for a variety of biological systems.