Gaussian accelerated Molecular Dynamics - Thermodynamic Integration (GaMD-TI): Improved alchemical free energy calculations with enhanced sampling

It is valuable to calculate alchemical free energy changes in drug discovery and development. Thermodynamics Integration (TI) has been widely used in computational chemistry for estimating free energy changes with alchemical transformations. However, TI based on usually short Molecular Dynamics (MD) simulations often suffers from insufficient conformational sampling. Here, we have integrated Gaussian accelerated MD and TI (GaMD-TI) to enhance the conformational sampling and improve accuracy of free energy calculations. GaMD-TI has been demonstrated in model systems of alchemical changes in the Valine dipeptide and mutation cycle of the Alanine Valine Isoleucine (AVI) residues. Simulations showed that when GaMD boost potentials followed near-Gaussian distribution, the free energy change could be reweighted accurately through generalized cumulant expansion to the second order. The total free energy change often exhibited faster convergence using Selective GaMD (SGaMD) than using conventional MD (cMD). Accuracy of the free energy estimates from SGaMD-TI simulations was similar to or higher than those from cMD-TI simulations, although the differences were subtle for these small model systems. Meanwhile, dihedral angles in the model systems underwent significantly more frequent conformational transitions in SGaMD than in cMD, indicating improved sampling. Future studies are planned on larger systems with more complicated alchemical changes, such as ligand binding to proteins/nucleic acids and mutations at biomolecular binding interfaces. GaMD-TI should be broadly applicable to alchemical free energy calculations and therapeutic design.