Perturbation Free-Energy Toolkit: Automated Alchemical Topology Builder and Optimized Simulation Update Scheme

Free-energy calculations play an important role in the application of computational chemistry to a range of fields, including protein biochemistry, rational drug design or material science. Importantly, the free energy difference is directly related to experimentally measurable quantities such as partition and adsorption coefficients, water activity and binding affinities. Among several techniques aimed at predicting the free-energy differences, perturbation approaches, involving alchemical transformation of one molecule into another through intermediate states, stand out as rigorous methods based on statistical mechanics. However, despite the importance of efficient and accurate free energy predictions, applicability of the perturbation approaches is still largely impeded by a number of challenges. This study aims at addressing two of them: 1) the definition of the perturbation path, i.e., alchemical changes leading to the transformation of one molecule to the other, and 2) determining the amount of sampling along the path to reach desired convergence. In particular, an automatic perturbation builder based on a graph matching algorithm is developed, that is able to identify the maximum common substructure of two molecules and provide the perturbation topologies suitable for free-energy calculations using GROMOS and GROMACS simulation packages. Moreover, it was used to calculate the changes in free energy of a set of post-translational modifications and analyze their convergence behavior. Different methods were tested, which showed that MBAR and extended thermodynamic integration (TI) in combination with MBAR show better performance as compared to BAR, extended TI with linear interpolation and plain TI. Also, a number of error estimators were explored and how they relate to the true error, estimated as the difference in free energy from an extensive set of simulation data. This analysis shows that most of the estimators provide only a qualitative agreement to the true error, with little quantitative predictive power. This notwithstanding, the preformed analyses provided insight into the convergence of free-energy calculations, which allowed for development of an iterative update scheme for perturbation simulations that aims at minimizing the simulation time to reach the convergence, i.e., optimizing the efficiency. Importantly, this toolkit is made available online as an open-source python package (https://github.com/drazen-petrov/SMArt).