An Open Source Graph-Based Weighted Cycle Closure Method for Relative Binding Free Energy Calculations

Free energy perturbation-relative binding free energy (FEP-RBFE) prediction has shown its reliability and accuracy in the prediction of protein-ligand binding affinities, which plays a fundamental role in structure-based drug design. In FEP-RBFE predictions, the calculation of each mutation path is associated with a statistical error, and cycle closure (cc) has proven to be an effective method in improving the calculation accuracy by correcting the hysteresis (summation of errors) of each closed cycle to the theoretical value 0. However, a primary hypothesis was made in the current cycle closure method that the hysteresis is evenly distributed to all paths, which is unlikely to be true in practice and may limit the further improvement of the calculation accuracy when better error estimation methods are available. Moreover, being a closed source software makes the current cycle closure method unachievable in many studies. In this paper, a newly implemented open source graph-based weighted cycle closure (wcc) algorithm was developed and introduced, not only including functions from the original cc method but also containing a new wcc method which can consider different error contributions from different paths and further improve the calculation accuracy. The wcc program also provides a new path-independent molecular error calculation method, which can be quite useful in many studies (like structure-activity relationship (SAR)) compared with the path-dependent method of the original cc program.