Leveraging a separation of states method for relative binding free energy calculations in systems with trapped waters

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Abstract
Methods for calculating the relative binding free energy (RBFE) between ligands to a target protein are gaining importance in the structure-based drug discovery domain, especially as methodological advances and automation improve accuracy and ease of use. In an RBFE calculation, the difference between the binding affinities of two ligands to a protein is calculated by transforming one ligand into another, in the protein-ligand complex, and in solvent. Alchemical binding free energy calculations are often used for such ligand transformations. Such calculations are not without challenges, however; for example, it can be challenging to handle interfacial waters when these play a crucial role in mediating protein-ligand binding. In some cases, the exchange of the interfacial waters with solvent water might be very infrequent in the course of typical molecular simulations, and such interfacial waters can be considered trapped on the simulation timescale. In these cases, RBFE calculation between two ligands, where one ligand binds with a trapped water while the other ligand displaces it, can result in inaccuracies if the surrounding water structure is not sampled adequately for both ligands. So far, a popular choice for treating the trapped waters in RBFE calculations is to combine free energy calculations with enhanced sampling methods that insert/delete waters in the binding site. Despite recent developments in the enhanced sampling methods, they can result in hysteresis in the RBFE estimate, depending on whether the simulations were started with or without the trapped waters. In this study, we introduce an alternative method, separation of states, to calculate the RBFE between ligand pairs where the ligands bind to the protein with different numbers/positions of trapped waters. The separation of states approach treats the sampling of the trapped waters separately from the free energy calculation of the ligand transformation. In our method, a trapped water in protein's binding site is decoupled from the system first, and the cavity created by its decoupling is stabilized. We then grow a larger ligand into this cavity-- a ligand that is known to displace the trapped water. In this study, we show that our method results in precise and accurate estimates of RBFEs for ligand pairs involving the rearrangement of trapped water via RBFE calculations for five such ligand pairs. We have optimized our simulation protocol to be suited for large distributed computational resources and have automated our RBFE calculation workflow.

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