Title: Towards more robust and efficient methods for the calculation of Protein-Ligand binding affinities
Description: Biological processes often depend on protein-ligand binding events, so that accurate prediction of protein-ligand binding affinities is of central importance in structural based drug design. Although many techniques exist for calculating protein-ligand binding affinities, ranging from techniques that should be accurate in principle, such as free energy perturbation (FEP) theory, to relatively simple approximations based on empirically derived scoring functions, the counterbalancing demands of speed and accuracy have left us with no completely satisfactory solution thus far. This thesis will be focused on the methodology development towards more robust and reliable Protein-Ligand binding affinity calculation. In Part I, we will present the WaterMap method, which will bridge the gap between the efficiency of empirical scoring functions and the accuracy of rigorous FEP methods. Unlike most other methods with the main focus on the direct interaction between the protein and the ligand, the WaterMap method we developed considers the explicit driving force from the solvent, in which several individual water molecules in the binding pocket play an active role in the binding process.

We demonstrate that protein may adopt active site geometries that will destabilize the water molecules in the binding pocket through hydrophobic enclosure and/or correlated hydrogen bonds, and displacement of these water molecules by ligand groups complementary to protein surface will provide the driving force for ligand binding. In some extreme cases, the interactions are so unfavorable for water molecules that a void is formed in the binding pocket of protein. Our method also considers the contribution from occupation of ligand atoms in the dry regions of binding pocket, which in some cases provides the driving force for ligand binding. FEP provides an in-principle rigorous method to calculate protein-ligand binding affinities within the limitations of the potential energy model and it may have a potentially large impact on structure based drug design projects especially during late stage lead optimization when productive decisions about compound modification are made . However, converging explicit solvent simulations to the desired precision is far from trivial, especially when there are large structural reorganizations in the protein or in the ligand upon the formation of the binding complex or upon the alchemical transformation from one ligand to another.

In these cases, there can be large energy barriers separating the different conformations and the ligand or the protein may remain kinetically trapped in the starting configuration for a very long time during brute-force FEP/MD simulations. The incomplete sampling of the configuration space results in the computed binding free energies being dependent on the starting protein or ligand configurations, thus giving rise to the well known quasi-nonergodicity problem in FEP. In Part II, we will present a new protocol called FEP/REST, which combines the recently developed enhanced sampling technique REST (Replica Exchange with Solute Tempering) into normal FEP to solve the sampling problem in brute force FEP calculation. The computational cost of this method is comparable with normal FEP, and it can be very easily generalized to more complicated systems of pharmaceutical interest. We apply this method to two modifications of protein-ligand complexes which lead to significant conformational changes, the first in the protein and the second in the ligand.

The new approach is shown to facilitate sampling in these challenging cases where high free energy barriers separate the initial and final conformations, and leads to superior convergence of the free energy as demonstrated both by consistency of the results (independence from the starting conformation) and agreement with experimental binding affinity data. Part III focus on two topics towards the foundational understanding of hydrophobic interactions and electrostatic interactions. To be specific, the nonadditivity effect of hydrophobic interactions in model enclosures is studied in Chapter 9, and the competition between hydrophobic interaction and electrostatic interaction between a hydrophobe and model enclosure is studied in Chapter 10. The approximations in popular implicit solvent models, like the surface area model in hydrophobic interaction, and the quadratic dependence of electrostatic interaction on the magnitude of charge are investigated. Six of the Chapters (Chapter 2-4, Chapter 6, and Chapter 9-10) have been published and the other one (Chapter 7) has been accepted for publication and currently is in press.

Each Part begins with its own introduction. Each chapter also contains its own abstract and introduction, and focus on one specific topic. They all share the common theme, that is to develop more robust and reliable methods to calculate protein-ligand binding affinities. The conclusions and discussions about future research directions are presented in Part IV.