Force fields for biomolecular simulations: from supra-molecular bio-inspired catalysts to protein- inhibitors complexes

Abstract

Over the past decades, molecular modelling and molecular dynamics (MD) simulations have become well- established disciplines, providing special tools for the study of chemical and biological processes. To perform classical MD simulations, a clear description of the connectivity and the electrostatic behaviour of the system is required. This is done with the use of Force Fields (FF), sets of parameters and functions, which allow the calculation of the potential energy of the molecular system of interest. The work in this thesis demonstrates the development of FF parameters and computational methods to model and analyse molecular systems that vary from supra-molecular host-guest complexes to protein -inhibitor systems.

The supra- molecular nano- capsule under study consists of four 3- pyridine ditopic organic ligands bridged together with two Pd2+ ions and it shows catalytic activity. Initially, parameterisation of the molecular building blocks of the system (Pd2+, host ligands, guest molecules, solvent and counter-ions) was conducted using the OPLS-AA FF and the paremeters were validated against experimental data. Then, alchemical free energy calculations were run to estimate the absolute binding free energies for a set of seven guest molecules to the host using the Sire OpenMM Molecular Dynamics (SOMD) software of the Sire MD Framework. The results were then compared with available experimental binding affinity data. The initial runs using the OPLS-AA non-polarisable FF, failed to reproduce the experimental trends. However, after modifications were introduced to the charges of the guest molecules, the calculated binding free energies managed to reproduce the experimental trends. The most striking observation to emerge from this study is the importance of the quality of the FF parameters to accurately describe a molecular system and predict its properties.

The need for an accurate description of the system under study, has pushed the scientific community into developing FFs that are system- bespoke, such as the QUBE FF, which derives parameters solely from Qunatum Mechanical (QM) calculations. The aim of my work is to modify the source code of Sire MD framework, to allow the incorporation of the QUBE FF for alchemical free energy calculations. New features, such as inclusion of the geometric combining rules and XML file parsing were incorporated using Python and C++ programming languages. The implementation was tested by calculating Hydration Free Energies (HFE) for a set of small molecules using SOMD. The results were in agreement with HFE calculated with the GROMACS MD package (MAE = 0.15 kcal/mol). Furthermore, relative binding free energy calculations were conducted, for HIV-Reverse Transcriptase (HIV-RT), and two sets of its inhibitors. Both the enzyme and the ligands were parameterised using the QUBE and the Amber FFs and the results were compared with available pEC50 data. Both FFs managed to reproduce experimental trends, however the performance of the FFs was found to depend on the molecule under study. Nonetheless, integrating the QUBE FF into the Sire MD framework provides a stable, adaptable platform with GPU-accelerated dynamics, which can significantly increase our ability to evaluate and apply customised QM-derived parameters for drug design.

To further improve the accuracy of the QUBE FF, off-center charges (virtual sites) were introduced to account for polarisability effects. Functionality in Sire was further extended to include virtual sites in MD simulations, which are also supported by the QUBE FF. The new feature of Sire was tested by calculating Single Point Energies (SPEs) and HFEs for a set of small molecules and comparing them with available experimental data. Finally, the induced myeloid leukemia cell differentiation protein (Mcl-1) and a set of its inhibitors were parameterised using the new QUBE FF that includes virtual sites. Absolute and relative binding free energy calculations were conducted and compared with results from previous studies which use the Amber FF, as well as with experimental assays. Both Amber and QUBE were found to overestimate the binding strength of the three inhibitors (MAEQUBE = 4.74 kcal/mol, MAEAmber = 4.15 kcal/mol). This discrepancy from the experimental data was attributed to the vdW interactions between the ligand and the hydrophobic binding pocket of the protein.

Analysis of the RBFE results revealed that Amber outperformed QUBE with VS inclusion (MAEQUBE = 0.91 kcal/mol, MAEAmber = 0.75 kcal/mol). However, the evidence from this study suggests that alchemical free energy calculations which model anisotropy can be conducted accurately and fast with SOMD, providing another useful tool to the scientific community for drug design purposes.