Fox, Stephen J.
(2012)
Protein-ligand binding affinities from large-scale quantum mechanical simulations.
*University of Southampton, Chemistry, Doctoral Thesis*, 255pp.

## Abstract

The accurate prediction of protein-drug binding affinities is a major aim of computational drug optimisation and development. A quantitative measure of binding affinity is provided by the free energy of binding, and such calculations typically require extensive configurational sampling of entities such as proteins with thousands of atoms. Current binding free energy methods use force fields to perform the configurational sampling and to compute interaction energies. Due to the empirical nature of force fields and the neglect of electrons, electron polarisation and charge transfer are not accounted for explicitly. This can limit the accuracy with which interactions are calculated and consequently the free energies obtained. Ideally ab initio quantum chemistry approaches should be used as these explicitly include the electrons. However, conventional ab initio approaches are not suitable due to their prohibitively high computational cost and unfavourable scaling.

In this thesis we use large-scale ab initio quantum chemistry calculations within the Density Functional Theory (DFT) method to address the above mentioned limitations of force fields. To obtain quantitative results with ab initio approaches it is important to converge the calculations with the size of the basis set. For this reason we have used the ONETEP program, which is capable of linear-scaling DFT with near-complete basis set accuracy.

A well known binding free energy approach is the Molecular Mechanics Poisson-Boltzmann Surface Area (MM-PBSA), which obtains free energies from evaluation of the energy of configurations in an implicit solvent model. We present the first application of a “QM-PBSA” approach to a protein-ligand system containing over 2600 atoms. In this QM-PBSA approach the energies of the configurations in vacuum are evaluated with ONETEP. The solvation energies were also obtained with ONETEP using a minimal parameter implicit solvent model within the self-consistent calculation. Large-scale DFT calculations were also applied within a more theoretically rigorous free energy approach which can, in principle, obtain the full entropic contributions to free energy change. The method performs a mutation from a molecular mechanical (MM) description to an quantum mechanical (QM) description of a system. As a result a QM correction is added to the relative binding free energy obtained from a thermodynamic integration calculation within the MM description.

This approach was combined with an electrostatic embedding model within ONETEP and used to calculate the hydration energies of small molecules. As well as the computation of more accurate energies, large-scale DFT calculation compute the electron density of the entire system. Using electron density analysis approaches, such as the Hirshfeld density analysis, in combination with energy decomposition approaches, such as a second order perturbation estimate of natural bond orbital interactions, both qualitative and quantitative understandings can be gained into the contributions of particular chemical functional groups that define protein-ligand interactions. These two approaches where applied to study complexes of the Phosphodiesterase type 5 protein and used to rank ligand binding affinities that agree well with then experimentally observed trends.

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