A first-principles approach to protein–ligand interaction

Abstract: It is still impossible to make an accurate, purely theoretical prediction of the free energy of a ligand binding to a protein in aqueous environment. The two main problems are the immense number of nuclear configurations contributing to the binding free energy and the impossibility to apply accurate quantum-chemical methods to such a large system, even for a single configuration. In this thesis, the second of these problems is addressed by exploring various ways of approximating the quantum-chemical interaction energy without introducing experimental data in the models.

The use of quantum chemistry to derive parameters for advanced molecular mechanics models is explored. First, models for the repulsion term, based on either orbital overlap or electron density overlap, are compared. The latter models are found to be inaccurate for certain interactions, although they perform well on average. Second, the distributed multipoles and polarizabilities required for the electrostatic and induction terms are assessed, the result suggesting that the newly developed LoProp method is an improvement on earlier methods.

The accuracy of various approximations inherent in the polarizability model are also tested. It is found that the neglect of Pauli effects is a severe approximation, but that the polarizability model nevertheless gives reasonable results, owing to error cancellation. As a basis for future polarization models that avoid such cancellation, a quantum-chemical model is introduced, in which Pauli effects from surrounding molecules are included through a pseudopotential.

Finally, a method for protein–ligand interactions is developed, in which the protein is divided into fragments and the pair potentials between the ligand and each fragment is calculated by quantum chemistry, whereas the non-additivity is modeled by multipoles and polarizabilities. This and further approximations are tested, allowing for a full protein–ligand interaction energy to be computed at an unprecedented level of theory. The method is applied in an approximate calculation of binding free energies for a set of ligands to avidin, unfortunately giving poor results. A possible reason for this failure is the treatment of solvation.