QM and QM/MM studies of ligand binding to myoglobin and haemoglobin
Strickland, Nikola Elisabeth #
Myoglobin (Mb) and haemoglobin (Hb) are haem proteins that are fundamental to the life of aerobic organisms. The main function of Mb is to store oxygen in the muscles and the main function of Hb is to transport oxygen in the blood. They carry out their functions by reversibly binding molecular oxygen to an iron atom at the centre of their haem groups. Other small ligands, such as CO and NO, can also bind reversibly to the haem group. Both haem proteins are used as models for understanding the relationship between protein structure, function and dynamics. At present there is some ambiguity about how Mb and Hb influence the ligand binding properties of their haem groups.
Before using quantum mechanical (QM) or hybrid quantum mechanical/molecular mechanical (QM/MM) methods to investigated the ligand binding properties of the haem group we first tried to gain a better understanding about how accurately density functional theory (DFT) predicts properties of haem molecules. We calibrated DFT bond dissociation energies (BDEs) and relative energies of different spin-states against highly accurate coupled cluster (CC) values, for two small haem compounds. We also assessed the accuracy of DFT optimised geometries for larger haem models by structural comparison against similar crystal structures.
We then carried out DFT calculations in order to better characterise the intrinsic potential energy surfaces (PESs) of the reactions of CO, NO and H2O with a gas-phase haem group. The spin-state of the iron atom changes upon association or dissociation of these ligands and this may introduce energy barriers into the reaction. We used a previously developed algorithm to directly calculate the minimum energy where the system crosses from the PES corresponding to one spin-state changes to a PES corresponding to another spin-state (and hence the value of any energy barrier during the course of the reaction). These model reaction PESs and their minimum energy crossing points may one day be compared to the PESs for the same reactions in Mb or Hb. In this thesis the impact of the protein environment on the ligand binding properties of the haem group was evaluated by comparison of the Fe-CO and Fe-O2 BDEs in the gas-phase haem groups to those in the proteins.
Fe-L BDEs were calculated in Mb and Hb using a quantum mechanical/molecular mechanical (QM/MM) method. For Mb the Fe-CO and Fe-O2 BDEs were predicted for 22 conformations of the protein, which were generated using molecular dynamics (MD) simulations. For Hb the key Fe-O2 BDEs were calculated for structures based on the two main quaternary states of the protein. For both proteins we calculated the amount that the protein stabilised or destabilised ligand binding by comparing the protein Fe-L BDEs to those calculated for the gas-phase models. The various structural and electronic causes of this discrimination were also analysed. For carbonmonoxy-Mb and oxy-Mb we also attempted to gain a better understanding about the relationship between the protein structure and function by examining the 22 conformations for any correlation between structural parameters and the BDEs. Finally the sensitivity of our QM/MM BDEs were assessed, with respect the atoms assigned to the QM region and the haem parameters used in the force-field of the MD simulations.