Microscopic model of carbon monoxide binding to myoglobin

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Abstract
We present a microscopic model of carbon monoxide (CO) binding to myoglobin which reproduces the experimentally observed Arrhenius pre-exponential factor of 10 9 s −1 and activation enthalpy distribution centered at 12 kJ/mol. The model is based on extensive ab initio calculations of CO interacting with a model heme-imidazole group which we performed using a fully quantum mechanical Hartree–Fock/density functional theory (HF/DFT) hybrid method. We fit the HF/DFT calculated energies, obtained for over 1000 heme-CO structures with varied CO and iron positions and orientations for both high (S=2) and low (S=0) spin states, to a model potential function which includes a bonding interaction in both of the spin states, electrostatic, and anisotropic Lennard-Jones-type interactions. By combining the x-ray determined protein structure with this potential and protein-CO interactions and internal heme interaction potentials obtained from established molecular dynamics literature, we calculate the energy required for the CO to reach the spin crossing from the heme pocket. We find that the transition between the two spin states occurs when CO and iron have activation enthalpies of 8 kJ/mol and 3 kJ/mol, respectively, which are necessary to move CO towards the iron and the iron atom relative to the heme plane N pyr . At the same time we find that 1 kJ/mol is needed to move N ε of His-64 and C γ of Val-68 relative to the heme group. The requirement that these motions be synchronized reduces the Arrhenius pre-exponential by a factor of 150 from the 10 12 s −1 obtained from CO motion across the heme pocket, leaving a factor of ∼ 6 to account for CO orientation and nonadiabaticity of the electronic spin change. The observed width of the enthalpy distribution is reproduced by assuming a Gaussian distribution of the heme positions with a standard deviation of 0.2 Å. We characterize the conformational relaxation by calculating an enthalpy barrier using x-ray structures of myoglobin in both the MbCO photoproduct and deoxy conformations, and we find a small difference, ∼ 5 kJ/mol, between the two conformations.