Steric contributions to CO binding in heme proteins: A density functional analysis of FeCO vibrations and deformability

Non-local Density Functional Theory (DFT) is applied to the calculation of geometry and vibrational frequencies of Fe^II(porphine)(imidazole)(CO), a model for CO adducts of heme proteins. Bond distances and angles are in agreement with crystallographic data, and frequencies are correctly calculated for C-O and Fe-C stretching and for Fe-C-O bending. This last mode is actually the out-of-phase combination of Fe-C-O bending and Fe-C tilting coordinates, which are heavily mixed because of a large bend-tilt interaction force constant. The in-phase combination is predicted at a very low frequency, 73 cm^-1, and to have a low infrared intensity; attempts to detect it in far-IR spectra via ¹³C¹⁸O isotope sensitivity have been unsuccessful. The stretch-bend interaction lowers the energy required for FeCO distortion. A soft potential may account for the wide range of crystallographically determined Fe-C-O displacements and orientations in myoglobin (Mb). The minimum energy path for displacement of the O atom from the heme normal was calculated by relaxing the structure while constraining only the O atom displacement from the heme normal. Energies of 0.2 to 3.5 kcal mol^-1 are required for the range of reported displacement, 0.3-1.3 Å. However, vibrational spectroscopy limits the allowable displacement to the low end of this range. The O atom displacement is computed via DFT to be 0.6 Å for a 7° angle of the C-O stretching IR dipole relative to the heme normal, the maximum value compatible with IR polarization measurements on MbCO. FeCO distortion is predicted to diminish both ν_CO and ν_FeC, thereby producing deviations from the well-established backbonding correlation; the scatter of the data permits a maximum displacement of 0.5 Å. This displacement would cost about 1.6 kcal mol^-1 of steric energy. A small distortion energy is consistent with the CO affinity changes produced by mutations of the distal histidine residue in Mb. Taking the leucine mutant as reference, we estimate the 1.6 kcal mol^-1 affinity loss in the wild-type protein to be the resultant of a 0.0-1.6 kcal steric inhibition, a 0.5 kcal mol^-1 attraction of the distal histidine sidechain for the bound CO [weak H-bond], and a 0.5-2.1 kcal mol^-1 attraction of the same side-chain for a water molecule in the deoxy protein. The observed 2.3 kcal mol^-1 O₂ affinity increase in the wild-type protein relative to the leucine mutant then implies a 2.8-4.4 kcal mol^-1 attraction of the histidine sidechain for bound O₂, consistent with a substantial H-bond interaction with the distal histidine. Thus steric inhibition can account for only a minor fraction of the discrimination factor against CO and in favor of O₂ which is produced by the heme-myoglobin interaction.