The phonon-assisted Mössbauer effect is used to determine the partial phonon density of states of the iron within the active center of deoxymyoglobin, carboxymyoglobin, and dry and wet metmyoglobin between 40 and 300 K. Between 0 and 1 meV the iron density of states increases quadratically with the energy, as in a Debye solid. Mean sound velocities are extracted from this slope. Between 1 and 3 meV a nearly quadratic “Debye-like” increase follows due to the similar strength of intermolecular and intramolecular forces. Above 3 meV, optical vibrations are characteristic for the iron-ligand conformation. The overall mean square displacements of the heme iron atom obtained from the density of states agree well with the values of Mössbauer absorption experiments below 180 K. In the physiological temperature regime the data confirm the existence of harmonic vibrations in addition to the protein specific dynamics measured by Mössbauer absorption. In the Debye energy regime the mean square displacement of the iron is in agreement with that of the hydrogens measured by incoherent neutron scattering demonstrating the global character of these modes. At higher energies the vibration of the heavy iron atom at 33 meV in metmyoglobin is as large as that of the lightweight hydrogens at that energy. A freeze dried, rehydrated $(h=0.38\mathrm{}\mathrm{g}$ ${\mathrm{H}}_2\mathrm{O}/\mathrm{g}$ protein) metmyoglobin sample shows an excess of states above the Debye law between 1 and 3 meV, similar to neutron scattering experiments. The room temperature density of states below 3 meV exhibit an increase of the density compared to the low temperature data, which can be interpreted as mode softening.

• Received 9 July 2001

DOI:https://doi.org/10.1103/PhysRevE.65.051916