Protein dynamics. Vibrational coupling, spectral broadening mechanisms, and anharmonicity effects in carbonmonoxy heme proteins studied by the temperature dependence of the Soret band lineshape.

In this work we study the temperature dependence of the Soret band lineshape of the carbonmonoxy derivatives of sperm whale myoglobin, human hemoglobin, and its isolated alpha and beta subunits. To fit the observed spectral profile we use an analytic expression derived for a system whereby a single electronic transition is coupled to Franck-Condon active vibrational modes, within the adiabatic and harmonic approximation. The vibronic structure of the spectra arises from the coupling with high frequency modes; these modes contribute to the total line shape through a series of Lorentzians with peak positions at vibrational overtones and half width related to the time constant of the population decay of the excited electronic state (homogeneous broadening); moreover, the coupling with low frequency modes broadens each Lorentzian to a Voigtian. Inhomogeneous broadening is modeled as a gaussian distribution of the 0-0 transition frequencies and is therefore added as a constant term to the previous gaussian width. This spectral deconvolution enables us to investigate the different contributions to line broadening and the parameters that characterize the vibrational coupling, as well as their dependence upon protein and solvent composition. The investigation is carried out as a function of temperature in the range 20-300 K; relevant information is obtained by comparing experimental results with theoretical predictions. This work supports a description of the investigated proteins as heterogeneous systems, whose heterogeneity depends on the particular protein and on the composition of the external matrix. The delocalized pi electron cloud of the porphyrin ring is coupled not only to the high frequency vibrational modes of the active site but also to a "bath" of lower frequency modes that involve the entire protein; moreover at suitable temperatures (approximately 200 K), anharmonic motions, which are an obvious prerequisite for the jumping among different conformational substates, become evident.