Retinal vibrations in bacteriorhodopsin are mechanically harmonic but electronically anharmonic: evidence from overtone and combination bands

Vibrations of the chromophore in the membrane protein bacteriorhodopsin (BR), a protonated Schiff base retinal, have been studied for decades, both by resonance Raman and by infrared (IR) difference spectroscopy. In spite the light-induced IR difference spectrum between the K intermediate (13-cis retinal) and the initial BR state (all-trans retinal) being first published almost 40 years ago, we present here unreported bands in the 2500 to 1800 cm-1 region. We show that the bands between 2500 and 2300 cm-1 originate from overtone and combination transitions of retinal C-C stretches. We assigned some of the newly reported bands below 2300 cm-1 to the combination of retinal C-C stretches with methyl rocks and with hydrogen-out-of-plane vibrations. Remarkably, experimental C-C overtone bands appeared at roughly twice the wavenumber of their fundamentals, with anharmonic mechanical constants [≤] 3.5 cm-1, and in some cases of [~]1 cm-1. Comparison of combination and fundamental bands indicates that most of the mechanical coupling constants are also very small. Despite the mechanical quasi-harmonicity of the C-C stretches, the area of their overtone bands was only [~]50 to [~]100 times smaller than of their fundamental bands. We concluded that electronic anharmonicity, the second mechanism giving intensity to overtone bands, must be particularly high for the retinal C-C stretches. We corroborated the assignments of negative bands in the K-BR difference spectrum by ab initio anharmonic spectral calculations of all-trans retinal in BR, which also reproduced reasonably well the small experimental anharmonic and coupling mechanical constants. Yet, and in spite accounting for both mechanical and electronic anharmonicities, the intensity of overtone C-C transitions was underestimated by a factor of 4 to 20, indicating room for improvement in state-of-the-art anharmonic vibrational calculations.