Role of isomerization barriers in the pK_a control of the retinal schiff base: A density functional study

The barriers to the rotation of all conventional single and double bonds have been calculated in a model Schiff base which is structurally very close to the retinal Schiff base chromophore in bacteriorhodopsin (bR). The calculated values for the torsional barriers can be used, therefore, to estimate the corresponding values in the retinal Schiff base structure. The torsional barriers are calculated as the energy differences between the all-trans and 90°-rotated conformers, respectively, for optimized structures in both neutral and protonated species. To study the effect of the isomerization on the pK_a of the Schiff base, for each 90°-rotated conformer the gas-phase proton affinity of the system has also been calculated and compared with the proton affinity of the all-trans conformer. The results clearly show that protonation of the nitrogen in the Schiff base group has a profound effect on the barriers to the rotation around different bonds in the system. For 90°-twisted species, completely different mesomeric structures are predicted for single or double bond rotations as well as for the protonated and the neutral species. The C=N double bond and the double bond next to the Schiff base group in the protonated Schiff base (corresponding to the C₁₃=C₁₄ bond of the retinal Schiff base in the bR which is assumed to rotate during the photoisomerization) have the lowest isomerization barriers among the double bonds. In the neutral species, however, high barriers to these rotations are predicted. The proton affinity of the system decreases upon the isomerization around the single bonds, while the rotation around the double bonds significantly increases the calculated values for the proton affinities. This may be considered as one of the possible mechanisms by which the protein environment controls the pK_a of the retinal Schiff base chromophore. The predicted low barrier to the C₁₃=C₁₄ double bond rotation is needed for the ground-state isomerization of the chromophore in the last step of the bR photocycle and also in the dark adaptation of the pigment. Protonation of the retinal Schiff base chromophore, therefore, seems to be a prerequisite for these ground-state isomerization events in bR.