Hiroko Kakitani

ON THE MECHANISM OF WAVELENGTH REGULATION IN VISUAL PIGMENTS

Abstract— The contributions of different factors that might be responsible for the 500 nm absorption maximum of bovine rhodopsin are evaluated in detail. These include: (1) electrostatic interactions between the chromophore and a charged amino acid on the apoprotein; (2) exciton interactions with aromatic amino acids; (3) twisting about single bonds which have considerable double bond character; (4) weak interactions between the Schiff base and a putative counter‐ion. Analysis of these mechanisms in terms of theoretical and experimental results suggests that(2–4) are all capable of contributing to the protein induced spectral shifts. However, the “external point charge” model proposed previously, i.e. mechanism (1), appears to provide the crucial interaction. In this paper, the theoretical basis for this model is discussed in detail. The model is briefly evaluated in light of the amino‐acid sequence of bovine rhodopsin and possible implications for other visual pigments are considered.

Molecular Mechanism for the Initial Process of Visual Excitation. I. Model of Photoisomerization in Rhodopsin and Its Theoretical Basis by a Quantum Mechanical Calculation of Adiabatic Potential

A model for explaining the photoisomerization of the chromophore in rhodopsin molecule with a high quantum yield is proposed on the basis of the strain effect. Necessary conditions assumed in the model are shown to be satisfied by the calculation using a self-consistent HMO theory which is recently developed by one of the authors. It is also shown that when a double-bond is twisted by about 40°, a steep change occurs in the molecular geometry, and that calculated adiabatic potentials, absorption wavelengths and transition dipole moments show some anomalies, corresponding to the change. Calculated energy barriers for isomerization around single-bonds of Schiff-bases of retinal in the ground state are very small.

Molecular Mechanism for the Initial Process of Visual Excitation. : II. Theoretical Analysis of Optical Activity in Rhodopsin and Bathorhodopsin

The circular dichroism spectra in rhodopsin and bathorhodopsin are theoretically analysed in terms of intrinsic optical activity of the retinal chromophore according to a torsion model proposed in paper I. The self-consistent HMO method is used to treat the π-electron system of the chromophore. From the analysis of the α- and β-bands of optical absorption and circular dichroism spectra, the plausible conformation of the chromophore is predicted as follows. In rho-dopsin, 6s- cis , 11- cis protonated retinal Schiff-base 12s- trans form and the bonds 6C-7C, 11C-12C and 12C-13C are twisted in -, + and - directions, respectively, when torsional angles θs are measured clockwise from planar cis conformation. Although we cannot determine the values of θs definitely, the ranges of them are θ 6-7 =-40^°∼-120^°, θ 11-12 =30^°∼40^° and θ 12-13 =-130^°∼-150^°. In bathorhodopsin, the bond 11C-12C is isomerized to a trans form by the rotation of about 100∼120 around it in the plus direction.

Resonance Raman studies of bacteriorhodopsin analogues.

Abstract— We present the results of resonance Raman measurements on a series of bacteriorhodopsin (bR) analogues formed from synthetic retinals which have replaced the native chromophore in the active site. Specifically, 5,6‐dihydro‐bR, 13‐desmethyl‐bR, 10‐methyl‐bR, 14‐methyl‐bR, and 10.14‐dimethyl‐bR have been studied. All five analogues bind and form Schiff base retinal‐apoprotein linkages. While the Schiff base linkages of 5,6‐dihydro‐bR, 13‐desmethyl‐bR, and 10‐methyl‐bR are protonated, like the native chromophore, the 14‐methyl‐bR, and 10,14‐dimethyl‐bR Schiff bases are unprotonated. These results suggest that the binding site of bacteriorhodopsin near the Schiff base moiety is different from that of rhodopsin. The protonated Schiff base ‐C=NH‐ stretching frequency of 5.6‐dihydro‐bR lies at 1660 cm‐1 which is unusually high for a bacteriorhodopsin based pigment. The downward shift upon deuteration is 16 cm‐1, essentially identical to that measured for bacteriorhodopsin. This and the other analogue results strongly reinforce our previous arguments that the Schiff base stretching frequency is determined in large part by two factors, the C=N force constant and the stretch interaction with C=N‐H bend. On the other hand, the deuterium isotope effect is determined primarily by the stretch‐bend interaction.

Self-Consistent HMO Theory for the Excited State of Conjugated Molecules –Molecular Geometry, Molecular Vibration and Optical Spectra–

The self-consistent HMO theory is applied to the excited state of conjugated molecules with a small modification of an electron-electron correlation term. The calculated wavelengths of the fluorescence are considerably in good agreement with the experimental values except for some carotenoids. It is found that the Stokes shift is almost constant among aromatic molecules and among carotenoids. The origin of this property is qualitatively discussed. A simple method for the calculation of optical spectral curves of large conjugated molecules is proposed. Applying it to all-trans β-carotene, we find that the calculated absorption curves are in good agreement with the experimental data and are appreciably different from mirror images of the calculated fluorescence curves. The vibrational frequencies and the normal coordinates of the molecular vibration are considerably different between the ground and the excited states in many modes.

Theoretical Analysis of Resonance Raman Spectra of Rhodopsin and Isorhodopsin

Resonance Raman (RR) Spectra of rhodopsin and isorhodopsin are theoretically analyzed and compared with those of free protonated retinylidene Schiff bases (PRSB). We used the multibond twisted chromophore conformations of rhodopsin and isorhodopsin which were previously obtained through the optical spectral analysis. The calculated frequencies and relative intensities of RR spectra of rhodopsin and isorhodopsin are almost similar to those for the corresponding free PRSBs. Furthermore the correlation between the frequencies νs of normal modes and the maximum wavelength of the absorption λ is analyzed for the following three cases; a) torsion around a double bond, b) a counter-anion near N atom and c) an anion near C5 atom. As a result, the experimental fact that νs of C=C stretchings decrease considerably as λ increases and those of C–C stretchings increase is best reproduced in case a). The frequency of C=N + H stretching shows drastic decrease in case b), but moderate decrease in cases a) and c) with ...

Theoretical Studies of Photoisomerization in Visual Pigments. I. Formulation

General formulas for the non-radiative transition rate by the non-adiabatic multiphonon relaxation mechanism were obtained for the purpose of calculating the photoisomerization rate in visual system. A feasible method for calculating the electronic matrix element was also proposed. We could show that the thermal equilibrium was attained in the excited state before the non-radiative transition occurs in rhodopsin. So, the above theory must be useful for the investigation of the molecular mechanism which enables to explain the very specific photochemistry of visual pigments. Numerical calculations are presented in the succeeding paper.

Mechanism of Photoconversion among Rhodopsin, Bathorhodopsin and Isorhodopsin

Oseroff and Callenders experimental data of laser photolysis of rhodopsin at low temperature are analyzed in terms of a photoreaction scheme with two common states. Branch probabilities involved in the scheme are also estimated using the quantum yields evaluated by Strackee.

Theoretical Studies of Photoisomerization in Visual Pigments. II. Numerical Calculation

A general theory of the non-adiabatic multiphonon relaxation rate, which was developed in the preceding paper, was applied to the photoisomerization of visual pigments. We estimated the free energy relation among rhodopsin, bathorhodopsin, common state and transition state of thermal isomerization. We calculated microscopic parameters such as a displacement of the normal coordinate due to the transition and electronic coupling matrix element. We investigated how the non-radiative transition rate varies with the free energy gap. We analyzed molecular mechanisms which made photoisomerization of visual pigments very rapid compared with that of other organic molecules. It was clarified that the matching condition which corresponds to the maximum Franck-Condon overlap is almost satisfied in visual systems and it is the main reason for the very rapid non-radiative transition.

Difference between Frequencies of Optical Absorption and Circular Dichroism Maxima : One Mode Approximation

Theoretical analysis is made for the electron-vibration interaction effects on frequencies ν max A and ν max C D of optical absorption and circular dichroism maxima. Simple formulae of the frequency difference ν max C D - ν max A are obtained in terms of electron-vibration interaction parameters for the case that one specific vibrational mode is important. Application of the theory is made for visual pigments.