Impact of the Protein Environment on Two-Photon Absorption Cross-Sections of Type I and Type II Retinal-Containing Proteins

The prediction and optimization of properties of retinal-containing proteins under two-photon excitation conditions is an important issue for the practical application of channelrhodopsins in optogenetics. Nonlinear two-photon absorption can also lead to photoactivation of visual rhodopsins in the IR range within 950–1000 nm. The factors that influence the two-photon absorption cross section of type I and type II retinal-containing proteins during transition to the first singlet electronically excited state are analyzed in this study with high-level quantum chemistry methods. It is shown that two channels through permanent dipole moments of the initial and final states make the main contribution to the two-photon absorption cross section during the S₀ → S₁ transition in the case of rhodopsins. A fast numerical convergence of the sum-over-states formalism provides direct evidence for the applicability of the two-level model for calculating TPA cross-sections in rhodopsins. This is due to the high transition dipole moment and significant redistribution of electron density during the S₀ → S₁ transition. An unambiguous correlation between the calculated cross section values and the difference in average dipole moments of the initial and final states makes it possible to explain the strong dependence of the cross section on the protein environment of the chromophore group in various rhodopsins (340–610 GM). It also allows us to predict the influence of the protein electrostatic field on the nonlinear photophysical properties of retinal.