Mimicking photoinduced processes in bR is not a trivial task since the resulting outcome is sensitive to the amount of the protein environment, which has to be taken into account for calculations. For this purpose, Molecular Dynamics (MD) simulations have been intensively used previously [4, 27-37]. Indeed, the rotation of the Schiff base as a result of the retinal isomerization can be obtained by modeling the retinal with its protein environment [34, 35]. However, in order to achieve it, many strong approximations should be used due to the lack of computational resources. One very crucial approximation suggests that the retinal structure can be subdivided into Quantum Mechanics (QM) and Molecular Mechanics (MM) segments, and the division between them is set across covalent bonds. The different QM/MM simulations have different approximations used for the description of MM and its connections to the QM. The QM−MM boundary major problem is the treatment of covalent bonding and adaptative schemes [4, 33, 37] Hayashi, et al., [34, 35] exploited only a part of retinal structure using the QM approach, while the other part of the molecule was parametrized. The full retinal in QM simulations is complicated by not demonstrating rotations as expected from experimental data [36, 37]. The later studies showed that the SB bound to retinal does not rotate in the vacuum models but instead, only the β-ring is rotating in the excited state [38, 39]. Starting from the excited state, structure optimization of the ground state headed back to the initially optimized ground state structure, which implies that the minima of the ground- and excited-state potential energy surfaces are not separated by any significant energy barrier .
In the vicinity of the local minimum of the S1 state, the retinal coupled to the SB remains almost planar, but the single and double bonds turn to become inverted according to the MD simulations and ab initio modeling [29, 30, 32, 37, 40]. As follows from these data, the existence of a small barrier between trans and cis structures in the excited states could partially explain the fluorescence effects related to the structural evolution of retinal bound to the protonated SB in bR . Our studies of the retinal-type conjugated systems indicate similar results: the S1 excited state demonstrates an inversion between single and double bonds, which should be caused by the presence of the S2 (also called 11Bu+) excited state properties, known for polyene and carotenoid molecules . According to our EOM-CCSD data, the lowest excited state of the retinal bound to the protonated SB is of a similar origin to that of the polyene type 11Bu+ state, while the excited state of the retinal bound to the non-protonated SB of the same origin (as in the polyene type 11Bu+ state) was above the excited state of the optically forbidden state 11Ag¯, which can be predicted only by taking into account the electron correlations. The EOM-CCSD is computationally expensive and the excited state energies are largely overestimated. Thus, the lowest S1 state of the deprotonated SB should be of the 11Ag¯ symmetry for the polyene while the lowest S1 state of the protonated SB should be of the 11Bu+ symmetry. On the other hand, the retinal energy surfaces should be more complicated if we join our studies of the retinal isomerization and possible flexibility of helices. There we would expect some additional energy transfer mechanisms which fix the retinal 13-cis,15-syn and 13-cis,15-anti configurations, and finally pass the absorbed light energy from the retinal into the helices.
Deprotonation of the SB initiates the first proton transfer step in bR . Protonation of Asp-85 upon deprotonation of the SB together with the all-trans to 13-cis photoisomerized retinal is followed by the release of a proton from a location within a network of protein residues and bound water [43-48] to the extracellular membrane surface. As follows from studies based on theoretical calculations, there should be various possible pathways for retinal deprotonation in the ground state what at moderate approximations agrees with the experimental data [40, 49]. The possibility to understand the detailed mechanism of proton pumping across the bR membrane as a result of the photoexcitation of the retinal chromophore is the aim of our consideration. The retinal deprotonation in the excited state would be the simplest model for explaining the irreversible mechanism without the requirement for the retinal 13-cis,15-syn isomer to exist in the ground state (Figure 2). Here we show possible energetic surfaces of the proton transfer from SB to ASP85 group which could open the proton transfer pathway, if the retinal 13-cis,15-syn isomer would be stable in the ground state.
4.2. Modeling of retinal isomerization
According to crystallographic data (PDB ID: 2NTW ), the photoisomerized 13-cis retinal in L is twisted at the C13 = C14 and C15 = N16 double-bonds resulting in the formation of retinal 13-cis,15-syn isomer. The protonated SB is connected to the proton acceptor Asp-85 via the water (W402) molecule. In the vicinity of the active center involved in the photoinduced proton transfer, additional water molecules, W401 and W406, are also present. The retinal is surrounded by the protein residuals TRP86, TRP182, and TYR185. In modeling, the all-trans retinal was taken from crystallographic data (PDB ID:1C3W). For QM calculations, the DFT modelling approach was performed in terms of Gaussian  by using HSEH1PBE and B3LYP functionals with cc-pVDZ basis set. The used HSEH1PBE and CAM-B3LYP functionals involve the long-range corrections. According to our study, the HSEH1PBE functional did not affect the results comparing with that of B3LYP functional. The CAM-B3LYP functional resulted in the β-ring rotation when all-trans retinal was optimized in the excited state what is out of the scope of this paper study.
It follows that the trans-retinal (corresponding to the ground state) had only one global minimum in the rotational pathway while optimization of the structure in the excited state showed two possible minima (Figure 3A). One of these minima is at about -92°, which correlates with the structure defined by the crystallographic data 2NTW. Moreover, the ground state in this configuration was also reorganized what suggested a conical intersection between these two states. The retinal 13-cis,15-syn isomer existed in the excited state only when TRP86, TRP182, and TYR185 structures defined according to crystallographic data were taken into account (Figure 3B). However, the optimization procedure in the ground state always resulted in the configuration of the trans-retinal. The same results were also obtained from QM/MM or QM/QM (ONIOM) studies by adding TRP86, TRP182, and TYR185 structures or even more structural data into the calculation scheme using molecular mechanics UFF or semiempirical PM6. Thus, minima corresponding to the excited states of the retinal 13-cis,15-syn isomer are available by using the supermolecular approach containing retinal and TRP86, TRP182, and TYR185 residuals in accord to the earlier suggestion . However, this was obtained for the case of the ground state, while our calculations support this conclusion for the excited state minima (Figure 3). Evidently, additional important effects should be taken into account to obtain minima of retinal 13-cis,15-syn isomer in the ground state. Thus, we fixed retinal 13-cis,15-syn isomer (Figure 4) in order to mimic the active center caused by the protein.
4.3. Modelling of the Initial Step of Proton Transfer
Part of the structures taken from the crystallographic data as shown in Figure 2 and Figure 4 was analyzed in terms of the QM calculations. The first step of the proton transfer is caused by the photoexcitation of the SB with its subsequent rotation towards the active canter where the water molecule, which can meditate the Asp-85 structure, is positioned as shown in Figure 4. We did the QM studies of the part of this structure; the results are presented in Figure 5. Initial trans-retinal (0°) should change into the 13-cis structure (-92.4°) after the light-induced transition into optically allowed excited S1 state.
To model the initial stage of the proton transfer, let us keep the key atoms taken from the crystallography data (with retinal in the13-cis-configuration, PDB ID: 2NTW ) fixed. In order to mimic the protein environment, the ASP85 and water molecules (except W402) were also kept in fixed positions (Figure 4). The modeling data demonstrate the proton displacement from W402 to the Asp-85 group (Figure 5A) what opens the pathway of the proton transfer from the SB to W402 (Figure 5B).
Thus, the presence of the water molecules of W401 and W406 is crucial for the proton transfer from W402 to Asp-85 group (Figure 5A). These molecules make an essential influence on the energy surfaces meaning that they open the protonation pathways which could be controlled by the protein of bR. This could explain the subsequent pathway of the protonation of Asp-85 by the SB in the L→M stage of the photoreaction of bR.