MECHANISM OF PROTON TRANSFER IN BACTERIORHODOPSIN

2.1. Charge transfer

Modelling of charge transport is usually based on the assumption that the system can be effectively separated into the dynamical part and the environment. This assumption is at the heart of the Marcus theory of electron transfer with the  transfer rate given by

where |H₁₂| is the coupling between the initial and final states, λ is the total reorganization energy of the  environment, k_B is the  Boltzmann constant, T is the absolute temperature, and ΔG⁰ is the total Gibbs free energy change for the transfer reaction. It was shown that such an approach can be successfully used to describe proton transport as well [17, 18]. However, there are two caveats for a specific bR case, both of them related to the smallness of the system and the corresponding impossibility of the separation of the dynamical subsystem and its environment. First, it is very difficult to define the reorganization energy, with all the bR residues reacting to the  proton transfer events in a  rather dynamical, not statistical manner. Second, in the  calculation of the  differences of free energies between the initial and final states, the direct electrostatic interaction between the transferring proton and charges on the residues provides an essential impact on the  result. In previous works based on the energy conceptions [19, 20], these both aspects are not taken into account properly. Free energies corresponding to proton sites (based on the related pK_a factors) are usually calculated with the  electrostatic interactions considered. The rest of the system is included by calculating the  reorganization energy and non-vacuum dielectric permittivity, the  electrostatic interaction of the protons with electrons being completely ignored, in particular. Water molecules, which are shown to be crucial for the proton transfer in bR [21–23], are considered electrically neutral, non-dissolved and dipole-less. While this approach can be appropriate for large protein systems [24], its applicability for relatively small systems, such as bR, is questionable.

A proper description of the  full bR dynamics could be based on the inclusion of the influence of all helixes and residues into the  Gibbs free energy and the  consideration of various vibrational degrees of freedom as the environment. In this case, the reorganization energy would be small, and the functional form of Eq. (1) becomes close to a delta-function. With small dissipation, the  transfer between the  states would be almost resonant, but slightly downhill with respect to the energy of the full system. As mentioned above, the bR complex is too large for such quantitative treatment, but this approach might be used for qualitative discussion. In particular, if the  exact dynamics of some fragment of the  full complex is being calculated, the  initial and final energies of this fragment alone do not have to be minimal for given configurations, as the  requirement of the energy minimum for the relaxed system applies only to the whole complex. Moreover, when two final states are available, the system can have a higher probability to be transferred to the more energetic of the  two, because it is impossible to unload a large amount of energy to the vibrational environment in order to proceed to the minimal energy state, i.e. if the  system is in the  inverted Marcus regime. In some sense, our approach is comparable to the  ‘reaction coordinate models’ [25, 26] where strongly-coupled environmental degrees of freedom (often high frequency modes) were specifically included into the  dynamical part.

2.2. Molecular dynamics and quantum chemical calculations

Mimicking photoinduced processes in bR is not a trivial task since the resulting outcome is sensitive to the protein environment, that has to be taken into account properly. For this purpose, molecular dynamics (MD) simulations have been intensively used [4, 27–37]. Indeed, the rotation of SB as a  result of the  retinal isomerization (see Fig. 2) can be obtained by modelling the  retinal with its protein environment [34, 35]. However, in order to achieve it, multiple approximations should be used due to the limits of computational resources including algorithms themselves. 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. For QM/ MM simulations various approximations can be used for the  description of MM and QM counterparts. The  definition of the  QM–MM boundary is the major problem by constructing covalent bonding and adaptative schemes [4, 27, 33, 37]. Hayashi and co-authors [34, 35] exploited only a part of the retinal structure with the attached SB using the QM approach, while the rest of the molecule was parameterized. QM simulations of full retinal do not demonstrate isomerization and/or rotations of some parts of the molecule as follows from experimental data [36, 37]. Moreover, the SB bound to the retinal does not rotate in the vacuum models but instead only the rotation of the β-ring is obtained in the excited state of retinal [38, 39]. Starting from the excited state, the structure optimization procedure restores the  initially optimized ground state structure, which implies that the  minima of the  potential energy surfaces in the ground- and excited-states are not separated by any significant energy barrier. Furthermore, by analyzing the isomerization process of retinal up to 90 deg, it was concluded that the DFT methodology is not applicable due to the fact that the system is reaching the conical intersection region in the course of isomerization [40].

Molecular dynamics simulations with molecular mechanics force fields are performed in order to relate deformations of the bR helices to the proton transfer mechanism by assuming that the  L-intermediate follows from the  retinal alltrans to 13-cis photoisomerization step corresponding to the K-intermediate [41, 42]. If the water molecules (especially W402) are not taken into account, the retinal pumping of the proton is expected from the 13-cis,15-anti structure and not from the 13-cis,15-syn, in opposite to the crystallographic data [42]. Other studies based on three transfer mechanisms in terms of QM/MM calculations [43] also indicate the presence of the 13-cis,15-anti configuration. More accurate approach for the simulation of the protonated retinal active centre is based on the force field methodology. The water molecular clusters with additional possible water molecules in accordance with several crystallographic data were taken into consideration [44]. As follows from this type of studies, the proton transfer from retinal interacting with the water molecule (W402) is more complicated since the presence of the energy barrier appears for the proton pathway [45], while the NMR studies report opposite evidences [46].

The protonated retinal after its excitation is known as the J state of bR corresponding to a complication of the excitation dynamics of the retinal [45-47]. In the  vicinity of the local minimum of the first singlet excite state (S₁), 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 modelling [29, 30, 32, 37, 48]. 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 [29]. Our studies of the retinal-type conjugated systems support this conclusion: the  excited state S₁ demonstrates an inversion between single and double bonds, that should be caused by the  presence of the  second singlet excited state (S₂) properties (also known as 1¹B_u⁺ type state, corresponding to its symmetry according to polyene models), appropriate for polyene and carotenoid molecules [49]. It follows from the equation-of-motion coupled cluster singles and doubles model (EOM-CCSD) approach [50] that the  lowest excited state of the  retinal bound to the protonated SB is of a similar origin to that of the polyene type 1¹B_u⁺ state. In the case when retinal is bound to the non-protonated SB, the  optically forbidden state of symmetry 1¹A_g^– turns to be the lowest excited state due to the electron correlations. The  EOM-CCSD is computationally expensive and the excited state energies are largely overestimated. The  lowest S₁ state of the  retinal bound with the  deprotonated SB should be of the 1¹A_g^– symmetry while the lowest S₁ state of the retinal bound to the protonated SB should be of the  1¹B_u⁺ symmetry. Thus, the  retinal energy surfaces should be more complicated by considering the retinal isomerization together with the  possible flexibility of helices. Thus, energy transfer channels, which might fix the retinal in the 13-cis,15-syn and 13-cis,15-anti configuration (Fig. 2), and finally pass the absorbed light energy from the  retinal into the  helices, are expected.

Deprotonation of the  SB is usually attributed to the first proton transfer step in bR [10]. The protonation of Asp-85 upon the deprotonation of SB together with the photoisomerization of retinal from the initial all-trans configuration to the 13-cis configuration is followed by the release of a proton via a network of protein residues and bound water molecules [51–56] to the extracellular membrane surface [57, 58]. As follows from studies based on theoretical calculations, various possible pathways for retinal deprotonation in the ground state, which at moderate approximations agrees with the  experimental data [48, 59], are expected.

4.1. Modelling of retinal isomerization

The proton transfer correlates with the photoinduced transition of the  retinal from its initial trans-configuration to the  13-cis,15-syn isomer on µs timescale [65]. Thus, first, we consider the photoisomerization process in terms of QM/MM by taking into account the  structural details of the  part of the  protein from the  vicinity of the photoactive centre (retinal) as follows from crystallographic data [5, 64]. The protonated SB, which is a  proton donor, becomes connected to the  proton acceptor Asp-85 via the  water molecule (labelled W402) as a  result of the  retinal isomerization. Additional water molecules, labelled W401 and W406, as well as the protein two tryptophan residues labelled Trp-86, Trp-182 and tyrosine residue (labelled Tyr-185) are also present in the vicinity of the active centre and might play a decisive role in the photoinduced proton transfer. In order to repeat calculations with a higher basis set the  threonine residue (labelled Thr-90) may also be required. The all-trans configuration of the  retinal together with the  protein residues and bound water molecules mentioned above is taken from the crystallographic data.

As follows from the calculations, the all-trans retinal (corresponding to the  ground state) contains only one global minimum along the rotational pathway, while the optimization in the excited state results in the presence of two possible minima (Fig. 3(a)). One of these minima is at about –92 deg that correlates well with the structure defined from the  crystallographic data 2NTW [64]. Moreover, the ground state in this configuration can also be found when the protein residues Trp-86, Trp-182, and Tyr-185 are taken into account, thus, suggesting a conical intersection between these two states (Fig. 3(b)). Similar results are obtained both in QM/MM or QM/QM (ONIOM) studies by adding Trp-86, Trp-182, and Tyr-185 residues into the calculation scheme and using molecular mechanics UFF and in the semiempirical PM6 calculations. Thus, the minima corresponding to the excited states of 13-cis,15-syn isomer of the retinal appear within the supermolecular (several molecules in the same QM calculations) approach containing the retinal Trp-86, Trp-182, and Tyr-185 residues in agreement with the earlier suggestions for the ground state stability. However, this structure does not follow from the calculations of the ground state, so it can be obtained for the excited state minima only (Fig. 3). Accordingly, to obtain the minimum for the 13-cis,15-syn isomer of retinal in the ground state, additional interactions should be taken into account.

Thus, to examine the stability of the configuration of active centre corresponding to the retinal in the 13-cis,15-syn configuration, we initially fix this configuration and use the QMD simulations of the structure at different temperatures (Fig. 4).

The initial structures used for the calculations are chosen to be optimized either in the ground state or in the first excited state with the SB rotated by 90 deg. The results presented in Fig. 4 demonstrate that the ground state structure (E0) remains almost the same, while in the excited state (E1), this structure reaches other values of the rotational angle (retinal of cis isomer) on the time scale less than 0.5  ps at low temperatures. At higher temperatures (70 and 300  K), the  isomerization process starts at around 30  fs and experiences transition into another structural arrangement in about 100 fs and, thus, the initial state evidently cannot survive for several µs, as expected from the  experimental observations. Accordingly, we conclude that QMD simulations do not support the  evidence of the  appearance of 13-cis,15-anti retinal isomer without taking into account the essential interaction with the protein environment that has been ignored so far.

4.2. Initial step of proton transfer

To model the initial stage of the proton transfer, let us keep the key atoms taken from the crystallography data (with the  retinal in the  13-cis, 15-syn configuration and water molecules as it is in 2NTW [64]) fixed (see Fig. 5). The modelling data obtained by using QM calculations demonstrate the  proton displacement from W402 to the Asp85 group (Fig. 6(a)) that opens the pathway of the proton transfer from the SB to W402 (Fig. 6(b)).

Since the proton transfer is initiated by the photoexcitation of the retinal bound to SB, it subsequently rotates towards the  active centre where the water molecule mediating the Asp-85 residue is positioned, as shown in Fig. 5.  Thus, the photoexcitation of the retinal molecule causes the transition from the trans retinal (0 deg) to 13-cis configuration (–92.4 deg) in the excited S₁ state.

In this case, the  proton transfer starts from the  water molecule (W402) to Asp-85 residue with a subsequent proton transfer from the protonated SB to the  formed temporary hydroxide (OH^–). This explains the  pathway demonstrating the  role of water molecules as follows from the energy surface scans shown in Fig. 6(a). It should be mentioned that the presence of water molecules W401 and W406 is crucial for the proton transfer from the W402 to the Asp-85 group (Fig. 6(a)). These molecules make an essential influence on the energy surfaces by opening protonation pathways in bR.

5.1. Energy redistribution during the photocycle

Let us discuss now how the  energy supplied by the  photon is redistributed over various degrees of freedom in the  transitions between the  intermediates shown in Fig.  7, keeping in mind that these transitions are almost resonant with a small dissipation. Immediately after the photon absorption, the  energy is entirely in the  electronic degrees of freedom of the excited state of the retinal. The excited electronic state cannot relax back to the all-trans ground state because the internal degrees of freedom are not able to accept all the energy of the electronic excitation. Instead, the conformation to the  13-cis form (J to K transition) allows the excitation energy to be transferred to the  strain of the  retinal. It should be noted that the part of the energy is still contained in the electronic subsystem, as the  ground state energy of the 13-cis isomer is larger than that of all-trans. In the consequent transition between K and L intermediates, the retinal is more relaxed and the energy is redistributed to the  protein resulting in bending of the C-helix and thus in modification of the energies of the Coulomb interaction between residues [63, 66].

These modified interactions compensate for the  huge acid dissociation constant (pK_a) differences between the SB and Asp-85 (more than 11 and 2.5, respectively, for the bR states) and allow the  initial proton transfer between these residues (L to M₁ transition). To make the transfer possible, the pK_a factors of both protonable sites are modified bringing them to the pK_a of about 6.5. Accordingly, the energy delivered to the proton is much less than half of the electron-volt as follows from the initial pK_a difference. The protonation of Asp-85 modifies the electrostatic interactions in the proton release group, so the  corresponding proton energy becomes larger than the chemical potential of the extracellular space and the proton can be released (M₁ to M₂ transition). The deprotonation of SB leads to conformational changes (relaxation of the C-helix and bending of B- and F-helices), which, in turn, allow both the increase of the pK_a of SB to 8.3 and the decrease of the pK_a of Asp-96 to 7 [8]. Moreover, it leads to the penetration of water molecules in the space between the Asp-96 residue and SB. As a result, the reprotonation of the SB from Asp-96 via the water bridge becomes energetically favourable (M₂ to N₁ transition). Consequently, the proton energy level of Asp-96 again becomes smaller than the chemical potential of the cytoplasmic side and the Asp-96 residue is reprotonated (N₁ to N₂ transition). Accordingly, in the  series of events the  bR complex releases the  high-energy proton to the extracellular side and takes the low-energy proton from the  cytoplasmic side, i.e. the  proton is effectively pumped. The energy gain can be estimated from the difference between the pK_a of Asp-96 residue at the initial state (about 11) and the potential of the hydrogen (pH) factor of extracellular space, which is about 0.3 eV for pH = 5. The proton translocations from and to Asp-96 give rise to a new sequence of conformational changes, such as the relaxation of B- and F-helices, and the modifications of electrostatic interactions, so the retinal reisomerization to the  all-trans configuration is now possible (N₂ to O transition). The reprotonation of SB leads to the decrease of the pK_a of Asp-85 and its proton is slowly transferred downhill to the proton release group (O to bR transition) completing the photocycle.

5.2. General description of energy redistribution processes

Let us discuss now how the obtained results of our calculations of the initial step of proton transfer are related to a  general description of the  energy redistribution processes. Proton transport correlates with the protein conformational changes at various bR stages during the  photocycle, especially with the  bending of C- and F-helices (Fig.  7). In particular, the proton transfer to the extracellular side is related to the C-helix, while the proton uptake from the cytoplasmic side is related to the F-helix.

As follows from our quantum chemistry studies, the rotation energy surface cannot explain the initial energy transfer without the account of interaction with the protein helices. Indeed, the protonated 13-cis,15-syn retinal configuration cannot occur without the support of the protein because it is absent in the ground state structure (Fig. 3(a)), while the relevant minima might be present in the first excited state if three structural parts from the bR are taken into account (Fig. 3(b)). Thus, the energy should be evidently translocated to the C-helix for the rearranged positions of three water molecules (Fig. 6(a)), which appear as a result of the isomerization in the vicinity of the protonated Schiff base. This complex dynamics of molecules and protein residuals in the vicinity of the excited retinal could result in irreversible proton transfer by (i) temporary shifting the  OH- group from W402 and subsequently protonating Asp-85 (Fig.  6(b)) and (ii) translocating the proton from the SB group to W402 (Fig. 6(a)). Thus, the initial energy should be transferred to the protein in the initial step.

As a  result of such configuration changes, the energy of the electronic states of retinal should be modified as schematically shown in Fig. 8. According to our calculations, the proton should be transferred to Asp-85 (with the help of the water molecule) from the  13-cis,15-syn configuration, which is not of the lowest energy state of the retinal taken alone. To have the retinal fixed in this configuration, we have to postulate that the energy of this state is decreased as a result of the electrostatic interaction with the bent helices. The ground state of the  retinal at the  13-cis,15-syn conformation with the account of this interaction should be almost at the same energy level as it is for cis/trans minima. Thus, we should have two similar centres, which differ by the  water translocation but with similar structural parts causing different irreversible proton transfer events (Fig. 8).

The energy translocation from the retinal to protein helices in the primary step allows us to qualitatively determine the energy swap in the protein, as shown in Fig. 8. Proton transport is initiated from the middle of the structure by step-by-step pushing and uptaking protons over all the bR proteins resulting in pK_a changes.