12124
J. Phys. Chem. B 2008, 112, 12124–12133
Trapped Water Molecule in the Charge Separation of a Bacterial Reaction Center Nikolai Ivashin*,† and Sven Larsson‡ Institute of Physics, National Academy of Sciences, Nezalezhnasti AVenue 70, 220072 Minsk, Belarus, Department of Physical Chemistry, Chalmers UniVersity of Technology, S-41296, Go¨teborg, Sweden ReceiVed: December 20, 2007; ReVised Manuscript ReceiVed: June 4, 2008
Low-frequency oscillations in the absorption spectrum at 1020 nm, connected to the primary charge separation process in Rhodobacter sphaeroides, have been shown by Yakovlev et al. to be caused by rotational motion of an interstitial water molecule called “water-A”. The same water molecule was shown by Potter et al. to increase the rate of charge separation by a factor of 8. We have carried out geometry optimization of water-A and its nearest atoms in the protein pocket, using density functional theory (DFT). There are strong hydrogen bonds to the axial imidazol group of the B part of the special pair (P ) PAPB) and to the keto carbonyl group of ring V of the accessory chlorophyll (BA). Rotation of water-A is thus impossible in the electronic ground state. We have tried to support our speculations on other possible mechanisms by calculations. The P+BAcharge transfer state is stabilized by proton transfer from water-A and simultaneous proton transfer from the axial group of PB to water-A. After double proton transfer the hydrogen bond to the keto group disappears whereby a possibility opens up for almost free water rotation. The results therefore would explain the 32 cm-1 oscillation of Yakovlev et al. The proposed mechanism assumes, however, that the general assumption that the activation energy disappears in the primary charge separation of bacterial photosynthesis, holds also for this special case. I. Introduction A bacterial photosynthetic reaction center (RC) was structurally determined about twenty years ago1,2 (Figure 1). The charge separation process is known in some details, as reviewed for example by Shuvalov and Yakovlev.3 The lowest locally excited-state is of the type P* ) (PAPB)* where PA and PB are two bacteriochlorophyll (BChl) molecules which form the “special pair” (P). Electron transfer (ET) occurs at the avoided crossing between P* and the charge-separated state (P+BA-) where BA is the accessory BChl on the active A-side.4,5 The lifetime of P* is approximately τ ) 3 ps.4-7 The electron thus first moves to BA, where the lifetime is less than 1 ps. The electron subsequently continues to pheophytin (HA) where τ ) 200 ps. Although the localization of the electron on the accessory BChl was suggested in the first measurement of the charge separation rate,4 there was for a long time no proof of the presence of the state P+BA- as an intermediate in the charge separation process. Finally such evidence and proof was provided by Holzapfel et al.5 The calculated electronic coupling between P and HA is actually too small to permit direct transfer from P to HA in a short time.8,9 High charge separation rate may thus be achieved with an accessory BChl (BA) as the first acceptor of the electron. Moreover, if the coupling would have been large enough to allow direct ET in short times, the rate of back-transfer to the locally excited triplet state would also have been large.9,10 About 15 years ago, Vos et al. discovered subpicosecond oscillations in the stimulated emission spectra of P11-13 in a modified RC of Rhodobacter sphaeroides where charge separation is prevented. Similar experiments were subsequently carried out by others.14,15 The system was seen to move as a wave packet on the multidimensional potential energy surface (PES) † ‡
Institute of Physics, National Academy of Sciences. Department of Physical Chemistry, Chalmers University of Technology.
of the excited state. The emission intensity varied in time in an oscillatory manner, corresponding to coherent motion of a wave packet and very likely related to frequencies (energies) of vibrational modes. The energies were obtained from the measured intensity variations by a Fourier transformation. Oscillations in ∆A were found in different regions of the spectrum, indicating for example charge separation processes. Oscillations in the region between 920 and 1100 nm were connected to the absorption of BA,16-20 measuring the rate of the charge separation process P*BA f P+BA-. The frequencies of the oscillations range from 0.4-10 ps-1 (corresponding to 13-333 cm-1 in EM radiation). The nature of the oscillations is uncertain. Motions in the protein,21,22 in the cofactors and their side groups10 have been suggested.23-26 Coupled motion between the two monomers in the special pair (SP), producing a rich dimer resonance Raman spectrum27,28 and introducing oscillations in the energy of the P* state relative to the charge separated P+BA- state, is another very likely source.10,22-29 Streltsov et al. found a distinct oscillation at 12 ( 2 cm-1 and another at 30 ( 3 cm-1.16-18 More recently a 32 cm-1 oscillation was found in the work of Yakovlev et al. and connected to ET.30 Strong evidence was provided that it is related to motion of a water molecule (water-A) in the protein structure30,31 (Figure 2). In our view motions in the protein should be localized to molecules and groups in the ET pathway, such as the mentioned water molecule, while oscillatory motion in the protein as a whole should be less important. There is general agreement that the oscillations are activated by changes in the geometry when a molecule is excited or when the electron moves from one cofactor to the next. In the case of excitation these geometry changes are responsible for the Stokes shift of the transition. The Stokes shift is the result of geometry changes of all possible modes and is equal to the reorganization energy for the excitation. If the change of equilibrium energy for a particular mode is large compared to
10.1021/jp711924f CCC: $40.75 2008 American Chemical Society Published on Web 08/30/2008
Trapped Water Molecule
Figure 1. Schematic view of the cofactors and the important amino acids in the reaction center of Rb. sphaeroides.
Figure 2. Position of the water-A molecule between P and BA.
the vibrational width, there is a possibility for wave packet formation and coherent motion before decay to the lowest vibrational state. In the RC the contributions to the reorganization energy generated by bond length changes in the bacteriochlorophylls are probably of less importance than the contribution due to side group motion, relative motion in the dimer, and in the protein around RC. Reorganization energies have been studied and calculated in detail by Reimers and Hush.24 Only modes coupled to the charge distribution should be of any importance for the charge separation () electron transfer, ET). Probably the most important source for wave packet formation is motions in the dimer.21-30 The locally excitedstate P* of the dimer contains attractive components due to excitonic coupling and also charge transfer components which are likely to change the equilibrium distance between the dimer halves compared to the ground state.32 In fact the electronic spectrum of P is rather different from the standard dimer spectrum for a case of parallel, stacked monomer planes, since this type of stacking geometry implies low intensity in the lowest excited state.8 This indicates strong interactions between the monomers, as is also borne out by the crystallographically determined coordinates corresponding to the P+ state.33 It would
J. Phys. Chem. B, Vol. 112, No. 38, 2008 12125 be expected that modes where the monomers are moving against each other are of special importance. In the case of P, the spectrum corresponding to stimulated emission from P* contains at least three strong modes in the region 90-150 cm-1, which may be connected to interactions between the monomers of P or between P and the protein.34 The oscillation frequencies of interest in the BA- spectrum and in the stimulated emission spectrum very likely originate in the same mode, where the dimer halves are moving against each other. It is expected that bacteriochlorophyll and large cyclic π systems in general, do not change bond lengths very much if the system is reduced or oxidized. This depends simply on the fact that the bond order changes when the system is oxidized or reduced are distributed on many bonds. The binding between the two monomers in a dimer on the other hand, may be much affected by occupancy since the highest occupied orbital is very likely bonding and the lowest unoccupied orbital very likely antibonding between the monomers in the dimer. Thus the energies of the P*BA and P+BA- states are both strongly dependent on the distance between the dimer halves (and the distance between P and BA). Therefore mode energies between 125 and 130 cm-1 have been implicated as connected to dimer binding21-30 and the origin of both the oscillations in the emission spectrum of the P*BA excited-state and the absorption spectrum of the P+BA- charge transfer state. Robert and Lutz first suggested the possibility of a water molecule in the structure between the keto carbonyl of BA (ring V), His M202 (the axial ligand of PB), and Gly M203.35 In later X-ray work water-A was indeed found.33,36 Since this water molecule is bridging P and BA, it was included in our calculations of electronic coupling, but no contribution to the coupling was found.9 Water-A was not included in our calculation of the vibrations, however, since that calculation only involved the structure of a single BChl molecule.10 New calculations have now been performed which include water-A, hydrogen bonded to BChl, but these results will be published elsewhere. Streltsov et al. connected an oscillation in the 865 nm absorption with the frequency near 30 cm-1 to P+BA-.14 Yakovlev et al. found very strong evidence that water-A provides a large part of the oscillations in the ∆A spectrum monitored at 1020 nm. The experimental frequencies suggest that water-A rotates freely.30,31 The authors showed that the absence of water-A in dry films leads to a much reduced intensity of the 32 cm-1 oscillation. The latter oscillation also disappears if a mutation of glycine M203 to leucine (M203G f L) is carried out, in which case there is no space available for a water molecule.31,37 Very few other changes take place in this mutation and the protein continues to work properly, although charge separation becomes slower by a factor of 8.37 Dynamics related to water-A thus appears to promote a high charge separation rate and be advantageous for the species. Other mutations involving water molecules have been tried.38 Further support for the water rotation mechanism was provided by HD and D2 isotope exchange.30,39 The shift is consistent with a picture where the oscillations are caused by rotation of water-A.30,39 Due to the fact that there are normally frequent possibilities for hydrogen bonds in a protein, free water rotation has to be considered as a great surprise. Yakovlev et al. also showed30 that several processes are correlated with stabilization of P+BA-: disappearance of P* emission, appearance of BA- absorption at 1020 nm, and HAabsorption at 760 nm. From that we may conclude that water-A
12126 J. Phys. Chem. B, Vol. 112, No. 38, 2008 rotations appear after ET to BA, while the 130 cm-1 oscillation is connected to the immediate appearance of P*. In our previous work we determined which modes are activated in different processes by calculating the geometry before and after ET.10 We also made an extensive calculation of the vibrational spectrum of a BChl molecule to assign the modes of the vibration spectra to structural oscillations. In general there is reasonable agreement with the experimental frequencies,10 but, as mentioned above, water-A or any other surrounding molecule in the protein were not included in the calculations. At least two different theoretical possibilities have been mentioned in the literature to explain the connection between the vibration modes on one hand and the charge separation rate and spectral oscillation on the other. One suggestion is that some molecular group oscillates in the activated mode, whereby the distance and orbital overlap along the ET pathway also varies, making the electronic coupling time-dependent. For example in the protein dynamics work by Parson and Warshel et al.21,22 an oscillation at 17 cm-1 has been suggested as a cause, but strong support from experimental data appears to be absent. In principle, however, the relative position of the special pair and the accessory BA may be affected and cause oscillations in the coupling that promote ET. Oscillations in the coupling along the ET pathway, however, may also be caused by rotation of side groups of the cofactors or in fact by water-A. The latter has been suggested to be a “door” which opens and closes with the oscillations.30,31 This is in disagreement with our calculations of the electron transfer coupling via water-A, however, which is negligible. The other possibility is that motions in the protein induce electric fields which affect the free energy and hence the thermal reaction barrier. Even in this case protein motion has been suggested as the cause since it provides a temporal variation in activation energy and hence reaction rate, but as mentioned above such motion should only be important close to the ET pathway, in the cofactors or water-A, since these groups are directly affected by large changes in equilibrium geometry at ET. As will be shown here in the case of water-A, there is a change in geometry after the electron has transferred to BA. Rotatory motion becomes possible and leads to a time dependent field which modifies the probability for ET. The oscillations in water-A are probably of little importance as a mechanism for providing fast ET, but a correct description of them may improve our understanding of the charge separation process and the feasibility of a coherent quantum mechanical process. In this paper we will examine the water-A pocket in a great detail and find at least two strong hydrogen bonds. We will then consider the possibility for opening of the cavity and activation of partial water-A rotation. As required in the rotation model of Yakovlev et al.,30,31 at least one hydrogen bond, probably the bond to the keto group of ring V of the accessory BA, has to be removed. No explanation of the Yakovlev results in terms of electron structure was found, until concerted proton transfer was tried. This “double proton transfer” mechanism would provide a new pocket with a single hydrogen bond and a possibility for water-A to rotate. It leads to a stabilization of the charge separation and prevents charge recombination. The final test of this mechanism depends on whether the short time scale necessary for this proton transfer can be ascertained. II. Methods and Results All calculations were performed using Gaussian 03 electronic structure package.40 Geometry optimizations were carried out
Ivashin and Larsson
Figure 3. Atoms included in the calculation of the ground-state pocket model.
using the DFT method with the B3LYP hybrid functional.41 The calculations on neutral, anion radical and protonated forms of the BChl molecule used 6-31 g(d) basis set on all atoms. It is known that use of extended basis sets in DFT with diffuse functions leads to an accurate description of hydrogen-bonding interactions.42 B3LYP/6-311++G(2d,2p) calculations were successfully applied by Lii et al.43 to hydrogen-bonded systems such as the water dimer and carbohydrates. We use the same basis set for all atoms of water-A and the nearest atoms of the pocket that are involved in hydrogen bonds with water-A to optimize its position. The water position is determined by short-range repulsive interactions and interactions of hydrogen bond type. Since we do not have access to the total energy of the system we will use the Natural Bond Orbital (NBO) analysis44 of the water intermolecular interactions. It is well-known that this approach allows estimating the short-range strong (chemical) part of the interactions that our pocket model describes correctly. The method has been successfully applied to a number of molecular clusters with intermolecular hydrogen bonding.44 NBO theory44 allows the transformation of canonical molecular orbitals into an orthonormal set of one- and two-center localized orbitals (NBOs) analogous to traditional Lewis-type orbitals. It is possible to estimate the energy lowering, E(2), caused by CT interactions by performing second-order perturbation analysis. E(2) values are directly proportional to the overlap integral, S(a,b), between preorthogonalized NBOs (pre-NBOs) and inversely proportional to the energy difference between corresponding NBOs. The calculated E(2) energies were used for characterization of the water molecule intermolecular interactions in the pocket. To predict the charge transfer states it would have been necessary to include three chromophores in the calculation (P+B-). This cannot be done at the present using accurate ab initio methods. For this reason the ZINDO/S method,45 as implemented in Gaussian 03, was also employed. Interactions of the Water Molecule in the Pocket. The position of the oxygen atom of the water molecule is slightly different in different crystallographic studies, while the positions of the hydrogen atoms cannot be determined by X-ray crystallography. To study the possibilities for free rotation it is necessary to get more correct and detailed information on the water-A coordinates and its interactions in the pocket. DFT calculations were carried out on a model (Figure 3) of the water-A pocket, constructed on the basis of the crystallographic positions of Rh. sphaeroides.33,36 The model was chosen to include all possible hydrogen bonds within a radius of about 8 Å from the water-A oxygen, including BA. To take into account the remaining sterical interactions that determine the water position, PheM197 and a part of the peptide chain linking with HisM202 were also included. The noninteracting side groups
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TABLE 1: Water-A (HOH or HHO) Hydrogen Bond Lengths in the Ground State after Geometry Optimization in the PBA Ground State, the P*BA State, and the P+BA- Statea hydrogen bond state of special pair and accessory BChl (PBA)
BA(CdO) · · · HOH
HHO · · · HisM202(NH)
PheM197(CdO) · · · HOH
2.89 (1.93) 2.98 (2.02) 2.91 (1.94) 2.67 (1.70)
3.05 (2.05) 3.13 (2.13) 3.27 (2.30) 3.06 (2.06)
3.42 (2.60) 3.21 (2.36) 3.14 (2.23) 3.60 (2.70)
b
ground state ground statec excited-state P*BAd charge separated stateP+BA- d
a BA(CdO) refers to the carbonyl group of ring V and NH belongs to the imidazol axial ligand of PB. Distance in parentheses is the distance between the hydrogen atom and the heavy atom. b Water-A pocket constructed on the basis of ref 36. c Water-A pocket constructed on the basis of ref 33. d Water-A pocket constructed on the basis of the P+Q- data of ref 33.
TABLE 2: Distance between Water-A atoms and Closest Atoms in the Pocket (Dotted) before and after Double Proton Transfera modeling state P+BA- state after double proton transfer with fixed water-A oxygen
ground state
a
water-A intermolecular contacts
d (Å)
E(2) (cm-1)
d (Å)
E(2) (cm-1)
BA(CdO) · · · HOH BA(CdO)H · · · OH2 His(NH) · · · OHH His(N) · · · HOH Phe(CdO) · · · HOH
1.93 2.05 2.60
2290 3237 109
2.35 2.05 2.49
290 4501 273
E(2) values refer to the NBO analysis.
of BA were replaced by hydrogens. This structure was partially geometry optimized. Only the atoms of water-A and those involved with it in the hydrogen bonds (C and O atoms on ring V of BA; N, H atoms on HisM202; protein C and O atoms neighboring to PheM197) were involved in the geometry optimization. The data of the optimization and following NBO analysis44 of the hydrogen bond energies (E(2) values) are summarized in Tables 1 and 2. During geometry optimization the water-A molecule takes a position with the oxygen atom hydrogen bonded to the oxygen atom of ring V of BA and to the N atom of the free NH group of the imidazol side chain of HisM202, which is also the axial ligand of PB. The second hydrogen atom of the water-A molecule was directed to the peptide carbonyl of PheM197, but the corresponding E(2) energy is very low, consistent with a long hydrogen bond. The data obtained show that rotation or any other significant motion of the water molecule in the groundstate of RC is impossible because of the two strong hydrogen bonds. The results obtained reflect the well-known unique properties of the water molecule to interact with the protein. Rotation in the ground-state is very unlikely. The question is whether rotation is possible in the excited P* or P+BA- states and, if so, what causes its activation. Unfortunately neither excitation nor charge transfer can be simulated easily in the present simplified model. If the number of electrons is increased the new electron localizes itself on BA. Renewed optimization leads to a shortening of the hydrogen bond between water-A and ring V of BA. The same situation prevails if Stowell′s coordinates36 corresponding to the equilibrium structure of P+Q-, are used. The hydrogen bond between the ring V keto group of BA and water-A is increased but the interaction between water-A and HisM202 is also increased. It follows that the pocket size changes estimated at BA reduction cannot by themselves eliminate the hydrogen bonds. There is still a possibility, however, that the optimized geometry minimum is a local energy minimum and that a lower global minimum is obtained after large moves corresponding
to proton transfer. Full single proton transfer may be considered energetically impossible, since an OH- would be left behind, indicating a situation with a high free energy. There are strong indications, however, that double proton transfer is energetically possible and this will be considered next. Only One Hydrogen Bond Remains after Double Proton Transfer. In the experiments of Yakovlev et al.,30,31 an oscillation corresponding to a wavenumber of 130 cm-1 explains the initial part of the ∆A kinetics. As mentioned above, it is very likely, and in fact commonly accepted, that this is one of many possible dimer modes23,24 that affects the orbital energy of the electron to be transferred from P. As described by Yakovlev et al.30 this initiates a wave packet motion toward an avoided crossing with the P+BA- state. If the system ends up in the P+BA- state, the conditions for proton transfer completely change, particularly since the BA state is negatively charged. Therefore, motions associated with the stabilization of the BAare important. We will study a particular mechanism: concerted proton transfer at the water-A molecule, equivalent to a double proton transfer in the two strongest hydrogen bonds of water-A. As discussed above water-A must regain the proton in the other hydrogen bond, the hydrogen bond between water-A and the NH of the axial imidazol ligand of PB, the side group of HisM202. Below we will check the energetics of double proton transfer model to explain the water molecule rotation. The following system was studied: An additional electron was added to the system to give a possibility to simulate BA reduction. The positions of the protons were changed consistent with double proton transfer model. This stabilizes the additional electron on the part of the system that simulates BA. The hydrogen nuclei are geometry optimized in their new equilibrium positions in the pocket. The geometry optimization corresponds to a motion on the picosecond scale of the protons. The latter are the only nuclei that may be accelerated during relatively short time. The heavier oxygen atom on the other hand is still considered as fixed due to its larger mass and is not geometry
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Figure 5. Rotational axis of the water molecule in the pocket.
at the equilibrium position corresponding to the charge separated state P+BA-. The Water Rotational Coordinate. The rotational constant (2B) for a water molecule, corresponding to a rotation axis in the water molecular plane, directed at the same angle (52.25°) to the two OH bonds, and with the OH distance R ) 0.9572 Å, is Figure 4. Result of double proton transfer geometry optimization. Note that water-A is not oriented in a favorable way to form a strong hydrogen bond interaction with (BA)OH.
optimized. Optimization of the keto atoms and the imidazol nitrogen did not lead to any significant changes. We believe that the optimized structure corresponds closely to the enolate ion form of reduced bacteriochlorophyll. After the protons have been allowed to relax in a structure that corresponds to double proton transfer, there are two protons bonded to the oxygen of water-A (Table 2). One of these protons is still very weakly hydrogen bonded to PheM197. The other proton is the one received from the imidazol axial ligand of PB in a concerted process with the proton transfer from water-A to BA. Water-A is thus still a water molecule but one of the protons is located at the other side of the oxygen atom compared to where there was one before. As can be seen from Table 2 and Figure 4, model optimization does not lead to any new strong hydrogen bond between water-A and BA. After the proton has transferred to the carbonyl group in its double well hydrogen bond potential, the corresponding electronic state and PES change character so that the expected hydrogen bond disappears. The heavy atoms in the original hydrogen bond CdO · · · H · · OH were more or less linear, and the hydrogen bond O · · · H · · · O angle equal to 169°, which is thus quite close to 180°. After proton transfer to BA, the geometry is determined by the BChl macrocycle, which forces a much smaller angle, only 114.2°. Such a small angle is very different from what is expected from a strong hydrogen bond (Figure 4). We may therefore conclude that at short times after the electron has arrived at BA, double proton transfer takes place in which only one hydrogen bond remains, the one to the axial ligand. The other one is lost after it has been transferred to the keton at ring V and appeared in a geometry which does not allow a hydrogen bond to water-A. This also means that the lowest energy states of the system are not vibrational states but rotational states. The low-lying states after ET will determine the reaction path and character of the wave packet that is formed at t ) 0 (defined as the time when the electron has arrived at BA). This motion is dephased
2B )
2p ) 29.2 cm-1 4πcI
where I ) 2µ(R sin 52.25)2 (1)
This rotation is hindered in the pocket due to lack of space. Furthermore there would be no dipole moment change during this type of rotation, but this is required for an “energetics” explanation of the oscillations. The double proton transfer model considered above opens the door for water rotation around the remaining hydrogen bond with imidazole (where the proton is now bonded to water-A and bonded with a hydrogen bond to the nitrogen atom of the imidazol axial ligand of PB). If free rotation of the oxygen atom and the free hydrogen atom is allowed in the presence of one hydrogen bond, the frequency may be calculated to 43 cm-1. The strongly hydrogen bonded H atom is then modeled with an atomic mass equal to 1000. In this case the rotation axis passes close to the oxygen nucleus, since the latter is sixteen times heavier than the weakly hydrogen bonded hydrogen atom. However, the radius of the rotating free hydrogen atom is too large for this rotation to fit into the pocket. To obtain a smaller rotation cylinder for the almost free hydrogen atom we consequently have to pass the rotation axis closer to this hydrogen atom (Figure 5). Such a motion has a smaller radius and is possible in a space-restricted pocket. If the rotation radius is reduced by about 25% by assuming a direction of the rotation axis closer to the other hydrogen (0.23 Å from the O atom), full rotations become possible. The oxygen of water-A is further from the axis and the moment of inertia higher, making the rotation constant smaller than 43 cm-1, in fact close to the experimental 32 cm-1. The calculation for the fully deuterated water molecule gives the frequency also in agreement with experiment (24 cm-1). The conclusion is that rotation of the water molecule around a single hydrogen bond (with deprotonated imidazole) is allowed after double proton transfer. To check this possibility further we made four single point calculations followed by NBO analysis for the pocket using the water rotating cylinder mentioned above. The data obtained are summarized in Table 3. The largest barrier for rotation around the remaining hydrogen bond occurs at the weak hydrogen bond with E(2) ) 260 cm-1 with Phe(CdO). This value remains small (or even smaller) if small changes, consistent with the inaccuracy in the X-ray
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TABLE 3: Hydrogen Bond E(2) energies (cm-1) of NBO analysis for different rotation angles θa
TABLE 5: Excited State of Charge Transfer Character in ZINDO Calculation on the System PBAa geometry
ν˜ (cm-1)
∆ν˜ (cm-1)
X-ray coordinates after double proton transfer + rotation 90° + rotation 180° + rotation 270°
14350 12386 12133 11546 11837
-1964 -2217 -2804 -2513
water-A rotation angle water-A intermolecular contacts Phe(CdO) · · · HOH BA(COH) · · · OHH His(N) · · · HOH a
0°
90°
180°
270°
260 49 (-211) 70 (-190) 0 (-260) 266 175 (-91) 224 (-42) 280 (14) 3619 3684 (65) 3514 (-105) 3556 (-63)
a
In parentheses: change compared to θ ) 0.
TABLE 4: Calculated (B3LYP/6-31G((d)) Energies of Protonated and Deprotonated Species taking Part in Charge Separationa system optimized
Energy (H)
BChl-ImBChl-Im- protonated, enol BChl-Im- protonated, enolate P+, including Im P+, including Im, deprotonated
-1682.0698 -1682.5824 -1682.5613 -3363.8310 -3363.3596
Difference -0.5126 -0.4915 0.4714
The structures of BChl-Im and protonated BChl-Im- were fully optimized to obtain the enol form (see section III). In the more realistic enolate form only the hydrogen connected to the keto carbonyl was allowed to move. P+ was partly optimized with the distance between the macrocycles maintained according to x-ray data. a
-
structure, are performed. Taking this fact into account, we may propose that immediately after ET and double proton transfer the barrier for water rotation is negligible. Energetics of Double Proton Transfer. To get an idea of whether double proton transfer is possible energetically, we calculate whether the energy lowering when a proton is added to the negative ion of BChl is sufficient to remove a proton from the imidazole axial ligand. The first system studied consists of BChl and imidazole at the appropriate distance in RC, with one electron added. The energy lowering when one proton is added to this system at the CO carbonyl is -0.5126 au if the structure is completely reoptimized. This corresponds, however, to the enol form, that is inaccessible during the short time scale of 1 - 0.1 ps during which the electron is present on BA. In this shorter time scale the enolate form is of interest. Therefore we carried out another calculation where only the position of the new proton close to the keto group was varied. The energy obtained is -0.4915 au (Table 4). Next we studied a system which consists of the cationic form of the special pair. When a proton is removed from the axial imidazole ligand, the energy is raised by 0.4714 au. If the energy gain at the keto group in the previous calculation is added, there is a total stabilization of the total energy by 0.02 au (≈ 0.5 eV ≈ 50 kJ mol-1). This is sufficient to overcome the increase in energy due to the break of one of the hydrogen bonds of the water molecule and due to loss of Coulomb interaction energy between BA- and P+, caused by proton transfer. Another attempt to calculate the energy of double proton transfer was done using the ZINDO/S method.45 This approach allowed us to study the charge separated state behavior after double proton transfer. The structural model used in the calculations included the truncated forms of the special pair and accessory bacteriochlorophyll using the X-ray coordinates.33 Truncations were made for peripheral groups which are not part of the macrocycle. All imidazole axial ligands were kept. The water molecule position, the keto carbonyl of group V and its protonated form were modified in accordance with the optimized data obtained for the pocket model. The calculations of the
The positions of the two protons are changed according to geometry optimization and subsequent rotation in the pocket (see text).
charge transfer (CT) state were done using Gaussian 03 implementation of the ZINDO/S method. All orbitals were involved in the configuration interaction treatment. As can be seen from Table 5, double proton transfer and the subsequent relaxation lead to evident stabilization of the CT state. The data obtained predict some further lowering of the CT state as the result of rotation of the water molecule. The largest effect, unsurprisingly, takes place at 180° rotation. Therefore the water-A molecule is not completely free to rotate in the charge separated state in this semiempirical study but the rotational barrier is less than 600 cm-1. This is still a very small barrier although it may be questionable whether the quantum states may still be regarded as rotational. III. Discussion Charge separation in a bacterial RC takes place at the avoided crossing between the P* and P+BA- potential surfaces. The latter state is characterized by absorption in the region 920-1100 nm and modified equilibrium geometries after ET. Vibrational manifolds are accessed if the corresponding equilibrium coordinate is much changed in the ET. The high-energy vibrations are generally inaccessible since their corresponding shifts in equilibrium position in BChl are too small to be relevant for any wave packet motion. A small shift in equilibrium position combined with high vibrational energy cannot lead to the formation of any coherent wave packet. Coherent Motion. The dynamics of ET has been discussed in the literature with emphasis on the possibility for a coherent wave packet motion.46-49 If the vibrational energy is small compared to the reorganization energy due to shift in equilibrium position, there should be no obstacle to formation of wave packets which remain coherent for some time. There is evidence for coherent motion from other systems,50 and hence such a motion cannot be excluded in the primary charge separation. Relevant (for excitation and ET) vibrational manifolds in the P+BA- electronic state are due to side group oscillations, relative motion between the cofactors, or other motion in the cofactors that do not exist in the monomeric form. Possibly the protein cannot be fully excluded as a source of the oscillations. In a wider perspective the presence of low-energy as compared to high energy vibrational modes in the charge separation process gives a slower dynamics of the charge separation but saves energy, since the reorganization energy may remain small. A large reorganization energy gives a large activation barrier unless the free energy of reaction ()loss of energy) is also very large in the Marcus model.51 Since biological charge separation processes have to be fast to avoid competing waste processes (for example triplet formation), it is important that molecular systems are used which can accomplish sufficiently fast charge separation without too high a loss of free energy. The price to pay is that low-frequency modes have to be used. The dynamics
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therefore has to be in a time window between several picoseconds and up to thousand times faster. The main motion to accomplish charge separation, as suggested by Yakovlev et al.,30 is a motion with a wavenumber around 125 cm-1. The frequency of 125 cm-1 fits the behavior close to t ) 0 for the oscillatory spectrum obtained at 1020 cm-1 by them.30 The latter authors propose that the 125 cm-1 vibration is transformed to the 32 cm-1 vibration, however, without giving any details on how this transformation takes place. In any case the 32 cm-1 mode is apparently absent at t ) 0. Possible Reason for Water-A Rotations. We have shown that double proton transfer is energetically possible only after ET and reduction of the accessory BChl. Double proton transfer provides a lock prohibiting the electron from returning to the special pair. It is trapped with a completely novel manifold of eigenstates. Since the ground-state PES is flat in the pocket, the lowest energy quantum states involve rotational excitations. Normally rotational eigenfunctions do not occur in a protein, but in this particular case water-A apparently looses one of only two strong hydrogen bonds and is free to rotate in the P+BAelectronic state. The original ground-state wave function Ξ°, including the proton wave functions for water-A, may be expanded in nuclear motion of time dependent wave functions (wave packets) where the new quantum states (Ξi) are used:
Ξ0 )
∑ CiΞi exp(iωit)
(2)
i
In particular, eq 2 describes the motion of the proton close to the oxygen atom of water-A. In the normal case of charge separation the vibrational functions are essentially the same as in the ground-state with the same vibrational energies. In the present case the vibrations are replaced by rotations or pseudorotations at a low energy in eq 2. Concerning the motion of the proton around water-A, the PES of the excited-state P+BAis thus essentially flat, allowing for rotational instead of vibrational wave functions. We thereby provide an explanation for the unique and surprising result of Yakovlev et al.30,31 of a rotational motion inside the protein. This rotational motion is thus possible in the charge separated state, but not in the ground state. If the states in the right member of eq 2 belong to the rotational manifold of water-A, particularly |C1|2 and |C2|2 have to be large. The wave packet Ξ° describes the proton which is on the BA side of the oxygen atom and is thus composed of the first two vibrational functions with J ) 0 and J ) 1. After ET to BA the proton is changed in position to the other side, close to PB. This means that one of the two rotational functions have to change sign at t ) 0. The wave packet will start to move in accordance with this. The oscillations seen in ∆A at 1020 nm are the oscillations of a rotating water-A and the most prominent frequency in the Fourier transformed spectrum is due to the transition between J ) 0 and J ) 1. This is thus a reasonable explanation for the oscillation spectrum (including overtones in some cases) seen by Yakovlev et al.30,31 The appearance of the oscillations is special for this RC of Rb. sphaeroides, since a third hydrogen bond is already very weak, thus leaving only a single strong hydrogen bond. Protonation of the Carbonyl. It is likely that the 131-keto carbonyl group of P+BA- is protonated and the axial imidazol ligand of PB deprotonated in a concerted reaction after ET to BA, but in a way that does not permit the enolate state to change into the enol state due to shortage of time for this process.
Figure 6. Comparison of water-A pockets in B. Viridis (thin line) and Rb. Sphaeroides (thick line). The water-A positions are marked by circles.
Although we are unable to calculate at the moment the free energy change of P+BA-, it is obvious that the free energy is considerably lowered by the double proton transfer reaction. Since the final P+BAHA- state is at about 0.15 eV lower free energy than the P* state, there appears to be no risk that the electron is trapped at the accessory BA molecule, but will continue to HA. The reorganization energy is small since PES is essentially flat. We conclude that the explanation of the promotion of charge separation by water-A is not in being a bridge for ET, providing electronic coupling, but possibly in a lowering of the reaction barrier. Furthermore it is likely that double proton transfer locks the electron on the accessory chlorophyll and thereby prevents back transfer to the special pair. The suggested mechanism may be tested by removing the water molecule by mutation. This has already been done in the work of Yakovlev et al.30,31 and Jones et al.37,38 If water-A is removed by mutation (whereby the remaining structure remains intact) the 32 cm-1 oscillation disappears. If water-A is replaced by heavy water-A the frequencies change as predicted by the mass dependence in the rotational levels, as we showed in section II. Removal of water-A leads to a lower reaction rate.37 This is likely due to the stabilization of the P+BA- state when water-A is present, as was also expressed by Jones et al.37,38 It is generally accepted that the activation energy essentially disappears in the primary charge separation step. In the Marcus model this means that some stabilization of the P+BA- state must occur to compensate for the reorganization energy of the process. Comparison to Blastochloris Wiridis. (Figure 6) In B. Viridis (formerly Rhodopseudomonas Viridis) the rate of charge separation is about the same as in Rb. sphaeroides.52 The second ET step is slightly faster: 0.65 in B. Viridis compared to 0.9 ps.52 No oscillations corresponding to a water-A at about 32 cm-1 are visible.53 This may be explained partly as due to a shorter residing time on BA. There is a much simpler and better explanation, however. The hydrogen bond that corresponds to the one between water-A and PheM197 is likely to be much stronger in B. Viridis than in Rb. sphaeroides (since it is shorter; see Table 6). In B. Viridis water-A is therefore completely fixed in its pocket by at least two hydrogen bonds even after charge separation and double proton transfer. Reaction Rate. It is important to discuss whether coherent motion increases or decreases the reaction rate.46-49 It is difficult to give a general answer to this problem. Very likely the differences between coherent and incoherent rates are not great in most cases. In the first step of charge separation, wave packet motion is likely since the distances between the atoms of the monomers are changed as a result of the excitation. The energy
Trapped Water Molecule
J. Phys. Chem. B, Vol. 112, No. 38, 2008 12131
TABLE 6: Comparison of interatomic Distances in the Water Pockets of Rb. Sphaeroides and B. Wiridis Rb. Sphaeroides36
B. Viridis60
atoms
A-side
B-side
A-side
B-side
O(CdO) · · · O(protein) O(CdO) · · · N(His) N(His) · · · O(protein) O(H2O) · · · O(CdO) O(H2O) · · · N(His) O(H2O) · · · O(protein)
5.68 4.94 5.45 2.77 2.81 3.76
4.73 4.76 4.30 2.84 2.47 4.20
5.39 4.84 5.12 3.03 3.05 2.85
4.60 4.70 4.46 2.68 2.36 3.03
a
L168 His f Phe mutant.
of the dimer is temporarily increased, setting in motion a vibronic wave packet formed from (in what concerns the electronic components) the orbitals on P and BA. After the wave packet has arrived at BA, it is stabilized by double proton transfer. In the case of incoherent transfer, which is the usual case in the ground state, it is appropriate to use the model of Bixon and Jortner54,55 which goes back to the theory of Kubo and Toyozawa,56 for low temperatures (nuclear tunneling model), and the Marcus model51 for higher temperatures. In the case of the bacterial primary charge separation, the former model has been used also to show that the rate is reduced at a higher temperature.6 To apply the theory to get the latter result it is necessary to assume that the potential energy surface for the charge separated state intersects the potential energy surface for the locally excited state (S1) at the new equilibrium geometry for all relevant modes. This appears to us as less likely. Normally occupation of higher vibrational levels leads to a higher rate, converging to the Marcus high temperature limit (activated behavior). At a low temperature nuclear tunneling leads to a higher rate than the standard Arrhenius type theory due to Marcus, but still to a lower rate at a low temperature than at a higher temperature. We believe that a more likely explanation of a higher rate at a lower temperature is in fact coherent ET. This is very clear in the Viridis data,53,57 where the oscillation peak at 150 cm-1 is much more pronounced at a low temperature, signaling wave packet motion. At a higher temperature the rate decreases to the incoherent limit given by standard theory.51,55,56,58 In the case of double proton transfer and the rotations of the water-A molecule the primary problem is not whether the motion is coherent or incoherent. Coherence is in that case introduced by ET and can hardly increase the reversible ET rate. The increase of the (irreversible) rate is very likely due to the stabilization of the state P+BA- state after ET. Protein dynamics. The basic reason for the oscillations are either a more or less harmonic motion which is activated because the equilibrium positions are changed in the new electronic state, or motion such as the one in water-A, that has been started because of electron transfer. We do not see any great role for the traditional protein motion, although this would be possible in principle. A much greater role is ascribed to the protein dynamics in a recent paper59 in the interpretation of a rate experiment, where the absorbance changes after excitation at 860 nm of the RC in Rh. sphaeroides and several mutations, due to tryptophan residues around 280 nm, were probed.59 Since all systems showed the same rate of the protein relaxation kinetics, it was argued that ET was set in motion by the latter, with due regard to differences in free energies, rather than by individual ET steps. The latter have very different rates for different mutations. (A possible consequence of this theory would be
that the old stride on whether the electron is at all on BA would become meaningless.) At a long distance from the protein there should be a rather negligible change in the field due to a charge separation of a few Å close to the special pair, if the opposite charges created are screened equally. If the negative charge is screened first, there will be a ∆A in the absorption around 280 nm, since indole behaves in this particular way (see ref 59 for further information). We believe that the electron is quickly screened, for example due to double proton transfer, while the screening of the essentially immobile positive charge, with a very long lifetime, depends on heavier negative ions or groups and therefore on the kinetics typical for the whole protein. IV. Conclusion Our calculations show that the interstitial water-A molecule does not have any free rotation in the ground state. This is unsurprising, but in any case an important result in view of the fascinating and well supported experimental results of particularly of Yakovlev et al.30,31 that are still virtually unexplained theoretically. We are able to conclude that rotation of water-A is possible in the charge transfer excited-state P+BA- in Rh. sphaeroides provided that double proton transfer takes place as a part of the reorganization around the accessory BA chromophore in the primary charge separation. One of the three hydrogen bonds of water-A, the one to PheM197, remains very weak. Rotational motion in a protein requires that a second hydrogen bond is also eliminated. We have shown that the hydrogen bond between water-A and the carbonyl of ring V of BA disappears after double proton transfer, giving a possibility for free rotation around the third hydrogen bond. Double proton transfer stabilizes the P+BA- state according to our calculations, and if this stabilization is reversible, it would explain why the reaction rate increases when water-A is present, since back transfer to P is made more difficult. It is not yet clear whether other natural RC’s perform using similar mechanisms. There appears to be no advantage with a rotating water-A as opposed to a fixed water-A. Water-A seems to be conserved in similar types of cavities in a number of well functioning reaction centers.37 In B. Viridis the same mechanism may be present, since the water-A pocket is similar (Table 6), although water rotations similar to those in Rb. sphaeroides apparently are absent.57 As pointed out by Potter et al.,37 the water-B side also appears to be conserved in efficiently working RC’s, but water-B cavities are indeed different from water-A cavities. It is in fact more likely that water-B is oriented in a way that opposes charge separation. Work is in progress where we hope to be able to confirm that water-B cavities (Table 6) are incapable to perform double proton transfer, at least not in the same way as the water-A. It will be necessary to establish whether reversibility and sufficiently high rate can be achieved in a double proton transfer step. This process has to be dynamically consistent with the subsequent step in the primary charge separation: BA-HA f BA HA-. Since it would take us too far to try to straighten out all relevant details in the present paper, we refer to the free energy surfaces given Figure 7. The double proton transfer (DPT) states are given in the middle of the figure. ET leads to a lowering of the DPT state in such a way that the activation energy disappears. This is consistent with previous assumptions and molecular dynamics calculations on the primary charge separation.21,22 A problem with
12132 J. Phys. Chem. B, Vol. 112, No. 38, 2008
Figure 7. Accepted view of potential energy surfaces P* and P+BA-. The x-axis is the reorganization coordinate, that is here modeled as double proton transfer. The protons are thus moving toward BA in a fast motion since the activation energy disappears. PBA is a hypothetical double proton transfer state without ET. The dashed states are hypothetical enol states.
DPT is that transfer from the enolate form BA--p+ assumed here to the enol form pBA (dashed curves; p is the proton) is possible. If a proton appears in the vicinity of the keto group on reduced BA this enolate state may become stabilized as an enol state where the keto group has been replaced by a hydroxyl group. The enol state has other bond lengths in the whole macro-cycle and is therefore connected with large reorganization energy as is indicated in Figure 7 by a high activation barrier. The protons are thus moving toward BA in a fast motion since the activation energy disappears, but the system is hindered to enter the enol state immediately, even if this might be energetically possible. The energies of the latter states are hypothetical. Unfortunately a full understanding of the charge separation process in photosynthesis requires very extensive calculations involving three or more cofactors. Acknowledgment. N.I. would like to thank the Belarus State Program “Bioengineering and Biosafety” for support. We also want to thank the Royal Academy of Science of Sweden (KVA) and the Swedish Science Council (VR) for continuous support. References and Notes (1) Deisenhofer, J.; Epp, O.; Miki, K.; Huber, R.; Michel, H. J. Mol. Biol. 1984, 180, 385. Deisenhofer, J.; Epp, O.; Miki, K.; Huber, R.; Michel, H. Nature 1985, 318, 618. Michel, H.; Epp, O.; Deisenhofer, J. EMBO J. 1986, 5, 2445. (2) Chang, C. H.; Tiede, D.; Tang, J.; Smith, U.; Norris, J. R.; Schiffer, M. FEBS Lett. 1986, 205, 82. Allen, J. P.; Feher, G.; Yeates, T. O.; Rees, D. C.; Deisenhofer, J.; Michel, H. Proc. Natl. Acad. Sci. USA 1986, 83, 8589. (3) Shuvalov, V. A.; Yakovlev, A. G. FEBS Lett. 2003, 540, 26–34. (4) Shuvalov, V. A.; Klevanik, A. V.; Sharkov, A. V.; Matveetz, Yu.A.; Krukov, P. G. FEBS Lett. 1978, 91, 135–139. (5) Holzapfel, W.; Finkele, U.; Kaiser, W.; Oesterhelt, D.; Scheer, H.; Stilz, H. U.; Zinth, W. Chem. Phys. Lett. 1989, 160, 1. Holzapfel, W.; Finkele, U.; Kaiser, W.; Oesterhelt, D.; Scheer, H.; Stilz, H. U.; Zinth, W. Proc. Natl. Acad. Sci. U.S.A. 1990, 160, 5168–5172. (6) Fleming, G. R.; Martin, J. L.; Breton, J. Nature 1988, 333, 190– 192. (7) Breton, J.; Martin, J. L.; Migus, A.; Antonetti, A.; Orszag, A. Proc. Natl. Acad. Sci. U.S.A. 1986, 83, 5121–5125. (8) Larsson, S.; Braga, M.; Broo, A.; Ka¨llebring, B. Int. J. Quantum Chem. 1991, 18, 99–118.
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JP711924F
