Study of Electronic Structures and PigmentâProtein Interactions in the

Article pubs.acs.org/JPCB

Study of Electronic Structures and Pigment−Protein Interactions in the Reaction Center of Thermochromatium tepidum with a Dynamic Environment Fulu Zheng,† Mengting Jin,† Tomás ̌ Mančal,‡ and Yang Zhao*,† †

Division of Materials Science, Nanyang Technological University, Singapore 639798, Singapore Faculty of Mathematics and Physics, Charles University in Prague, Ke Karlovu 5, 121 16 Prague 2, Czech Republic

‡

S Supporting Information *

ABSTRACT: On the basis of the recently reported X-ray crystal structure of light-harvesting complex 1−reaction center (LH1-RC) complex from Thermochromatium tepidum, we investigate electronic structures and pigment−protein interactions in the RC complex from a theoretical perspective. Hybrid quantum-mechanics/molecular-mechanics methods in combination with molecular dynamics simulations are employed to study environmental effects on excitation energies of RC cofactors with the consideration of a dynamic environment. The environmental effects are found to be essential for electronic structure determination. The special pair, a dimer of bacteriochlorophylls which serves as the primary electron donor in the bacterial RC, is our focus in this work. The first excited state of the special pair is found to have the lowest excitation energy of all molecules in the system, making it the most likely populated site after the excitation transfer. The transition charges from electrostatic potentials and the point dipole approximation have been applied to calculate the electronic coupling between individual pigments and that between the special pair and other pigments. Stronger electronic coupling is obtained between the PM molecule and the L branch pigments than that between the PM and the pigments in the M branch. Quantum chemical calculations reveal charge transfer characteristics of the first excited state of the special pair. It follows that charge separation takes place along the L branch in the RC. Spectral densities for all the cofactors are also calculated.

I. INTRODUCTION Photosynthesis is one of the most important biological proceses on Earth in which solar energy is harvested by light-harvesting antennas with excitation energy transferred to the reaction center (RC), followed by charge separation (CS) and electron transfer (ET).1 The excitation energy is eventually converted into chemical energy with nearly 100% quantum efficiency.2−4 A deeper understanding of the efficient energy transfer in natural photosynthesis would be extremely beneficial to the design of artificial photosynthetic devices with high efficiency and robustness. Purple bacteria are considered to have the oldest and the simplest photosynthetic apparatus of all photosynthetic organisms.5 Since the first report of the X-ray crystal structure of the reaction center from Rhodopseudomonas (Rps.) viridis,6−8 the purple bacterial RC has been used extensively as a model system for the investigation of photosynthetic energy transduction and principles governing biological electron transfer. This is mainly due to its robust, tractable membrane protein.9,10 Thermochromatium (Tch.) tepidum is a thermophilic purple sulfur bacterium species discovered in the Mammoth Hot Springs of the Yellowstone National Park where it endures temperatures of up to 58 °C, the highest known of all thermophilic bacteria.11,12 In the photosynthetic systems of Tch. tepidum, the solar energy is mainly absorbed by two light-harvesting antenna complexes: the light-harvesting complex 1 (LH1) and the light-harvesting © 2016 American Chemical Society

complex 2 (LH2). The excitation energy is transferred from LH1 and LH2 to a third pigment−protein RC complex which is located at the center of LH1. Reported crystal structures of the photosynthetic systems in this species13−16 provide invaluable structural information for further theoretical investigations of the mechanism of excitation energy transfer and ET in these systems. Similar to the RC complex from Rhodobacter (Rb.) sphaeroides,17−20 three protein subunits, the so-called L, M and H subunits, and the protein of Cytochrome (Cyt) are included in the RC complex from Tch. tepidum. All these RCs also contain the same cofactors,13,16,21 namely, four bacteriochlorophylls (BChls), two bacteriopheophytins (BPhes), one spirilloxanthin (SPX), one menaquinone (MQ), one ubiquinone (UQ) and four heme molecules.22 One non-heme iron (assigned to be a ferrous ion) located between two quinone molecules and a calcium ion at the interface of the Cyt and M subunits were also found in the RC complex of Tch. tepidum from the crystal structure of LH1-RC complex with a resolution of 3.0 Å.16 Four BChls and two BPhes are arranged in two quasi-symmetric branches, the L and M branches which are associated with polypeptides L and M, respectively. These Received: July 1, 2016 Revised: September 1, 2016 Published: September 5, 2016 10046

DOI: 10.1021/acs.jpcb.6b06628 J. Phys. Chem. B 2016, 120, 10046−10058

Article

The Journal of Physical Chemistry B

purple bacteria.32,33 Compared to the experiments on the RC from Tch. tepidum, theoretical investigations of the asymmetric pathway selection remain elusive. The electronic coupling and the pigment-environment coupling are two fundamental factors affecting the dynamics of excitation energy transfer in photosynthetic complexes.46 To our knowledge, no theoretical studies on electronic coupling and pigment−environment coupling have been reported on the RC complex from Tch. tepidum. Classical molecular dynamics (MD) simulations allow investigations of arrangements, conformational motion, and electronic ground state properties of systems with sizes comparable to, or larger than, typical light-harvesting systems.47 The quantum mechanics/molecular mechanics (QM/MM) approach has been widely employed to elucidate environmental effects on the preferential selection of energy transfer pathway at different photosynthetic systems.48−54 For instance, Gao et al.48 employed the QM/MM method combined with MD simulations to find that the pigment−environment coupling plays an important role in determining excitation energy transfer pathways in Fenna−Matthews−Olson (FMO) light harvesting complex in green sulfur bacteria. Zhang et al.49 constructed an exciton model via extensive QM/MM calculations based on MD simulations to investigate the environmental effects on the preferential selection of the CS and ET pathways of the RC from PS II. In this paper, we apply a combination of classical MD simulations and semiempirical quantum chemistry methods to study influences of the environment on the electronic structures of the pigments in the RC from Tch. tepidum. The pigment-environment coupling strength of the system is also calculated based on the trajectories from the MD simulations. The determination of the environmental effects on the unidirectionality of the CS and ET will be discussed for the RC from Tch. tepidum. The paper is organized as follows. Section II describes the details of computational methods employed in this work. The main results are collected in section III including the excitation energies, electronic coupling, and the spectral densities of all the cofactors. Finally, conclusions are drawn in section IV.

pigments are labeled as PL, PM, BChL, BChlM, BPhL, and BPhM with PL and PM standing for the two BChls which form the special pair P. BChL and BChlM are called accessory bacteriochlorophylls (Acc. BChls). The arrangements of all the cofactors in the RC complex from Tch. tepidum are shown in Figure 1.

Figure 1. Structure of the RC from Tch. tepidum extracted from the LH1-RC complex (PDB ID: 3WMM).16 Different protein subunits are labeled and distinguished by different colors, i.e., Cyt in blue, L in pink, M in green, and H in red. Six cofactors, i.e., two BChls composing the special pair (PL and PM, red), two accessory BChls (BChL and BChlM, royal) and two BPhes (BPhL and BPhM, green) are embeded in the proteins. Two quinones (UQ and MQ, purple), four heme molecules (heme-1, -2, -3, and -4, gray), one spirilloxanthin (SPX, orange), and two ions (Ca2+ and Fe2+) are also included in the simulations.

Even with two quasi-symmetric branches, CS and ET mainly occur asymmetrically through the L branch which is correspondingly called the active branch9,23−31 in the purple bacterial RCs. The primary phase of CS mainly occurs at the special pair, located close to the periplasmic side of the membrane, which is the primary electron donor.22,32 Then the electron is rapidly transferred to BPhL via BChL within 5 ps33 at room temperature, before arriving at MQ, also located at the L branch, and it is finally picked up by UQ which transports two electrons and two protons away from RC to the cytochrome bc1 complex on the other side of the membrane.2,31 Various CS processes have been reported for different types of RCs with different pigment configurations. For the RCs in photosystem II (PS II),34−39 neighboring pigments have similar intermolecule distances, and multiple CS pathways initialized from different primary exciton-charge-transfer states40−43 were proposed. Recently vibronic coherence has been detected from the two-dimensional electronic spectroscopy experiments on the PS II RCs and the presence of specific nuclear modes was predicted to enhance the efficiency of CS in this system.44,45 On the basis of quasi-symmetric pigment arrangements and asymmetric pathway selection of two branches, different surroundings of the pigments in two branches are proposed to underlie the unidirectionality of the CS and ET in RCs from

II. COMPUTATIONAL DETAILS Structure of the RC complex used in this work is extracted from the crystal structure of LH1-RC complex of Tch. tepidum (PDB ID: 3WMM) at 3.0 Å resolution.16 As is shown in Figure 1, three protein subunits in RC, i.e., the L, M, and H subunits, and the protein of Cyt are included in our system as well as all the cofactors, i.e., four BChls, two BPhes, one SPX, two quinones (MQ and UQ), and four heme molecules. One calcium ion and one non-heme iron ion are also included in the simulation. The system is neutralized by adding five chloride ions and solvated into a water box composed of TIP3P water molecules with 15 Å from the boundaries of the complex to the edges of the box. The size of the simulation box is 125.0 Å × 106.5 Å × 153.0 Å with 190989 atoms in total. All simulations are performed with the NAMD package with the CHARMM27 force field55−57 for the protein and the ions. The force field parameters for the cofactors (BChl, BPhe and heme) and UQ molecule are from the literature.58 The parameters for MQ and SPX molecules are obtained from the CGenFF program.59,60 After 20000 steps of energy minimization, the system is gradually heated up from 30 to 270 K in 90 ps and equilibrated at 300 K for 200 ps in an NVT ensemble, followed by two separate simulations for 300 and 77 K, respectively. As to the 10047


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III. RESULTS AND DISCUSSION Excitation Energies. From the two sets of 6 ns NPT simulations at 77 and 300 K, 2000 snapshots are extracted from the trajectories of the last 4 ns with one snapshot recorded every 2 ps. Excitation energies of the cofactors are obtained as the average of results calculated for all the snapshots. We first calculate the site energies for all the individual cofactors, i.e., PL, PM, BChL, BChlM, BPhL and BPhM, at 77 and 300 K. In Figure 2, the site energies for these cofactors in

simulation at 300 K, a 6 ns NPT run (T = 300 K, P = 1 bar) is performed directly, while for the 77 K case, the system is first simulated in another NVT ensemble at 77 K for 200 ps followed by 6 ns simulation under NPT ensemble (T = 77 K, P = 1 bar). A time step of 2 fs is applied for all MD simulations. Calculated root-mean-square deviations (RMSDs) of the protein backbones and the cofactors are used to verify system equilibration (see Figure S1 in the Supporting Information). The energy gaps between the ground states and the first excited states of the cofactors are calculated individually. The Zerners intermediate neglect of differential orbital with parameters for spectroscopic properties (ZINDO/S)61,62 combined with the configuration interaction singles (ZINDO/S-CIS) method (implemented in ORCA program version 2.863,64) is adopted to calculate the excitation energies. An active space spanned by the 10 highest occupied and the 10 lowest unoccupied orbitals is applied to describe the configuration interaction. Configurations extracted from the equilibrated trajectories are utilized to prepare input files for excitation energies calculations. Besides numerous applications of this method to site energy calculations of various photosynthetic pigments,48−50,52−54,62,65−73 the ZINDO method has also been successfully applied to establish the electronic structure of the special pair from the bacterial RCs.74−77 In this work, we also adopt the ZINDO/S-CIS method to calculate excited state energies of the special pair in the RC of Tch. tepidum. To investigate the influence of the environment on the excitation energies of the cofactors, two sets of excitation energy calculations are performed. We first calculate the excitation energies for the cofactors with different configurations without the consideration of the environment. Another set of calculations is done by modeling the surrounding atoms of the target cofactor (within a cutoff radius) as atomic point charges (PCs). This treatment has been widely applied to obtain the electronic structure of the pigments in various photosynthetic systems, such as LH2, FMO, and PSII.48−50,72,73 The effect of the cutoff radii on the electronic structure was investigated recently50 and a cutoff radius of 20 Å was adopted to calculate the excitation energies of the LH2 pigments. In order to determine if a cutoff radius is sufficiently large for calculations in this work, we performed calculations of the excitation energy of the PL pigment with larger cutoff radii. Only minor changes in the average excitation energy are found when the cutoff radius is larger than 20 Å, and therefore, a cutoff radius of 20 Å is also applied in this work. Fully dynamic PCs which are updated for every snapshot are selected and used for the calculations in our work. The calculations for all snapshots can also be performed with the same PCs which are selected from a certain snapshot and called “frozen PCs”.65 Even though the “frozen PCs” can take the surrounding environment of the pigments into consideration, the same PCs for all the snapshots represent a “frozen” environment and the fluctuations of the excitation energy are mainly induced by the different configurations of the pigments. In contrast to the “frozen PCs”, both the total number and the coordinates of the PCs in our calculations are distinct for each snapshot. As a result, calculated excitation energies in this paper have larger fluctuations compared to those obtained with “frozen PCs”. We use dynamic PCs in all calculations to subject the cofactors to a realistically fluctuating environment.

Figure 2. Excitation energies of the cofactors in the RC with (magenta) and without (cyan) the consideration of surrounding environment at 77 and 300 K. For the separated pigments, i.e., PL, PM, BChL, BChM, BPhL, and BPhM, the excitation energies are the energies of the first excited states. For the special pair (P), the excitation energies for P1 and P2 are energies of the first and second excited states of P, respectively. All the results are averaged over 2000 configurations extracted from 4 ns production simulations with the blue lines being the standard deviations.

vacuum (without considering the surrounding environment) are depicted. We can see that the site energy differences between the L branch cofactors and their M branch counterparts are originated in different protein environments and different configurations of the pigments. For the vacuum case, the cofactors in the L branch have similar site energies as their counterparts in the M branch. This indicates that the fluctuations in the pigment configurations in the two branches have similar influences on the pigment excitation energies. Compared to Acc. BChls, BPhes have lower site energies in vacuum at both 77 and 300 K. However, the BPhes have a shorter wavelength absorption band (755 nm) than Acc. BChls (800 nm) in the RC according to measured absorption spectra.78 Therefore, it is essential to include environmental effects in electronic structures calculations of the RC complex. Taking into account the surrounding atoms within 20 Å of the cofactors, the site energies for most cofactors show obvious corrections compared to those calculated in vacuum. For PL and PM which compose the special pair, PCs surrounding them contribute to an increase in their site energies by 47 and 104 meV at 300 K, and by 28 and 63 meV at 77 K, respectively. An increase in the site energy induced by the PCs is also found for BPhL (BPhM) by 33 meV (87 meV) at 300 K, and 21 meV (91 meV) at 77 K. Except for the slightly lower site energy of BPhL at 77 K, both BPhL and BPhM have larger site energies than BChL and BChlM in most cases, a finding that is consistent with published results.78,79 The special pair in the RC from Tch. tepidum serves as the primary electron donor, and the BChls of the special pair have the longest absorption wavelength (885 nm) according to measured spectra.78 Contradictorily, the two BChls composing the special pair, i.e., PL and PM, have higher site energies than two Acc. BChls at both 77 and 300 K when the surrounding 10048


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Table 1. Electronic Coupling (Unit: cm−1) with both PDA and TrEsp Methods, Center-to-Center Distances (Unit: Å), and Angles between the Transition Dipole Moments (Unit: deg) of the Separated Pigments in the RC at 300 and 77 K 300 K PL−PM PL−BChL PL−BChM PL−BPhL PL−BPhM PM−BChL PM−BChM PM−BPhL PM−BPhM BChL−BChM BChL−BPhL BChL−BPhM BChM−BPhL BChM−BPhM BPhL−BPhM

77 K

VTrEsp mn

VPDA mn

Rmn

angle

VTrEsp mn

VPDA mn

Rmn

angle

339.65 −50.64 −152.17 −15.74 41.97 −144.74 −66.89 39.63 −13.51 18.11 162.72 −10.16 −8.97 174.7 7.64

535.31 −13.65 −85.83 −6.04 20.12 −73.84 −15.48 19.33 −8.72 11.03 112.04 −5.34 −5.08 131.23 3.49

7.69 11.35 13.34 16.41 19.82 13.84 10.40 19.51 16.48 22.39 10.37 25.24 24.50 10.40 23.84

137.76 135.18 7.25 96.18 129.20 11.63 141.67 120.96 87.56 140.23 116.13 93.78 94.67 122.99 64.68

308.13 −67.82 −144.77 −11.19 42.42 −171.57 −53.38 39.97 −15.86 18.49 184.25 −11.47 −7.84 143.37 6.85

635.54 −23.68 −81.96 −3.80 20.05 −94.39 −6.58 19.33 −8.65 11.77 125.78 −6.12 −4.45 118.08 2.82

7.33 10.68 13.48 16.41 20.20 12.88 10.73 19.23 16.86 21.81 10.51 24.83 24.42 10.63 23.87

136.82 131.72 8.41 94.60 134.46 10.54 142.29 121.30 83.76 138.53 118.26 91.66 92.77 126.29 70.83

conjectured that the two BPhes play a crucial role in the determination of pathways for CS and ET in the RC complex of Tch. tepdium as the asymmetric environment of BPhL and BPhM will most likely affect the charge-transfer states. As to the temperature effects on the site energies of the cofactors, it is found that a higher temperature leads to larger fluctuations in the results. The special pair P has more atoms and more PCs surrounding it, such that flexibilities are included in the calculations, producing a larger standard derivation of the excitation energy than other cofactors. Electronic Coupling. In addition to the site energies of the RC cofactors, we also calculate electronic interactions between the cofactors. Because of a sufficiently large interpigment distance and a lack of orbital overlaps, electronic coupling between pigments in photosynthetic systems can be often calculated with the point dipole approximation (PDA) as

PCs are included in the calculations and the pigments are treated as separate units (see Figure 2). Digging into the crystal structure of the RC complex, we can explore the spatial arrangements of PL and PM. These two BChls are relatively close to each other with a distance of 7.7 Å between the magnesium atoms of the two molecules. The porphyrin rings of these two BChls are nearly parallel. On the basis of the configurations of the special pair, we can expect not only strong resonance coupling leading to a loss of individuality of the two molecules, but also a non-negligible orbital overlap between the two molecules. To facilitate excitation energy calculations we treat PL and PM as one aggregate P. Because of the strong electronic coupling within the two monomers of the special pair, the first excited states of PL and PM will split into two energy levels of P,80 denoted as, P1 and P2. The same calculation method as introduced above has been applied to obtain the excitation energies for the first two excited states of P. At both 77 and 300 K, excitation energies calculations of P with and without the consideration of surrounding PCs have been performed for 2000 snapshots and the averaged results are shown in Figure 2. As the first excited state, P1 has the lowest energy of all pigments, responsible for the longest wavelength absorption band in the absorption spectrum of the RC complex.78,79 The excitation energies of P1, 1.427 ± 0.124 eV at 300 K and 1.426 ± 0.056 eV at 77 K, show excellent agreement with that from the measurements (1.40 eV). The red shift of the excitation energy of P1 and the blue shift of P2 with respect to PL and PM are attributed to strong electronic coupling and energy level splitting. As shown in Figure 2, BChL and BChlM have very similar site energies even when the surrounding PCs are included in the calculations, and the differences are only 0.6 meV at 77 K and 4.3 meV at 300 K. This indicates that the environment-induced site energy difference between BChL and BChlM is negligible. In contrast, the site energies of BPhL and BPhM show larger changes after the inclusion of their environments. BPhL has lower site energies than BPhM with a gap of 60.7 meV at 77 K and 44.6 meV at 300 K. This means that the surrounding environments of BPhL and BPhM have totally different influences on these two pigments. The asymmetric electronic structure of BPhL and BPhM will contribute to the asymmetry of the two branches. On the basis of our calculated results, it is

PDA Vmn =

fmn μm μn 4πε0 R mn3

[em̂ ·en̂ − 3(em̂ ·emn ̂ )(en̂ ·emn ̂ )]

(1)

where μm (μn) is the magnitude of the Qy transition dipole moment of pigment m (n) pointing along the unit vector êm (ên), Rmn is the center to center distance between pigments m and n, and êmn is the unit vector pointing from pigment m to n, ε0 is the dielectric constant, and f mn is a factor to account for the influence of the solvent on the electronic coupling. This method has been widely applied to calculate electronic coupling of pigments from various photosynthetic systems, such as LH1,81 LH2,66−68 FMO,48,82−84 and RC82 complexes. However, the method is only valid for pigments separated by large intermolecular distances,85 and it overestimates the electronic coupling for densely packed pigments,82 such as PL and PM. For closely packed pigments, Renger and co-workers calculated interpigment electronic coupling using transition charges from the electrostatic potentials (TrEsp) method82,86 TrEsp Vmn

=

fmn 4πε0

∑ I ,J

qIm ·qJn |RmI − RnJ|

(2)

Here, RmI (RnJ ) is the coordinate of atom I (J) in pigment m (n), and qmI (qnJ ) is the transition charge which is obtained by fitting the electrostatic potentials of the transition densities.82 10049


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coupling than that in PL−BChL (PM−BChM) although the intermolecular distance in PL−BChM (PM−BChL) is larger than that in PL−BChL (PM−BChM). Similar to PL−PM, short interpigment distances in BChL−BPhL and BChM−BPhM give rise to relatively strong coupling. Large intermolecular distances and nearly perpendicular arrangements of transition dipole moments produce relatively weak electronic coupling for BChL−BPhM and BChM−BPhL. Among all the pigments, BPhL and BPhM have the weakest electronic coupling which results from a large interpigment distance, an unfavorable angle between the two transition dipole moments, and a smaller transition dipole moment of BPhe molecules than that of the BChl molecules. PM presents stronger electronic coupling with the pigments in the L branch (BChL and BPhL) than that with the M branch pigments. Strong electronic coupling between PM and the L branch pigments will contribute to the directionality of the CS and ET process along the L branch as there are charge transfer characteristics of the first excited state of the special pair (from PL to PM), which will be discussed below. We also calculate the electronic coupling between P and other four pigments (BChL, BChM, BPhL and BPhM). We first construct an excitonic Hamiltonian

In this study, we apply quantum chemistry calculations to obtain the transition charges of BChl and BPhe molecules. The molecular geometry is first optimized by the density functional theory (DFT) method with the B3LYP functional and the 631G**basis set.49,82 The CHELPG program87 is then employed to obtained the transition charges based on the excitation transition density of the molecule calculated with the time-dependent density functional theory (TDDFT) on the optimized molecular structure. All DFT calculations are performed with the GAUSSIAN 09 package.88 In the calculations of transition charges, the phytyl tail is replaced with a CH3 group and the transition charges of the hydrogen atoms are added to the bonded carbon, oxygen and nitrogen atoms. The transition charges for individual BChl and BPhe molecules are shown in Table S1 of the Supporting Information. The measured magnitudes of the Qy transition dipole moments for the calculations of VPDA mn are 6.40 and 6.25 D for BChl and BPhe molecules, respectively.89 In this work, the calculated magnitude of BChl Qy transition dipole moment is 7.23 D which agrees well with other published results.90 For the BPhe molecule, the magnitude of the dipole moment associated with the Qy transition is 6.68 D. To match the experimental values, the transition charges for BChl and BPhe are rescaled by factors of 0.885 and 0.936, respectively.49,58,82 The screening factor f mn has been reported to be dependent on the center to center distance Rmn between two molecules as f mn = 2.68 × exp(−0.27·Rmn) + 0.54.91 The magnesium atom of BChl is taken as the pigment center, and the center of BPhe is taken as the center-of-mass of two nitrogen atoms [N2 and N4 atoms in Figure S2(b) of the Supporting Information]. The center of the magnesium atoms of PL and PM is treated as the midpoint between special pair P. Electronic coupling calculations have been performed on the same 2000 configurations used for the site energy calculations and final results are averaged along the trajectories. Both the PDA and the TrEsp methods are used to calculate the electronic coupling between six individual pigments at 300 and 77 K with the results shown in Table 1. At both 300 and 77 K, PL and PM have the strongest electronic coupling among all the cofactors, consistent with the analysis in the previous section. The electronic coupling between PL and PM calculated with the TrEsp method is comparable with what has been reported by other authors.79,92 Compared with the TrEsp method, the PDA method produces stronger electronic coupling for PL and PM at both temperatures, which is also consistent with the assertion that the PDA method overestimates the electronic coupling for the pigments separated by short distances.82 For other pigments, the trend is reversed. The electronic coupling of BChL−BPhL and BChM−BPhM obtained with the TrEsp method is in excellent agreement with the experimental value of ∼170 ± 30 cm−1,93 lending support to the validity of the TrEsp method.94 Separations and orientations of the transition dipoles are main factors that influence the coupling strength between two pigments. VPDA mn is determined by the coordinates of three atoms [Mg1, N3, and N5 atoms in Figure S2(a) of the Supporting Information] and is more sensitive to the interpigment distance than VTrEsp mn . The short intermolecular distance between PL and PM contributes to its strong electronic coupling. For each of the two methods, there are four other relatively strong electronic coupling strengths as shown in Table 1. Taking for example the results at 300 K, the smaller angle between the two transition dipole moments in PL−BChM (PM−BChL) leads to stronger

⎛ E P VP P ⎞ L L M ⎟ HP = ⎜⎜ ⎟ V E PM ⎠ ⎝ PMPL

(3)

for the special pair with EPL (EPM) being the site energy of PL (PM) including the consideration of PCs as obtained in the previous section. VPLPM is the electronic coupling between PL and PM, which is shown in Table 1. The two exciton states P− and P+ can be obtained by diagonalization of HP with a transformation matrix

⎛ α β⎞ ⎟⎟ S = ⎜⎜ ⎝− β α ⎠

(4)

yielding exciton state energies ϵP− and ϵP+. Three methods will be applied in this section to the calculation of electronic coupling between the special pair and the other pigments. The electronic coupling between the P− state and the other pigments is computed as well as that between the P+ state and the other pigments. In the first method, the transition dipole moments for the two exciton states of the special pair are constructed and utilized to compute the electronic coupling with the PDA method. With the coefficients α and β obtained from the diagonalizaton of HP, the transition dipole moments for P− and P+ can be expressed as μ⃗ P− = αμ⃗ PL − βμ⃗PM and μ⃗ P+ = βμ⃗PL + αμ⃗ PM where μ⃗PL (μ⃗PM) is the transition dipole moment of PL (PM) and α2 + β2 = 1.92,95−99 The PDA method is then applied to calculate the electronic coupling between the special pair and the other pigments. VTrEsp PL PM is chosen as the electronic coupling between PL and PM in the diagonalizaton of HP. The values for α and β are 0.8690 and 0.4948 at 300 K (0.8082 and 0.5889 at 77 K), respectively. We will use the acronym SP-PDA to refer to this method in the rest of this paper. The second method is based on the partial diagonalization of the complete excitonic Hamiltonian (PDH) for the RC system comprising six pigments. Similar to HP, we construct the excitonic Hamiltonian for the system of PL−PM−BChL− BChM−BPhL−BPhM as 10050


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Table 2. Electronic Coupling (Unit: cm−1) from the Methods of SP-PDA, PDH-PDA, PDH-TrEsp and SP-TrEsp between the special pair and the other pigments in the RC at 300 and 77 K 300 K P−−BChL P−−BChM P−−BPhL P−−BPhM P+−BChL P+−BChM P+−BPhL P+−BPhM

H=

77 K

VSP−PDA mn

VPDH−PDA mn

VPDH−TrEsp mn

VSP−TrEsp mn

VSP−PDA mn

VPDH−PDA mn

VPDH−TrEsp mn

VSP−TrEsp mn

78.47 −122.10 −21.26 28.13 -38.13 15.09 12.92 −0.73

30.61 -61.94 −15.94 21.52 -68.52 −61.44 12.49 4.24

27.32 -99.27 −33.23 43.14 -150.94 -133.13 26.73 8.91

66.66 -36.46 −43.26 39.33 -145.07 -176.42 16.17 24.88

98.87 -112.39 −20.04 27.32 -38.43 1.26 10.68 2.89

43.35 -58.01 −15.45 20.86 -87.12 −58.27 12.22 6.46

46.06 -85.68 −32.56 43.63 -178.67 -128.30 25.74 12.12

75.09 -42.49 −39.74 41.77 -178.82 -159.11 20.04 23.91

than P+ (P−). As shown in Table 1, PL−BChM (PM−BChL) has relatively stronger electronic coupling than PL−BChL (PM− BChM), and it follows that P−−BChM (P+−BChL) exhibits stronger coupling than P−−BChL (P+−BChM). Compared to the SP-PDA and PDH-PDA methods, the PDH-TrEsp and SPTrEsp methods lead to stronger coupling between the P+ state and the other pigments. This effect is due to the nearly antiparallel arrangement of transition dipole moments of PL and PM. In the SP-PDA method, the electronic coupling between the special pair and the other pigments is directly computed with the PDA method based on the transition dipole moments of the special pair. It is a crude approximation to construct the dipole moments of the excited states of the special pair from the transition dipole moments of single molecules (PL and PM), as the local excitation is assumed and the charge transfer characteristics cannot be captured. Additionally, the transition dipole for the P+ state is very small, which leads to underestimation of coupling between the P+ state and the other pigments. Another drawback induced by the small value of transition dipole of the P+ state is that its sign is very sensitive to the configuration fluctuations of individual molecules. A small configuration change of BChls of the special pair may flip the direction of the transition dipole moment of the P+ state. So the electronic coupling between the P+ state and the other pigments calculated with the SP-PDA method is not as accurate as those obtained with the other three methods (PDH-PDA, PDH-TrEsp, and SP-TrEsp). The sign of the electronic coupling may also be at variance with those from the other methods as a result of the small transition dipole moment of the P+ state which may flip its direction for different configurations. The results of the SP-TrEsp method are not affected by the biased site energies of PL and PM, and the constructions of the transition dipole moments for the two exciton states of the special pair (P− and P+). The SP-TrEsp method gives stronger electronic coupling for P−−BChL than P−−BChM. Stronger electronic coupling between P− and BChL favors the CS along the L branch from the excited special pair. The electronic coupling between the special pair and the other pigments calculated with the SP-TrEsp method will be applied for the further calculations below. The system of P−−P+−BChL−BChM−BPhL−BPhM can be described with the partially diagonalized Hamiltonian H′ in which the coupling between P− and P+ is zero. The site energies in H′ (diagonal entries) have been obtained in the previous section with the effects of the environments included (see the magenta columns in Figure 2). The electronic coupling between two individual pigments is calculated with the TrEsp method (shown in Table 1), and the SP-TrEsp method is applied to compute the electronic coupling between the special

∑ Em|m⟩⟨m| + ∑ Vmn|m⟩⟨n| m

m≠n

(5)

where Em is the averaged excitation energy of the state |m⟩ localized on cofactor m with the consideration of the surrounding environment, and Vmn is the electronic coupling between |m⟩ and |n⟩. HP is included in H as a 2 × 2 block. In order to obtain the two exciton states of the special pair, the HP block in the complete excitonic Hamiltonian is diagonalized within the framework of an expanded transformation matrix

⎛S 0⎞ ⎟ S′ = ⎜ ⎝0 I ⎠

(6)

where I is a 4 × 4 identity matrix and S is the transformation matrix to diagonalize HP. The complete excitonic Hamiltonian after partial diagonlization can be written as H′ = S′−1HS′

(7)

The electronic coupling between the special pair and the other pigments is included in the first two rows (columns) in H′, and the electronic coupling between any two of the other four pigments remains unchanged from the values in H. Both the TrEsp and the PDA method can be applied to compute the electronic coupling Vmn in eq 5. We denote the method as PDH-TrEsp (PDH-PDA) with Vmn obtained from the TrEsp (PDA) method. Similar to the TrEsp method applied for the individual pigments, we calculate the transition charges for the first two exciton states of the special pair from quantum chemistry, and the transition charges are then utilized to estimate the electronic coupling with the TrEsp method. We denote this method as SP-TrEsp. The transition charges for the first two excited states of the special pair are obtained with the CHELPG algorithm. The excitation transition density is calculated by the TDDFT with the wB97XD functional and the 6-31G** basis set to account for the charge transfer characteristics of the excited states. The transition charges for the first two excited states of P are shown in Table S1 of the Supporting Information. The transition charges are rescaled by the same factor (0.885) as that used for the single BChl. The electronic coupling between the special pair and the other pigments calculated by the above methods at both 77 and 300 K is shown in Table 2. From the results of the SP-PDA, PDH-PDA and PDH-TrEsp methods we can find that P−− BChM and P+−BChL have relatively stronger coupling than P−−BChL and P+−BChM, respectively. The reason is that all these three methods are based on the coefficients obtained from the diagonalization of HP in which PL has a lower site energy than PM, so P− (P+) has a larger population on PL (PM) 10051


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The Journal of Physical Chemistry B Table 3. Exciton Energies (eV) and Coefficients of P−−P+−BChL−BChM−BPhL−BPhM System at 300 and 77 K temp (K)

exciton level

exciton energies

P−

P+

BChL

BChM

BPhL

BPhM

300

1 2 3 4 5 6 1 2 3 4 5 6

1.425 1.499 1.502 1.541 1.578 1.619 1.424 1.486 1.513 1.535 1.568 1.665

0.988 −0.085 −0.127 0.008 −0.021 0.003 -0.985 0.150 0.074 −0.051 −0.020 −0.003

−0.003 −0.207 0.113 0.109 −0.082 -0.962 0.006 0.080 −0.138 −0.127 −0.038 0.978

−0.109 -0.708 −0.341 0.583 0.030 0.176 0.119 0.523 −0.041 -0.828 0.028 −0.156

0.065 -0.416 0.834 −0.051 −0.287 0.205 −0.064 0.008 -0.924 0.055 −0.346 −0.137

0.076 0.512 0.295 0.804 −0.001 0.015 −0.102 -0.836 −0.032 -0.539 0.003 −0.006

−0.044 0.122 −0.269 0.024 0.954 0.026 0.047 0.004 0.344 −0.041 -0.937 0.007

77

devoted to constructing the electronic structures of P and to explaining the directionality of CS and ET. Asymmetric charge density distributions on the two halves of P have been revealed as an intrinsic property of P,117,119 and observed in the ground and the excited state of P74,100−111,115−121,125 as well as in the cation radical of P.112,113,116,117 The symmetry breaking of the charge density distribution in PL and PM could result from various factors, e.g., different orientations of the side groups of two pigments105,116,117,119 and tuning effects of the surrounding protein residues.103,104,115,117,120 For the RCs from Rb. sphaeroides, PL (PM) has a higher electron density when P is in the ground (excited) state. The asymmetric charge distribution on P then gives rise to the P+LP−M charge transfer (CT) characteristics for the excited state of P. At the closing of this section, we present investigation of the special pair. In addition to the transition charges we also obtain the transition densities of the first two excited states of the special pair using quantum chemistry calculations. As illustrated in Figure 4, the plots of the transition densities for P− and P+ agree well with the analytical predictions. As discussed in the previous section, the P− state is an antisymmetric combination of the localized excited states on PL and PM with a transition dipole moment of μ⃗P− = αμ⃗ PL − βμ⃗PM, while the P+ state is a symmetric combination with a transition dipole moment of μ⃗P+ = βμ⃗ PL + αμ⃗PM. From the transition densities shown in Figure 4, it is found that the PL has an ordinary Qy excitation in the two states. PM presents a transition dipole opposite (parallel) to the Qy direction in the P− (P+) state. In order to investigate the transition characteristics of the first two excited states of the special pair, we calculate contributions from the orbital transitions to these two excited states, and the results are shown in the right column in Figure 4. The excitations to P− and P+ are mainly attributed to the transitions among the four molecular orbitals (as shown in Figure 4) including the highest occupied molecular orbital (HOMO) and lowest unoccupied molecular orbital (LUMO). The states of P− and P+ are mainly composed of two transitions of HOMO−1 → LUMO and HOMO → LUMO+1, and both transitions are local. The P− state also has a transition of HOMO → LUMO which possesses an intermolecular charge transfer component from PL to PM. Most of the excited states of the special pair, including the P+ state, have CT characteristics. Not listed in Figure 4 are transitions with a CT component and less than 10% contribution to the P+ state. The CT characteristics of the P− state and the strong electronic

pair and the other pigments (shown in Table 2). Diagonalizing the Hamiltonian H′ we obtain the eigenvalues εM and the corresponding eigenvectors ξm(M) as shown in Table 3. Eigenvalue εM is the energy of the delocalized exciton state |M⟩ and ξ(M) m is the coefficient that represents the contribution of the localized excited state on cofactor m to the exciton state |M⟩. As shown in Table 3, the lowest and highest exciton states are mainly localized on P− and P+, respectively. Both the second and the fourth exciton states are delocalized on BChL and BPhL. In contrast, the third and the fifth exciton states are mostly localized on BChM and BPhM, respectively. With the exciton energy εM and the expansion coefficient ξ(M) m we can calculate the excitation probability of the localized excited state on cofactor m which is defined as49 Pm =

∑ f (M)|ξm(M)|2 M

(8)

where f(M) is the Boltzmann factor for the exciton state |M⟩ with energy of εM. The excitation probabilities of all the cofactors in the RC are plotted in Figure 3 at both 300 and 77

Figure 3. Excitation probabilities of the cofactors in the RC at 300 and 77 K.

K. Compared with the Acc. BChls and BPhes, the P− state exhibits the highest probability to be excited at 300 K (PP− ≈ 87%) and 77 K (PP− ≈ 97%) and is the most probable site for initial excitation. As a result of the highest excitation energy, P+ state has very low probability to be excited at both 77 and 300 K. As the primary electron donor in the bacterial RCs, the special pair has been a paradigm for investigations of asymmetric CS and ET in the RCs. Tremendous experimental100−113 and theoretical74,97,114−127 efforts have been 10052


Article

The Journal of Physical Chemistry B Cm(ti) = ⟨δEm(ti)δEm(t0)⟩ =

1 N−i

N−i

∑ δEm(ti + tk)δEm(tk), (10)

k=1

where the summation is over the N configurations extracted from MD trajectories. Then the spectral density Jm(ω) can be written as65,71,132,133 Jm (ω) =

βω π

∫0

∞

dt Cm(t ) cos(ωt )

(11)

where β = 1/(kBT) is the inverse temperature. A total of 50000 configurations are extracted from the 100 ps NPT production simulation at 300 K and used for the excitation energy calculation with a time step of 2 fs between adjacent snapshots. Time windows of 4 ps are prepared to calculate the correlation functions with a spacing of 400 fs between adjacent time windows. There are 241 4 ps-long time windows along a trajectory of 100 ps and the final correlation functions are averaged over the correlation functions calculated for all the time windows. We multiply the correlation function by a Gaussian window function in order to avoid the spurious effects in the numerical Fourier transformation of the correlation function.53,132,133 This corresponds to a convolution of the actual spectral density with a Gaussian function with standard deviation of 7.4 cm−1. Calculated spectral densities for all cofactors in the RC are shown in Figure 5. For the two pigments PL and PM, which Figure 4. Transition density (left column) for the first two excited state of the special pair in the bacterial RC and the contributions to these excited states from the transitions between different orbital pairs (right column). HOMO and LUMO stand for the highest occupied molecular orbital and lowest unoccupied molecular orbital for the special pair, respectively. In the dimer, the left monomer is PL and the right one is PM.

coupling of PM−BChL favor the CS along the active (L) branch in the RC from Tch. tepidum. Spectral Densities. A key quantity in the description of system-bath coupling is the spectral density. In this section, our focus is the RC spectral density, which quantifies the pigment− protein coupling for all cofactors, using the combined QM/ MM approach. Kleinekathöfer and co-workers have calculated spectral densities for pigments in LH2,58 FMO69 and PE54565 from pigment excitation energy fluctuations calculated by quantum chemistry approaches. Renger et al. proposed a charge density coupling (CDC) method83,86,128,129 to obtain excitation energy fluctuations, which has been applied to calculate spectral densities for the pigments in FMO130,131 and RC70 from Rb. sphaeroides. In this work, site energies are calculated for the pigments in the RC based on the trajectories from MD simulations, and site energy fluctuations are utilized for spectral density estimation for all cofactors in the RC. The excitation energy fluctuation δEm(ti) for cofactor m is defined as δEm(ti) = Em(ti) − Em̅

Figure 5. Spectral densities of the cofactors in the RC based on the MD simulations at 300 K. The excitation energy for the first excited state of P is used to calculate the spectral density for P.

compose the special pair, the spectral densities have similar shapes while the coupling to the surrounding environment of PM is slightly stronger than that of PL. As a result of the short distance between PL and PM, a large number of surrounding atoms of the two pigments are the same, which leads to similar coupling of the two molecules to nuclear modes. We also calculate the spectral density for the first excited state of the special pair P which is shown as the solid red line in Figure 5a. Besides the intramolecular vibrational modes of BChls, the intermolecular modes between PL and PM also contribute to the

(9)

where Em(ti) is the site energy at time ti, and E̅m is the averaged site energy of cofactor m with the consideration of its protein environment. The autocorrelation function of the excitation energy fluctuation for cofactor m is defined as58 10053


Article

The Journal of Physical Chemistry B spectral density of P. As an aggregate of PL and PM, the special pair P has more surrounding atoms included in the site energy calculations than individual pigments (PL and PM), which produce larger fluctuations of its site energy. Both factors give rise to larger amplitudes of the spectral density of P for most frequencies than those of single PL and PM. Among the cofactors, Acc. BChls have the minimal spectral density amplitudes. The position and the amplitudes of the peaks of the spectral density for BChL are similar to those of BChM, indicating that BChL and BChM are coupled to similar environmental modes with similar strengths. This is in agreement with the results from site energy calculations, from which we find that the surrounding environments of BChL and BChM have nearly the same influences on the two pigments. Comparing the spectral densities of BPhes in Figure 5c to those of all the other cofactors, one can find that BPhes have the strongest pigment−protein coupling strengths of all the cofactors in the RC. BPhM is coupled to its surrounding more strongly than BPhL, and differences in amplitude between the spectral densities of the two BPhes are larger than those for Acc. BChls. The strong pigment−protein coupling of BPhes is consistent with the large fluctuations of the site energies of these two pigments. BPhL and BPhM are coupled to their respective protein environments with different coupling strengths, a finding that also leads to differing environmental effects on the site energies of BPhL and BPhM (see Figure 2) and the branch selectivity of the CS and ET in the RC. Corresponding coupling strengths to a specific vibration mode for all the cofactors can be extracted from the calculated spectral densities and made use of in theoretical modeling of the CS and ET dynamics including full details on the nuclear degrees of freedom in these processes. In principle, spectral densities should be independent of temperature and this issue has been discussed in details in recent literature.131,132 We also calculate spectral densities for all the cofactors based on the MD simulations at 77 K with a similar procedure as described above. Results are shown in the Figure S3 in the Supporting Information. The overall shape of the spectral densities is temperature independent. Only for a few pigments, magnitudes of spectral densities show minor difference between different temperatures. In a recent study on the spectral densities of the FMO pigments,53 obvious variations in magnitude are found for the spectral densities calculated from the ZINDO calculations at different temperatures. The spectral densities from ZINDO calculations are also revealed to be dependent on the initial conditions for the production run in MD simulations.53 In current work, variations in magnitudes of the spectral densities at different temperatures may rise from the fact that the production trajectories in MD simulations are initialized from different configurations at 300 and 77 K.

been calculated for all cofactors, quantifying thus the pigment− protein interactions. It is found that only when the environmental effects are included in the calculations, we can obtain reliable electronic structures of pigments in the RC. Treating PL and PM as a single aggregate−the special pair P, we have obtained excitation energies for the first two excited states of P. The first excited state of P is found to have the lowest energy among all the cofactors, which makes it the most probably excited state after the energy transfer process is finished. Two methods, namely, PDA and TrEsp, are applied to calculate the electronic coupling between the individual pigments. Stronger electronic coupling between PM and the pigments in the L branch is obtained than that between PM and the M branch pigments. This finding favors the asymmetric CS along the L branch as quantum chemistry calculations reveal a CT component (PL to PM) in the first excited state of P. The transition charges for the first two excited states of the special pair are calculated using TDDFT and are used, via the TrEsp method, to estimate the electronic coupling between the special pair and other pigments. The SP-TrEsp method produces stronger electronic coupling of P−−BChL than that of P−− BChM which also contributes to directional CS along the L branch. The spectral densities of the cofactors show that two BPhe molecules are more strongly coupled to their surroundings than other cofactors. Both the site energies and the spectral densities of BPhes indicate that the respective environments of BPhL and BPhM have different influences on the target pigments. It is predicted that BPhes also play a crucial role in the determination of the CS and ET pathways. It is our hope that the parameters obtained in this work will find their applications in simulation of CS and ET dynamics as well as in determination of vibrational influences on directionalities of these processes in the RC of Tch. tepidum. Work in this direction is in progress.

IV. CONCLUSION Hybrid QM/MM methods combined with MD simulations have been employed in this work to investigate electronic structures and pigment−protein interactions in the RC complex from Tch. tepidum, using the recently reported 3 Å X-ray crystal structure of the LH1-RC complex. The semiempirical ZINDO/S-CIS method is applied to calculate excitation energies for all cofactors in the RC considering the surrounding environmental atoms within a cutoff radius of 20 Å. On the basis of the site energy fluctuations obtained from the quantum chemistry calculations, spectral densities have also

Corresponding Author

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ASSOCIATED CONTENT

S Supporting Information *

The Supporting Information is available free of charge on the ACS Publications website at DOI: 10.1021/acs.jpcb.6b06628. Molecular structures for the BChl a and BPhe a pigments in the RC of Tch. tepidum, the RMSDs of the protein backbones and cofactors for the production simulations at both 77 and 300 K, the spectral densities of the cofactors in the RC based on the MD trajectory at 77 K, and transition charges in atomic unit for the heavy atoms of BChl a and BPhe a pigments in the RC from Tch. tepidum (PDF)

■

AUTHOR INFORMATION

*(Y.Z.) E-mail: [email protected]. Telephone: +65 6513 7990. Fax: +65 6790 9081. Notes

The authors declare no competing financial interest.

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ACKNOWLEDGMENTS We are grateful to Ulrich Kleinekathöfer for sending us force field parameters of the cofactors. Support from the Singapore National Research Foundation through the Competitive Research Programme (CRP) under Project No. NRF-CRP510054


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2009-04 and from the Singapore Ministry of Education Academic Research Fund Tier 1 (Grant No. RG106/15) is gratefully acknowledged. T.M. acknowledges the kind support of the Czech Science Foundation (GACR) through Grant No. 14-25752S. F.Z. thanks Jing Lu for useful discussion on quantum chemistry calculations.

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