Elastic Vibrations in the Photosynthetic Bacterial Reaction Center

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Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach Georgy E. Milanovsky, Vladimir A. Shuvalov, Alexey Yu. Semenov, and Dmitry A. Cherepanov J. Phys. Chem. B, Just Accepted Manuscript • DOI: 10.1021/acs.jpcb.5b03036 • Publication Date (Web): 06 Jul 2015 Downloaded from http://pubs.acs.org on July 9, 2015

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The Journal of Physical Chemistry

Elastic Vibrations in the Photosynthetic Bacterial Reaction Center Coupled to the Primary Charge Separation: Implications from Molecular Dynamics Simulations and Stochastic Langevin Approach Georgy E. Milanovsky1, Vladimir A. Shuvalov1,2, Alexey Yu. Semenov1,2, Dmitry A. Cherepanov*1,3. 1

- A.N. Belozersky Institute of Physical–Chemical Biology, Moscow State University, Moscow,

Russia 2

- N.N. Semenov Institute of Chemical Physics, Russian Academy of Sciences, Moscow,

Russia. 3

- A.N. Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of

Sciences, Moscow, Russia.

KEYWORDS: photosynthetic bacterial reaction center, Rhodobacter sphaeroides, electron transfer, photoinduced charge separation, oscillatory kinetics, molecular dynamics, Langevin equation.

ACS Paragon Plus Environment

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Primary electron transfer reactions in the bacterial reaction center are difficult for theoretical explication: the reaction kinetics, almost unalterable over a wide range of temperature and free energy changes, revealed oscillatory features observed initially by Shuvalov and coauthors (1997, 2002). Here the reaction mechanism was studied by molecular dynamics and analyzed within a phenomenological Langevin approach. The spectral function of polarization around the bacteriochlorophyll special pair PLPM and the dielectric response upon the formation of PL+PM− dipole within the special pair were calculated. The system response was approximated by Langevin oscillators; the respective frequencies, friction and energy coupling coefficients were determined. The protein dynamics around PL and PM were distinctly asymmetric. The polarization around PL included slow modes with the frequency of 30-80 cm-1 and the total amplitude of 130 mV. Two main low-frequency modes of protein response around PM had the frequencies of 95 and 155 cm-1 and the total amplitude of 30 mV. In addition, a slowly damping mode with the frequency of 118 cm-1 and the damping time >1.1 ps was coupled to the formation of PL+PM− dipole. It was attributed to elastic vibrations of alpha-helices in the vicinity of PLPM. The proposed trapping of P excitation energy in the form of the elastic vibrations can rationalize the observed properties of the primary electron transfer reactions, namely, the unusual temperature and ∆G dependences, the oscillating phenomena in kinetics and the asymmetry of the charge separation reactions.


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Introduction The primary electron transfer (ET) reactions in the photosynthetic bacterial reaction center (BRC) are initiated by photo-excitation of the bacteriochlorophyll dimer P (the special pair) consisting of two monomers PL and PM, which are bound to protein subunits L and M, respectively1. The subunits L and M obey a high structural symmetry and include two branches of redox-cofactors, namely, the neighboring to P monomeric bacteriochlorophylls BL and BM (see Figure 1), more distant bacteriopheophytin molecules HL and HM, and two quinone acceptors, which are out of scope of this work. Despite the structural symmetry, only the branch L is active in the wild type BRC with regard to ET2. In the BRC from Rhodobacter sphaeroides bacteriochlorophyll BL operates as an intermediate carrier between the special pair P and bacteriopheophytin HL3,4; the sequential reductions of BL and HL: P* → P+BL−→ P+HL− have lifetimes of ~2.3 ps and ~0.9 ps, respectively5. In the neutral ground state the monomer PL is strongly disturbed and an excess negative charge is localized on its porphyrin ring6. The spectral structure of the P → P* transition reveals strong vibronic features which indicates the coupling of P excitation to nuclear vibrations7–9. The electronic absorption line shape and Stark spectrum of the lowest energy P → P* transition revealed that within the excited special pair P*, the partial charge transfer state PL+PM- has a larger contribution in the excited state than the PL-PM+ state, and the respective change in dipole moment between the ground and excited states |∆µ| is about 7 D10. Ab initio molecular dynamics (MD) of the special pair and neighboring amino acid residues showed that low-frequency vibrations within this complex are coupled to considerable changes of the electrical dipole within the special pair11. As a consequence, the excitation of special pair is associated with the


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formation of primary electric dipole P* ↔ PL+δ PM-δ with the partial charge δ of about 0.2 units of the elementary charge.

Figure 1 Because the reaction BL−HL → BLHL− is faster than the preceding process P* → P+BL−, the reduction of BL could not be revealed by conventional subpicosecond techniques, and the formation of P+HL− dipole is usually the first observable charge-separated state in the BRC from the wild type of purple bacteria. The HL reduction does not slow down at cryogenic temperature: at liquid helium the primary charge separation in the BRC is even twofold faster than at room temperature12. In addition, reaction is poorly described by homogeneous exponential kinetics13. Several site-specific modifications of BRC in the vicinity of P have been constructed, where the redox potential Em(P/P+) changed as compared to the wild type in the range between -100 and +260 mV14. In the mutant L168HF, where Em(P/P+) decreased by ~95 mV, increasing the driving force of the primary ET, the charge separation at room temperature was approx. twofold faster than in the wild type (t1/2 ≈ 1.5 ps)15, but at 10 K the primary charge separation occurred with the same rate and matched the reaction in the wild type BRC at this temperature16. In the double mutant L131LH+M160LH, where Em(P/P+) increased by ~130 mV, decreasing the driving force, the charge separation at room temperature was ~5-fold slower (t1/2 ≈ 15 ps) than in


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the wild type RC14. It is noteworthy that in this mutant the charge separation at 10 K was only 4fold

slower

(t1/2

≈

60

ps)

than

at

room

temperature16.

In

the

triple

mutant

L131LH+M160LH+M197FH, where Em(P/P+) increased by ~260 mV14, the charge separation was completely blocked even at room temperature17. Taking these data all together, the primary charge separation in BRC seems challenging and raises several fundamental questions regarding its physical mechanism: (i) why the ET takes place along the cofactors of branch L but not along the branch M; (ii) why the primary ET, being so fast in the wild type, proceeds without an activation barrier when the reaction driving force changes in the range from -100 to +130 meV; and (iii) what is the role of observed oscillatory features in the mechanism of the primary charge separation. Whereas some features of BRC structure might presumably account for the functional asymmetry of ET18, the last two problems pose a great challenge for theoreticians19. It is worth noting that the further increase of ∆G by ~260 meV in the triple mutant completely inhibits the reaction and switches it to a conventional mechanism described by the Marcus-Dogonadze theory20. In this paper we analyze the oscillatory mechanism of primary charge separation in BRC, which has been originally suggested by Shuvalov and co-authors8,21 as the phenomenological wave-packet motion model and later supported by experiments of Vos et al.22 For this purpose we use MD simulations of BRC and theoretical approach based on the Langevin stochastic dynamics23.

Materials and methods Molecular dynamics simulations


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MD simulations were carried out with the model built using the crystal structure of BRC from the purple bacterium Rhodobacter sphaeroides (PDB code: 2gnu)24. The structure included three protein chains (subunits H, L and M), 4 bacteriochlorophylls, 2 bacteriopheophytins and 2 ubiquinones. Reaction center was surrounded by water molecules to fill the rectangular cell (approx. 84×74×80 Å), after that K+ and Cl- ions were added to make the system electrically neutral (the ion strength of 0.1 M). Parameterization of atomic interactions for the protein was based on AMBER molecular potentials25. The molecular potentials of bacteriochlorophylls, bacteriopheophytins and ubiquinones have been computed by ab initio methods26 and used for calculation of the dielectric linear response of BRC protein27. The partial charges of the cofactors in neutral, oxidized and reduced states were derived by Mulliken population analysis using the density functional approximation PBE028,29 with the GAMESS program30. MD simulations were conducted using the NAMD 2.7 program31 on the "Chebyshev" supercomputer in the Moscow State University Computing Center. After equilibration of the solvent around BRC in the constrained crystallographic conformation, the BRC together with a thin surrounding water layer (~0.3 nm thickness) was embedded into a hydrated lipid bilayer, which was constructed from a typical bacterial phospholipid, 1-palmitoyl-2-oleoyl-sn-glycero-3phosphocholine and equilibrated. The system included 125 molecules of phospholipid, 8300 water molecules and 60 monovalent ions, ~55000 atoms in total. The consequent equilibration of the system was carried out in three stages: first, the lipid was relaxed at the fixed conformation of protein and constrained water positions, then the water was relaxed but the general conformation of BRC was conserved by applying restrictions to Cα atoms of backbone, and finally a free simulation of the system at 300 K was performed for 5 ns. The subsequent 5 ns long free


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dynamics was used for the analysis, and no drift of potential energy or systematic changes of the system volume were observed. The integration step was 1 fs. 100 conformations from this trajectory, 50 ps apart from each other, were used as initial states for subsequent analysis. Each system was cooled to the temperature of 100 K for 40 ps; afterwards, short (3.2 ps) and long (32 ps) simulations in the neutral (all cofactors uncharged) and charge-separated (PL+PM-) states were carried at the constant volume without temperature control. We simulated the charge separation inside the special pair or chlorophylls, considering that chlorophyll PL has +1 charge and chlorophyll PM has -1 charge after excitation (the partial charge of ~0.8 at a monomer has been recently determined for the charge-separated state of special pair by Stark spectroscopy32). Atom coordinates were recorded every 1 fs in short 3.2 ps simulations and every 10 fs in longer 32 ps simulations, resulting in 3200-frames long trajectories. The primary analysis of trajectories files (retrieval of atomic coordinates in explicit form) was carried out in MATLAB using scripts from the MatDCD package of MD Tools suite developed by the Theoretical and Computational Biophysics group at the Beckman Institute, University of Illinois. All further calculations were performed in MATLAB with custom scripts. Electric potential from different parts of the system (protein, ligands, water box centered on protein complex) on the π-electron conjugated rings of PL, PM, BL and BM was calculated for all trajectories. The spectral function of BRC was calculated as squared modulus of Fourier transform of electric potential (from protein part of the system, including ligands) at different cofactors and averaged over 100 independent trajectories, as described above.

Results and discussion


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1. Analysis of polarization dynamics within the Langevin approach The ET reactions in BRC are accompanied by a dielectric polarization of protein and other polar components of the system. The dynamics of electric potential is governed by structural properties of the protein matrix. Due to the long-range nature of electrostatic interactions, an appropriate analysis of dielectric response must incorporate not only the contributions from closest neighboring but also from the distant protein parts and surrounding water. The MD simulations of BRC provide a microscopic treatment of ~105 atoms and could not be directly linked to the kinetic modeling of ET reactions. In order to correlate the processes of ET with the polarization dynamics, we approximated the changes of electric potential φA(t) at the cofactor A with a phenomenological model consisting of m Langevin oscillators and n Debye relaxation modes. In the simplest case, single mode accounts for the changes of electric potential φA(t) at the cofactor A due to the motion of charge q:

q q  x(t )  ≈ 1 −  r + x (t ) r  r 

ϕ A (t ) = r r

(1)

In general, mode i reflects the stochastic motion of an effective particle with charge qi and mass mi in a harmonic potential Vi ( x) = 1/ 2ki ( x − xi ) in accordance with the Langevin equation 2

mi &x& + γ i x& + ki ( x − xi ) = (2γ i kBT ) F (t ) 1/ 2

(2)

The random force F(t) satisfies the conditions F (t ) = 0 and F (t1 )F (t2 ) = δ (t1 − t2 ) . The oscillating mode i is characterized by the self-frequency ωi = ki mi and the friction time

τ i = mi γ i . The solution of Langevin equation could be found by the Fourier transform of eq 233. ) The square of solution xi (ω ) , known as a spectral function, has the Lorentzian form and characterizes on the average stochastic dynamics:


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| xˆi (ω ) |2 =

2k BT 1 ⋅ miτ i ωi2 − ω 2 2 + τ i−2ω 2

(

(3)

)

Treating φA(t) in accordance with eq 1 as a linear function of x(t), the ith component of spectral function can be written in the following form: S iosc (ω ) =| ϕˆ i (ω ) | 2 = 2 k B Te −1 ⋅ τ iφ i ⋅

ω i2

(4),

τ i2 (ω i2 − ω 2 ) + ω 2 2

where e is the electron charge and φi is the response of ith mode upon the cofactor A charging:

φi =

eqi2 ki ri 4

(5)

The Debye mode j is characterized by the relaxation time t j = γ j k j , the respective spectral function reads −1 S rel j (ω ) = 2k BTe ⋅ t jφ j ⋅

1 1 + t 2j ω 2

(6)

The full spectral function of the system is the sum of oscillation and relaxation components:  ω i2 S A (ω ) = ∑ | ϕˆ k (ω ) |2 = 2 k BTe −1  ∑ τ iφ i k τ i2 ω i2 − ω 2  i

(

)

2

+ω2

+ ∑ t jφ j j

 1 2 2  1 + t j ω 

(7)

In general, the spectral function could be inferred from equilibrium MD simulations in the ground state of the system34–37 using discrete Fourier transforms of potential changes N −1

ϕˆt (ωk ) = ∑ ϕ (t + t n ) exp(−iωk t n ) , which are calculated over a set of intervals t n = n ⋅ δt and n=0

−1 frequencies ωk = 2πk ( N ⋅ δt ) ( k , n = 0,1,2,..., N − 1 ). The spectral function is obtained by

averaging over MD trajectory: S A (ωk ) = ϕˆt (ωk )

2

(8) t


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The spectral function reflects stochastic dynamics of the system in a complex multidimensional non-harmonic potential. According to the fluctuation-dissipation theorem38, the system relaxation after a small perturbation could be related to the polarization dynamics due to spontaneous thermal fluctuations39. However, the fluctuation-dissipation theorem relates the linear response and the polarization spectral function under an assumption, that the harmonic modes are fully independent of each other. This might be not true for proteins: for example, low-frequency fluctuations of the protein conformation might modulate the characteristics of high-frequency modes, such as local vibrations of individual hydrogen-bonded groups, or large domain motions. Besides, deconvolution of φA(t) into the functional form (7) is not uniquely defined. In accordance with the general functional approach based on the spin-boson model, the dynamic properties of dielectric polarization could be specified with the spectral function of the following form38,40: S (ω ) =

π

∑ (C 2

2 j

)

m jω j δ (ω − ω j )

(9)

j

It represents a set of harmonic oscillators ωj linearly interacting with the spin subsystem (e.g., an electron transferring cofactor); Cj are the respective coupling coefficients. If the number of oscillators is large, this model exhibits a dissipative behavior. Unfortunately, the general form of S(ω) remains unknown, it may be obtained either from an appropriate microscopic model, or from phenomenological assumptions40,41. The coefficients C 2j m j ω j in eq 9 and the factors τ iφi in eq 7 of the Langevin model are essentially different, since the parameter ωj is the self-frequency of the oscillator whereas τi is the respective friction time. Thus, the question remains: to what degree the protein dynamics can be approximated by a set of linear harmonic oscillators? To check the consistence of the


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representation of the system dynamics by eq 7, we calculated the mean reaction field ΦA(t) in BRC upon appearance of a charge at the cofactor A: Φ A (t ) = ∆ ϕ A (t )

(10)

∆q A =1

The respective differential equation for the field ФА(t) can be obtained by averaging eq 2:

&& + τ −1Φ & + ω 2 (Φ − Φ ) = 0 Φ i i 0

(11)

2. Molecular dynamics model and spectral analysis

MD model of bacterial photosynthetic reaction center from Rhodobacter sphaeroides was constructed using the crystallographic structure with 2.2 Å spatial resolution24 (PDB code 2gnu). Protein complex was embedded into a lipid bilayer and solvated within a rectangular water box; the system dimensions were approx. 84×74×80 Å. The modeled structure included ~13 000 atoms of protein complex (chains L, M and H and the ligands), 125 molecules of 1-palmitoyl-2oleoyl-sn-glycero-3-phosphocholine, ~8300 water molecules and 60 monovalent ions. In accordance with the conditions of experiments, where the oscillating features of BL− formation kinetics were observed most distinctly42,43, we analyzed the system at 100 K and averaged the results over 100 independent trajectories. We studied the dielectric polarization of BRC and surrounding water coupled to the charging of monomers within BChl special pair PL+PM−. Two complementary approaches were employed: • the analysis of thermal dynamics of the electrostatic potential φ(t) at the BChl cofactors in the neutral ground state; • the analysis of system polarization dynamics in response to the PL+PM− dipole formation. 2.1 Spectral function of the BRC dielectric polarization


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We checked the possible role of particular vibration modes in the primary events of charge separation in BRC. The spectral function of BRC polarization was determined using the equilibrium MD simulations. Namely, thermal changes of the electrical potential φ(t) at the individual cofactors (PL, PM, BL, BM) as induced by different polar components of the system (protein, with differentiation up to individual amino acids; water; ligands) were calculated from 100 independent trajectories (of 32 ps length). For this set of data, the spectral function S(ω) was calculated by averaging the Fourier transforms of φ(t) components in accordance with eq 7. To elicit the magnitude of energy coupling given by the coefficients C 2j in eq 9, the spectral functions were multiplied by frequency, and the products ω•Sp(ω) were plotted in Figure 2A by thin lines for the cofactors PL (yellow) and PM (green), respectively. The spectral functions in Figure 2A reveal several main contributions to the dielectric response. The sharpest peak is observed at 1050 cm-1, two less prominent bands are positioned at 800 and 730 cm-1 and the third broad band is located in the long-wave region below 200 см-1. There is also a large set of smaller bands distributed in the range between 400 and 1600 cm-1. The spectral functions in Figure 2A were approximated by Langevin model as described below; the components of such deconvolution are presented in Table 1.


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Figure 2 We made an attempt to assign the bands in Figure 2A to the elements of BRC structure. For this purpose, we first divided the total function S(ω) into the components arising from the motion of protein backbone and of side amino acid residues. The sharpest peaks in the spectral function of amino acids side chains are mostly governed by vibrations of histidines – axial ligands of magnesium atoms of bacteriochlorophyll molecules PL and PM (HisL173 and HisM202 for chains L and M, respectively, see Figure 1) – with two most prominent modes with frequencies of 1050 cm-1 and 725 cm-1 and two minor peaks at 1130 and 540 cm-1. The other amino acid side


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chains with different characteristic vibration frequencies constitute a broad low-amplitude spectrum ranging from 200 to 700 cm-1. A sharp peak at 730 cm-1 and several low-frequency peaks between 30 and 200 cm-1 were revealed in Raman spectra of the primary electron donor P obtained at 278 K44. The Raman cross sections of the special pair were by an order of magnitude smaller as compared to the cross sections of BChl and BPhe monomers in BRC at room temperature and did not increase at 95 K. Such behavior suggests that the excited state of P (P*) is very effectively coupled to some relaxation processes (with damping time of 200 fs. The small magnitude of dielectric losses is in line with the activationless character of the primary charge separation and small reorganization energy of the reaction. In contrast, the dielectric response at the monomer PL is much larger, and we examined the impact of slow modes at the monomer PL indicated in Figure 3B on the photoinduced electron transfer. In the ground state of the special pair, the monomer PL carries an excessive negative charge caused by charge donation from the axial histidine6. Upon excitation, the formation of the charge-separated state PL+δPM−δ is coupled with dynamics of HisM202 – the axial ligand of monomer PL11,63. The results of our MD simulations (Figure 3B) revealed that the rotation of HisM202 by ~60° in the excited state of P observed in ab initio MD simulations11 occurred at the same time scale of ~300 fs as the slow polarization response at monomer PL (Figure 3A). It seems plausible that elastic protein vibrations in the vicinity of PM caused by the rotation of HisM202 would provide potential oscillations which promote the subsequent electron transfer from PM to BL. Thus, the dielectric asymmetry manifests itself even at the earliest steps of ET. The results of MD simulations presented in this study reveal microscopic details of the phenomenological mechanism described above. The most notable contributions to protein


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polarization in the vicinity of PLPM arise from: (i) high-frequency modes (>200 cm-1) responsible for the fast potential jump; (ii) low-damped oscillations (the main frequency 118 cm-1) of helices cd at the hinge joint between helices cd and D and movements of the trans-membrane helices E

of both monomers perpendicular to PL-PM axis (Figure 4A); (iii) low-frequency vibrations (1.1 ps was observed in the protein response upon the formation of PL+PM− dipole. It was attributed to elastic vibrations of


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alpha-helices in the vicinity of PLPM (Figure 4A). As a whole, the domain formed by helices cdM, DM and EM is more rigid owing to a more dense system of hydrogen bonds formed by polar

amino acid groups in this region. The fluctuation-dissipation theorem relates the stochastic polarization dynamics in the ground state of the system with the dielectric response upon a charge separation treated as perturbation of the system. We compared the spectral functions of PL and PM monomers calculated in the ground state of the BRC complex with the reaction field dynamics upon the formation of PL+PM− dipole. The spectral function characterizes accurately the fine structure of polarization spectrum (the self-frequencies of individual modes), but is less precise in the estimation of the friction coefficients arising due to the non-harmonic effects in the system dynamics. The coupling coefficients of polarization modes could be calculated with the spectral function only by taking into account strong dynamic correlations which appear after charging of closely located monomers of the special pair. Summarizing the findings that follow from the oscillating modes observed in the transition spectra of BRC variants of Rhodobacter sphaeroides 42,43,58 and the specific modes found by MD simulations in combination with the Langevin analysis (this work) we conclude that: (1) Femtosecond absorption spectroscopy and MD simulations demonstrate the existence of similar nuclear coherent oscillations in the range between 50 and 250 см-1. Since the experimental data were obtained by selective femtosecond excitation of the special pair bacteriochlorophyll P, the observed oscillations are associated with the formation of excited state P*, the preliminary charge separation within the special pair, and the following ET to BL and HL.


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(2) The experimental processes are adequately reproduced by means of MD simulations connecting the polarization response of the whole BRC protein with the formation of PL+PM− dipole. (3) The symmetry between L and M branches is already broken at the stage of the charge separation within the bacteriochlorophyll dimer P: the polarization response in the vicinity of PL stabilizes the formation of primary PL+PM− dipole, whereas the slow potential oscillations induced by the elastic protein vibrations in the vicinity of the monomer PM promote the ET from PM to BL. (4) The proposed vibrational mechanism of electro-elastic coupling could rationalize the experimentally observed properties of BRC charge separation, namely, the unusual temperature and ∆G dependences, the oscillating phenomena in kinetics and the asymmetry of the charge separation reactions. The elastic vibrations coupled to the formation of excited state P* may determine thereby ultrafast, extremely effective and asymmetric primary charge separation.


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FIGURE LEGENDS Figure 1. General arrangement of the primary ET cofactors in the BRC. Special pair of BChl molecules (PL, PM), accessory BChls (BL, BM), their axial ligands (HisL173, HisM202; HisL153, HisM182 – partially obscured by accessory BChls) and side-ligand (HisL168) are shown. The functionally active cofactors in the branch L are colored yellow, the symmetrical non-active branch M is marked green. Two water molecules, which form bonds between the axial histidines and the accessory BChls, are shown by red spheres. Figure 2. (A) Spectral functions of protein electric field fluctuations at monomers PL (yellow) and PM (green) of the special pair, calculated from equilibrium MD simulations of BRC in the neutral state at 100 K (dots) and by the Langevin model (solid lines). (B) Correlation of the axial ligands HisL172/HisM202 rotation with the reaction filed dynamics after the PL+PM− dipole formation at 100 K. The spectral function of the model for reaction filed dynamics (black dashed line; 16 modes), and the spectral functions of HisL173 (yellow) and HisM202 (green) rotations calculated from MD simulations in the neutral state are shown. Figure 3. The reaction field dynamics of BRC polarization induced by the formation of PL+PM− dipole. The electric potential changes (red solid lines) at the monomers PL (A) and PM (B) were calculated from 100 independent MD trajectories and fitted by a sum of 16 Langevin oscillators (solid black). Thin dashed lines show the potential standard error of mean over 100 trajectories. Contributions of different modes with high damping (thin solid lines) and the mode of 118 cm-1 frequency with small damping (blue line) are shown. Three individual trajectories (solid, dashed and gray lines) illustrate the variance of reaction field dynamics at the monomer PL (C) due to stochastic fluctuations of the system.


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Figure 4. Structural elements of the BRC protein undergoing the elastic vibrations with selffrequencies of 115-125 cm-1 (A) and the damped Debye-type dynamics (B). BChls of the L and M chains are shown in yellow and green, respectively. Alpha-helices around the BChl special pair (blue) are responsible for the coherent low-frequency potential oscillations at PM, whereas a loose hydrophobic region localized around PL (orange) is accountable for the Debye-type relaxation at this cofactor. Figure 5. Tentative energy diagram for the transitions between states PBL, P*BL and P+BL− during the primary ET events in BRC. The multidimensional potential energy surfaces for these states are shown as one-dimensional energy terms (see section 4 of Results for details). Figure 6. Oscillatory motion of cdL/cdM helices (marked by solid arrows) around “hinges” between cd and D helices (marked by ellipses), whose elastic vibrations are proposed to be coupled to the rotation of HisL173/HisM202 imidazole rings (marked by dashed arrows) upon excitation of the special pair. The symmetric domains of the L and M branch are shown in orange and green.


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Table 1. Parameters of the Langevin model of BRC polarization in the vicinity of the special pair, obtained by the deconvolution of PL and PM spectral functions as acquired from equilibrium MD simulations.

Mode

1

2

3

4

5

6

7

8

9

10

11

12

13

14

15

16

Frequency, cm-1

1129

1050

945

796

725

697

604

540

440

390

165

147

125

117

57

30

Friction time, fs

89

989

65

150

577

102

32

272

30

63

136

494

44

280

117

195

PL

10

22

23

68

12

24

23

10

59

0

35

3

396

34

160

112

PM

11

21

16

65

11

20

27

0

52

18

24

18

463

4

21

62

Amplitude, mV

Table 2. Langevin model of polarization dynamics induced by the formation of PL+PM− dipole. Mode

1

2

3

4

5

6

7

8

9

10

11

Frequency, cm

1110

1030

794

715

426

155

118

95

81

43

28

Friction time, fs

380

36

160

170

16

260

1130

180

60

240

250

PL

1

11

11

6

42

1

9

6

47

35

47

PM

1

3

7

4

36

11

3

19

3

5

3

-1

Amplitude, mV


34

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AUTHOR INFORMATION

Corresponding Author *e-mail: [email protected]

Author Contributions The manuscript was written through contributions of all authors. All authors have given approval to the final version of the manuscript.

Funding Sources This work has the support from the Russian Science Foundation (grant 14-14-00789). Experimental results considered in section 4 were obtained with support from the Russian Foundation for Basic Research (grants 15-04-04252, 13-04-40297 and 13-04-40299)

Acknowledgements The authors thank Victor Nadtochenko and Vladimir Novoderezhkin for valuable discussions. The authors express gratitude to Massimo Marchi for the provided parametrization of BRC cofactors.

ABBREVIATIONS ET, electron transfer; BRC, bacterial reaction center; BChl, bacteriochlorophyll; MD, molecular dynamics; P, special pair of bacteriochlorophylls; PL and PM, bacteriochlorophyll monomers of special pair from chains L and M, respectively; BL and BM, accessory bacteriochlorophylls from chains L and M, respectively; HL and HM, bacteriopheophytins from chains L and M, respectively.


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Table of Contents Graphic and Synopsis

Primary electron transfer reactions in the bacterial reaction center are difficult for theoretical explication: the reaction kinetics, almost unalterable over a wide range of temperature and free energy changes, revealed oscillatory features observed initially by Shuvalov and coauthors (1997, 2002). Here the reaction mechanism was studied by molecular dynamics and analyzed within a phenomenological Langevin approach. The spectral function of polarization around the bacteriochlorophyll special pair PL/PM and the dielectric response upon the formation of PL+/PM− dipole within the special pair were calculated. The system response was approximated by Langevin oscillators; the respective frequencies, friction and energy coupling coefficients were determined. The protein dynamics around PL and PM were distinctly asymmetric. The polarization around PL included slow modes with the frequency of 30-80 cm-1 and the total amplitude 130 mV. Two main low-frequency modes of protein response around PM had the frequencies of 95 and 155 cm-1 and the total amplitude 30 mV. In addition, a slowly damping mode with the frequency of 118 cm-1 and the damping time >1.1 ps was coupled to the formation


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of PL+PM− dipole. It was attributed to elastic vibrations of alpha-helices in the vicinity of PLPM. The proposed trapping of P excitation energy in the form of the elastic vibrations can rationalize the observed properties of the primary electron transfer reactions, namely, the unusual temperature and ∆G dependences, the oscillating phenomena in kinetics and the asymmetry of the charge separation reactions.

Cover art.


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Biographies

Georgy E. Milanovsky graduated from Moscow State University, faculty of bioengineering and bioinformatics in 2010 and is currently pursuing PhD in laboratory of electrogenic photoprocesses of A.N. Belozersky Institute of Physical-Chemical Biology under prof. Alexey Yu. Semenov. His research interests include studies of electron transfer in photosynthetic complexes with molecular dynamics.

Vladimir Shuvalov graduated from Moscow State University in 1965, obtained PhD in 1969, Doctor of Science degree in 1982, awarded State prize in 1991. Academician of RAS since 1997. Since 1972 he has been working at the Institute of Fundamental Problems of Biology, Russian Academy of Sciences. He conducted research in Kettering Laboratory (USA, 1978), the University of Washington (USA, 1980), the University of Leiden (Netherlands, 1985-1986). His research interests include molecular basis of photosynthesis, namely, the mechanisms of proteins-chlorophyll interaction in plants and photosynthetic bacteria.


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Alexey Yu. Semenov obtained his M.S. degree in 1973 and his Ph.D. degree in Biochemistry in 1978 from the Moscow State University. He is the head of laboratory and Professor of Biochemistry and Biophysics at A.N. Belozersky Institute of Physical-Chemical Biology, Moscow State University. From 2006 till 2014 he was the President of the Russian Photobiological Society. His current research interests are the study of molecular mechanisms of the primary charge transfer reactions in photosynthetic reaction centers.

Dmitry A. Cherepanov obtained his Ph.D. degree in theoretical biophysics in 1988 from the Moscow State University. Since 1988 he is working in A.N.Frumkin Institute of Physical Chemistry and Electrochemistry, Russian Academy of Sciences, Moscow. In 1999-2002 he was awarded by Alexander von Humboldt Fellowship, in 2003-2004 by the Mercator Visiting Professorship from German Research Foundation and worked in the University of Osnabrueck, Germany. His research interests are theoretical biophysics, theory of charge transfer reactions in proteins and molecular dynamics simulations.


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Figure 1. General arrangement of the primary ET cofactors in the BRC. Special pair of BChl molecules (PL, PM), accessory BChls (BL, BM), their axial ligands (HisL173, HisM202; HisL153, HisM182 – partially obscured by accessory BChls) and side-ligand (HisL168) are shown. The functionally active cofactors in the branch L are colored yellow, the symmetrical non-active branch M is marked green. Two water molecules, which form bonds between the axial histidines and the accessory BChls, are shown by red spheres 55x36mm (300 x 300 DPI)



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Figure 2. (A) Spectral functions of protein electric field fluctuations at monomers PL (yellow) and PM (green) of the special pair, calculated from equilibrium MD simulations of BRC in the neutral state at 100 K (dots) and by the Langevin model (solid lines). (B) Correlation of the axial ligands HisL172/HisM202 rotation with the reaction filed dynamics after the PL+PM- dipole formation at 100K. The spectral function of the model for reaction filed dynamics (black dashed line; 16 modes), and the spectral functions of HisL173 (yellow) and HisM202 (green) rotations calculated from MD simulations in the neutral state are shown. 141x202mm (300 x 300 DPI)


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Figure 3. The reaction field dynamics of BRC polarization induced by the formation of PL+/PM− dipole. The electric potential changes at the monomers PL (A) and PM (B) were calculated from 100 independent MD trajectories (black dotted lines) and fitted by a sum of 16 Langevin oscillators (red). Thin dashed lines show the potential standard error of mean over 100 trajectories. Contributions of different modes with high damping (thin solid lines) and the mode of 118 cm-1 frequency with small damping (blue line) are shown. Three individual trajectories (solid, dashed and gray lines) illustrate the variance of reaction field dynamics at the monomer PL (C) due to stochastic fluctuations of the system. 223x488mm (300 x 300 DPI)



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Figure 4. Structural elements of the BRC protein undergoing the elastic vibrations with self-frequencies of 115-125 cm-1 (A) and the damped Debye-type dynamics (B). BChls of the L and M chains are shown in yellow and green, respectively. Alpha-helices around the BChl special pair (blue) are responsible for the coherent low-frequency potential oscillations at PM, whereas a loose hydrophobic region localized around PL (orange) is accountable for the Debye-type relaxation at this cofactor. 162x320mm (300 x 300 DPI)


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Figure 5. Tentative energy diagram for the transitions between states PBL, P*BL and P+BL- during the primary ET events in BRC. The multidimensional potential energy surfaces for these states are shown as onedimensional energy terms, see section 4 of Results for details. 57x40mm (300 x 300 DPI)



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Figure 6. Oscillatory motion of cdL/cdM helices (marked by solid arrows) around “hinges” between cd and D helices (marked by ellipses), whose elastic vibrations are proposed to be coupled to the rotation of HisL173/HisM202 imidazole rings (marked by dashed arrows) upon excitation of the special pair. The symmetric domains of the L and M branch are shown in orange and green. 167x145mm (300 x 300 DPI)


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Elastic Vibrations in the Photosynthetic Bacterial Reaction Center

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