Static and Dynamic Disorder in Bacterial Light-Harvesting Complex

Article pubs.acs.org/JPCB

Static and Dynamic Disorder in Bacterial Light-Harvesting Complex LH2: A 2DES Simulation Study Olga Rancova* and Darius Abramavicius* Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio av. 9 III bld., LT-10222 Vilnius, Lithuania ABSTRACT: Two-dimensional coherent electronic spectroscopy (2DES) is a powerful technique in distinguishing homogeneous and inhomogeneous broadening contributions to the spectral line shapes of molecular transitions induced by environment fluctuations. Using an excitonic model of a double-ring LH2 aggregate, we perform simulations of its 2DES spectra and find that the model of a harmonic environment cannot provide a consistent set of parameters for two temperatures: 77 K and room temperature. This indicates the highly anharmonic nature of protein fluctuations for the pigments of the B850 ring. However, the fluctuations of B800 ring pigments can be assumed as harmonic in this temperature range.

■

INTRODUCTION The peripheral light-harvesting complex LH2 of purple bacteria1,2 is often titled one of the most studied photosynthetic complexes. The LH2 photosynthetic complex stands out because of high symmetry of its structure resolved by X-ray crystallography3−7 and atomic force microscopy.8 Depending on bacterial species, LH2 complexes are cylinders formed by either eight or nine equal segments of transmembrane proteins (Figure 1A). Each segment contains two low-weight proteins that coordinate three bacteriochlorophyll a (BChl) molecules and one or two carotenoids. BChls form two concentric rings. Nine weakly interacting horizontally oriented BChls form a ring at the cytoplasmic side of the transmembrane complex, whereas 18 vertically oriented tightly packed and strongly interacting BChls form a ring on the opposite side of the complex. The rings are conventionally named B800 and B850, respectively, because of the peak positions in nanometers of their BChl Qy absorption bands at room temperature. The Frenkel exciton theory successfully describes spectroscopy experiments of LH2 in this wavelength region. A combination of considerably strong and weak excitonic couplings between BChls in the complex is a remarkable property of LH2 complexes. Pigments in the B850 ring demonstrate one of the strongest nearest neighbor excitonic coupling in the range from 250 to 420 cm−1 in the photosynthetic antenna complexes evaluated as shown by analysis and parametrization of different experimental data.9−13 The pigments in B800 rings are coupled rather weakly in the range of 25−30 cm−1.14−16 The excitonic coupling of the nearest pigments from different rings is of the same order. The accurate circular symmetry of the interacting pigments implies the optically forbidden lowest energy excitonic state. However, even at low temperatures the LH2 complexes demonstrate superradiance17 suggesting that seemingly sym© 2014 American Chemical Society

metric rings of pigments have inhomogeneous properties. This assumption is confirmed by the single-complex spectroscopy.18 In order to simulate and interpret this effect, the static disorder is introduced. These properties of LH2 bring a lot of parameters to the excitonic model, while their values used by different scientific groups to describe various spectroscopic features of LH2 complexes are rather diverse (see for example15,19−23) and hence call for revisiting. Recently developed two-dimensional coherent electronic spectroscopy (2DES) rephasing technique has been applied to measure LH2 (Rhodobacter sphaeroides species) 2D spectra at room temperature.25−28 A few years earlier the experimental rephasing 2DES spectra of the spectral variant of the LH2 complex (B800−820) of Rhodopseudomonas acidophila strain 7050 have been measured at 77 K.28 According to the experimental setup, values on the horizontal ω1 axis correspond to the excitation frequencies and vertical ω3 axis contains detection frequencies. The 2D spectra allow visualization of not only the excited states of the system but also various types of static and dynamic correlations between the pigments. Simulation of the 2D spectra should be able to reduce the uncertainty of excitonic parameters described above. In this paper we focus on the parameters responsible for spectral broadening, namely, the reorganization energy of fast fluctuations (or the dynamic disorder) and the static energy disorder variance for a given Hamiltonian.30 Received: May 2, 2014 Revised: June 19, 2014 Published: June 19, 2014 7533

dx.doi.org/10.1021/jp5043156 | J. Phys. Chem. B 2014, 118, 7533−7540

The Journal of Physical Chemistry B

Article

Here Em is the excitation energy (or site energy) of pigment m, Vmn is the resonant interaction between the sites, and the conjugate operators B̂ †m and B̂ m create and annihilate an excitation on site m. Only one excitation is allowed per site, so the operators satisfy the Pauli commutation relations [B̂ n,B̂ †m] = δmn(1 − 2B̂ †mB̂ m). The Hamiltonian (eq 1) describes block matrices with a given number of excitations. Diagonalization of these blocks provides the multiexcitonic basis for modeling of the spectroscopic responses. Single and double excitations are important for the 2DES spectra.31 In the previous research30 we obtained the single-exciton matrix elements Em and Vmn of the Frenkel exciton Hamiltonian using the structural data of the LH2 complex of the purple bacteria Rps. acidophila5 and the electrostatic theory.32−35 The excitonic couplings were calculated by the transition charges from electrostatic potential (TrEsp) method.32 The site energies were calculated by the charge density coupling (CDC) method.33 On the microscopic level the transition charges were rescaled to obtain the intradimer coupling of B850 pigments close to the value of 300 cm−1 22,36 and the protonation pattern of the poorly defined histidine states was adjusted to get the proper absorption and circular dichroism (CD) spectra. Since all B800 pigments on average have the same environment, the site energies of the B800 pigments in the reference Hamiltonian (eq 1) are set to the same 12 500 cm−1 value; the other values are from ref 30. Relaxation and dephasing processes, responsible for the homogeneous broadening, are included by assuming the linear coupling of the excitations with coordinates of an infinite number of harmonic oscillators representing protein environment at constant temperature as described in ref 37. The fluctuations of the site energies caused by these oscillators are uncorrelated. In this case the environment-related parameters are reduced to site energy fluctuation spectral densities C″n (ω) for each site that describes the spectral contents of the environment. During the simulations, the site basis Hamiltonian eq 1 and the accompanying site energy fluctuation amplitudes are then transformed into the eigenstate basis, where one obtains the mean diagonal Hamiltonian and the

Figure 1. (A) LH2 complex of the purple bacteria Rhodopseudomonas acidophila created with VMD.24 (B) Modeled absorption spectrum at 77 K. (C, D) Modeled 2DES rephasing spectrum at 77 K: (C) real part of the signal; (D) absolute value of the signal.

■

MODEL AND SET OF SIMULATION PARAMETERS To start with the simulations, we assume that the system of the pigments is described by the Frenkel exciton Hamiltonian in the pigment (site) representation Ĥ 0 =

†

m≠n

†

∑ EmBm̂ Bm̂ + ∑ VmnBm̂ Bn̂ m

mn

(1)

Figure 2. (A) Spectral density function (eq 3 with An = 1) (solid line) compared with log-normal shape from ref 43 (dashed line). Log-normal parameters are σ = 0.75, ωc = 38 cm−1, and the Huang−Rhys parameter is 1.6. In the inset a low-energy part is zoomed in. In parts B−E the modeled rephasing 2DES of one site without static energy disorder is shown: (B, C) 77 K; (D, E) room temperature; (B, D) real part of the signal; (C, E) absolute value of the signal. 7534



Article

fluctuation amplitude matrix which contains as diagonal as offdiagonal elements. These off-diagonal elements cause energy transport (relaxation), which is included in Redfield theory. The remaining diagonal fluctuations of the eigenstate basis are accounted for by the cumulant expansion approach.31,38 For instance, this gives the spectral shape of the absorption peak of an eth exciton in the form Ge(ω) =

∫0

widths of the Gaussian disorder is usually assumed to be different for the two rings as well (see, for example, refs 12 and 36). Therefore, two variances for the Gaussian distributions of the static site energy disorder for the B800 pigments σ800 and B850 pigments σ850 should be defined independently. Hence, given the Hamiltonian matrix and the shape of the fluctuation spectral density, we remain with four undefined protein related parameters: A850, σ850 for the B850 ring and A800, σ800 for B800 ring.

∞

dt exp[i(ω − εe)t − ge(t ) − t /τe]

■

(2)

SIMULATED LH2 SPECTRA AT ROOM TEMPERATURE Absorption spectroscopy is the foundation of spectroscopy experiments. Unfortunately for the LH2 it leads to a highly smooth double-peak result that obscures the underlying microscopic dynamics. The quantities, such as the width of the static disorder and the homogeneous line width, cannot be unambiguously ascribed, since both contribute to the spectral line width. While the CD spectrum is a sensitive probe of excitonic parameters and it has been used to fine-tune the Hamiltonian parameters,30 the inhomogeneous and homogeneous broadenings become convoluted in CD as well. 2DES spectroscopy can help to directly distinguish between contributions of different parameters on the resulting spectra obscured in the absorption.39,44,45 In the present research we model the signal in the so-called rephasing direction where the signal wave vector is ks = −k1 + k2 + k3. Here subscript indices on the right-hand side denote the wave vectors of the three incident pulses.37 The Fourier transformation of the delay times between first and second pulses (t1) and third and probe pulses (t3) to the frequency domain then gives the (ω1, ω3) frequency grid for the 2D heterodyne signal map. The remaining t2 delay time between the second and third pulses is then a parameter of the obtained 2D map. In this setup the homogeneous broadening widens the spectral line in all directions on the 2DES spectrum. The inhomogeneous broadening affects only the diagonal elongation in the rephasing 2DES. Thus, the inhomogeneous and homogeneous broadening of the spectral line can be approximately associated with the diagonal and antidiagonal elongations of the diagonal peaks at zero delay time. Because of the large amount of computational resources requisite to simulate the 2D spectra, we further limit ourselves to zero t2 delay time, although the experimental rephasing spectra at zero t2 delay are always contaminated by nonrephasing contribution due to overlap of realistic pulses. However, our simulations do not show appreciable differences between t2 = 0 and 20 fs (the published rephasing spectrum is at 20 fs waiting time delay in ref 25), so we can safely use zero delay for fitting purposes. The room temperature 2DES spectra of LH2 have been reported.25−28 The corresponding 2D map at 77 K is published for the similar B800−820 complex,29 where the homogeneous broadening is clearly reduced by lower temperature. Using this information, we can make some restrictions of disorder parameters of the LH2 aggregate as follows. The structural and spectroscopic information suggests that the 800 nm band of both LH2 and its spectroscopic variant B800−820 has the same peak position and line width. Therefore, the spectral properties of 800 nm band of both LH2 and B800−820 complexes in 2DES should be similar as well. Since the rephasing spectrum at 77 K of B800−820 system has clear features at zero delay time (well-resolved elliptical peak shape without cross-peaks), we can establish the ratio of diagonal and

where ge(t) is the temperature-dependent homogeneous spectral line shape function and τe is the exciton lifetime. These parameters are given by the spectral density functions as described in refs 31 and 18. Expression of a single peak in 2DES is more complicated,39 while it is also defined by ge(t) functions. Several different forms of the spectral density function, obtained by fitting the experimental data and modeling, have been suggested for LH2 complexes.19,22,40−42 It has been argued that the form of the spectral density function especially in the vicinity of the zero frequency is crucial for the correct modeling of the coherences and thermalization processes in the photosynthetic complexes, and the log-normal shape due to its adjustable asymmetry and asymptotic convergence has been suggested.43 Unfortunately there are no parameters presented for this form of the spectral density function in the case of LH2 complex. In the present modeling we use a similar spectral density function from ref 22 of the form 2 ⎛ ω⎞ as Cn″(ω) = A n ∑ |ω|s + 1 exp⎜ − ⎟ ω ( s 1) !·ωcss + ⎝ ⎠ cs s=1

(3)

with parameters adapted from the experimental LH2 line shape studies.22 With a scaling constant An = 1 this spectral density gives the reorganization energy of 90 cm−1. Note that both spectral density functions can be brought to a similar shape as shown in Figure 2A. However, we have found that at temperatures from 77 to 300 K either of these spectral densities gives the same temperature dependent single pigment absorption. The single pigment absorption spectrum modeled with the spectral density function (eq 3) is an asymmetric Gaussian with 210 cm−1 (77 K) and 430 cm−1 (room temperature) fwhm line width. Correspondingly 2DES rephasing spectra at two temperatures are demonstrated in Figure 2B−E and show a diagonally elongated peak shape, which indicates an interplay of fast and slow fluctuations coming from high and low frequency components, respectively. Different spectral density functions for B800 and B850 pigments were derived using the combined molecular dynamic simulations and quantum chemistry methods for the LH2 complex of a purple bacterium Rhodospirillum molischianum.42 Instead we assume that the shape of the spectral density function is the same for both B800 and B850 pigments, but the coupling strength is different. Scaling constants An in eq 3 take into account the differences as suggested in ref 19. We use factors A850 and A800 as fitting parameters. Beside these effects we consider some static inhomogeneities within the pigment−protein complexes (like conformational changes of the proteins or solvent effects) to occur on a much slower time scale. This causes the static disorder of the site energies having the Gaussian distribution. So each site energy in the reference Hamiltonian (eq 1) is additionally randomly shifted. Then the simulated spectrum is given by the ensemble average over the different realizations of the static disorder. The 7535



Article

antidiagonal peak line widths and define the dynamic and static disorder parameters for the B800 ring. As seen from the 2D map for the B800 peak,29 the ratio of the peak widths at halfmaximum along and across diagonal is approximately 3:1. With the above-described exciton model and the spectral density function eq 3 we obtain A800 = 0.5 and σ800 = 60 cm−1 for the B800 pigments to best fit the experimental 2DES B800 band at 77 K. This leaves us with only two undefined parameters A850 and σ850 for the LH2. Using the typical disorder parameters (A800 = 0.5 and σ800 = 60 cm−1, and A850 = 1.5 and σ850 = 280 cm−1),12,36,46 we calculated the absorption and 2DES spectra first at 77 K. The spectra are shown in Figure 1B−D. The peak shapes and peak intensities of 2DES can be compared with B800−B820 experiment and show qualitatively good match. However, as protein environment of B820 (B850) pigments is different for LH2 and B800−820 complexes, only qualitative comparison applies here. Unfortunately this qualitatively good match turns out not to be true for the room temperature spectra. The B800 band in absorption and 2DES with above given parameters at room temperature shows proper lineshapes, while B850 band appears incorrect. Additional fitting is necessary to determine the parameters of B850 band at room temperature. The whole twodimensional space of A850 and σ850 values appears impossible to scan and try by fitting the 2D spectra because of the long computational time. Hence, we first impose restrictions using the absorption spectra of the whole LH2 complex at room temperature. The benchmark for this fit is the experimental absorption spectrum at 300 K presented in ref 47. We found the whole range of the parameters allowing simulation of the absorption spectrum of LH2 complex at 300 K with minimal error. The results are presented in Figure 3. As seen from the absorption spectra obtained with all presented sets of parameters shown in the inset of Figure 3, the spectra are

very similar. In the inset one may see that the parameter values A850 and σ850 which fit absorption are correlated almost linearly. This finding allows us to reduce the parameter space from 2D to 1D. We have then simulated 2D rephasing spectra of LH2 complex at room temperature with several sets of broadening parameters from Figure 3. The results of these simulations are presented in Figure 4. In the figure the real part of the signal is presented in the upper row of maps and the absolute value of the signal in the lower row of maps. As seen from a comparison of Figure 2 and Figure 3, there are striking differences between the 2D rephasing spectra. On one extreme with the B850 parameters A850 = 0.5 and σ850 = 330 cm−1 (Figure 4A) the intensity of the B800 peak in absolute value of the signal is approximately 0.05 of the B850 peak intensity. While on the other extreme (A850 = 4.5 and σ850 = 30 cm−1, Figure 4E) the B800 peak intensity is 0.7. We find that the set A850 = 3.5 and σ850 = 130 cm−1 (Figure 4D) leads to the relative peak intensity of B800 equal to 0.5 of B850 intensity which closely matches the experimental spectrum obtained at room temperature and 20 fs delay time.25

■

DISCUSSION While LH2 has quite a long history of studies, the question of protein fluctuations is still puzzling. Recent development of 2D coherent spectroscopy has the potential to help in characterizing properties of the static and dynamic disorders. According to our study, the presence of two groups of pigments in the structure becomes advantageous in this quest because we can adjust B800 parameters independently and later fit B850 with respect to the B800. Simulations with the typical parameters12,36,46 provide reasonable absorption and 2DES spectra at 77 K (Figure 1B−D), which resemble the experiment of B800−82029 However, room temperature is characterized by a different set of parameters. Notice the huge asymmetry of system− environment couplings for B800 and B850 pigments at room temperature. The B800 ring is known from experiments to demonstrate more regular temperature behavior than B850 ring.47−49 This enables us to conserve parameters of B800 and then focus on B850 ring. The obtained disorder values of the B850 parameters at the room temperature are quite extreme: A850 = 3.5 and σ850 = 130 cm−1 compared to the values for the B800 ring of A800 = 0.5 and σ800 = 60 cm−1. Hence, the reorganization energy of dynamic fluctuations of the B850 pigments becomes ∼7 times larger than that of B800 pigments. Also, the static energy disorder of B850 pigments is smaller than that evaluated in other investigations (see, for example, refs 12, 36, and 46), where the disorder parameters are in the range of the ones of Figure 4A (A850 = 0.5 and σ850 = 330 cm−1) and Figure 4B (A850 = 1.5 and σ850 = 280 cm−1). However, Figure 4D matches the room temperature experiment.25 Additional pecularity in Figure 4A−D is the interplay of B800 and B850 peak intensities in 2DES. The peak amplitude in 2DES scales as the fourth power of the transition dipole in the eigenstate representation. Since the exciton is more delocalized in the B850 ring, its corresponding transition dipoles are stronger than the ones of B800 band where the exciton is more or less localized. So while the B800 and B850 peaks in absorption have approximately the same strength, we find that the B850 peak becomes much stronger than the B800 in 2DES spectrum when peaks have the same homogeneous line widths. Static diagonal disorder broadens B850 peak in one dimension, but that is not enough to reduce its amplitude to

Figure 3. Modeled absorption spectra of LH2 complex at room temperature with fixed parameters of B800 pigments (A800 = 0.5 and σ800 = 60 cm−1) and nine different sets of disorder parameters of B850 pigments (spectra plotted in different colors). The corresponding values of disorder parameters A850 and σ850 are given in the inset graph. The ensemble spectra are averaged over 2000 realizations of the static energy disorder. The experimental absorption spectrum from ref 47 is plotted by dotted line. 7536



Article

Figure 4. Simulated 2D rephasing spectra of LH2 complex (reduced six-unit model) at room temperature and 0 delay time: top row, real part of the signal; bottom row, absolute value of the signal corresponding to experiment of ref 25. Parameters of the B800 pigments are fixed at A800 = 0.5 and σ800 = 60 cm−1. Parameters of B850 pigments left to right are the following: (A) A850 = 0.5 and σ850 = 330 cm−1; (B) A850 = 1.5 and σ850 = 280 cm−1; (C) A850 = 2.5 and σ850 = 220 cm−1; (D) A850 = 3.5 and σ850 = 130 cm−1; (E) A850 = 4.5 and σ850 = 30 cm−1.

the required level. Only by broadening the B850 peak in two dimensions by means of dynamic disorder (large homogeneous broadening) are we able to reduce its amplitude and make both B850 and B800 of comparable amplitude so that both become visible. Our set of parameters, which fit room temperature spectra, do not lead to proper absorption or 2D spectra at 77 K temperature. Hence, the 2D spectra uncover the complexity of the B850 ring whose environment-related parameters must be temperature dependent. There are numerous experiments investigating how different spectroscopic properties of LH2 complexes depend on external parameters, such as pressure, temperature, solvent.12,23,47,48,50,51 The analysis of the experimental data shows that often these dependencies are neither linear nor simple. In the Frenkel exciton model these effects could be responsible for the temperature dependent site energies of the pigments or their excitonic couplings or the temperature dependent spectral density function or the systembath coupling strength or the temperature dependent static disorder effects or any combination of them. Some of the temperature effects are implemented in the recently proposed dichotomous model,49 where protein is described by two conformational states with temperature dependent populations or in the simpler temperature dependence of the complex size.22 Most of these effects can be attributed to the temperature dependent protein properties. For our simulations we observe that the static disorder and dynamic disorder are both temperature-dependent. At low temperature (77 K) the static disorder dominates with small homogeneous broadening, while at room temperature the homogeneous broadening covers the whole exciton bandwidth. Surprisingly (or not) this cannot be described by a model of a harmonic environment. Anharmonicity of the protein fluctuations can explain our observations. A sketch of the anharmonic bath potential energy surface is drawn in Figure 5. At low (77 K) temperature we observe one set of fluctuation frequencies and the homogeneous broadening of the spectral line is small. Some population of the higher-energy protein states gets trapped in some local

Figure 5. Sketch of the B850 environment anharmonicity. Thermally populated energy levels are shown in blue for low temperature (TL) and red for high (room) temperature (TH). The static disordered energy states are denoted a, b, c, d, and e for low temperature, which turn into states A and B at high (room) temperature.

minima of the free energy potential and thus contributes to the static energy disorder. However, at high temperatures higherenergy protein states become thermally activated and now have enough energy to fluctuate and turn from static into dynamic. Thus, the dynamic disorder becomes significantly larger at room temperature than at 77 K. Within such anharmonic picture we can thus have temperature-dependent static disorder and fluctuation magnitude. Notice that this effect applies to B850 pigments, while the environment of the B800 pigments seems to be nearly harmonic. One reason for such different behavior is the fact that the B850 pigments are tightly packed and squeezed into the protein frame. The crystallographic results show that the electron density within B850 dimers could be considered as continuous.4 Thus, B850 pigments are very sensitive to any changes in their surrounding, whereas the B800 pigments have more freedom in the LH2 structure, and thus, their environment is more like having a single minimum in free energy. To summarize these considerations, it seems necessary to use the temperature dependent spectral density functions (at least amplitudes) and temperature-dependent disorder for B850 pigments. Here further development of the dichotomous 7537



Article

inseparable. As the number of interaction configurations (Liouville-space pathways) scales with the number of pigments at least as N3, for the full LH2 complex consisting of 27 pigments the calculation of the 2D spectrum including the static energy disorder becomes intractable. In the study of closely related B800−820 complex containing the same number of pigments the size of the problem was reduced by splitting the complex into two excitonically independent B800 and B820 blocks with only Förster energy transfer between them.29 As described above, this approach is hardly justified. We have chosen to compromise on some parameters by reducing the number of BChls in the LH2 complex. Instead of nine symmetric elements, we used the excitonic double-ring system with only six symmetric elements. To conserve the same excitonic properties, we kept the same values of the diagonal and off-diagonal elements in the Frenkel exciton Hamiltonian. Hence, we included only six B800 pigments and correspondingly 12 B850 pigments. For the transition dipoles we redistribute the symmetric units, so they again form the closed rings of pigments with adjusted orientations of the transition dipoles. The comparison of the trial simulations of the complete nine-unit complex and reduced six-unit complex showed that for both linear absorption and the 2DES spectrum the differences are minimal. In Figure 7 the LH2 2DES (real

model and inclusion of the temperature dependent different spectral density populations would probably help. The tight packing of B850 BChls leads to exciton delocalization.13,17,52,53 We can estimate it from our simulations. Examining the shape of the diagonal B850 peak in the 2DES real-value spectra (Figure 4, upper row), one may notice the negative side peak of excited state absorption (ESA) up from the diagonal, similar to peak shapes of disordered Jaggregates.45,54 This property of the diagonal + ESA peaks is the function of the exciton delocalization, determined by the ratio |J|/disorder, where J denotes the excitonic coupling between the pigments and the disorder should include both static and dynamic contributions. In Figure 6 we present

Figure 6. Antidiagonal cuts of the B850 peak of 2DES spectra at two temperatures. The disorder parameters are A850 = 1.5 and σ850 = 280 cm−1 for 77 K simulation and A850 = 3.5 and σ850 = 130 cm−1 for 293 K.

antidiagonal cuts of the B850 peak of 2DES spectra at two temperatures, 77 and 293 K, clearly showing the asymmetry of side peaks. If there was no excited state absorption, both the above-diagonal (high energy) and below-diagonal (low energy) side peaks would have the same intensity due to dispersive component. 2D peak shape analysis analogous to the one in ref 54 indicates that the exciton delocalization is approximately 3− 4 for B850 ring, which is comparable to that suggested in refs 13 and 53, and ∼1 for B800 ring is conserved at both 77 K and room temperature. This can be explained by the fact that the increase of one type of disorder (dynamic) is accompanied by the decrease of another type (static), as seen from the inset of Figure 3. Thus, the total limiting effect of the disorder remains similar. In the present research the modeling of the 2D spectra with both B800 and B850 pigments appears to be a big computational challenge due to proper account of spectral lineshapes, so the limitations of the modeling must be discussed. First issue is related to the size of the system: the LH2 system is “really big” for the 2DES simulations with proper account of lineshapes in terms of the number of pigments. Also B850 ring is composed of dimers of BChls with slightly different properties. The site energies of B850α and B850β BChls differ by approximately 300 cm−1. Additionally the intermolecular coupling shifts the excitation energies even further away. So the excitonic states of B850 ring appear in the B800 region. This makes the B850 and B800 ring subsystems

Figure 7. LH2 absorption (upper line) and 2DES rephasing (real part) (lower line) spectra simulated for six-unit (A) and nine-unit (B) complexes at room temperature with A850 = 3.5 and σ850 = 110 cm−1.

part) simulated for six-unit and nine-unit complexes at room temperature analogous to Figure 4D are shown. In the simulated 2DES the amplitude of the B800 peak is approximately 10% larger for nine-unit complex than for sixunit LH2 complex. Trial calculations (results not shown) with smaller ensemble averaging showed that the same effect of dependency on the disorder parameters as in Figure 4 can be observed for nine-unit complexes. It has been already noticed that the resonance interactions of the pigments both within and between the rings should not be ignored.16,25,55−57 So we must simulate the system with pigments interacting strongly and rather weakly. This raises the question of possible approximations. Förster theory is often sufficient for B800 pigments, while Redfield theory should be suitable for B850 pigments. Additionally, the dynamic exciton self-trapping in the B850 ring after a few hundreds of femtoseconds22,51,58 due to strong interaction with the phonon bath has been suggested, seemingly ruling out the Redfield 7538



Article

Complex from the Purple Bacteria Rhodopseudomonas acidophila Strain 7050. Biochemistry 2001, 40, 8783−8789. (7) Koepke, J.; Hu, X.; Muenke, C.; Schulten, K.; Michel, H. The Crystal Structure of the Light-Harvesting Complex II (B800−850) from Rhodospirillum molischianum. Structure 1996, 4, 581−597. (8) Scheuring, S.; Sturgis, J. N. Atomic Force Microscopy of the Bacterial Photosynthetic Apparatus: Plain Pictures of an Elaborate Machinery. Photosynth. Res. 2009, 102, 197−211. (9) Wu, H.-M.; Reddy, N. R. S.; Small, G. J. Direct Observation and Hole Burning of the Lowest Exciton Level (B870) of the LH2 Antenna Complex of Rhodopseudomonas acidophila (Strain 10050). J. Phys. Chem. B 1997, 101, 651−656. (10) Ketelaars, M.; van Oijen, A. M.; Matsushita, M.; Köhler, J.; Schmidt, J.; Aartsma, T. J. Spectroscopy on the B850 Band of Individual Light-Harvesting 2 Complexes of Rhodopseudomonas acidophila I. Experiments and Monte Carlo Simulations. Biophys. J. 2001, 80, 1591−1603. (11) Freiberg, A.; Rätsep, M.; Timpmann, K.; Trinkunas, G.; Woodbury, N. W. Self-Trapped Excitons in LH2 Antenna Complexes between 5 K and Ambient Temperature. J. Phys. Chem. B 2003, 107, 11510−11519. (12) Urboniene, V.; Vrublevskaja, O.; Trinkunas, G.; Gall, A.; Robert, B.; Valkunas, L. Solvation Effect of Bacteriochlorophyll Excitons in Light-Harvesting Complex LH2. Biophys. J. 2007, 93, 2188−2198. (13) Pullerits, T.; Chachisvilis, M.; Sundströ m, V. Exciton Delocalization Length in the B850 Antenna of Rhodobacter sphaeroides. J. Phys. Chem. 1996, 100, 10787−10792. (14) Sundström, V.; Pullerits, T.; van Grondelle, R. Photosynthetic Light-Harvesting: Reconciling Dynamics and Structure of Purple Bacterial LH2 Reveals Function of Photosynthetic Unit. J. Phys. Chem. B 1999, 103, 2327−2346. (15) Krueger, B. P.; Scholes, G. D.; Fleming, G. R. Calculation of Couplings and Energy-Transfer Pathways between the Pigments of LH2 by the ab Initio Transition Density Cube Method. J. Phys. Chem. B 1998, 102, 5378−5386. (16) Cheng, Y. C.; Silbey, R. J. Coherence in the B800 Ring of Purple Bacteria LH2. Phys. Rev. Lett. 2006, 96, 028103. (17) Monshouwer, R.; Abrahamsson, M.; van Mourik, F.; van Grondelle, R. Superradiance and Exciton Delocalization in Bacterial Photosynthetic Light-Harvesting Systems. J. Phys. Chem. B 1997, 101, 7241−7248. (18) van Oijen, A. M.; Ketelaars, M.; Köhler, J.; Aartsma, T. J.; Schmidt, J. Unraveling the Electronic Structure of Individual Photosynthetic Pigment−Protein Complexes. Science 1999, 285, 400−402. (19) Jang, S.; Newton, M. D.; Silbey, R. J. Multichromophoric Förster Resonance Energy Transfer from B800 to B850 in the Light Harvesting Complex 2: Evidence for Subtle Energetic Optimization by Purple Bacteria. J. Phys. Chem. B 2007, 111, 6807−6814. (20) Hofmann, C.; Aartsma, T. J.; Köhler, J. Energetic Disorder and the B850-Exciton States of Individual Light-Harvesting 2 Complexes from Rhodopseudomonas acidophila. Chem. Phys. Lett. 2004, 395, 373− 378. (21) Linnanto, J.; Korppi-Tommola, J. Modelling Excitonic Energy Transfer in the Photosynthetic Unit of Purple Bacteria. Chem. Phys. 2009, 357, 171−180. (22) Pajusalu, M.; Rätsep, M.; Trinkunas, G.; Freiberg, A. Davydov Splitting of Excitons in Cyclic Bacteriochlorophyll a Nanoaggregates of Bacterial Light-Harvesting Complexes between 4.5 and 263 K. ChemPhysChem 2011, 12, 634−644. (23) Timpmann, K.; Ellervee, A.; Pullerits, T.; Ruus, R.; Sundström, V.; Freiberg, A. Short-Range Exciton Couplings in LH2 Photosynthetic Antenna Proteins Studied by High Hydrostatic Pressure Absorption Spectroscopy. J. Phys. Chem. B 2001, 105, 8436−8444. (24) Humphrey, W.; Dalke, A.; Schulten, K. VMDVisual Molecular Dynamics. J. Mol. Graphics 1996, 14.1, 33−38. (25) Harel, E.; Engel, G. S. Quantum Coherence Spectroscopy Reveals Complex Dynamics in Bacterial Light-Harvesting Complex 2 (LH2). Proc. Natl. Acad. Sci. U.S.A. 2012, 109, 706−711.

theory at longer times. To avoid these problems, we studied only zero delay time 2DES spectra where coherence signals up to 500 fs are important and polaron formation could be neglected. It must be also noticed that the simulation includes additional approximation in the formulation of excited state absorption. It is known that the single chlorophyll shows the induced absorption from its singly excited state, while chlorophyll aggregates demonstrate exciton annihilation through its higher lying excited states; hence, it should be treated as at least a three-level system.52,59 The excited state absorption of a BChl molecule (ESA-BChl) is not included in our modeling (eq 1) based on the assumption that the number of combination bands, where two pigments are singly excited (|mn⟩), scales with number of pigments as N × N, while the number of “overtones” (|n2⟩) scales as N. So for LH2 with the number of pigments N being 27, the effect of ESA-BChl should be small. In conclusion, we have performed analysis of the static and dynamic disorder of the exciton model for the LH2 aggregate. We find that the disorder parameters must carry temperature dependence so that the spectra become much more homogeneous at room temperature compared to the 77 K temperature. This cannot be explained by a harmonic environment model and suggests that protein environment of the crowded B850 ring is highly anharmonic. Meanwhile the exciton delocalization turns out to be temperature independent. Hence LH2 has evolved to maintain its properties in a broad range of temperatures.

■

AUTHOR INFORMATION

Corresponding Authors

*O.R.: e-mail, olga.rancova@ff.vu.lt. *D.A.: e-mail, darius.abramavicius@ff.vu.lt Notes

The authors declare no competing financial interest.

■ ■

ACKNOWLEDGMENTS This research was funded by the European Social Fund under the Global Grant Measure (No. VP1-3.1-ŠMM-07-K-01-020). REFERENCES

(1) Cogdell, R. J.; Gall, A.; Köhler, J. The Architecture and Function of the Light-Harvesting Apparatus of Purple Bacteria: From Single Molecules to in Vivo Membranes. Q. Rev. Biophys. 2006, 39, 227−324. (2) Hu, X.; Ritz, T.; Damjanovic, A.; Autenrieth, F.; Schulten, K. Photosynthetic Apparatus of Purple Bacteria. Q. Rev. Biophys. 2002, 35, 1−62. (3) McDermott, G.; Prince, S.; Freer, A.; Hawthornthwaite-Lawless, A.; Papiz, M.; Cogdell, R.; Isaacs, N. Crystal Structure of an Integral Membrane Light-Harvesting Complex from Photosynthetic Bacteria. Nature 1995, 374, 517−521. (4) Prince, S.; Papiz, M.; Freer, A.; McDermott, G.; Hawthornthwaite-Lawless, A.; Cogdell, R.; Isaacs, N. Apoprotein Structure in the LH2 Complex from Rhodopseudomonas acidophila Strain 10050: Modular Assembly and Protein Pigment Interactions. J. Mol. Biol. 1997, 268, 412−423. (5) Papiz, M.; Prince, S.; Howard, T.; Cogdell, R.; Isaacs, N. The Structure and Thermal Motion of the B800-850 LH2 Complex from Rps. acidophila at 2.0Å Resolution and 100K: New Structural Features and Functionally Relevant Motions. J. Mol. Biol. 2003, 326, 1523− 1538. (6) McLuskey, K.; Prince, S. M.; Cogdell, R. J.; Isaacs, N. W. The Crystallographic Structure of the B800-820 LH3 Light-Harvesting 7539



Article

(26) Fidler, A. F.; Singh, V. P.; Long, P. D.; Dahlberg, P. D.; Engel, G. S. Time Scales of Coherent Dynamics in the Light-Harvesting Complex 2 (LH2) of Rhodobacter sphaeroides. J. Phys. Chem. Lett. 2013, 4, 1404−1409. (27) Fidler, A. F.; Singh, V. P.; Long, P. D.; Dahlberg, P. D.; Engel, G. S. Probing Energy Transfer Events in the Light Harvesting Complex 2 (LH2) of Rhodobacter sphaeroides with Two-Dimensional Spectroscopy. J. Chem. Phys. 2013, 139, 155101. (28) Fidler, A. F.; Singh, V. P.; Long, P. D.; Dahlberg, P. D.; Engel, G. S. Dynamic Localization of Electronic Excitation in Photosynthetic Complexes Revealed with Chiral Two-Dimensional Spectroscopy. Nat. Commun. 2014, 5, 3286. (29) Zigmantas, D.; Read, E. L.; Mančal, T.; Brixner, T.; Gardiner, A. T.; Cogdell, R. J.; Fleming, G. R. Two-Dimensional Electronic Spectroscopy of the B800−B820 Light-Harvesting Complex. Proc. Natl. Acad. Sci. U.S.A. 2006, 103, 12672−12677. (30) Rancova, O.; Sulskus, J.; Abramavicius, D. Insight into the Structure of Photosynthetic LH2 Aggregate from Spectroscopy Simulations. J. Phys. Chem. B 2012, 116, 7803−7814. (31) Abramavicius, D.; Palmieri, B.; Voronine, D. V.; Šanda, F.; Mukamel, S. Coherent Multidimensional Optical Spectroscopy of Excitons in Molecular Aggregates; Quasiparticle Versus Supermolecule Perspectives. Chem. Rev. 2009, 109, 2350−2408. (32) Madjet, M. E.; Abdurahman, A.; Renger, T. Intermolecular Coulomb Couplings from ab Initio Electrostatic Potentials: Application to Optical Transitions of Strongly Coupled Pigments in Photosynthetic Antennae and Reaction Centers. J. Phys. Chem. B 2006, 110, 17268−17281. (33) Adolphs, J.; Müh, F.; Madjet, M. E.; Renger, T. Calculation of Pigment Transition Energies in the FMO Protein. From Simplicity to Complexity and Back. Photosynth. Res. 2008, 95, 197−209. (34) Renger, T. Theory of Excitation Energy Transfer: From Structure to Function. Photosynth. Res. 2009, 102, 471−485. (35) Renger, T.; Müh, F. Theory of Excitonic Couplings in Dielectric Media. Photosynth. Res. 2012, 111, 47−52. (36) Scholes, G. D.; Fleming, G. R. On the Mechanism of Light Harvesting in Photosynthetic Purple Bacteria: B800 to B850 Energy Transfer. J. Phys. Chem. B 2000, 104, 1854−1868. (37) Valkunas, L.; Abramavicius, D.; Mančal, T. Molecular Excitation Dynamics and Relaxation; Wiley-VCH Verlag GmbH & Co. KGaA: Weinheim, Germany, 2013. (38) Abramavicius, D.; Butkus, V.; Valkunas, L. Interplay of Exciton Coherence and Dissipation in Molecular Aggregates. In Semiconductors and Semimetals; Würfel, U., Thorwart, M., Weber, E. R., Eds.; Elsevier: San Diego, CA, 2011; Vol. 85; pp 3−46. (39) Butkus, V.; Valkunas, L.; Abramavicius, D. Molecular VibrationsInduced Quantum Beats in Two-Dimensional Electronic Spectroscopy. J. Chem. Phys. 2012, 137, 044513-9. (40) Renger, T.; Marcus, R. A. On the Relation of Protein Dynamics and Exciton Relaxation in Pigment−Protein Complexes: An Estimation of the Spectral Density and a Theory for the Calculation of Optical Spectra. J. Chem. Phys. 2002, 116, 9997−10019. (41) Novoderezhkin, V. I.; Rutkauskas, D.; van Grondelle, R. Dynamics of the Emission Spectrum of a Single LH2 Complex: Interplay of Slow and Fast Nuclear Motions. Biophys. J. 2006, 90, 2890−2902. (42) Olbrich, C.; Kleinekathöfer, U. Time-Dependent Atomistic View on the Electronic Relaxation in Light-Harvesting System II. J. Phys. Chem. B 2010, 114, 12427−12437. (43) Kell, A.; Feng, X.; Reppert, M.; Jankowiak, R. On the Shape of the Phonon Spectral Density in Photosynthetic Complexes. J. Phys. Chem. B 2013, 117, 7317−7323. (44) Mukamel, S. Multidimensional Femtosecond Correlation Spectroscopies of Electronic and Vibrational Excitations. Annu. Rev. Phys. Chem. 2000, 51, 691−729. (45) Abramavicius, D. Exciton−Exciton Scattering in a OneDimensional J Aggregate. Europhys. Lett. 2013, 101, 57007. (46) Freiberg, A.; Timpmann, K.; Ruus, R.; Woodbury, N. W. Disordered Exciton Analysis of Linear and Nonlinear Absorption

Spectra of Antenna Bacteriochlorophyll Aggregates: LH2-Only Mutant Chromatophores of Rhodobacter sphaeroides at 8 K under Spectrally Selective Excitation. J. Phys. Chem. B 1999, 103, 10032−10041. (47) Trinkunas, G.; Zerlauskiene, O.; Urboniene, V.; Chmeliov, J.; Gall, A.; Robert, B.; Valkunas, L. Exciton Band Structure in Bacterial Peripheral Light-Harvesting Complexes. J. Phys. Chem. B 2012, 116, 5192−5198. (48) Zerlauskiene, O.; Trinkunas, G.; Gall, A.; Robert, B.; Urboniene, V.; Valkunas, L. Static and Dynamic Protein Impact on Electronic Properties of Light-Harvesting Complex LH2. J. Phys. Chem. B 2008, 112, 15883−15892. (49) Meldaikis, J.; Zerlauskiene, O.; Abramavicius, D.; Valkunas, L. Manifestation of Protein Conformations in the B850 Absorption Band of Light-Harvesting Complex LH2. Chem. Phys. 2013, 423, 9−14. (50) Wu, H.-M.; Rätsep, M.; Jankowiak, R.; Cogdell, R. J.; Small, G. J. Comparison of the LH2 Antenna Complexes of Rhodopseudomonas acidophila (Strain 10050) and Rhodobacter sphaeroides by HighPressure Absorption, High-Pressure Hole Burning, and TemperatureDependent Absorption Spectroscopies. J. Phys. Chem. B 1997, 101, 7641−7653. (51) Freiberg, A.; Rätsep, M.; Timpmann, K. A Comparative Spectroscopic and Kinetic Study of Photoexcitations in DetergentIsolated and Membrane-Embedded LH2 Light-Harvesting Complexes. Biochim. Biophys. Acta 2012, 1817, 1471−1482. (52) van Amerongen, H.; Valkunas, L.; van Grondelle, R. Photosynthetic Excitons; World Scientific: Singapore, 2006; p 590. (53) Dahlbom, M.; Pullerits, T.; Mukamel, S.; Sundström, V. Exciton Delocalization in the B850 Light-Harvesting Complex: Comparison of Different Measures. J. Phys. Chem. B 2001, 105, 5515−5524. (54) Han, J.; Zhang, H.; Abramavicius, D. Exchange Narrowing and Exciton Delocalization in Disordered J Aggregates: Simulated Peak Shapes in the Two Dimensional Spectra. J. Chem. Phys. 2013, 139, 034313. (55) van Oijen, A. M.; Ketelaars, M.; Köhler, J.; Aartsma, T. J.; Schmidt, J. Spectroscopy of Individual Light-Harvesting 2 Complexes of Rhodopseudomonas acidophila: Diagonal Disorder, Intercomplex Heterogeneity, Spectral Diffusion, and Energy Transfer in the B800 Band. Biophys. J. 2000, 78, 1570−1577. (56) Agarwal, R.; Yang, M.; Xu, Q.-H.; Fleming, G. R. Three Pulse Photon Echo Peak Shift Study of the B800 Band of the LH2 Complex of Rps. acidophila at Room Temperature: A Coupled Master Equation and Nonlinear Optical Response Function Approach. J. Phys. Chem. B 2001, 105, 1887−1894. (57) Novoderezhkin, V.; van Grondelle, R. Spectra and Dynamics in the B800 Antenna: Comparing Hierarchical Equations, Redfield and Forster Theories. J. Phys. Chem. B 2013, 117, 11076−11090. (58) Polívka, T.; Pullerits, T.; Herek, J. L.; Sundström, V. Exciton Relaxation and Polaron Formation in LH2 at Low Temperature. J. Phys. Chem. B 2000, 104, 1088−1096. (59) Boni, L. D.; Correa, D. S.; Pavinatto, F. J.; D. S. dos Santos, J.; Mendonca, C. R. Excited State Absorption Spectrum of Chlorophyll a Obtained with White-Light Continuum. J. Chem. Phys. 2007, 126, 165102.

7540


Static and Dynamic Disorder in Bacterial Light-Harvesting Complex

Recommend Documents