J. Phys. Chem. B 2008, 112, 15883–15892
15883
Static and Dynamic Protein Impact on Electronic Properties of Light-Harvesting Complex LH2 O. Zerlauskiene,† G. Trinkunas,† A. Gall,‡ B. Robert,‡ V. Urboniene,§ and L. Valkunas*,†,| Institute of Physics, SaVanoriu 231, LT-02300 Vilnius, Lithuania, CEA, Institut de Biologie et Technologies de Saclay, and CNRS, 91191 Gif sur YVette Cedex, France, Department of General Physics and Spectroscopy, Vilnius UniVersity, Sauletekio 9, LT-10222 Vilnius, Lithuania, and Department of Theoretical Physics, Vilnius UniVersity, Sauletekio 9, LT-10222 Vilnius, Lithuania ReceiVed: April 21, 2008; ReVised Manuscript ReceiVed: July 12, 2008
A comparative analysis of the temperature dependence of the absorption spectra of the LH2 complexes from different species of photosynthetic bacteria, i.e., Rhodobacter sphaeroides, Rhodoblastus acidophilus, and Phaeospirillum molischianum, was performed in the temperature range from 4 to 300 K. Qualitatively, the temperature dependence is similar for all of the species studied. The spectral bandwidths of both B800 and B850 bands increases with temperature while the band positions shift in opposite directions: the B800 band shifts slightly to the red while the B850 band to the blue. These results were analyzed using the modified Redfield theory based on the exciton model. The main conclusion drawn from the analysis was that the spectral density function (SDF) is the main factor underlying the strength of the temperature dependence of the bandwidths for the B800 and B850 electronic transitions, while the bandwidths themselves are defined by the corresponding inhomogeneous distribution function (IDF). Slight variation of the slope of the temperature dependence of the bandwidths between species can be attributed to the changes of the values of the reorganization energies and characteristic frequencies determining the SDF. To explain the shift of the B850 band position with temperature, which is unusual for the conventional exciton model, a temperature dependence of the IDF must be postulated. This dependence can be achieved within the framework of the modified (dichotomous) exciton model. The slope of the temperature dependence of the B850 bandwidth is then defined by the value of the reorganization energy and by the difference between the transition energies of the dichotomous states of the pigment molecules. The equilibration factor between these dichotomous states mainly determines the temperature dependence of the peak shift. Introduction The absorption spectrum of a particular molecule, electronic excitation transfer between molecules, and/or photochemical reactions are strongly influenced by the molecular environment. This influence manifests itself in the absorption/fluorescence spectra via the dispersive shift phenomenon and the spectral broadening as a result of well-defined electron-phonon interactions in a solid state.1 The spectral shift due to differences in the local environment of the molecule is usually associated with the so-called inhomogeneous distribution of the transition frequencies. The electron-phonon interaction manifests itself in the line-shape of the electronic transition as a result of phonon side bands in addition to the zero-phonon transition. In the case of protein-bound chromophores, their surroundings cannot be considered as a rigid matrix. The dynamics of proteins proceeds on time scales ranging from femtoseconds to hundreds of nanoseconds.2 Therefore, the static (inhomogeneous) and dynamical components of the spectral broadening of the electronic transitions contribute combined. The concept of the line-shape function of an absorption spectrum originates from the pioneering theoretical description developed by Lax in terms of a two-level system coupled with * To whom correspondence should be addressed. Tel: +370-52661640. E-mail:
[email protected]. † Institute of Physics. ‡ CEA, Institut de Biologie et Technologies de Saclay. § Department of General Physics and Spectroscopy, Vilnius University. | Department of Theoretical Physics, Vilnius University.
harmonic oscillators.3 Further development of the theory has been based on the stochastic approach,4,5 by taking into account anharmonicity6 and by using the Brownian oscillator model to characterize the phonon system.7 This approach has also been used by describing the absorption line shapes of (bacterio)chlorophyll molecules in photosynthetic pigment-protein complexes of the light-harvesting (LH) antenna and reaction centers.8-12 However, due to the resonance interactions between pigment molecules in photosynthetic pigment-protein complexes, the excitonic effects play a dominant role in determining the optical spectra and the excitation energy transfer.13 As a result, the pigment-protein complex should be considered as a multilevel system of exciton states coupled to a large manifold of phonons. This coupling originates the population relaxation of exciton states as well as the exciton dephasing. To describe the line shape of an absorption spectrum of excitonically coupled molecular aggregates, various theoretical approaches are used. For disconnected molecules, or impurity centers in a crystal, the spectral density function (SDF) and the inhomogeneous distribution function (IDF) are typically the basic quantities that characterize the dynamical and inhomogeneous broadening of the line shape of their absorption spectra.8,10,14-17 As has been demonstrated by analyzing the J-aggregate at a fixed temperature, the absorption spectrum is sensitive to variations of the parameters that determine the SDF in the case when the IDF is small, and this sensitivity is absent when the IDF becomes the dominating factor.18 However,
10.1021/jp803439w CCC: $40.75 2008 American Chemical Society Published on Web 11/14/2008
15884 J. Phys. Chem. B, Vol. 112, No. 49, 2008 temperature variation can strongly influence population relaxation rates of exciton states19 along with definitions of the IDF and SDF in proteins, thus perturbing the parameters determined from fitting of the experimental spectra. This kind of analysis on the sensitivity of parameters has been applied by describing the temperature dependence of the spectra of chlorophyll dimers in a water-soluble pigment-protein20 and has not been carried out by explaining the temperature dependence of the spectra of larger aggregates so far. The structure of the LH2 (or peripheral light-harvesting) complex of Rhodoblastus (Rbl.) acidophilus21 was elucidated over a decade ago.22 This complex is arranged as a highly symmetric ring of 9 protein-pigment subunits, each containing two helical trans-membrane polypeptides, the R-polypeptide on the inner side and the β-polypeptide on the outer side of the ring. The carboxy-terminal domain of this protein binds, in the hydrophobic membrane phase, a ring of 18 tightly coupled bacteriochlorophyll (Bchl) molecules with a center-to-center distance of less than 1 nm between neighboring pigments. This ring is responsible for the intense absorption of LH2 at 850 nm (the so-called B850 ring). Due to the relatively small distances between the pigments in the B850 rings the interaction between them will play an important role in determining their spectroscopic and functional properties. Indeed, the magnitude of the resonance interaction between the nearest neighbors was estimated to be ∼300 cm-1 (e.g., see refs 13, 23-27). A second ring of 9 weakly interacting Bchls is bound by the aminoterminal domain of LH2 (pigment-pigment distance of about 2.1 nm) and is largely responsible for the absorption at 800 nm (B800 ring). The availability of detailed structural information for LH2 has stimulated efforts to model the electronic properties of the Bchl molecules using the exciton theory.13,28 Like the peripheral light-harvesting complex from Rbl. acidophilus, the LH2 from Rhodobacter (Rba.) sphaeroides is also nonameric and is believed to have the same overall structure.29 However, the LH2 complex from Phaeospirillum (Phs.) molischianum, which also exhibits typical 800 and 850 nm electronic absorption transitions, contains one less protein-pigment subunit making it an octameric structure.30 The temperature dependence of the absorption spectra of detergent-purified LH2 complexes from Rbl. acidophilus23 and Rba. sphaeroides in a glycerol-water mixture and in native membranes14,17 can qualitatively be explained in terms of the exciton model invoking the defined structural data. However, according to the thorough analysis recently presented,14,17 the experimentally observed temperature dependence of the spectral parameters deviates from the theoretical predictions, especially at highest temperatures. From the spectral analysis of the LH2 complexes from Rba. sphaeroides, it has been concluded that the IDF and the resonance interaction between pigments in the B850 ring should be slightly modified at high temperatures. The variability of the resonance interaction as compared to their values obtained at lower temperatures might be qualitatively attributed to changes of the dielectric screening of the resonance interaction in the glycerol-water solution with temperature.14 However, the temperature dependence of the IDF was lacking a proper mathematical model. The above analysis was based on the assumption that the population relaxation rates are temperature independent. Here, we present further analysis of the absorption spectra of the LH2 complexes by taking into account the explicit temperature dependence of the population relaxation rates in terms of the modified Redfield theory.31,32 Comparative analysis between the LH2 spectra from different species, namely, Rba. sphaeroides, Rbl. acidophilus, and Phs.
Zerlauskiene et al.
Figure 1. Absorption spectra as a function of temperature for the LH2 complexes from (a) Rba. sphaeroides (b) Rbl. acidophilus, and (c) Phs. molischianum. The arrows indicate the spectral changes with increasing the temperature.
molischianum is present. In order to explain the continuous blue shift of the B850 band with temperature, a novel model explaining the temperature dependence of the IDF is proposed. Materials and Methods Phs. molischianum, Rba. sphaeroides 2.4.1, and Rbl. acidophilus were grown photosynthetically under strict anaerobic conditions in the light at 30 °C.33,34 The isolation of detergentpurified LH2 complexes from whole cells was based on a previously defined protocol35 where the photosynthetic membranes were solubilized with the detergent N,N-dimethyldodecylamine-N-oxide (LDAO) (Fluka, Buchs, Switerland). For electronic absorption experiments, the LH2 samples were prepared in 60% (v/v) glycerol (Sigma, St Quentin, France), 0.1% (w/v) LDAO (Fluka, Buchs, Switerland), 20 mM Tris.Cl, pH 8.5. Since glycerol-water solutions exhibit a phase transition around 200 K, the complete temperature cycle could only be measured by progressively decreasing the temperature. Absorption measurements in the 4-200 K range were also achieved by slowly raising temperature. The temperature of the samples was maintained by a Helium bath cryostat (Maico Metriks, Tartu, Estonia). In order to ensure the equilibrium between the sample and the helium bath, the sample was stabilized at each measured temperature for at least 15 min. Electronic absorption spectra were collected using a Cary E5 spectrophotometer (Varian, Les Ulis, France). Absorption Measurements The near-infrared spectra of the LH2 complexes (650-920 nm) from Rba. sphaeroides, Rbl. acidophilus, and Phs. molischianum obtained at different temperatures are presented in Figure 1. As was already mentioned above, the two major electronic transitions corresponding to the B800 and B850 bands arise from the rings of weakly and strongly interacting Bchl molecules, respectively. The bandwidths of both B800 and B850 increase with temperature (Figure 2, parts a and c) and the maxima of these bands shift slightly, the B800 band shifts toward longer wavelengths (see Figure 2b) and the B850 band
Protein Impact on Light-Harvesting LH2
J. Phys. Chem. B, Vol. 112, No. 49, 2008 15885 obtained for J-aggregates, where it is attributed to the exciton coupling with acoustic phonons.19 Thus, this difference can evidently be related to the pigment-protein interaction.17 The temperature dependence of the B850 band position is the weakest in the LH2 complex from Rba. sphaeroides and is almost identical in the other two pigment-protein complexes. Modified Redfield Theory for Exciton Spectra Calculations The absorption spectrum of the molecular aggregate usually is attributed to the exciton model in combination with the modified Redfield theory.31,32 The excitonic energies and wave functions are obtained from the diagonalization of the exciton Hamiltonian:
Figure 2. Temperature dependences of the bandwidths [(a), (c)] and peak positions [(b), (d)] of the absorption spectra shown in Figure 1 of LH2 complexes from Rba. sphaeroides (squares), Rbl. acidophilus (circles), and Phs. molischianum (triangles). The dashed lines in (c) correspond to fitting results according to eq 1. The fitting parameters are given in Table 1.
TABLE 1: Fitting Parameters According to Eq 1 for Three Different LH2 complexes. Rba. sphaeroides Rbl. acidophilus Phs. molischianum
A
B
C
221 265 330
1.24 1.57 1.52
0.83 0.83 0.873
toward the shorter wavelengths (Figure 2d) for all complexes under consideration. The temperature dependences of the bandwidths of the B800 band are similar for all three bacterial complexes. At 4 K, the B800 bandwidth from Rba. sphaeroides and Rbl. acidophilus LH2 complexes are very similar, whereas in the Phs. molischianum antenna, it is twice as large. The temperature dependences of the B800 band-shift for Rba. sphaeroides and Phs. molischianum are similar and stronger than that observed in the LH2 complex from Rbl. acidophilus. The bandwidths of the B850 band also increase with temperature; however, this dependence is weaker (Figure 2c). The temperature dependence of the B850 bandwidths can be described well by the power law:17
Γ850(T) ) A + BTC
(1)
The slopes of the temperature dependence of the bandwidths are well described by eq 1 for lower temperatures. Clear changes in the behavior of the bands with temperature at ∼200-230 K may indeed be roughly considered as an inflection point. It is worthwhile to mention that the temperature dependence of the B850 bandwidth speeds up upon reaching ∼200 K for Rba. sphaeroides and slows down for Rbl. acidophilus and Phs. molischianum when compared with the temperature dependence defined by eq 1 (see Figure 2c). The fitting parameters for the three LH2 complexes determined according to eq 1 are presented in Table. 1. The smallest values determining the spectral bandwidth (parameters A and B in Table 1) correspond to the LH2 complex from Rba. sphaeroides and the largest values qualifying the bandwidth correspond to Phs. molischianum LH2 complex, respectively. The slopes of the temperature dependence of the bandwidth are the same for the LH2 complexes from Rba. sphaeroides and Rbl. acidophilus and slightly steeper in the case of Phs. molischianum. This type of the temperature dependence is essentially weaker in comparison with the slope
H)
N
N
n)1
n,m)1
∑ (εn + qn)|n〉〈n| + ∑
Vnm|n〉〈m| + Hph
(2)
where εn is the electronic transition energy, qn are collective coordinates of the thermal bath describing the modulations of the diagonal energies in molecular representation, |n〉 and 〈n| are the ket and bra vectors, respectively, of the n-th molecule in the aggregate (the Bchl molecule in the B850 ring). Matrix elements Vnm denote the energies of the resonance interaction between the n-th and the m-th pigments, which can be calculated from the available LH2 structure files 22,30 or determined semiempirically by fitting the experimental observations. Due to the ensemble of the LH2 complexes considered, the excitation energy εn is assumed to be the Gaussian random variable with mean ε0 and the full width at half-maximum (fwhm) Γinh of the IDF:
finh(εn) )
(
4ln(2)(εn - ε0)2 2 ln(2) 1⁄2 exp Γinh π (Γinh)2
( )
)
(3)
Hph is a free phonon Hamiltonian. All relevant information about the molecular interaction with the bath consists in the correlation function of this energy fluctuation, the Fourier transform of which is related to the SDF of a separate Bchl molecule. Assuming that the baths acting on different molecules are uncorrelated, the latter is defined as follows:
Cn,n(ω) )
∫-∞∞ dt exp(iωt)〈[qn(t), qn(0)]〉
(4)
where the bath average is taken in respect of the free phonon Hamiltonian Hph. Additionally assuming also that baths for all molecules are equivalent, the following simplification can be used:
Cn,n(ω) ≡ C(ω)
(5)
Introducing exciton states, N
|k〉 )
∑ ckn|n〉
(6)
n)1
where ckn is the coefficient describing the participation value of the n-th excited molecule in the k-th exciton state, the exciton energy states Ek enumerated by the k-quantum number can be determined as a result of diagonalization of the electronic part of the exciton Hamiltonian (eq 2). By applying the same exciton representation for the correlation function defined by eq 4, we will get:
15886 J. Phys. Chem. B, Vol. 112, No. 49, 2008
Zerlauskiene et al.
N
Ckkkk(ω) )
* Cn,n(ω) ∑ cknc*k'ncknck′′′n
(7)
n)1
The modified Redfield theory is based on the approach when the diagonal term of the exciton-phonon coupling with the bath can be taken into account explicitly while the nondiagonal coupling is accounted for perturbatively.31,32 The absorption spectrum corresponding to a particular configuration of the Bchl molecules in the fixed substates can be calculated by using the cumulant expansion technique and within the frame of the modified Redfield theory, thus, given by:16,17,31,32
σa(ω) ) 〈ω
∑ |µk| Re[∫0
∞
2
i(ω-Ek)t-gk(t,T)-Rkkkkt
]〉IDF (8)
dt e
k
where N
Ek )
N
∑ |ckn| εn + ∑
c*kmcknVmn
(9)
n,m)1
µk ) ∑n µnckn is the transition dipole moment of the k-exciton state, which is related to the transition dipole moment of the n-th molecule, µn, and the spectral (homogeneous) broadening function gk(t) is determined by the correlation function of a collective coordinate of the thermal bath, qn:
gk(t, T) ) gkkkk(t, T)
gkkkk(t, T) )
∫
2πω
{ ( ) coth
pω [1 2kBT
1 π
Ckkkk(ω) is the imaginary part of the Fourier transform of the correlation function in the exciton representation (eq 7), which by taking into account eq 5, is given as follows:
qn )
(12)
In terms of the modified Redfield theory the Redfield relaxationtermRkkkk shouldsatisfythefollowingrelationships:16,17,31,32
∑ Rkkkk
(13)
k′
Rkkkk ) -2Re
W(ωkkt){g¨kkkk(t) - {g˙kkkk(t) ∫0∞ dt ˆ g˙kkkk(t) + 2iλkkkk} × ×{g˙kkkk(t) - g˙kkkk(t) + 2iλkkkk}} (14)
ˆ W(ωkkt) ) exp{-iωkkt - gkkkk(t) - gkkkk(t) +
J(ω) )
(19)
∑ g2ξδ(ω - ωξ)
(20)
ξ
Therefore, the relationship between C′′(ω) and the SDF function holds accordingly:
where 1 ∞ C kkkk(ω) λkkkk ) dω π 0 ω
(16)
which is analogous to the molecular reorganization energy in the exciton representation. Indeed, by substituting the imaginary part of the correlation function in the site representation (eqs 5 and 7) into eq 16, we will obtain the molecular reorganization energy modified by the amplitudes of the exciton wave functions.
(21)
Recently, the SDF was determined in a parametric form for the B777 subunit by analyzing the fluorescence line narrowing spectra.8,36 This subunit, containing a single Bchl molecule bound to a single R-helix (either an R- or β-polypeptide) is obtained by dissociating the LH1 complex (also called the core light-harvesting complex) by titration with increasing detergent concentration.37 Therefore, the SDF from B777 is characterized solely by the pigment-protein interaction with some effect caused by the presence of the detergent. The obtained SDF can be also approximated in an elementary function form:8
s1ω3
[( )]
ω J(ω) ) exp 4 ω 7!·2·ωS1 S1
+ 2gkkkk(t) + 2i(λkkkk - λkkkk)t} (15)
∫
∑ gξpωξqξ
C(ω) ) ω2J(ω)
n)1
Rkkkk ) -
(18)
ξ
N
∑
∫0∞ dω C ω(ω) ≡ aω1 + bω2
where gξ is the strength of the excitation energy coupling with a particular vibrational mode ξ of frequency ωξ, the SDF describing the distribution of phonon/vibration modes can be determined as follows:
}
* cknc*k'nck''nck'''n
(17)
The two exponent terms in eq 17 can be also interpreted thus as contributing from two distinct spectral distribution modes. The imaginary part of the correlation function C′′(ω) can be related to the SDF. By introducing the following relationship between the excitation energy fluctuations qn and phonon/ vibration modes:
cos(ωt)] + i[sin(ωt) - ωt] (11)
Ckkkk(ω) ) C(ω)
( )
where the four variable parameters a, b, ω1, and ω2 are directly related to the reorganization energy in the site representation λ according to the definition given by eq 16:
(10)
where
Ckkkk(ω) ∞ dω 2 -∞
( )
ω2 ω ω + πb exp ω1 ω2 ω2
C(ω) ) πaω exp -
λ)
2
n)1
The strength of the resonance interactions determining the exciton Hamiltonian (eq 2) can be found semiempirically, for instance, from the fit of the ensemble averaged LH2 absorption, linear dichroism and circular dichroism spectra. During the numerical calculations, the imaginary part of the correlation function in the site representation C′′(ω) can be approximated and expressed in a more convenient parametric form:10
1⁄2
+
s2ω3 7!·2·ω4S2
×
[( )]
exp -
ω ωS2
1⁄2
(22)
The normalization factor introduced in eq 22 is chosen to fulfill the definition of the Huang-Rhys factor S as a sum of the corresponding factors of two distinct spectral distribution modes, s1 and s2:
S)
∫0∞ dωJ(ω) ) s1 + s2
(23)
It is noteworthy that the Huang-Rhys factor determines the strength of the exciton interaction with the vibrational/phonon modes, that is,
Protein Impact on Light-Harvesting LH2
J. Phys. Chem. B, Vol. 112, No. 49, 2008 15887
TABLE 2: Best-Fit Parameters of the Temperature Dependence of the B850 Bandwidth and the Peak Position Obtained Using Different SDF Functions. SDF used to fit the temperature dependence of the B850 bandwidth V (cm-1) λ (cm-1) λ/2V Γinh (cm-1) Γinh/V Rba. sphaeroides SDF determined by fitting B850 taken from ref 17 SDF determined by fitting the B800 band SDF determined by fitting the FLN of the B777 band taken from ref 8 SDF determined according to ref 40
C′′(ω) function parameters a
b
ω1 (cm-1) ω2 (cm-1)
342 342 342
220 150 90
0.32 0.22 0.13
362 527 499
1.1 1.53 1.41
4.911 5.696 0.173 0.78 0.417 0.483
10 10 100
30 190 100
342
135
0.2
499
1.44
0.484 0.297
115
267
Rbl. acidophilus SDF determined by fitting the B800 band
360
180
0.25
606
1.65
0.013 1.058
5
170
Phs. molischianum SDF determined by fitting the B800 band
400
200
0.25
702
1.72
0.016 1.284
10
140
S)
∑ g2ξ
(24)
ξ
Thus, the SDF can be defined unambiguously by using the approximation for C′′(ω) (eq 17) from the relationship given by eq 21, or by using its direct approximation (eq 22). By also applying the approximate series expansion for coth (pω/2kBT), analytical integration for the spectral broadening function gk(t,T) can be then easily performed giving algebraic expressions with the help of the approximation for C′′(ω), as given by eq 17.38 Therefore, the form of eq 17 has been used for further simulations. Analysis of the Experimental Data For simulating the absorption spectra, the following set of parameters is critical. The resonance coupling V between nearest neighbor Bchl molecules bound to the R and β polypeptides in the heterodimeric protein subunit and the bandwidth of the IDF, Γinh, defined by eq 3, which are parameters determining the exciton energy states of the molecular aggregate with the diagonal disorder of the molecular transitions, must be taken into account. According to the structural organization, the Bchl molecules in the B850 ring are situated in two inequivalent (R and β) positions.22,30 Thus, in addition to the inhomogeneity of the molecular excitations the different transition energies that are considered as a mean excitation energies of the corresponding Bchl molecules, ε0 + ∆/2 (in the R position) and ε0 - ∆/2 (in the β position) have to be postulated implicitly. The value ∆ ) 300 cm-1 has been suggested from the analysis of the circular dichroism spectrum of the LH2 from Rba. sphaeroides.26 As has been demonstrated38 the variability of the resonance coupling for quite a wide range does not affect the excitonic energy distribution in the lower Davydov sub-band. Therefore, as in our previous temperature dependence studies of the absorption spectrum of the LH2 complexes from Rba. sphaeroides, the value of 340 cm-1 was chosen for the resonance coupling between the nearest neighbor Bchls. Recently it has been found that the resonance interaction between the Bchl molecules in the B850 ring can be estimated by determining the energy gap between the main absorption maximum at 850 nm and the absorption maximum at the upper edge of the exciton band.39 Since the gaps between the maxima of the optical transitions serve as the measure of the excitonic bandwidths, this procedure has been used to determine the corresponding values of the resonance interaction for Rbl. acidophilus (360 cm-1) and for Phs. molischianum (400 cm-1). The values characteristic for the exciton spectrum chosen for calculations are given in Table 2.
Figure 3. C′′(ω) and J(ω) functions for the B850 band obtained by neglecting the temperature-dependence of the Redfield relaxation parameters17 (dashed-dotted-dotted line), for the B800 band (dasheddotted line) and from calculations of J(ω) by describing the FLN of the B777 complexes (dashed line (b), adapted with permission from,8 copyright (2002) American Chemical Society), C′′(ω) as follows from the FLN of the B777 complexes (dashed line (a)), C′′(ω) for the overdamped Brownian oscillator model used in ref 41 (solid line) and J(ω) determined from the FLN experiments for the B850 for the Rba. sphaeroides LH2 complexes in 66% buffer-glycerol solution (solid line) determined40 together with its fitting using the SDF shape determined by eq 22 (dotted line), which is presented for the reference.
The other group of parameters qualifies the strength of the exciton-phonon coupling. The reorganization energy λ and parameters of the correlation function C′′(ω) (the parameters of the SDF) determine the dynamical broadening of the absorption spectrum. All of these values as well as the IDF bandwidth Γinh defined above have been used as variable parameters during the simulation. Rba. sphaeroides. The shapes of the B800 and B850 bands are sensitive to variation of both the SDF and IDF.14,17 Since the Bchl molecules in the B800 ring is weakly interacting, the B800 band can be well characterized as the inhomogeneously broadened molecular transition with a slight perturbation by the transition into the higher Davydov subband of the exciton band corresponding to the B850 ring.39 The SDF determined by fitting the experimental spectra is the dashed-dotted line in Figure 3. λ ) 112 cm-1 and Γinh ) 120 cm-1 were determined from fitting the B800 band temperature dependence.17 Because of the weakness of the intermolecular interaction, this result is not sensitive to the population relaxation. By assuming the same shape of the SDF and permitting the variability of the strength of the exciton-phonon interaction
15888 J. Phys. Chem. B, Vol. 112, No. 49, 2008
Figure 4. Temperature dependences of the fwhm (a) and absorption maxima (b) of the B850 band of the LH2 from Rba. sphaeroides (filled squares) and calculated with the SDF obtained by fitting the FLN of the B777 complexes:8 λ ) 90 cm-1 and Γinh ) 499 cm-1 (open circles); with the SDF determined from the FLN spectra of the LH2 complexes: 40 λ ) 135 cm-1 and Γinh ) 499 cm-1 (open diamonds); with the SDF obtained by fitting the B800 band: λ ) 150 cm-1 and Γinh ) 527 cm-1 (open triangles). By using the SDF obtained from fitting the temperature dependence of the B800 band and additionally by taking into account the two conformational states for each pigment molecule with the following chosen parameters: λ ) 150 cm-1, Γinh ) 510 cm-1, ∆E ) 90 cm-1 when k1/k2 ) 0.3 at 100 K, k1/k2 ) 0.32 at 150 K, k1/k2 ) 0.4 at 200 K and k1/k2 ) 0.45 at 250 K, the fit is presented by open stars.
(changing λ), the best fit of the temperature dependence of the B850 bandwidth and the peak position can be obtained by using two adjustable parameters, which are λ ) 150 cm-1 and Γinh ) 527 cm-1, as shown in Figure 4. To demonstrate the sensitivity of the calculated absorption spectra to the shape of the SDF we compared different SDF functions obtained by fitting different experimental data. The SDF was defined (i) from fitting the absorption spectrum by neglecting the Redfield relaxation terms17 (Figure 3, dashed-dotted-dotted line), (ii) from fitting the fluorescence line narrowing (FLN) spectra of the B777 band, which corresponds to the single Bchl molecule in the protein8 (Figure 3, dashed line), and (iii) from the FLN spectra of LH240 (Figure 3, dotted line). To fit the temperature dependence of the absorption spectrum by neglecting the temperature dependence of the Redfield terms, the SDF should be taken as a very narrow function of the frequency with the maximum at 10 cm-1 17 (see Figure 3). However, this narrow SDF is no longer suitable when the temperature dependence of the Redfield terms is taken into account (Figure 5). In order to fit the temperature dependence of the bandwidth of the B850 band the SDF function should be assumed to be substantially broader with the maximum shifted to larger frequencies (for instance, at about 60 cm-1 in the case of the SDF determined from fitting the temperature dependence of the B800 band). Similar results can be also obtained with the SDF determined from fitting the FLN spectra of B7778 or from fitting the FLN spectra of LH240 as shown in Figure 4. The fitting results were adjusted to the experimental data by changing the reorganization energy λ and the width of the IDF (see Table 2). The shift of the band position above 180 K cannot be obtained with any of the chosen SDF values and should be attributed to the phase transition of the solvent and to changes in the surrounding protein scaffold.17 Rbl. acidophilus. Similar analysis of the temperature dependence of the absorption spectra shown in Figure 1 was carried
Zerlauskiene et al.
Figure 5. Temperature dependences of the fwhm (a) and absorption maxima (b) of the measured B850 band of the LH2 from Rba. sphaeroides (filled squares) and calculated with Rkkkk ) 50 cm-1 (open circles), with modified Redfield tensors (open triangles) when the fitting parameters are chosen λ ) 220 cm-1, Γinh ) 362 cm-1.
Figure 6. Temperature dependences of the fwhm (a) and absorption maxima (b) of the measured B850 band of the LH2 from Rbl. acidophilus (filled circles) and calculated with the SDF determined by fitting the temperature dependence of the B800 band: λ ) 180 cm-1, Γinh ) 606 cm-1 (open triangles), calculated with parameters corresponding to the SDF determined in ref 41 according to the overdamped Brownian oscillator model (open circles), and calculated with the SDF obtained from fitting the temperature dependence of the B800 band and additionally by taking into account the two conformational states for each pigment molecule: λ ) 180 cm-1, Γinh ) 430 cm-1, ∆E ) 180 cm-1 when k1/k2 ) 0.6 at 150 K, k1/k2 ) 0.68 at 200 K, k1/k2 ) 0.78 at 250 K and k1/k2 ) 0.85 at 300 K (open stars).
out for the temperature dependence of the LH2 absorption spectrum from Rbl. acidophilus. The temperature dependence of the B850 bandwidth can be well described by using any of the broad SDFs shown in Figure 3, for instance by using the SDF defined from fitting the temperature dependence of the B800 band of the LH2 complexes from Rbl. acidophilus. The fitting results are presented in Figure 6. The temperature dependence of the B850 bandwidth is well described by using the same free fitting parameters: λ ) 180 cm-1 and Γinh ) 606 cm-1, which are slightly larger in comparison with the values obtained for Rba. sphaeroides. The temperature dependence of the band position can be related to the exciton model at lower temperatures and cannot be explained within the framework of
Protein Impact on Light-Harvesting LH2
J. Phys. Chem. B, Vol. 112, No. 49, 2008 15889
Figure 8. Modified Redfield tensors of a single realization of the spectral disorder for the B850 band using the SDF from the B800 band. Numbers label the excitonic levels in the ascending energy order. The data correspond to the calculated absorption spectra shown in Figure 9(c).
Figure 7. Temperature dependences of the fwhm (a) and absorption maxima (b) of the measured B850 band of the LH2 from Phs. molischianum (filled triangles) and calculated with the SDF determined by fitting the temperature dependence of the B800 band: λ ) 200 cm-1 and Γinh ) 702 cm-1 (open triangles), and calculated with the SDF obtained from fitting the temperature dependence of the B800 band and additionally by taking into account the two conformational states for each pigment molecule: λ ) 200 cm-1, Γinh ) 600 cm-1, ∆E ) 170 cm-1 when k1/k2 ) 0.6 at 150 K, k1/k2 ) 0.7 at 200 K and k1/k2 ) 0.9 at 300 K (open stars).
the exciton model at higher temperatures as was already outlined when fitting this dependence for Rba. sphaeroides.17 However, the deviation of the fitting results from the experimental data is even more pronounced in the case of Rbl. acidophilus, since the temperature dependence of the peak shift starts to deviate from the theoretical predictions even at lower temperatures (∼100 K). This deviation cannot be attributed only to the phase transition of the solvent but predominantly to the changes in the protein scaffold and/or to differences in the origin of the electronic transitions for different monomers (for instance, with different degrees of mixing with the CT states). Phs. molischianum. The temperature dependence of the bandwidth of the LH2 spectra from Phs. molischianum can be also well described in terms of the SDF determined from fitting the B800 band with the simplified model of noninteracting Bchl molecules. The temperature dependence of the B850 bandwidth is also well described (see Figure 7) by using two free fitting parameters: λ ) 200 cm-1 and Γinh ) 702 cm-1, which are evidently the largest among three species under consideration. The temperature dependence of the band positions is similar to Rbl. acidophilus and should be attributed to the changes in the protein scaffold and/or to differences in the origin of the electronic transitions for different monomers (for instance, with different degrees of mixing with the CT states). Discussion In this work, we show that the temperature dependence of the B800 bandwidth can be attributed to the temperaturedependent population of the phonon bath modes described by the SDF, while the size of the bandwidths from different species is defined by the corresponding IDF. Slight variation of the slope of the temperature dependence of the B800 bandwidths from different bacterial species follows the changes of the values of the reorganization energies and characteristic frequencies corresponding to the SDF. As already demonstrated,17 two different SDF functions for the B800 and B850 bands have to be assumed upon fitting the absorption spectra of the LH2 complexes from
Figure 9. Single realization of calculated absorption spectra of the B850 band obtained with the B800 SDF when (a) Rkkkk)0 cm-1, (b) Rkkkk)50 cm-1, and (c) with Redfield tensors presented for the temperatures 77, 180, and 300 K. Note the logarithmic scale of amplitudes used for better view of spectra.
Rba. sphaeroides where a wide temperature range is considered if the temperature dependence of the Redfield relaxation rates is deliberately neglected. This assumption of the temperature independence of the Redfield relaxation rates was considered as a justified approach since the IDF functions for both bands are essentially broader than the homogeneous bandwidths,18 as defined from fitting the spectra. However, the temperature dependence of the B850 bandwidth calculated with the same narrow SDF (see Figure 3) alters somewhat when the temperature dependence of the Redfield relaxation terms are taken into account (see Figure 5). This change of the temperature dependence results from the progressive homogeneous broadening of the higher exciton states due to the Redfield relaxation terms. This relaxation-linked broadening becomes comparable upon the spacing between the exciton states at higher temperatures (see Figure 8). Indeed, the exciton states responsible for the absorption spectrum that are well separated at low temperatures starts to strongly overlap when the temperature is increased (see Figure 9 for a particular realization selected from the ensemble of the inhomogeneously distributed LH2 complexes). Moreover, the absorption spectrum for a particular realization is essentially distinct from each other by using different assumptions concerning the temperature dependence of the Redfield relaxation rates (Figure 9). It is noteworthy that this statement is relevant for all realizations from the ensemble since the temperature dependence of the Redfield relaxation terms is qualitatively similar in all cases. Evidently, the ensemble averaged absorption spectrum should demonstrate the strong temperature dependence caused by the Redfield relaxation terms
15890 J. Phys. Chem. B, Vol. 112, No. 49, 2008 if their values become comparable with the splitting values between the exciton states. This statement is justified even in the case when the inhomogeneous broadening is substantially larger (at low temperatures) than the homogeneous bandwidth of the spectrum when the temperature dependence of the absorption spectrum is considered. The temperature dependence of the B850 bandwidth can be well described by using broader SDF functions with the maxima shifted to larger frequencies and is not very sensitive to any particular SDF line shape (Figure 3). The slope of the temperature dependence is defined mainly by the values of the reorganization energies and characteristic frequencies of the SDF function (see Table 2). Thus, the reorganization energy determined as a fitting parameter is of a reasonable value (of the order of 100 to 200 cm-1) for all broad distributions (when the Redfield relaxation rates are taken into account) and is slightly larger if the narrow distribution function is chosen (by neglecting the Redfield relaxation). All used SDF functions provide a good description of the bandwidth temperature dependence and a similar temperature dependence of the absorption maximum of the B850 band from Rba. sphaeroides (see Figure 4), which indicates that the reduction of the exciton coherence size with temperature due to the population relaxation (Figure 8) is not sufficient to reach a substantial blue shift of the spectrum. The temperature dependence of the B850 bandwidths for Rbl. acidophilus (Figure 6) and Phs. molischianum (Figure 7) are also well described using the same broader SDF defined from fitting the temperature dependence of the B800 band. Then the slope of the temperature dependence is also defined by the value of the reorganization energy λ while the IDF value can be chosen to reach the full width. The lowest values are obtained for Rba. sphaeroides, and the largest values for Phs. molischianum (see Table 2). An additional demonstration of the sensitivity of the temperature dependence to the chosen values is shown in Figure 6 for Rbl. acidophilus. As was already mentioned above the SDF and IDF parameters can be postulated from fitting the absorption spectrum at a fixed temperature. However, the fitting result is ambiguous. Indeed, by taking the SDF and IDF postulated by fitting the absorption spectrum at room temperature,41 the obtained bandwidth fits well with our experimental data at room temperature; however, it does not give the proper slope for the temperature dependence (see open circles in Figure 6). Evidently, this ambiguity in determining the SDF and IDF can be resolved by analyzing the temperature dependence of the absorption spectrum. The temperature dependence of the maximum position of the B800 band (Figure 2b) can be attributed to the changes of the dispersion interaction with the surrounding environment.17 The temperature dependence of the maximum position of the B850 band is well described at low temperatures (less than 150 K) for Rba. sphaeroides (see Figure 4), (less than 100 K) for Rbl. acidophilus (Figure 6) and Phs. molischianum (Figure 7). However, the exciton model does not explain the drastic changes at higher temperatures. For instance, by using the SDF and IDF chosen from fitting the absorption spectrum at room temperature,41 the calculated high temperature slope of the maximum position is the same as that defined by using the SDF and IDF parameters from fitting the temperature dependence of the bandwidth. The fit can be obtained by assuming the temperature dependences for the dielectric constant of glycerol, the dispersion interaction, and the IDF all together.17 The latter can be explained on the basis of the modified (dichotomous) exciton model recently developed to describe the spectral dynamics of a single LH2 fluorescence spectrum at room temperature.42,43
Zerlauskiene et al.
Figure 10. Temperature dependence of the fwhm (a) and maxima (b) of the IDF defined in the frame of the dichotomic exciton model of LH2 with two conformational states for every molecule (c), when assuming ∆E ) 90 cm-1 (filled squares); ∆E ) 180 cm-1(open squares) The model of the ground and excited-state potential surfaces of the B850 ring pigment in the protein surrounding (c). The potential surface is shown along the conformational coordinate of the protein. Both in the ground and excited states the protein can be in two conformational states denoted “1” and “2”, separated by the energy barrier. In the absence of the light excitation transitions between the conformational states are spontaneous and occur in the ground state (k1 and k2).
This dichotomous exciton model suggests that each Bchl molecule can be in two conformational states that are determined by the protein scaffold. Transitions between these conformational states modulate the transition energies of the Bchl molecules. Evidently, then the IDF becomes sensitive to the ratio of the transition rates between these two states, which characterizes every molecule (Figure 10). Thus, let us modify our model accordingly assuming that each Bchl molecule can be in two conformational states with the different transition energies (see Figure 10), which differ from each other by the ∆E value. Postulating also that the transition rates between these conformational states as k1 and k2, the IDF then should vary when changing the ratio k1/k2 (see Figure 10). Evidently, some additional input to the IDF caused by the ensemble distribution of the LH2 complexes has to be also taken into account. Thus, by changing these additional values ∆E and k1/k2 with the adjustment of the IDF the temperature dependence of the bandwidths and band maxima can be obtained as indicated by the open stars in Figures 4, 6, and 7. Attributing the changes of the ratio k1/k2 to the temperature effect (due to the changes in the equilibration conditions between these two states in each monomer), the different temperature dependences of the bandwidth and the maxima positions for the B850 bands from the different species can be described. A more elaborate analysis by using the dichotomous exciton model, including the temperature dependence of the k1/k2 ratio, is outside the scope of this present work and will be presented elsewhere. In the present work, we have clearly pointed out that the different LH2 proteins, which have slightly different pigment environments, exhibit different deviations from the temperature dependence of the bandwidths from the behavior described by eq 1. This is attributed to differences in the equilibration ratio k1/k2 obtained for each LH protein. Thus, according to our calculations, the bandwidth of the IDF caused by the ensemble averaging, Γinh, have to be assumed to be slightly smaller (by the value of 150 cm-1 and less) in comparison with those determined from the conventional model (see Table 2). The additional broadening comes from the ∆E value. Since there is some difference between the ∆E values obtained from the different species,
Protein Impact on Light-Harvesting LH2 changes of Γinh also varies. The λ value identifies the amount of the input from the SDF into the bandwidth and together with the ∆E value (see Figure 10 b) are the main factors determining the slopes of its temperature dependence. Thus, we conclude that the λ value are assumed to be similar (of the order of 150-200 cm-1) for the LH2 complexes from all species under present consideration, λ being smallest for Rba. sphaeroides and largest for Phs. molischianum. The same conclusion is also obtained by determining the ∆E value, the smallest value of 90 cm-1 was determined for Rba. sphaeroides while the other species it is twice as large. The deviation of the temperature dependence of the B850 bandwidth from the temperature dependence as defined by eq 1 is achieved by changing the equilibration ratio k1/k2. In order to obtain a stronger temperature dependence, as is the case for Rba. sphaeroides (see Figure 2), this ratio should be smaller than 0.5 (see Figure 10 a). For deviations in the opposite direction, which is the case for Rbl. acidophilus and Phs. molischianum, the k1/k2 ratio should be larger than 0.5. The same type of asymmetry in population of both dichotomous states is also concluded from fitting the fluorescence excitation spectral changes of a single LH2 from Rbl. acidophilus.42,43 However, the obtained values are somewhat different from those that follow from fitting the absorption spectra. Thus, by fitting the time-dependence of the fluorescence spectra of a single complex, the ∆E value is assumed to be almost the same and λ ∼ 2× larger than the value determined from the absorption studies, while k1/k2 is smaller and equals to 0.5. Moreover, the excitation energy of all Bchl molecules had to be assumed to be shifted by -110 cm-1, similar to the conclusion obtained by fitting the temperature dependence of the fluorescence spectra of the ensemble averaged LH2 complexes.17 It is noteworthy that the chosen set of parameters gives us the chance to fit the temperature dependence of the B850 band position. The conclusions about the degree of protein impact (Viz., primary sequence to quaternary structure) on the spectral properties of the B850 band correlate well with results obtained from Stark-spectroscopy, which demonstrates that the smallest Stark effect occurs in Rba. sphaeroides, while it is twice as large in the other two species.44 Finally, it is worth admiting that the ratios λ/2V and Γinh/V define the concurrence between the exciton phonon coupling and the effect of the disorder with pure excitonic measures. In spite of the differences in the absolute values of the resonance interactions, the reorganization energies and the widths of the IDF, both rations are very similar for all three LH2s (see Table 2): the exciton-lattice coupling is weak (λ/2V ≈ 0.25) and the static diagonal disorder is comparable to the resonance coupling (Γinh/V ≈ 1.5) for all species. Conclusions As demonstrated in our previous studies,14,17 the temperature dependence of the absorption spectrum of the LH2 complex from Rba. sphaeroides can be explained by assuming that the resonance interactions between pigments in the B850 ring and the IDF should be assumed to be temperature dependent, while the shift of the B800 band with temperature could be attributed to the changes in the dispersive interaction. This conclusion was obtained by neglecting the temperature dependence of the Redfield relaxation terms describing the population relaxation of the exciton states. Moreover, the SDF had to be essentially different by describing the temperature dependence of the B800 and B850 bands. In order to understand the protein input (Viz., primary sequence to quaternary structure) on the spectral properties of the LH2 complexes the comparative analysis of
J. Phys. Chem. B, Vol. 112, No. 49, 2008 15891 the LH2 complexes from different species, namely, from Rba. sphaeroides, Rbl. acidophilus, and Phs. molischianum is presented here. We have qualitatively demonstrated that the temperature dependence is similar in all three species. The spectral bandwidths of both B800 and B850 bands increases with temperature while the band positions shift in opposite directions: the B800 band shifts slightly to the red, while the B850 band to the blue in the temperature rage from 4 to 300 K. We have shown that by taking the temperare dependence of the Redfield relaxation terms into account the SDF for the B850 band should be the same (or similar) to that as obtained for B800 band. In order to explain the temperature dependence of the B850 bandwidth and shift, the modified dichotomous exciton model validated from the analysis of the single molecular fluorescence spectra,42,43 is suggested. Thus, the slope of the temperature dependence of the B850 bandwidth is defined by the value of the reorganization energy λ, and the difference between the dichotomous tranistion energines of the pigment molecules. The temperature dependence of the B850 absorption peak shift is completely determined by the equilibration factor between the dichotomous states and the total amount of the bandwidth is attributed to the inhomogeneous broadening caused by the ensemble averaging. Acknowledgment. This research was supported by the Lithuanian State Science and Studies Foundation, by a Gilibert project in support of the France-Lithuanian scientific collaboration, and by the ECONET program of the French Ministery of Foreign Affairs. We also acknowledge support from the European Union (A.G., Contract No. MEIF-CT-2004-00951; B.R., V.U., Contract No. HPMT-CT-2000-00162). A.G. is grateful for the support provided by his laureate (BiophysMembProts) from the L’Agence Nationale de la Recherche, France. References and Notes (1) Agranovich, V. M.; Galanin, M. D. Excitation Energy Transfer in Condensed Matter; North-Holland: Amsterdam, 1982. (2) Parak, F. G. Rep. Prog. Phys. 2003, 66, 103. (3) Lax, M. J. Chem. Phys. 1952, 20, 1752. (4) Anderson, P. W.; Weiss, P. R. ReV. Mod. Phys. 1953, 25, 269. (5) Kubo, R. Fluctuation, Relaxation and Resonance in Magnetic Systems; ter Haar, D., Ed.; Oliver and Boyd: Edinburgh, 1962. (6) Georgievskii, Y.; Hsu, C.-P.; Marcus, R. A. J. Chem. Phys. 1999, 110, 5307. (7) Mukamel, S. Principles of Nonlinear Optical Spectroscopy; Oxford University Press: New York, 1995. (8) Renger, T.; Marcus, R. A. J. Chem. Phys. 2002, 116, 9997. (9) Novoderezhkin, V.; van Grondelle, R. J. Phys. Chem. B 2002, 106, 6025. (10) Jang, S.; Silbey, R. J. J. Chem. Phys. 2003, 118, 9324. (11) Renger, T. Phys. ReV. Lett. 2004, 93, 188101. (12) Mancal, T.; Valkunas, L.; Fleming, G. R. Chem. Phys. Lett. 2006, 432, 301. (13) van Amerongen, H.; Valkunas L.; van Grondelle, R. Photosynthetic Excitons; World Scientific, Singapore, 2000. (14) Urboniene, V.; Vrublevskaja, O.; Gall, A.; Trinkunas, G.; Robert, B.; Valkunas, L. Photosynth. Res. 2005, 86, 49. (15) Schro¨der, M.; Kleinehatho¨fer, U.; Schreiber, M. J. Chem. Phys. 2006, 124, 084903. (16) Schro¨der, M.; Schreiber, M.; Kleinehatho¨fer, U. J. Luminesc. 2007, 125, 126. (17) Urboniene, V.; Vrublevskaja, O.; Gall, A.; Trinkunas, G.; Robert, B.; Valkunas, L Biophys. J. 2007, 93, 2188. (18) Ohta, K.; Yang, M.; Fleming, G. R. J. Chem. Phys. 2001, 115, 7609. (19) Heijs, D. J.; Malyshev, V. A.; Knoester, J. Phys. ReV. Lett. 2005, 95, 177402. (20) Renger, T.; Trostmann, I.; Theiss, C.; Madjet, M. E.; Richter, M.; Paulsen, H.; Eichler, H. J.; Knorr, A.; Renger, G. J. Phys. Chem. B 2007, 111, 10487. (21) Imhoff, J. F. Int. J. Syst. EVol. Microbiol. 2001, 51, 1863.
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