Letter pubs.acs.org/JPCL
How Photosynthetic Proteins Switch Leonas Valkunas,*,†,‡ Jevgenij Chmeliov,†,‡ Tjaart P. J. Krüger,∞ Cristian Ilioaia,∞,∥ and Rienk van Grondelle∞ †
Center for Physical Sciences and Technology, Institute of Physics, Savanoriu Avenue 231, LT-02300 Vilnius, Lithuania Department of Theoretical Physics, Faculty of Physics, Vilnius University, Sauletekio Avenue 9, Building 3, LT-10222 Vilnius, Lithuania ∞ Department of Physics and Astronomy, Faculty of Sciences, VU University Amsterdam, De Boelelaan 1081, 1081 HV Amsterdam, The Netherlands ∥ Institut de Biologie et de Technologies de Saclay, CEA, UMR 8221 CNRS, Université Paris Sud, CEA Saclay 91191 Gif sur Yvette, France ‡
ABSTRACT: Recent time-resolved studies have revealed the switching behavior of single photosynthetic light-harvesting complexes. In this work, we suggest a diffusion-controlled model describing essential protein dynamics underlying this switching. The calculated blinking statistics are compared with the experimental result and not only reproduce the power-law behavior at intermediate times, but also follow the experimentally observed deviations from such behavior on a shorter time scale. We propose that the coupling of fast protein dynamics to a specific slow coordinate is at the basis of regulatory switching.
SECTION: Biophysical Chemistry and Biomolecules of plant photosynthesis under fluctuating light intensities, even at very high intensities.17 Consequently, LHCs responsible for quenching must be able to switch quickly and reversibly between an almost perfect light-harvesting state and an almost perfect quenching state, as was demonstrated by means of a simple thermodynamic approach.18−20 Recent time-resolved studies of the major antenna complexes from plants (LHCII trimers) have allowed the detection of the intermittency of the fluorescence signal originating from single complexes, when no averaging over the whole ensemble was performed.5,6 The results have revealed many details of the switching behavior of LHCIIs, again supporting the proposal that such behavior is their intrinsic ability. Moreover, it was found that the switching rate and the dwell time in either the light-harvesting state or quenched state were under environmental control. For these reasons we have proposed that regulation of such switching behavior of LHCIIs is a direct reflection of the NPQ process.21 Therefore we postulated that the fluorescence intermittency observed from LHCII trimers could be attributed to a diffusioncontrolled process of transitions between strongly and weakly fluorescing states on the potential energy surface of LHCII.5 This conceptual approach can be well demonstrated on the simplified two-dimensional projection of LHCII’s multidimen-
he flexibility of protein structures is a fundamental feature that probably has been utilized by nature to select and optimize biologically relevant structural configurations.1 Once several such functionally different states are identified, transitions between them cannot be realized by means of random dynamics on the multidimensional energy landscape reflecting all the possible conformational states.2,3 In order to be able to access the functional states efficiently and quickly when required, the protein should behave as a switching device between active and inactive states, employing only a few degrees of freedom controlled by the changes in the external conditions. Such type of switching has recently been observed in single photosynthetic light-harvesting complexes (LHCs) from plants4−8 and bacteria.9,10 These photosynthetic LHCs are composed of aggregates of pigment molecules ((bacterio)chlorophylls and carotenoids) bound to a protein scaffold, and their spectroscopic properties serve as effective reporters of the protein’s conformational changes. As a result, transitions between such conformational states are reflected in their absorption and/or fluorescence spectra.4,7−14 Photosynthetic LHCs are responsible for the collection of solar energy and its subsequent delivery to the reaction center, where this energy is stabilized in the form of a trans-membrane electrochemical potential.15,16 However, LHCs have another (regulatory) function: they dissipate the excess excitation energy as heat via nonphotochemical quenching (NPQ) and thus protect the whole photosynthetic apparatus from photodamage as well as ensure an optimal efficiency and robustness
T
© 2012 American Chemical Society
Received: July 19, 2012 Accepted: September 10, 2012 Published: September 10, 2012 2779
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the equilibrium position of the second potential; and U0 is the vertical difference between the potential minima. According to this description, the system resides mainly in the vicinity of the U1 potential well when the y values are small, and the transition into the minimum of the U2 potential well occurs by increasing the y value (when y0 > 0). Since the LHCII trimer can be found only in one of these two states at any given time, a random walk in the phase space of the coordinates x and y will lead to a random switching between the on and off states. The dynamics of these transitions should then resemble the experimentally observed dynamics of fluorescence intermittency.5,6 Changes in the environmental conditions might induce some variation of the potential surface, which will result in a shift of the dynamic equilibrium to either the on or the of f state. We can safely assume that transitions between the on and off potential surfaces occur strictly vertically, meaning that the coordinates x and y do not change during the transition, as shown in Figure 1. The rate of the downward transition from point A on the on potential surface to point B with the same coordinates on the off potential surface is equal to k1. Similarly, the rate of the downward transition C → D from the of f to the on potential surface is denoted as k2. In addition, both relaxation rates should contain the factor exp(−α|ΔU|/(ℏω0)) reflecting the so-called energy gap law.22 Here ω0 is the dominant frequency responsible for the transitions between the points on the energy surfaces under consideration, and α is some function, weakly (logarithmically) dependent on the potential energy difference |ΔU| between those points, so that we can treat it as some constant parameter (α ≅ 1 ÷ 3). The ratio of the upward and downward transition rates is defined by the detailed balance relationship via the corresponding /ki = exp(−|ΔU|/(kBT)), where kB is Boltzmann factor: k(up) i the Boltzmann constant and T denotes temperature. The time-dependent probability density ρi(x,y,t) for finding the system at the point with coordinates x and y at time t when the system is either in the on (i = 1) or off (i = 2) potential surface obeys the following diffusion equation:23,24
sional surface, where one axis reflects a fast reaction coordinate corresponding to inter- and intramolecular vibrations, and the other axis corresponds to some specific slow conformational change of the protein under consideration that stabilizes the quenched state. Here we formulate the corresponding physical model and present some modeling results. We conclude that the model gives an excellent description of the switching process as observed in LHCII. This could imply that nature has learned to select and control specific protein motions to make an efficient switch between the light harvesting and quenched states. The simplest model demonstrating the switching ability via the fluorescence intermittency in LHCII complexes5 assumes that, depending on the protein structural arrangement, the LHCII trimer can be found in two states: either a light (on) state, when the fluorescence signal from the irradiated LHCII trimer is clearly detected, or a dark (of f) state, when the fluorescence is almost switched off. If one projects the manifold of all rapid molecular vibrations in the LHCII onto a single reaction coordinate x, then the on and off states of the LHCII trimer mentioned above would correspond to two minima on the configurational potential energy surface of the protein. Possible transitions between these two states can be attributed to another generalized coordinate y reflecting some specific slow protein conformational change that disturbs the energy balance between different pigments involved in the lightharvesting and quenching process. To characterize the transition rates between the two (on and off) states, the potential energy surfaces attributed to each of them can be separately defined as independent potential wells (see Figure 1), which in the harmonic approximation are given by 1 2 1 2 λ1x + γ1 y 2 2 1 1 U2(x , y) = λ 2(x − x0)2 + γ2(y − y0 )2 + U0 2 2 U1(x , y) =
(1)
where indices ‘1’ and ‘2’ denote on and of f states, respectively; λi and γi determine the reorganization energies in the ith potential along the coordinates x and y, respectively; x0 and y0 indicate
∂ρi ∂t
= [Dix 3x + Diy 3 y − kiHi(x , y)]ρi (x , y , t )
(2)
where Dix and Diy are the diffusion coefficients in the ith potential along the x and y directions, respectively; 3 x and 3 y are the corresponding diffusion operators: ⎡ ∂2 1 ∂ ∂Ui(x , y) ⎤ 3 zρi (x , y , t ) = ⎢ 2 + ⎥ρ (x , y , t ), kBT ∂z ∂z ⎦ i ⎣ ∂z i = 1, 2; z = x , y
and H1(x , y) = e−α |ΔU | / (ℏω0)·min{1, e(U1− U2)/(kBT )}, H2(x , y) = e−α |ΔU | /(ℏω0)·min{1, e(U2 − U1)/(kBT )}.
(3)
Assuming that the diffusion along the x coordinate is much faster than along the y coordinate, the terms determining fast dynamics can be adiabatically eliminated from eq 2. In this case, the x-dependence of the probability densities approaches the stationary (Gaussian) distribution exponentially fast, thus integration of eq 2 yields
Figure 1. Potential surfaces of the on and of f states in the phase space of the x and y coordinates. k1 and k2 denote the relaxation rates of the on → of f and of f → on transitions, respectively. 2780
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The Journal of Physical Chemistry Letters ∂ρi̅ (y , t )
=
∂t
∂ ∂t
Letter
∫ dx ρi (x , y , t ) = (Diy 3 y − κi(y))ρi̅ (y , t ) (4)
where κ1(y) = k1
λ1 2πkBT
∫ dx e−λ x /(2k T)H1(x , y)
κ2(y) = k 2
λ2 2πkBT
∫ dx e−λ (x−x ) /(2k T)H2(x , y)
2
1
B
(5)
2
2
0
B
(6)
The initial conditions of eq 4 can be chosen as follows. First we define the stationary solution ρ1̅ (st) of eq 4 when the transition to the of f state is inactive. Then, we multiply the obtained steady-state solution (the Gaussian distribution) by the effective rate κ1(y) given by eq 5. This function determines the initial distribution of the population of the off state. Similarly, the initial probability density for the population of the on state is given by the product ρ2̅ (st) (y)κ2(y). It is noteworthy that after substituting the expressions for Hi(x,y) (see eqs 3) and normalizing, both initial distributions coincide: ρi̅ (y , t = 0) ∝ ρi̅ (st) (y)κi(y) ∝
⎛
Figure 2. Experimental (squares and circles) and simulated (lines) probability densities of the dwell times in bright (a) and dark (b) states for two different acidity levels of the environment. For visual clarity, the upper data corresponding to pH 8 was multiplied by a factor of 100.
Table 1. Fitted Model Parameters value
⎞
∫ dx exp⎜⎝−α |ΔℏωU | ⎟⎠ 0
⎧ ⎛ U (x , y ) ⎞ ⎛ U (x , y ) ⎞⎫ × min⎨exp⎜ − 1 ⎟ , exp⎜ − 2 ⎟⎬ kBT ⎠ kBT ⎠⎭ ⎝ ⎩ ⎝ ⎪
⎪
⎪
⎪
(7)
∫ dy ρi̅ (y , t )
(8)
Finally, the quantity corresponding to the experimentally collected blinking statistics5 determining the probability Pi(t) that a transition from one state to another occurs within the time interval (t;t + dt), is defined as Pi(t ) = −
dSi(t ) , dt
i = 1, 2
pH 6
pH 8
model parameter
λ = λ 2 /λ1 γ = γ2/γ1
0.3 0.68
0.2 0.72
k1−1 k2−1
x0 λ1/kBT
1.0
1.4
(D1yγ1/kBT)−1 −1
pH 6
pH 8
190 ms 3.6 ms
430 ms 4.8 ms
2.4 s
3.8 s
y0 γ1/kBT
8.59
8.57
(D2yγ1/kBT)
1s
1.4 s
U0/kBT
0.5
1.5
ℏω0 /(αkBT )
0.4
1.0
of the environment, namely, at pH 6 and pH 8, are demonstrated in Figure 2, and the corresponding fitting parameters are presented in Table 1. The latter pH value corresponds to natural physiological conditions ensuring strong fluorescence of isolated trimers, while the former is similar to the one usually observed under NPQ conditions. It is clear that a description of all the possible conformational changes of the LHCII trimer using only two generalized coordinates and simple harmonic potential wells cannot reveal all the subtle details of the dynamic spectral properties of such a photosynthetic pigment−protein complex. Nevertheless, this simplified model with properly chosen parameters can very well reproduce the experimentally observed fluorescence intermittency on the whole experimentally accessible time scale, as demonstrated in Figure 2. From the obtained model parameters (Table 1) several interesting properties of the potential surfaces of the on and off states can be outlined. First of all, the potential energy surface of the off state is less steep than that of the on state, and its minimum is located slightly above the minimum of the on state. Furthermore, a clear dependence of the parameters on the environmental acidity is revealed. In more adverse environmental conditions at low pH level, the potential surfaces of both on and off states exhibit notable deformations. The potential well of the of f state becomes slightly steeper (along the fast x coordinate), and its minimum approaches the minimum of the on state, which results in an increased probability for the system to switch to the dark, nonfluorescing state. This effect is enhanced by a ∼2.3-fold increase of the on → off transition rate as the environmental acidity rises. On the other hand, the parameters describing slow conformational changes of the protein, namely, the ratio γ = γ2/γ1 and y0, are almost insensitive to the pH. While analyzing the model parameters that determine the transitions between the on and of f states, we first notice that the
A more detailed numerical analysis reveals that eq 7 defines a very sharp distribution with the maximum located near the intersection point y(0) of the one-dimensional functions U1(x = 0,y) and U2(x = x0,y), so that it might be well approximated as δ(y − y(0)). Solutions of eq 4 allow us to determine the survival probabilities on the on and off potential surfaces, Si(t), by integrating ρ̅i(y,t) over the y coordinate: Si(t ) =
value
model parameter
(9)
The presented model contains several parameters, which will be used for fitting the experimental data. Upon introducing relative representations of the coordinates determining both potential surfaces, five of them characterize the on and of f potential surfaces (λ = λ2/λ1, γ = γ2/γ1, x0, y0 and U0), while the other three determine the dynamics of the transitions between the on and of f states (k1, k2 and ω0). All these parameters were varied while fitting the experimental data of blinking statistics at various pH values.5 We note that the diffusion coefficients Diy only determine the time scale of the protein conformational changes, so they do not change the shape of the Pi(t) distributions on the logarithmic scale but only shift them along the time and probability-density axes. From the magnitude of those shifts, the diffusion coefficients were determined. The fitting results for data collected under two particular conditions 2781
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energy ℏω0 of the dominating phonon mode taking part in the transitions is on the order of the thermal energy kBT. The lower pH level determines a higher protonation of the system, which results in an increased effective mass of the vibrating molecules and therefore almost 2-fold drop of the frequency ω0 of their vibrations. The relatively high value of ℏω0 can explain the flattening of the calculated probability densities at longer dwell times (Figure 2), a somewhat different behavior compared to other existing models dealing with the power-law blinking statistics.23,25 As already mentioned, the initial population distribution ρ̅i(y,0) in phase space was chosen in the vicinity of the intersection point of the potential surfaces of the on and of f states, y(0). As a result, initially we have exp(−α|ΔU|/(ℏω0)) ≈ 1, and the transition probability is rather high. In the course of time the evolution of ρ̅i(y,t) reflects not only the spreading of this distribution along the y coordinate, but also the shift of its maximum toward the minimum of the corresponding potential. Since the distance between the potential minima is rather big, y0 ≈ 9(kBT/γ1)1/2, the maximum of the distribution function ρ̅i(y,t) diffuses sufficiently far from y(0) after some time, so that the factor exp(−α|ΔU|/(ℏω0)) → 0, which makes the survival probability and its probability density become almost independent of time. Reducing the distance y0 between the potential energy minima of the on and of f states can reduce or even completely remove this flattening effect; however, the time interval of the power-law behavior then shrinks noticeably, making way for an exponential distribution. Another interesting outcome is the notable differences between the diffusion and transition rates in the on and of f states. The rate of the transition from the on to the of f state is ∼50−90 times slower than that of the backward transition. Such a high ratio of the transition rates in opposite directions reveals why the population of the off states decreases in time much faster than that of the on states. After the transition to the dark state, the system usually remains in this state for a very short time, so that the measured fluorescence intermittency should resemble very short blinking events, rather than short flashes. A somewhat similar fluorescence blinking behavior was observed in many other fluorescing systems, ranging from simple single dye molecules26−28 and semiconductor quantum dots25,29−33 to a diverse range of more complex fluorescing systems.34−36 If the exponential switching behavior of single dye molecules observed on shorter time scales can be attributed to the quantum transitions between singlet and metastable triplet states,37,38 the power-law blinking statistics observed in various other systems still does not have a proper explanation. A diffusion-controlled electron-transfer model, suggesting onedimensional diffusion in energy space, was developed to explain the fluorescence blinking of single semiconductor quantum dots.23 However, despite a somewhat similar mathematical description, the physical basis of that model totally differs from the one presented here: for quantum dots, a charge quenching mechanism by surface states was assumed to be the dominant factor that determines fluorescence blinking.23 This mechanism explains why such robust systems as quantum dots usually follow power-law blinking statistics over a very broad interval of the dwell times the system spends either in the bright or in the dark states, ranging from microseconds to even several hours. For disordered biological systems, this range is noticeably narrower, and the power-law exponents strongly depend on the environmental conditions.5 The blinking effect observed to take place in single LHCIIs seems to be even more outstanding if
one takes into account the complex internal structure of these units containing more than 40 distinct pigments, each with its own spectral properties. If the fluorescence intermittency would be attributed to individual uncoupled chromophores, due to the stochastic nature of the blinking phenomenon, the averaged signal from all pigments would almost completely lack any noticeable blinking events. By contrast, experimental observations of fluorescence blinking support the significance of the protein scaffold binding all the pigments together and enforcing them to act as a whole quantum unit. It seems that during evolution the plants “have learned” to take advantage of the blinking of simple emitters and implemented this on a slightly more macroscopic level, when the protein’s motion and deformation influence the interpigment couplings, molecular fluctuations, and possible pathways for the excitation energy transfer. As a result, the switching behavior of the LHCIIs has become their intrinsic property governed by the lability and adaptability of the protein scaffold. The latter property not only determines the system evolution, but also manifests itself as system adaptation to the varying environmental conditions, such as acidity, illumination level, and so on. The origin of the on and off states could be caused by the modulation of the distance between a carotenoid (lutein (Lut) 1 molecule) and the cluster of three chlorophyll (Chl) a molecules located nearby, i.e., Chl a610−611−612, which are responsible for the long wavelength transition.39 Another possible effect could be due to lowering of the optically forbidden S1 state of Lut 1. In both cases, the excitation transfer rate from the cluster of Chls a to the Lut 1 molecule would change, so that self-regulating processes involved in the formation of the centers responsible for excitation energy quenching would shorten (or prolong) the mean excitation lifetime of the Chl molecules, and the intensity of the measured fluorescence would vary accordingly in time. Such attribution of the origin of the bright and dark states then implies that the mechanisms responsible for NPQ should be closely related to the phenomenon of fluorescence intermittency. To summarize, we have developed a simple two-state diffusion-controlled model that quantitatively explains fluorescence blinking in single LHCII trimers, demonstrating that the major part of the fluorescence reduction is governed by subtle conformational changes of the protein scaffold, disturbing the interpigment energetic pattern.5,18−20 The model is based on two-dimensional diffusion on the energy surface of LHCII, with one coordinate reflecting fast molecular vibrations and another determined by some slow specific structural change of the protein. The latter, reflecting changes in (some) interpigment distance, is thus coupled to rapid vibrational motions, which determine the modulating impact on the potential energy surfaces. This model explains the deviation of the fluorescence intermittency dynamics from the power-law blinking,5,6 which is typical for nanostructures of nonbiological origin. Quantitative reproduction of the experimental data strongly suggests that the intrinsic ability of proteins to act as an environmentally controlled switch makes them a suitable candidate to govern NPQ and fast reversible transitions between almost perfect energy-transfer and quenching states. Moreover, it is likely that similar switching mechanisms might exist for other biologically important proteins liable to some conformational changes that have an effect on their functional properties. 2782
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AUTHOR INFORMATION
Corresponding Author
*E-mail: leonas.valkunas@ff.vu.lt. Notes
The authors declare no competing financial interest.
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ACKNOWLEDGMENTS This research was partly funded by the European Social Fund under the Global Grant Measure (L.V., J.C.), EU FP6 Marie Curie Early Stage Training Network via the Advanced Training in Laser Sciences project (T.P.J.K.), TOP grant (700.58.305) from the Foundation of Chemical Sciences, part of the NWO (R.v.G.), and the advanced grant (267333, PHOTPROT) from the European Research Council (ERC) (R.v.G., T.P.J.K.).
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