How the molecular structure determines the flow of excitation energy in plant light-harvesting complex II
Introduction
The plant light-harvesting complex LHCII is the major photosynthetic antenna on earth. On one hand, it serves to absorb light and to transfer excitation energy to the reaction center of photosystem II. Here, the excitation energy is used to drive electron and proton transfer reactions that ultimately lead to water splitting and the creation of a proton-motive force used by the ATP-synthase to store chemical energy in the form of adenosine triphosphate (ATP). On the other hand, LHCII is able to regulate the excitation energy flow to the reaction center, protecting it under high-light conditions from receiving a poisonous overdose of excitations by non-photochemical quenching (NPQ) of excitation energy (Müller et al., 2001) and by state transitions (Wollman, 2001), in which the light-harvesting complex moves away from photosystem II to photosystem I. The molecular details of the light-harvesting reaction and its regulation are still unknown and a matter of active research. Knowledge about these details could guide us in the future to create artificial systems that are able to transform solar into storable chemical energy.
The pioneering work of crystallographers and spectroscopists has provided to us the crystal structure of LHCII (Liu et al., 2004, Standfuss et al., 2005) and its stationary (Hemelrijk et al., 1992, Pieper et al., 1999a, Pieper et al., 1999b) and time-resolved optical spectra (Visser et al., 1996, Kleima et al., 1997, Gradinaru et al., 1998, Novoderezhkin et al., 2005, Novoderezhkin and van Grondelle, 2010, Schlau-Cohen et al., 2009, Schlau-Cohen et al., 2010), respectively. A full elucidation of the structure–function relationship requires to perform structure-based calculations of optical spectra (Novoderezhkin and van Grondelle, 2006, Müh et al., 2010). Such calculations require a theory that takes into account the two principle types of couplings, that is, the excitonic coupling between pigments and the exciton-vibrational coupling between the electronic transitions of the pigments and the vibrations of the pigments and the protein. In addition, the parameters of the theory have to be calculated on the basis of the structure of the macromolecule to understand the molecular building principles. We refer to a recent review (Renger, 2009) for a more detailed introduction into these two aspects of the model building.
According to the recent crystallographic reports by Liu et al. (2004) and Standfuss et al. (2005), the LHCII consists of trimers, where each monomeric subunit binds eight Chla, six Chlb and four carotenoid molecules as photoactive cofactors. Whereas the Chls just serve as light-harvesting pigments, the carotenoids in addition fulfill at least three more tasks. They stabilize the structure, quench Chl triplet energy and most likely are involved in NPQ. The Chls are arranged in two layers (Fig. 1). The stromal layer contains a domain of strongly coupled Chla pigments (Chls a 610, 611, 612 in the nomenclature of Liu et al.) a Chlb domain, where Chlb 601 of one monomeric subunit is strongly coupled to Chls b 608 and 609 of the neighboring subunit, and two more weakly coupled Chls a 602 and 603. The stromal layer contains a dimer of Chls a 613 and 614 and more weakly coupled Chls b 605, 606, 607 and Chla 604. By using two different types of Chls, the absorbance cross section of the complex is considerably widened with Chls b and Chls a absorbing around 650 nm and 675 nm, respectively. This difference does not allow for strong exciton delocalization between two different types of Chls, as discussed in detail below. However, the close distances observed in the crystal structure between Chls a and b are expected to give rise to ultrafast excitation energy transfer.
Indeed, transient spectroscopic studies measured fast excitation energy transfer between Chlb and Chla on different timescales ranging from sub 100 fs (Schlau-Cohen et al., 2009) to 9 ps (Visser et al., 1996). As expected, Chlb to Chla transfer times measured on LHCII trimers, e.g., by Visser et al. (1996) (<0.3 ps, 0.6 ps, 4–9 ps) are similar to those measured on LHCII monomers (200 fs, 3 ps) (Kleima et al., 1997). It was more surprising that the slow 10–20 ps component assigned first to reflect excitation energy transfer between Chla in different monomers (Visser et al., 1996) was also found in isolated monomers, where exciton relaxation times between Chla states at 670 nm and 680 nm of 300 fs and 12 ps were reported (Gradinaru et al., 1998). It was concluded that exciton equilibration in LHCII monomers is practically identical to that found in trimers.
Another interesting finding concerns the 2–5 ps lifetimes detected for excited states absorbing in the intermediate spectral range around 660 nm between the Chla and Chlb regions (Visser et al., 1996, Gradinaru et al., 1998). At present, it is not clear whether these intermediate states are redshifted Chls b or blueshifted Chls a or both. Calculations by Novoderezhkin et al. (2005) identified these so-called bottleneck states as Chls a 604 and b 605. Wildtype-minus-mutant difference spectra indicated that Chls a 613 and 614 absorb in this spectral region (Rogl et al., 2002, Remelli et al., 1999), whereas structure-based calculations of site energies obtained a blueshifted Chlb 608 absorbing around 660 nm (Müh et al., 2010).
A difficulty when modeling excitation energy transfer in photosynthetic pigment protein complexes is the equal strength of excitonic and exciton-vibrational coupling. In standard Redfield theory, the excitonic coupling is taken into account non-perturbatively by diagonalizing an exciton matrix that contains in the diagonal the local transition energies of the pigments and in the off-diagonal the excitonic couplings between their optical transitions. A second-order perturbation theory in the exciton-vibrational coupling then yields the rate constants for relaxation between different delocalized states. In modified Redfield theory (Zhang et al., 1998, Yang and Fleming, 2002, Renger and Marcus, 2003), the diagonal part of the exciton-vibrational coupling is taken into account exactly, whereas still a second-order perturbation theory is used for the off-diagonal part of this coupling. In this way, it is possible to include multi-vibrational quanta transitions in the dissipation of excess energy of the excitons by the protein (Yang and Fleming, 2002, Renger et al., 2007).
However, a dynamic localization of the exciton wavefunction is still neglected. That is, if two pigments have the same site energy, but only a very weak excitonic coupling, their excited states will assumed to be delocalized in modified Redfield theory, whereas in reality, the exciton-vibrational coupling would dephase any coherences and thus would localize these states. To include such a dynamic localization requires a non-perturbative description also of the off-diagonal part of the exciton-vibrational coupling. In principle, the hierarchical equation of motion approach used by Ishizaki and Fleming (2009) contains such a description, at the expense of a large numerical effort. A simple method was introduced to investigate the temperature dependent localization of a mixed excited/charge transfer state of the special pair of the reaction center of purple bacteria (Renger, 2004). This method, however, contains an approximation that would not allow to describe exciton relaxation.
An alternative way to deal with this problem is to introduce domains of strongly coupled pigments and to use a delocalized basis only for the excited states of those pigments that are in the same domain (Yang et al., 2003, Raszewski and Renger, 2008). Excitation energy transfer between different exciton domains is then described by generalized Förster theory (Sumi, 1999, Scholes and Fleming, 2000, Jang et al., 2004, Raszewski and Renger, 2008). A question, related in spirit, concerns the inclusion of high-frequency intramolecular vibronic transitions of the Chls into a line shape theory of multi-pigment protein complexes. For a two-level system, representing a single pigment in a protein, these transitions may just be included in the spectral density of the exciton-vibrational coupling (May and Kühn, 2000). However, for an exciton domain containing a number of strongly coupled pigments, such a procedure would imply that not only the electronic transitions delocalize but also the vibronic transitions involving excited intramolecular vibrational states. However, the related Franck-Condon factors are very small (<0.1) (Pieper et al., 1999b) and, therefore, the respective excitonic couplings are small compared to the exciton-vibrational coupling. Along these lines, it seems to be the most reasonable approach to take into account delocalization of excitonic states only between 0-0 transitions and to use a localized basis for the vibronic transitions involving excited intramolecular vibrational states. A respective theory will be presented in this work.
We have recently reported structure-based calculations of the excitonic couplings and local transition energies (site energies) of the Chls in LHCII (Müh et al., 2010), using a methodology developed and tested earlier on a smaller system, the FMO protein (Müh et al., 2007, Adolphs et al., 2008). The three main results were: (i) the excitonic couplings that were calculated including the influence of the polarizability of the protein (by the Poisson-TrEsp method) justify a point dipole approximation with an effective dipole strength as used earlier (Novoderezhkin et al., 2005). (ii) The energy sink is located at Chla 610, in agreement with an earlier mutagenesis study (Remelli et al., 1999) and a fit of optical spectra (Novoderezhkin et al., 2005). Our calculations showed that the sink at Chla 610 is caused mainly by interactions with charged amino acid residues. (iii) The red-most Chlb is Chlb 608 absorbing in the intermediate spectral region around 660 nm, with the positive charge on Arg 70 contributing mostly to the redshift.
The linear optical spectra calculated with these parameters agreed qualitatively with experiments, and some deviations were removed by a refinement fit of the site energies (Müh et al., 2010). Here, we will take a different strategy. We apply the original directly calculated site energy shifts and improve the theory of optical spectra by including intramolecular vibronic transitions. In addition, nonlinear time-resolved spectra will be calculated and compared with experimental data in order to provide a link between the relaxation of excitation energy probed in these experiments and the structure.
This work is organized in the following way. A theory of linear optical spectra, including high-frequency intramolecular vibronic transitions, is presented first. This line shape theory is used next to derive expressions for a generalized Förster theory rate constant for excitation energy transfer. Afterwards, the theory is applied to calculate linear and nonlinear optical spectra of LHCII and to compare with experimental data. Finally, the results are discussed and conclusions are presented.
Section snippets
Hamiltonian
The Hamiltonian of LHCII is given as:The Chl-Hamiltonian Hchl contains the energies of the intramolecular electronic and vibrational states:where a counts the Chls, which may be in their electronic ground (k = g) or excited (k = e) state with energy , and the vibrational quantum numbers νi describe the excitation of the ith intramolecular vibrational mode with frequency .
The
Results
In this section, the theory is applied to calculate linear and non-linear optical spectra of LHCII. The excitonic couplings and site energy shifts ΔEi determined previously (Müh et al., 2010) by quantum chemical/electrostatic calculations based on the crystal structure of Liu et al. (2004) are used. The site energies Ei are obtained as , where is a reference energy that is equal for all Chla and is that of all Chlb. We determined these two energies from comparison of
Importance of intramolecular vibronic transitions of Chls
The inclusion of intramolecular vibronic transitions of the Chls allow to significantly improve the agreement between the experimental data and the linear optical spectra calculated previously (Müh et al., 2010) without these transitions (Fig. 3). Moreover, these transitions are also responsible for the fast dissipation of excess energy during the Chlb to Chla transfer (Fig. 4).
The importance of vibronic transitions was recognized early by Novoderezhkin, van Grondelle and coworkers in their
Conclusions
A theory was presented that includes intramolecular vibronic transitions in the description of optical spectra and excitation energy transfer between domains of strongly coupled pigments. The latter extension of generalized Förster theory was found to be important for excitation energy transfer between domains containing Chlb and those containing Chla. The intramolecular vibronic transitions allow for fast dissipation of excess energy during this transfer. In agreement with experimental data
Acknowledgment
Financial support by the German Research Foundation through Collaborative Research Center 429 (project A9) is gratefully acknowledged.
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