Excitation Energy Transfer and Electron Transfer Steps in Cyanobacteria Modeled with Rate Equations

The formalism based on rate equations as presented in chapters 1.3 and 1.4 was used in studies during recent years to model time dependent fluorescence data captured in form of time- and wavelength-correlated single photon counting (TWCSPC) or time dependent fluorescence quantum yield measurements covering 9 orders of magnitude in time. The described samples and experiments as partially described in (Schmitt, 2011) include:

  • 1) preparations of the phycobiliprotein (PBP) antenna from of Synechocystis sp. PCC6803 (Maksimov et al., 2013; 2014a) and A.marina (Theiss et al., 2007a, 2008, 2011; Schmitt et al., 2006; Schmitt, 2011);
  • 2) different solubilized and aggregated LHCII trimers from spinach (Lambrev et al., 2011),
  • 3) the water soluble chlorophyll binding protein (WSCP) that was genetically expressed in E.coli and reconstituted with Chl a, Chl b or mixtures of Chl a and Chl b (Theiss et al., 2007b; Schmitt et al., 2008; Renger et al., 2009, 2011; Pieper et al., 2011);
  • 4) artificial PPCs formed from eosin as chromophores bound to proteins (Barinov et al., 2009);
  • 5) semiconductor-pigment-protein-hybrid-complexes (Schmitt, 2010; Schmitt et al., 2011, 2012) and
  • 6) whole cells of different cyanobacteria, especially the cyanobacterium Acaryochloris (A.) marina (Petrasek et al., 2005; Schlodder et al., 2007; Schmitt et al., 2006, 2013; Theiss et al., 2007a; Theiss et al., 2007a, 2008, 2011);
  • 7) whole cells of the green algae Chlorella pyrenodoisa Chick and on the higher plant Arabidopsis thaliana (Belyaeva et al., 2008, 2011,
  • 2014, 2015) as well as fluorescence quenching in lichens (Maksimov et al., 2014b);
  • 8) the application of rate equations to describe the image signal gathered by modern microscopic techniques like photoacoustic imaging (Mark et al., 2015a, 2015b).

As an example in this chapter the fluorescence dynamics in the PBP complexes of A.marina and of whole cells of A.marina are analysed. The next chapter (2.7) focuses on the question how more complex systems like the whole Photosystem II dynamics of higher plants can be described with basically the same rate equation formalism (Belyaeva et al., 2008, 2011, 2014, 2015).

The main focus was not the spatial structure and dynamics of traceable fluorophores but the analysis of time resolved excitation energy transfer (EET) and electron transfer (ET) steps on the temporal scale of picoseconds.

The unusual cyanobacterium A.marina was discovered in 1996 and it is up today the only known organism which mainly contains Chl d instead of Chl a in the membrane intrinsic Chl antenna and reaction centers (Miyashita et al., 1996, 1997; Marquardt et al., 1997). This feature was reason enough for us to investigate EET and ET processes in A-marina with the technique of TWCSPC.

Figure 9 (see chapter 2.1.4), published in (Theiss et al., 2011), shows typical fluorescence decay curves of whole cells of A.marina collected after excitation with 632 nm at room temperature performed with TWCSPC (Schmitt, 2011). In Figure 9a, this data matrix is shown as a color intensity plot (CIP). A vertical plot at a constant time t0 results in the time-resolved emission spectrum F(t0, A) (Figure 9c) while a horizontal intersection delivers the fluorescence decay at a constant emission wavelength Ao (Figure 9b). Figure 9b shows the decay curves of A.marina at 660 nm and 725 nm. It is seen that the fluorescence at 660 nm decays much faster than the emission at 725 nm. A closer look at the emission maximum on top of Figure 9b reveals a very small temporal shift between the 660 nm and the 725 nm decay curves. The 725 nm decay is slightly shifted to later times in comparison to the 660 nm decay. A data fit shows that the small temporal shift in the following called “fluorescence rise kinetics” has a similar time constant as the fluorescence decay at 660 nm. Both curves are convoluted with the instrumental response function (IRF) which leads to the small visible difference.

The multiexponential fits of all decay curves measured in one time- and wavelength resolved fluorescence spectrum were performed as global fits with common values of lifetimes т. (linked parameters) for all decay curves and wavelength-dependent pre-exponential factors A. (A) (non- linked parameters, see Figure 9d representing “decay associated spectra” (DAS) thus revealing the energetic position of individual decay components (for details also see Schmitt et al., 2008).

In whole living cells of A.marina the average time constant for the excitation energy transfer (EET) between the uniquely structured and rod shaped phycobiliprotein (PBP) antenna and the Chl d containing membrane intrinsic antenna complex was found to occur within an overall time constant of 70 ps (Petrasek et al., 2005; Theiss, 2006; Theiss et al., 2011; Schmitt, 2011) (see Figure 9). This value is 3 times faster than in other cyanobacteria containing phycobilisomes (PBS) assembled from several PBP rod structures and Chl a containing membrane intrinsic antenna complexes (Glazer, 1985; Holzwarth, 1991; Mullineaux and Holzwarth, 1991; Trissl, 2003; Theiss et al., 2008).

Figure 40 represents DAS characterized by EET from PC and APC containing hexamers of the membrane extrinsic PBP antenna to spectrally red shifted APC molecules which are most probably located in the linker protein representing the so-called terminal emitter (TE). This EET was resolved to occur within 20 (±10) ps in A.marina. These values were found in living cells of A.marina. Further elucidation of the fast equilibration processes in the PBP antenna of A.marina is not easily possible with TWCSPC as can also be shown by numerical simulations of the expected time resolved spectra. Measurements of flash induced transient absorption changes performed in the fs-ps time domain by C. Theiss on isolated PBP complexes showed fast energy equilibration between different phycocyanin (PC) molecules (equilibration time <1 ps) which are bound to a hexameric protein structure in the PBP of A.marina and in PBS. The equilibration between the PC and the APC containing hexa- mers occurs with a time constant of 3-5 ps (Theiss et al., 2008, 2011).

Rate equations can now be used to simulate the exciton diffusion inside the rod-shaped structures of A.marina and to elucidate the real relationship between the observed fluorescence dynamics and intrinsic EET steps between single molecules or compartments. These simulations showed that the EET velocity depends critically on entropy effects caused by the small distance of the energetic states of the coupled PC chromo- phores. This effect is the main reason for slower exciton diffusion inside the PBS containing more than 300 PBP chromophores (Holzwarth, 1991) and additionally Chl a molecules, in contrast to the PBP complexes of A.marina containing 63 PC and 6 APC chromophores coupled to Chl d.

The geometry and small size of the A.marina antenna in contact to Chl d leads to faster energy transfer in comparison to the structure of the much larger PBS.

Decay associated spectra

Figure 40. Decay associated spectra (DAS) of a global fit (4 exponential components) of the fluorescence emission at 20 °C of whole cells of A.marina in the 640 nm - 690 nm range after excitation at 632 nm. The fluorescence below 645 nm is cut off by a long-pass filter. The graphics is redrawn from the data published in (Schmitt, 2011). Image reproduced with permission.

Entropy effects are the consequence of equation 10 (see chapter 1.3) indicating that the probability for a transfer towards a compartment is proportional to the quotient of the number of empty states that can take up the excitation energy in the acceptor compartment and the number of states for the exciton in the donor compartment. As there are 4 times more states in an antenna structure with 280 pigments as compared to an antenna with 70 pigments EET from such large antenna is delayed by 4 times even if the energetics and transition probabilities for all single transfer steps are the same in both cases which is the case if the coupling of all molecules is of similar strength.

As shown by the DAS depicted in Figure 40, the fluorescence dynamics in the PBP antenna of living cells is characterized by four exponential decay components with lifetimes of <20 ps, 80 ps (±10 ps), 180 ps (±100 ps) and 0.9 ns (±0.1 ns).

The DAS of the <20 ps component has a positive amplitude in the PC and APC emission band (645-660 nm) and a negative amplitude at

675 nm that is red shifted in comparison to the APC emission. This suggests that in living cells of A.marina the EET from PC to the most red chromophore of the PBP antenna occurs with a time constant of less than 20 ps. The 80 ps decay component reflects the EET from the PBP antenna to PS II (see below) and the slower components (180 ps, 0.9 ns) are probably due to conformationally distorted and/or functionally decoupled PBP complexes in A.marina (Schmitt et al., 2006).

Figure 41a shows a typical DAS gathered from TWCSPC spectroscopy on whole cells of A.marina.

a) Measured DAS o

Figure 41. a) Measured DAS of A.marina after excitation with 632 nm at room temperature. The simulated DAS is shown in panel b). The graphics was published in (Schmitt et al., 2011; Schmitt, 2011). Image reproduced with permission.

The values of the long decay components in the Chl d regime are given by time constants of 400 ps (blue triangles) and 900 ps (black circles) that differ slightly from the statistically evaluated data exhibiting time constants of 630 ps (±30 ps) and 1.2 ns (±0.1 ns) measured in 2005 (see Figure 9). It has to be pointed out that these values differ between different cells and different illumination conditions. The main focus of the simulated exciton dynamics is the fast fluorescence decay with time constants of 20 ps (green triangles in Figure 41a) and 80 ps (red squares Figure 41a). These values are found to be widely invariant between all investigated cells of A.marina. Therefore the mentioned deviations in the Chl d dynamics which are caused by the different redox states of the Chl containing reaction center are not relevant for the following conclusions.

The simulation shown in Figure 41b is based on the assumption, that the EET between the PC trimers occurs almost exclusively through the в-84 chromophores (see chapter 2.4.4; Mimuro et al., 1986; Holzwarth, 1991). In addition about 3-6 chromophores of the trimeric PC disk should be involved into the EET inside the PC disc which occurs from outside to inside of the PC trimer (Mimuro et al., 1986; Holzwarth, 1991). Therefore the excitation energy is trapped at the ^-84 chromo- phore inside of a trimer first and subsequently funneled to the APC chromophores and the terminal emitter (TE). The pathway of EET is guided by “fluorescing” chromophores in accordance with calculations of Suter and Holzwarth that were done for PBS (Mimuro et al., 1986; Suter and Holzwarth, 1987). The scheme that was used for the simulation shown in Figure 41b is presented in Figure 42.

Scheme for simulating the data presented in Figure 41a. The simulated DAS are shown in Figure 41b

Figure 42. Scheme for simulating the data presented in Figure 41a. The simulated DAS are shown in Figure 41b.

Figure 42 indicates the situation where 22 out of the 69 chromophores found in the PBP antenna of A.marina are assumed to be involved in EET along the PBP antenna of A.marina. The simulations were performed by a simplified model of the PBP antenna containing 17 PC chromophores with emission wavelengths between 638 nm and 654 nm, 5 APC chromophores with emission wavelengths between 660 nm and 680 nm, 5 Chl d pigments with emission wavelengths between 723 nm and 732 nm and two states of the radical pairs.

For the simulation the EET between different PC and APC molecules in the PBP antenna is set to 400 fs as found by Theiss (Theiss, 2006; Theiss et al., 2007a; Theiss et al., 2011). The EET from the “red” APC molecule (TE) to Chl d is set to 30 ps and the EET between the Chl d molecules in the Chl containing core antenna is set to 100 fs. For the sake of simplicity only four PC, two different APC molecules and four acceptor states of Chl d are explicitly shown in this scheme (Figure 42) while the rest of states added to the simulation is omitted and substituted by a series of black dots.

The simulation results presented in Figure 41b show that the experimental data can be explained by assuming equally coupled PC and APC molecules in the PBP antenna as shown in Figure 42. It turned out that all values found in the fluorescence decay kinetics should be understood as “effective” transfer times which cannot necessarily be identified with rate constants for single EET steps. The 2-3 ps kinetics most probably describe the overall relaxation between several PC pigments while the 20 ps component describes the overall relaxation from PC, APC and red APC (TE) in the linker protein. The exact value of the EET transfer step from the TE to Chl d depends on the number of chromophores involved in the EET. If only 8 instead of 17 PC molecules are used in the simulation, this value prolongates to 40 ps instead of 30 ps, respectively (data not shown). The TE, which most probably is the long wavelength APC around 680 nm (APClong ) found by Theiss et al. gives rise to the negative amplitude (rise kinetics) of the 20 ps component at 680 nm. Variations of the time constants in the model of Figure 42 reveal that the 20 ps component of the experimental data (Figure 41a) can be explained by EET along equally coupled PC/APC molecules. A rate limiting step between PC and APC or APC and APClong can also explain the 20 ps component (data not shown). But in all cases the overall EET time from the PBP to the Chl d is found to be 80 ps in the model only if a transfer time of max. 30-40 ps is set for the inverse transition probability between APClong and Chl d.

Finally the apparent time constants are not present on the molecular level in the PBP antenna of A.marina. They “emerge” from the coupling scheme and can already be explained by a simple rate equation system as it is a synergetic study of the whole complex. This example demonstrates how the underlying microscopic EET is hidden by a macroscopic observable that finally determines the behavior on dynamical time scales that are chosen for observation on a given system.

The decay time constants of the Chl d (400 ps and 900 ps at 725 nm) are explained by the electron transfer processes in the PS II (see Schmitt, 2011). The diffusion along the PC molecules leads to additional fast components of 2-3 ps with very small amplitude (cyan curve in Figure 41a) which can not be resolved in our experiment.

The simulation presented in Figure 41b fits the data presented in Figure 41a, except of the large amplitude of the 20 ps component (green curve) dominating in the measurement at 725 nm. This effect probably originates from PS I fluorescence at 725 nm. The simulations are performed for the dynamics of the PS II only and therefore can not reproduce the large fraction of the 20 ps component which mainly results from fast PS I fluorescence.

The simulation exhibits that in fluorescence spectroscopy the measurement data reflects apparent time constants for EET processes. If an ensemble of several energetic states couples to an acceptor then the fluorescence dynamics summarizes the diffusion of excitation in the donor states and the EET process. The 10-20 ps EET component (green curve of Figure 41) is also found in the fluorescence emission of isolated PBP. Therefore the fluorescence spectroscopic data reveals that the EET along the whole PBP antenna takes place within a time of about 20 ps. The overall EET from the PBP to the Chl d is found to appear as a 7080 ps component in the fluorescence data if the inverse transition probability between APClong (the TE) and Chl d is about 30 ps. The reason for this prolongated “apparent” decay time is the entropy effects of the degenerated PC states found in the PBP antenna structure.

In the PBP antenna of A.marina for example the equilibration between PC and APC molecules can still be resolved with a time constant of 20 (±10) ps. The information of faster equilibration processes simply cannot be found in the fluorescence dynamics observed by TWCSPC. In that case it is intrinsically impossible to extract information on the accurate values of the single energy transfer steps because the dynamics of different coupled states takes place in the same time domain between spectrally strongly overlapping chromophores. The states of the systems can mix in a way that makes it impossible to separate the processes even if the experimental resolution is high enough. This fact mostly limits the available information content. TWCSPC is principally limited by the amount of accessible information as shown with information theoretical approaches regarding single molecule fluorescence microscopy. The desired goal of the experimenter should be to extract all experimentally accessible information to have the general possibility to proof any predicted effect of an applied theory. In general the experimenter is not able to accumulate an infinite amount of information and it would be economic to choose exactly the right amount. Therefore the experimenter has to care that the accumulated information represents the accessible information.

An improvement can only be achieved by a study of the decomposed sample or by the employment of complementary experimental techniques which localise the observed state. But in both cases the experimental results might depend on the special configuration of the sample and the measurement setup and it is necessary to investigate the influence of the sample preparation and experimental manipulation onto the experimental results.

It might be useful to accomplish a kind of methodical statistics of the experimental techniques. Then the experimenter can shift systematic aberrations to statistical uncertainties to a certain amount. For this purpose the experimenter has additionaly to be able to reproduce the sample often enough without any variation.

In most cases the principal resolution is not limited by the setup but by the uncertainty of the sample. Doing high resolved fluorescence nano- scopy we shift the uncertainty from the optical wavelength representing our measurement setup to the observed states which is an ultimate resolution limit.

According to the presented results the excitation energy transfer in the antenna complexes of A.marina can be summarized as shown in Figure 43, left side. In this scheme it is assumed that the PBP antenna of A.marina resembles the rods of the phycobilisomes in common cyanobacteria with the main exception, that the hexamer closest to the thylakoid membrane is a heterohexamer consisting of one PC- and one APC-trimer as suggested by Marquardt et al. (1997). The EET from PC to Chl d is characterized by four kinetic components with lifetimes of <400 fs, 3 ps, 14 ps and 70 ps. The red arrows in Figure 43 exhibit our own evaluation results while literature values are marked black.

Figure 43, right side, shows a scheme with the range of time constants for EET processes in Synechococcus 6301 as reported in literature (black arrows) in comparison to our own findings obtained on Synechocystis (red arrows, compare Figure 44 and Figure 45). The equilibration along the trimeric PC disks in the PC containing rod appears with a typical rate of about (10 ps)-1 (Gillbro et al., 1985). Based on experimental results from ps-studies (Suter and Holzwarth, 1987) presented a random walk model for the EET in the PC rods of Synechococcus 6301 and calculated rates of (10 ps)-1 to (3.3 ps)-1 for single step EET between trimeric PC disks and about (25 ps)-1-(40 ps)-1 for the EET from the innermost PC trimer to the APC core. For the overall EET from a PC rod containing 4 hexamers to the APC core the literature reports rate constants of (80 ps)-1 to (120 ps)-1 (Gillbro et al., 1985; Suter and Holzwarth, 1987; Holzwarth, 1991; Mullineaux and Holzwarth, 1991) (Figure 43, right side).

Our own findings obtained at a slightly different organism, Synechocystis, did not resolve the involvement of an APC bound to the linker molecule but was sufficiently simulated with time constants of 70 ps for the EET from PC to APC and 280 ps from APC to the Chl a containing membrane integral antenna complex (Figure 44 and Figure 45).

In contrast, in A.marina where APC and PC share the same hexamer, the PC to APC EET occurs with a rate constant of only (3 ps)-1 (Figure 43, left panel). This is finally at least 8 times faster than the fastest EET rate reported from the innermost PC trimer to the APC core in phycobi- lisomes as reported in (Suter and Holzwarth, 1987) and even faster than the single step EET between adjacent trimers in pure PC rods of other cyanobacteria. The 14 ps component is observed in the DAS of the transient absorption spectra as a decay of a bleaching at 640 nm and a rise of a bleaching at 670 nm. We assign this component tentatively to an EET from APC (absorbing at 640 nm) to a low energy APC (bound to a linker protein) that transfers it's energy to Chl d with a time constant of 30-40 ps and therefore facilitates an efficient overall EET from the PBP antenna to Chl d which occurs with a rate constant of (70 ps)-1. This is more than three times faster than the EET transfer from the APC core to Chl a in Synechococcus 6301 which occurs typically with (170-120 ps)1 (Mullineaux and Holzwarth, 1991).

Kinetics of excitation energy transfer (EET) processes in A.marina and in the cyanobacterium Synechococcus 6301 as published in (Theiss et al., 2011). Left panel

Figure 43. Kinetics of excitation energy transfer (EET) processes in A.marina and in the cyanobacterium Synechococcus 6301 as published in (Theiss et al., 2011). Left panel: Model Scheme for the excitation energy processes (EET) inside the PBP antenna rod and between the PBP antenna and Chl d in A.marina. At the top the model scheme of the PC trimer with its bilin chromophores is shown. Right panel: Model Scheme and time constants for the EET inside the phycobilisomes of Synechococcus 6301 and from there to the RC giving a resume of the literature (Gillbro et al., 1985; Suter and Holzwarth, 1987; Holzwarth, 1991; Mullineaux and Holzwarth, 1991; Sharkov et al., 1994; Debreczeny et al., 1995a, 1995b). Image reproduced with permission.

The very fast EET in A.marina from PC to APC then to Chl d reflects the unique feature of A.marina due to its tiny rod-shaped PBP antenna where PC and APC share the same heterohexamer instead of huge phy- cobilisomes with rods containing PC only and an additional APC core.

As comparison we applied the formalism of rate equations onto the same problem (studying EET and ET transfer processes, in a different cyanobacterium, Synechocystis PCC 6803 available in our laboratory which should have similar properties like the above studied Synechococcus 6301).

The DAS of whole cells of Synechocystis are shown in Figure 44, upper panel. The energy transfer from PC to APC is associated with a characteristic fluorescence time constant of 60 ps (red curve in Figure 44). The fluorescence exhibits an additional 150 ps component (black curve) associated with an EET from the pigments around 640-660 nm (PC and APC) to Chl a of PS II (685 nm). The Chl a fluorescence decays with time constants of 300 ps (green curve) and 1 ns (blue curve).

Figure 44, upper panel, shows the result of a simulation that is performed according to the scheme given in Figure 45. The scheme comprises the photochemical light reaction in the PS II according to chemical equation 2 with an additional PC and APC containing PBS antenna.

In common Chl a dominated cyanobacteria such as Synechococcus 6301 (which exhibits a similar phycobilisome antenna like Synechocystis) the energy transfer from the PBS to PS II occurs on an at least 3 times slower time scale in comparison to A.marina. In these cyanobacteria the fluorescence decay of the PBS is characterized by multiphasic kinetics with lifetimes of typically 120 ps for the energy transfer from the PC-con - taining rods to the APC-core, 70 ps for the energy transfer from the APC- core to the terminal emitters and 200 ps for the energy transfer from the terminal emitter to Chl a of PS II.

Based on experimental results from ps-studies Holzwarth et al. calculated a time constant of 102 ps to 124 ps for the overall EET from a PC rod containing 4 hexamers to the APC core (Suter and Holzwarth, 1987; Holzwarth, 1991). Comparable rate constants found in literature are (80-120 ps)-1 (Gillbro et al., 1985) and (90-120 ps)-1 (Mullineaux and Holzwarth, 1991).

The simulation and the experimental results are in agreement if the EET time constant is set to 70 ps for the transfer from PC to APC which is slightly faster than the values given in literature, as mentioned above (see Figure 45). The time constant for the APC to Chl a transfer is simulated with 280 ps which resembles the sum of 70 ps for the energy transfer from the APC-core to the terminal emitters and 200 ps for the energy transfer from the terminal emitter to Chl a of PS II (Gillbro et al., 1985; Mimuro et al., 1986; Mullineaux and Holzwarth, 1991).

Upper panel

Figure 44. Upper panel: DAS of a measurement obtained on Synechocystis at room temperature after excitation with 632 nm laser light. The time constants of the components exhibit values of 60 ps with a minimum in the fluorescence regime of APC (670 nm, red curve), 150 ps with a minimum in the fluorescence regime of Chl a (680 nm, black curve) and additional positive time constants in the Chl a regime with 300 ps (green curve) and 1 ns (blue curve). Lower panel: Simulation of the DAS according to the scheme given in Figure 45, assuming a temperature of 300 K and a spectral bandwidth of the Gaussian emitter states of 25 nm. An edge filter width a cut off wavelength at 648 nm is simulated comparable to the edge filter used in the measurement data (DAS of the measurement is given in the upper panel).

Scheme for the simulation of the DAS shown in Figure 44, lower panel

Figure 45. Scheme for the simulation of the DAS shown in Figure 44, lower panel.

In addition a time constant of 230 ps is found for the primary charge separation and AG of the relaxed primary radical pair in comparison to the excited Chl state in the antenna system is found to be about 50 meV. The charge stabilisation (see also chemical equation 2) appears to be quite slow with 800 ps. Especially the time constant of the 1 ns component (see Figure 44) depends critically on this ET step. The reason for the high amplitude of the 1 ns component and the concomitant slow 800 ps charge separation may be the existence of partially closed reaction centers during the measurement.

The main difference of the simulated DAS (Figure 44, lower panel) and the measurement (Figure 44, upper panel) is the apparent amplitude deviation of the rise kinetics of the fast 60 ps term (red curve in Figure 44). The determination of the amplitude of the rise kinetics is very difficult and exhibits confidential intervals that are of comparable size to the amplitude itself. This situation is even more critical for the measurements presented in Figure 44, as there are two overlapping rise terms with time constants of 60 ps and 150 ps that are resolved in the DAS. Therefore the agreement between the experiment, Figure 44, upper panel and the simulation Figure 44, lower panel is sufficient within the confidence interval of the experimental results. The time constants determined as given in Figure 45 show that there is an agreement between the results obtained with our setup and the concomitant analysis via rate equations and literature values. Therefore our experiments and the theoretical approach are supported by the successful determination of the EET steps in the PBS of Synechocystis.

 
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