Excitation Energy and Electron Transfer in Higher Plants Modelled with Rate Equations

R. Steffen et al. developed a compact fluorescence spectroscopic setup suitable to monitor single (laser) flash induced transient changes of the fluorescence quantum yield (SFITFY) in cell suspensions and whole leaves in the time domain from 100 ns to 10 s (Steffen et al., 2001, 2005a, 2005b) (see Figure 46).

In our former studies we used data gathered by this setup to describe the PS II dynamics in whole cells of Chlorella pyrenoidosa Chick according to a reaction pattern based on the formalism of rate equations as described in chap. 1.3 and 1.4 (Belyaeva et al., 2008). Later it was shown that the intensity dependent pattern of SFITFY traces measured in whole leaves of Arabidopsis thaliana at four different intensities of the actinic laser flash can be described with one set of model parameters (Belyaeva et al., 2011). These findings are briefly outlined in this chapter and extended to an approach enabling the comparison of single transfer probabilities in different species. In (Belyaeva et al., 2014, 2015) a detailed comparison of the evaluated rate equation scheme of green alga and higher plants which was fit to the measured SFITFY curves of these species allowed for the comparison of single ET transfer steps in the proposed reaction scheme to distinguish the kinetics of single steps between green algae and higher plants. Details regarding the measurement setup (Steffen et al., 2001), the sample condition (Steffen et al., 2005a, 2005b) and the discussion of the metabolic relevance of the gathered results (Steffen et al., 2005a; 2005b) are described in the cited references. The following results are already published in (Belyaeva et al., 2014, 2015) and focus on the applicability of rate equation systems on the synergetic network analysis of ET steps in higher plants.

Experimental data of fluorescence yield changes

Figure 46. Experimental data of fluorescence yield changes (SFITFY curves) induced in whole leaves of Arabidopsis thaliana wild type plants by excitation with a single actinic 10 ns laser flash of different energy: 7.5-1016 photons/ (cm2-flash) (triangles), 6.2-1015 photons/ (cm2-flash) (circles), 3.0-1015 photons/ (cm2-flash) (squares) and 5.4-1014 photons/ (cm2-flash) (diamonds). The data are redrawn from (Belyaeva et al., 2011). The green arrow symbolizes the excitation by the actinic laser flash. Image reproduced with permission.

The time courses of the photosystem II (PSII) redox states were analyzed with a model scheme as shown in Figure 47. Patterns of Single Flash Induced Transient Fluorescence Yield (SFITFY) measured for leaves (spinach and Arabidopsis (A.) thaliana) and the thermophilic alga Chlorella (C.) pyrenoidosa Chick (Steffen et al., 2005a; Belyaeva et al., 2008, 2014, 2015) were fitted with this PS II model.

Figure 46 shows experimental SFITFY data of Steffen and coworkers (Steffen et al., 2005a) obtained by excitation of dark adapted whole leaves of Arabidopsis thaliana wild type with single actinic laser flashes of different energy. The signal Fq (-50 (is) before the actinic flash monitors the fluorescence induced by the weak measuring pulses. It reflects the normalized fluorescence quantum yield of dark adapted PS II complexes and is used to normalize the time dependent SFITFY curve monitored by a sequence of weak measuring light pulses in the range from 100 ns to 10 s after the actinic flash (which is symbolized by the green arrow in Figure 46). The photon densities per flash and unit area of the actinic laser flash of the four different SFITFY data sets were: 5.4 • 1014 (diamonds), 3 • 1015(squares), 6.2 • 1015 (circles) and 7.5 • 1016 (triangles) photons/(cm2-flash) (0.7%, 4%, 8% and 100% of reference).

The SFITFY patterns exhibit an “instantaneous” change of the fluorescence yield within 100 ns that strongly depends on the energy of the actinic flash (see Figure 46). This instantaneous change is a rise at low energies and turns into a drop below Fq at high energies of the laser flash. This drop is explained by the population of 3Car states that act as highly efficient quenchers of the fluorescence (Steffen et al., 2005a, 2005b; Belyaeva et al., 2008; 2011). A normalized maximum value Fmax(t)/F0 of about two is reached about 50 ps after the actinic flash. In the subsequent time domain the normalized fluorescence yield declines to a level slightly above its original value Fq.

Simulations based on a model of the PS II reaction pattern presented in Figure 47 provide information on the time courses of population probabilities of different PSII states. The appropriate application of the formalism of rate equations provides a flexible basis for comparative analyses of time dependent fluorescence signals observed on different photosynthetic samples under various conditions (e.g. presence of herbicides, other stress conditions, excitation with actinic pulses of different intensity and duration). The general formalism is principally suitable to describe any system that can be described by states and transitions between these states.

The kinetic scheme of Figure 47 allows the calculation of the transient PS II redox state populations ranging from the dark adapted state, via excitation energy and electron transfer steps induced by pulse excitation,

a. Kinetic scheme of Photosystem II as presented in (Belyaeva et al

Figure 47a. Kinetic scheme of Photosystem II as presented in (Belyaeva et al.,


2008, 2011, 2014, 2015). Each rectangle refers to one of the states. ^ P6g^/ denotes the total PS II chlorophyll including the antenna and the P680 pigments


and is used to determine singlet excited states 'Chl* delocalized over


all pigments in antenna and RC. Further components are P680 - photochemically active pigment, Phe - the primary electron acceptor pheophytin. QA and QB - the primary and secondary quinone acceptors. PQ — plastoquinone, PQH2 - plastoquinol; HL+ - protons, which are released into lumen, HS+ - protons in stroma. The letters above rectangles (xt, yt , zt, gt, i = 1, ..., 7) correspond to the model variables. Shaded areas symbolize the excited states that are capable of emitting fluorescence quanta. Dashed arrows designate fast steps (characteristic time values less than 1 ms). Bold arrows mark the light induced steps. Numbers at the arrows correspond to the step numbers. Dashed arcs designate two types of irreversible reactions of the processes of nonradiative recombination: Phe * with P680+* (42-45:= kPhe) and QA * with P680+* (46-49). Image reproduced with permission.

Figure 47b. The decay into ground state occurs via i) radiative fluorescence emission (kF), ii) nonradiative dissipation of excited chlorophyll singlets by quenching due to cation radical P680** and/or by the triplet states of carotenoids with rate constants kP680+ and k3Car, respectively and iii) radiationless dissipation of excitation to heat (kHD). Image reproduced with permission.

followed by final relaxation into the stationary state eventually attained under the measuring light. The shape of the actinic flash was taken into account by assuming that an exponentially decaying rate constant simulates the time dependent excitation of the PS II by the 10 ns actinic flash. The maximum amplitude of this excitation exceeds that of the measuring light by 9 orders of magnitude.

Figure 47 shows the whole scheme of redox states and their transitions as described in detail in (Belyaeva et al., 2011). Each box in Figure 47 represents the redox state of the corresponding component (compare


chap. 1.2): antenna and RC chlorophyll - (p^go/, pheophytin - Phe,

primary quinone acceptor - QA, secondary quinone acceptor - QB. The model comprises the processes of light induced charge separation (reaction numbers: 2, 9, 16, 29), charge stabilization by Qa * formation (reaction numbers 3, 10, 17, 30), electron transfer from Qa * to Qb (reaction number 7) and from Qa *Qb * to QbH (reaction number 14), protonation of QbH under PQH2 release (reaction numbers 21-27) and refilling of the empty QB-site with oxidized plastoquinones (PQ) (reaction numbers 34-40). For the sake of simplicity we assume that for each electron, transferred from the water oxidizing complex (WOC) via tyrosine Yz to the oxidized RC chlorophyll P680+* (reaction numbers 4, 11, 1g, 31), one proton is released into the lumen.

The model scheme of Figure 47a comprises 28 redox states of the PS II RC together with two states of the PQ pool. Therefore 30 variables (metabolites N,(t), i = 1...30) and a set of 30 differential equations describe the rate of production and consumption of N;(t) which is a function of the variables N (t) involved into population and deactivation of N;(t) (i, j = 1.30) and of the rate constants, i.e. probabilities for each transition per time unit kn, k_n (n = 1.49) for forward and backward transfer steps, respectively (see chapter 1.3 and 1.4). Some of the reactions in the model scheme (Figure 47a) involve protons in lumen and stroma ([Hi+] and [Hs+]) as model parameters.

The exact mathematical structure of the set of ordinary differential equations and the method of data variation and fitting is outlined in ref. (Belyaeva et al., 2008, 2011). The dissipative reactions (including

inter-system crossing), given by the rate constants kp680+, k3Car and ?hd, quench the fluorescence from PS II in addition to the photochemical quenching via electron transfer to the acceptor quinone molecule QA (see Figure 47b). The fluorescence emission is symbolized in Figure 47b by the radiative rate constant kF. Actinic flash induced formation and decay of non-photochemical quenching states P680 +*, 3Car and radiation-less dissipation as heat was the main focus of (Belyaeva et al, 2011).

The numerical fits of SFITFY data presented as colored solid lines on Figure 48 are seen to describe with high precision the SFITFY patterns at the four different values of the actinic flash energy. The energies of the actinic flashes and the corresponding relative values are compiled in columns 1 and 2 of Table 1. The maximal light constant values (kL-Max)

Simulation of the experimental SFITFY data of Figure 46 by the PS II model presented in Figure 47

Figure 48. Simulation of the experimental SFITFY data of Figure 46 by the PS II model presented in Figure 47 (a, b) (redrawn from Belyaeva et al., 2011). SFITFY curves in whole leaves of wild type plants of Arabidopsis thaliana are shown by symbols at the different laser flash energies: 7.5-1016 photons/cm2 flash (dark- blue), 6.2-1015 photons/cm2-flash (magenta), 3.0-1015 photons/cm^flash (beige) and 5.4-1014 photons/cm^flash (light-green). The numerical fits are shown accordingly by lines calculated with the rate constant fcL-Max values (see Table 1): 7.2-109 s_1 (dark-blue), 6.0-108 s_1 (red), 2.9-108 s_1 (brown), 5.2-107 s_1 (green) and the parameters as shown in Table 2. The dotted magenta lines represent the time courses of kL(t). The measuring light of low intensity was simulated with fcL-Min = 0.2 s_1 (see Table 1). Image reproduced with permission.

in column 3 imitate the rate of light quanta exciting the Chl molecules in the PS II model (Figure 47). The measuring light beam of the LED pulses, is not visible in Figure 48 because this value is smaller by several orders of magnitude compared to the activating actinic flash.

Table 1. Values of parameters used for the fitting of SFITFY data (see Figure 48) according to the model of PS II shown in Figure 47 as published in (Natalya, 2011). (PPFD stands for photosynthetic photon flux density; all other variables are described in the text).



. = 532 nm; fwhm = 10 ns

kn (s"1)


Var= 5.5 Ps












7.5 • 1016





2.08-109 1


20 (800)


6.2 • 1015





5.6-108 0.27











3.5-108 0.17


14 (500)


5.4 • 1014





1.2-108 0.06


14 (400)

Measuring. light PPFD 0.8 mol photons m“2 • s_1










Table 2. Values of parameters used for quantitative fits with the PS II model (Figure 47) simulations of SFITFY curves for whole leaves of Arabidopsis thali- ana plants (see Figure 48).

reaction number, n

kn (s ')


k_n (s ')



2, 9, 16, 29

3.2 • 10u/125


6.4 • 107

Charge separation (open RC) Charge separation (closed RC) (Schatz et al., 1988; Roelofs et al., 1992; Renger et al., 1995)

6, 13, 20, 33

2.56 • 109 / 2.25


1.14 • 108

3, 10, 17, 30

3 • 109



Charge stabilization on Qa_* (Schatz et al., 1988, Roelofs et al., 1992; Renger et al., 1995; Renger and Holzwarth, 2005)

4, 11, 18, 31

(3.3-M.5) • 107


Electron donation from tyrosine Z to P680+* (Renger, 2001)





ET from QA' to Qb ET from QA to Qb_’ (Renger and Schulze, 1985; Crofts and Wraight, 1983)





Table 2 shows the results gathered from the fit procedure for the values of PS II electron transfer parameters. The parameter values for processes of charge separation, stabilization and Qb -site reactions could be kept invariant to actinic flash energy without deviations between experimental data and the numerical fit using values from the literature (see column 5 of Table 2). In marked contrast the parameters of dissipative reactions in the antenna and PS II and the rate constant for charge recombination (flCar, ^hd, Figure 47b, kphe, Figure 47a) had to be changed when varying the relative actinic flash energy (see columns 4, 5, 6 of Table 1).

To simulate the fluorescence decay the values of AY (transmembrane electrical potential difference) and pHS (pH of the stroma) had to be varied lightly according to the values given in Table 1. The pH on the luminal side was set pHL = 6.5 for all energies of the actinic flash.

The SFITFY curves monitored in the range from 100 ns to 10 s after excitation of dark adapted samples with a single actinic flash of a definite energy can be explained by time courses of the PS II redox states that are illustrated in Figure 49a and Figure 49b for 100% light intensity and 4% light intensity, respectively. In closed RCs with reduced QA“the states P680+* PheQAare populated as a nonlinear process of two photon absorption during the actinic flash followed by a decrease due to the exponential decay of кг(0. Figure 49a (100% light intensity) shows full saturation (100%) of the closed RC and reduced overall Qa population (У Qa~ ). The value of 100% light intensity refers to the value &lmax =

7.5 • 109 s_1. ^Qa~ stays near 100% until the maximum of the SFITFY curve is reached at about 50 ps.

Using kLMAx = 6.2 • 108 s_1 (corresponding to 8%-light intensity) the level of ^Qa~ is still very close to saturation (95%) (data not shown). The calculations with ^lmax = 3 • 108 s_1 (4% light intensity) give rise to redox state population kinetics for ^Qa~ as shown in Figure 49b. Here the levels of maximal ^Qa~ are diminished to about 88%.

The results as presented in Figure 48 and Figure 49 (see summary in Table 2 and ref. Belyaeva et al., 2011) show that a consistent description of the experimental SFITFY data obtained at different excitation intensities can be achieved with invariant rate constants of electron transfer steps for all excitation pulse energies. In marked contrast, an increase of the actinic flash energy by more than two orders of magnitude from 5.4 • 1014 photons/ (cm2 flash) to 7.5 • 1016 photons/ (cm2 • flash), leads to an increase of the extent of fluorescence quenching due to carotenoid triplet (3Car) formation with factor 14 and of the recombination reaction between reduced primary pheophytin (Phe-) and P680+ with factor 3 while the probability for heat dissipation in the antenna complex remains virtually constant.

Calculated time course of normalized populations of different redox states in the PS II to simulate the SFITFY data of Figure 46

Figure 49. Calculated time course of normalized populations of different redox states in the PS II to simulate the SFITFY data of Figure 46 (circles) in whole leaves of A.thaliana wild type plants after illumination with an actinic laser flash (fwhm = 10 ns) at two different energies described by kL-Max values of 7.225 • 109 s_1 (panel a) and 2.9 • 108 s_1 (panel b) (redrawn from ref. Belyaeva et al., 2011). The measuring light is described by kL-Min = 0.2 s_1. The PS II model parameters used are presented in Tables 1, 2. The time courses of kL(t) are shown as dotted purple lines for kL-Max = 7.225 • 109 s_1 (panel a) and kL-Max = 2.9 • 108 s_1 (panel b). ?Qa * represents the sum of the closed RC states (x4 + g4 + y4 + z4 + x5 + g5 + y5 + z5) (dark green curve, see nomenclature in the scheme of Figure 47). All states including oxidized Chl a in the RC (P680 +*) are presented in the Fig.: P680 +* PheQA * denoting the sum of the closed RC states (x4 + g4 + y4 + z4) (light green curve), P680 +* Phe^Q^ — the sum of the closed RC states with reduced pheophytin (x7 + g7 + y7 + z7) multiplied with a factor 50 for better visibility (red curve). Image reproduced with permission.

However, when applying such a large parameter state as given in Figure 47 to fit a bunch of fluorescence curves as shown in Figure 46 and Figure 48 some of the parameters used to reproduce the measurements can be varied in a broad range without a significant change of the simulated SFITFY trace. Parameters describing fast processes (like e.g. kHD) do not influence the shape of the SFITFY decay on a longer timescale (and vice versa). This phenomenon offers the opportunity to analyze a wide range of processes occurring on different time scales simultaneously by precise evaluation of different time domains of the measured SFITFY data or TCSPC traces.

On the other hand, the analysis of processes taking place on similar timescales requires complementary information gathered from independent experiments if there is not a well defined parameter different for these processes (for example wavelength, polarization).

Thus, taking into account these properties, the PS II model offers new opportunities to compare electron transfer and dissipative parameters for different species (e.g. for the green algae and the higher plant) under varying illumination or growth conditions.

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