Introduction

When leaves are illuminated with strong light of the intensity of about 2–3 sunlight, Chl fluorescence initially rapidly increases during a few ms, but then stops on about a half-way and continues to increase with a slower rate—until it approaches the maximum Fm yield at about 200 ms (Schansker et al. 2011; Laisk and Oja 2018). Under ultrastrong microseconds-long xenon flashes of the intensity of a thousand sunlight Chl fluorescence reaches about the same level as during the first milliseconds under the lower light, but the additional rise to Fm does not happen (Joliot and Joliot 1964; Neubauer and Schreiber 1987; Samson and Bruce 1996). These two cases differ by the final state: the ST flash-induced induction ends with reduced QA, but oxidized QB and the rest of the ETC. The pulse-induced induction ends with the full reduction of QA, QB and the whole electron transport chain. This fact has induced a notion about a “thermal phase” of fluorescence rise, caused by release of a hypothetical quencher while ETC is being reduced (Delosme 1967; Schreiber and Neubauer 1987; Neubauer and Schreiber 1987; Koblížek et al. 2001; Vredenberg et al. 2009; Stirbet and Govindjee 2012). Multiple potential quenchers have been suggested (Vredenberg 2008; Stirbet and Govindjee 2012; Koblížek et al. 2001): (1) P680+ can quench Chl a fluorescence as efficiently as QA reduction; (2) P680 triplet, 3P680, most likely 3ChlD1 quenches in equilibrium with 3PD1; (3) carotenoid triplet 3Car is an efficient quencher in the antenna; (4) non-photochemical quenching by oxidized PQ molecules; (5) quenching by charge recombination from QB (Schreiber 2002); (6) reduced PheoD1 may be a quencher due to charge separation equilibrium P680* ↔ P680+Pheo−, shifted by transmembrane electric field (photo-electrochemical quenching (Vredenberg et al. 2009); (7) quenching by conformational changes in Chl proteins (Schansker et al. 2011); (8) fast recombination of separated charges in a cycle involving oxidized tyrosine Z (Laisk and Oja 2018). Contrary to the latter, (Prášil et al. 2018) showed that in Chlamydomonas reinhardtii donor side was not involved, but Fm was low when the QB binding site was occupied by PQ, and high when it was empty or occupied by DCMU or by PQH2.

Membrane energization by electric field as a factor controlling Chl fluorescence has been repeatedly emphasized (Schatz et al. 1987; Leibl et al. 1989; Keuper and Sauer 1989; Schreiber and Neubauer 1990; Schreiber and Krieger 1996; Vredenberg et al. 2009; Dau and Sauer 1992; Pospíšil and Dau 2002), but there is no direct evidence showing how the fluorescence yield of closed PSII centers is modulated by its presence. In the experimental part of this work, we first show that during low to high light induction, Chl fluorescence yield of closed reaction centers in sunflower leaves is not constantly Fm, but gradually increases, approaching the Fm value to the end of the induction. For explanation, we present a mathematical model similar to that of Schatz et al. (1988), but considering the repulsive force applied by an electric field on the radical pair. With this modification, the model predicts that the fluorescence yield of closed reaction centers increases during the induction, approaching the Fm level. According to this model, the ST flash-induced fluorescence level Ff is a fluorescence yield value, established in the state when QA has been reduced in most PSII, but the electric field, related to plastoquinone reduction and membrane energization, has not yet accumulated.

Materials and methods

Used leaves and measurement methods were essentially the same as those in (Laisk et al. 2012). Briefly, sunflower (Helianthus annuus L.) plants were grown in laboratory at a PFD of 450 µmol quanta m−2 s−1. O2 evolution was measured at 22 °C in the two-channel leaf gas exchange measurement system (Laisk et al. 2002), where the leaf was enclosed in a 32-mm diameter by 3-mm-deep chamber, flushed with gas at a flow rate 0.5 mmol s−1. The leaf chamber was illuminated through a branched fiber-optic light guide, producing uniform illumination of the adaxial leaf surface from three superimposable light sources. One branch was connected to a 630-nm LED light source providing a PFD of up to 8200 µmol quanta m−2 s−1 on the leaf surface. The second branch was used for far-red (FR) illumination. The third branch was connected to a xenon lamp, producing flashes of 7 µs half-width, photon dose of 76.7 µmol m−2 on the leaf surface, which saturated flash-induced O2 evolution. Leaf absorption was measured in a laboratory-made integrating sphere. Energy-calibrated actinic light spectra were measured by Miniature Fiber Optic Spectrophotometer PC2000 (Ocean Optic, Dunedin, FL). Photon fluence rate absorbed by the leaf in the photosynthetically active range was calculated as the product of the spectra of the incident light and leaf absorption from 400 to 700 nm. The red as well as FR light were integrated over their actual spectrum.

Oxygen evolution was measured in the flow-through system with a zirconium O2 analyzer (S-3A, Ametek, Pittsburgh, PA, USA) on a background of 10–20 ppm O2 in N2 and 200 ppm CO2. The MTP- and STF-induced O2 evolution was recorded as a bell-shape peak of 0.6 s half-width (for details see Oja et al. 2010). Integral O2 evolution from individual MTPs of gradually increasing length was approximated by a polynomial. Time-resolved ETR was calculated as four times the running slope of the polynomial. The rates are presented in µmol e− m−2 s−1 and sums in µmol e− m−2. The total per area density of PSII centers capable of water splitting was measured as four times O2 evolution from an individual saturating STF (Oja and Laisk 2000). Gradually decreasing density of open PSII centers during the induction was found by applying an STF at the end of MTPs of gradually increasing length. The difference in total O2 evolution from (MTP + STF) − MTP characterized the number of open PSII.

Chlorophyll fluorescence was excited by the same 630 nm LED light source that provided actinic (MTP) illumination. The fluorescence signal was collected from a 2 cm2 area of the leaf and recorded with a PIN diode sensor S3590-01 (Hamamatsu, Japan), whose signal was amplified by a THS 4601 chip connected to a laboratory-made DC amplifier (Oja et al. 2010). The sensor was protected from the excitation beam by a 750 ± 20 nm band-pass interference filter, a small cross-sensitivity signal was considered. The fluorescence excitation light was continuously recorded along with the fluorescence emission, using quantum sensor LI-190SA (LiCor, Lincoln, NE) connected to an amplifier. Fluorescence yield (in relative units) was calculated as the ratio of the fluorescence signal to the incident excitation intensity signal.

Results

Experimental approach

Before the application of MT pulses and ST flashes, leaves were stabilized under FR light, to keep the ET chain oxidized and S-states randomized due to the slow PSII excitation. Recorded fluorescence inductions (Fig. 1) began at the minimum value denoted Fo, but a little higher than the minimum fluorescence in the dark, rapidly increased during about 1 ms and then more slowly approached the maximum Fm level during the recording time of 300 ms.

Fig. 1
figure 1

Recorded fluorescence inductions (lines) at indicated light intensities (µmol m−2 s−1). These recordings lasted 300 ms, but for clarity only the initial part is shown. For O2 measurements, the pulses were repeated at length as indicated by data points. Each data point shows the actual fluorescence reached to this time moment in the particular recording. Dotted lines indicate Fm approached to the end of the recording (Fm is normalized to unity in figures below), Fo is the starting point of recordings (steady-state under low FRL), FPSI is PSI fluorescence

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O2 evolution could be recorded integrally from MT pulses of different lengths. The FR light was turned off simultaneously with the pulses and flashes, which was reflected as a step down in the reference O2 recording. Oxygen, evolved by the pulses and flashes, was superimposed on the reference transient (Fig. 2).

Fig. 2
figure 2

Example of O2 evolution measurements. A leaf was stabilized under FRL of 50 µmol m−2 s−1 to randomize S-states, activate ATP synthesis and carbon metabolism. The FRL-excited PSII generated steady-state O2 evolution, equivalent to ETR of 5.6 µmol e− m−2 s−1. Light pulses and flashes were superimposed on this state, simultaneously FRL was turned off. The corresponding transients in O2 evolution were measured and integrated. Denotations in the legend on the panel are the following: black (ref)—reference transient without pulsing; Xe (blue)—only xenon flash, inducing O2 evolution from 1/4 of active PSII centers in the leaf; MTP (red)—multiple-turnover pulses of different lengths and intensity (the example is a weak MTP, exciting less than all PSII units); MTP + Xe – a xenon flash was added at the end of the MTP with an aim to measure the fraction of still open centers. Point-by-point differences between the traces resulted in the following information: Xe—ref (blue), total number of active PSII; MTP—ref, summary electron transport during the applied MTP; (MTP + Xe) – MTP, fraction of PSII still open after the MTP

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The sum of O2 evolution induced by individual MT pulses of different photon dose was fitted by 6-th power polynomials (Fig. 3). The running O2 evolution rate was found as analytical derivative (slope) of the polynomial and multiplied by four to be presented as ETR. As this O2 evolution was produced by PSII still open during the induction, the rate reflects the quantum yield of all the PSII still open: the yield was maximal in the very beginning, but decreased towards saturation of the induction.

Fig. 3
figure 3

O2 pulses measured in response to MT light pulses of different intensity and length. Absorbed photon dose is on the abscissa, increasing as the pulse length was increased from 0.4 to 200 ms. Continuous lines are 6th power polynomials fitted to the data points. Different lines correspond to different PAD of the pulse light, indicated at the curves, µmol m−2 s−1. Inset shows details in the initial part of the curves, emphasizing intensity-independent initial slope

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The number of open PSII was derived from O2 evolution induced by a saturating ST flash applied at the end of the actinic MT pulse. The number of open PSII was maximal in the beginning, but decreased towards saturation of the induction. When the summary yield (rate during the MT pulse) was plotted against the fractional number of open PSII, the result indicated proportionality independent of the way the photons were applied—either during an intense short pulse or weaker longer pulse (Fig. 4). This shows that open centers operated at a constant quantum yield independent of the density of adjacent closed centers.

Fig. 4
figure 4

Decreasing rate of electron transport, supported by the gradually decreasing fraction of open PSII during low–high light induction. Proportionality indicates a constant yield. Arrow indicates direction of the induction

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Figure 5 represents the increasing fluorescence yield as measured from the leaf while the fraction of closed centers was growing during the induction. The curve begins at the minimum fluorescence slightly higher than the dark fluorescence of open centers Fo because of the slow excitation by FRL. Importantly, the curve is not linear—as expected assuming a constant Fm value for a closed center—but it curvilinearly increases as more PSII centers become closed. Proceeding from the fact that the quantum yield of open centers remained constant (Fig. 4), we assume that each open center keeps fluorescing at the initial yield during the whole induction. The blue line in Fig. 5 presents the decreasing summary fluorescence of open centers as their fraction decreases, being replaced by the growing fraction of closed centers. The final offset of the blue line characterizes PSI fluorescence (Peterson et al. 2014). This plot shows that fluorescence from closed PSII increases with an accelerating speed while more centers become closed during the induction.

Fig. 5
figure 5

Fluorescence yield during induction dependent on the fraction of closed PSII; color of data points indicates PAD. Fo is the summary fluorescence yield of open centers, linearly decreasing with the decreasing fraction of open centers (blue line, offset indicates PSI fluorescence)

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In Fig. 6, the total fluorescence yield of all closed centers—difference between the data points and the blue line in Fig. 5—was divided by the fractional amount of closed centers, revealing the fluorescence yield of a closed PSII center. Regulation of the fluorescence yield of closed PSII centers is best visible in the Panel A, where the light intensity was the highest. While electrons were transferred to reduce QA and QB, but not yet many electrons were reducing plastoquinone and PSI donor and acceptor side carriers, fluorescence yield of a closed PSII Fc was 0.55 of the final level denoted Fm. This yield is close to Ff, the one usually obtained after a ST flash. The yield was constant until 70% of PSII became closed due to reduction of their bound quinone acceptors, but not many electrons were yet transferred to PQ and other carriers of ETC. Fluorescence yield of closed PSII centers gradually increased, approaching the final Fm level when the whole ETC became reduced. At lower pulse light intensities the fraction of centers closed before the PSII ETR equilibrated with the reduction rate of PQ was smaller—e.g. 30% at the pulse light intensity of 2000 µmol m−2 s−1 and less at the still lower light intensities. At physiological light intensities Fc did not approach the high Fm reached at 8000 µmol m−2 s−1 of pulse PFD. At the typical growth light of 500 µmol m−2 s−1 closed centers emitted at the flash fluorescence Ff level, not showing a tendency to increase fluorescence during the 200 ms pulse—but it does not mean that a longer exposure at this PFD could not cause enhancement of fluorescence.

Fig. 6
figure 6

Fluorescence yield of closed reaction centers, Fc in relation to Fm = 1, dependent on the fraction of closed reaction centers during induction. Fluorescence yield was close to the flash-induced Ff = 0.55 Fm while the acceptor side carriers QA and QB were being reduced, but started to increase as soon as the whole electron transport chain became to be reduced. Different symbols indicate results obtained with different sunflower leaves

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Concluding this section, we have established that fluorescence yield of a PSII center getting closed by QA reduction in the state of unrestricted electron transport is 3.7 Fo. In the state of restricted electron transport, the whole ET chain becomes reduced, generating an allosteric effector that gradually increases the fluorescence yield of all closed centers—including those which had become closed earlier—to 6.7Fo.

Modeling the variable PSII fluorescence emission

Here, we present a simple model to explain mechanistic principles of the variability of fluorescence yield of closed PSII centers. The model (Fig. 7) is similar to that used by A. Holzwarth and coworkers (Schatz et al. 1987, 1988; Szczepaniak et al. 2008, 2009; Lambrev et al. 2012). For leaves, however, the 6-Chl PSII reaction center complex is joined with the large antenna as in (Holzwarth et al. 2009; Lambrev et al. 2012). There are two sites terminating excitation in this model. While randomly hopping in the antenna, excitation may be terminated as fluorescence emission or as heat generated either by internal conversion in an antenna pigment or via an intermediate triplet state. The other chance to terminate it is while excitation is deposited in the radical pair. In open centers, the most likely pathway for this is photochemical charge transfer to QA, but if the latter happens to be reduced, then excitation may be terminated by non-radiative recombination or recombination via a triplet state (Lambrev et al. 2012). The probability for being terminated rises with the time excitation is spending as the radical pair. By elevating the energy level of the radical pair (decreasing the free-energy difference with the antenna), electric field controls relative efficiencies of the two excitation termination sites: when the field is weak, the radical pair is a deeper trap, where excitation spends a longer part of its lifetime, offering a good chance for the photochemical charge transfer in open centers, or for non-radiative charge recombination in closed centers. When the field is strong, excitation spends little time in the shallow trap of the radical pair, but spends most of its lifetime randomly hopping in the antenna—with this increasing the chance of being terminated via fluorescence emission. Only one radical pair state is considered in this model, denoted Pheo−P680+. With this we smooth the initial ultrafast kinetic effects discernable by separating RP1 and RP2 (Pheo−ChlaccD1+ and Pheo−PD1+ Lambrev et al. 2012).

Fig. 7
figure 7

Model of excitation transfer within a PSII. Initially excitation is located in the pigment system of antenna + RC (black boxes); from there it moves to the Pheo−P680+ radical pair; the latter may recombine to the ground or excited levels, or the electron may move further to QA (blue boxes). In energized membranes with closed centers (red boxes), electric field pushes the radical pair to return excitation energy to the antenna. Rate constants are given in ns−1

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Mathematical analysis was executed by solving a system of linear differential equations, describing transformations between the states of PSII with differently located excitation. As an initial condition, the antenna was excited. With time the excitation could move to form the radical pair and later to reduce QA, but the excitation could competitively be terminated while being in the antenna or in the radical pair. In equation denotations, the A(ntenna)R(adical)Q(uinone) complex could be in states with antenna in excited, Ae, or ground, Ag, radical pair present, AgRQo, or absent, AeQo, and the quinone acceptor oxidized AgRQo or reduced, AgQr. Rate constants characterizing transformations between these states were evaluated, considering well-measured integrals—such as the maximum fluorescence Fm and the minimum fluorescence Fo (Fm/Fo = 6.7 in our leaves), and for the flash-induced fluorescence Ff/Fo = 3.7). Antenna fluorescence was emitted with the rate constant of 0.058 ns−1, but the excitation was competitively quenched by internal thermal conversion and via intersystem crossing to the triplet state, with the total rate constant of 0.23 ns−1. This rendered the excitation life-time in the antenna 3.5 ns and the absolute quantum yield for fluorescence emission 20%. Below we normalize calculated fluorescence yields in relation to this antenna yield, denoted Fmax = 1.

Excitation hopping time in the antenna was joined with the radical pair formation time, resulting in the rate constant ar = 6 ns−1 for the formation of the radical pair from antenna excitation. The radical pair could recombine into the excited state, sending the excitation back to the antenna. In leaves, the “entropic force” of the large antenna resulted in 1:1 equilibration of the radical pair state with the excited antenna state—in absence of the electric field excitation spent a half of its lifetime in the antenna, the other half in the radical pair. Competitively with the radiative recombination, the radical pair could rapidly donate its electron to QA with the rate constant of 5 ns−1. This rate constant determines the PSII photochemical quantum yield, found to be 0.65 in leaves (Laisk et al. 2014, see “Discussion”). Important was the role of the non-radiative recombination of the radical pair, quenching excitation in its non-fluorescent state. The corresponding rate constant of 2 ns−1 was chosen between the two exponentials reported in Schatz et al. (1987). Determined on the basis of integral fluorescence yields, these rate constants for the one-RP model are generally faster than those used for the two-RP model by Lambrev et al. (2012) for the wild-type arabidopsis in the dark-adapted (no NPQ) state. Slower rate constant values resulted in too high Fo, not compatible with the measured Fm/Fo and Ff/Fo ratios.

In this model, electric field was assumed to exert counter-pressure on the radical pair state, increasing the radiative recombination rate as follows:

$$\frac{ra}{ar}={\mathrm{e}\mathrm{x}\mathrm{p}\left(\frac{e\Delta E}{kT}\right)},$$
(1)

where ar is the antenna → radical pair rate constant, but ra is the reverse rate constant, ∆E is the effective potential difference, V, T is absolute temperature (300 K in calculations), e is electron charge, C, and k is Bolzmann constant J K−1. Increasing ∆E shifts the radical pair equilibrium towards the antenna, reducing the probability of the radical pair state and increasing the hopping time of excitation in the antenna—with this rising the fluorescence yield. In the Fm state, the 0.05 V potential difference increased the ra rate constant to 42 ns−1.

Calculations were carried out with rate constants fitted to reproduce the excitation kinetics for three PSII states: open or the Fo state, QA reduced or the Ff state, and maximum fluorescence, Fm state (Fig. 8). In the panel, the ordinate scale unit directly shows the relative population of excited antennas and the photochemical quantum yield for open centers, but for fluorescence the antenna yield Fmax, 0.2 in absolute units, is set to 1.0. Thus, the yields Fo, Ff and Fm are shown as a fraction of the theoretically possible maximum Fmax—the condition when the radical pair state is not populated. The initial state for integration was set with excitation in the antenna, but QA oxidized, AeQo = 1 for the open state, and AeQr = 1 for the closed state. No more excitations were added during the excitation transfer process, while every open PSII proceeded through the states AeQo ↔ AgRQo → AgQr and every closed PSII proceeded through the states AeQr ↔ AgRQr ↔ AgQr. During the excitation transfer process, the running probability for fluorescence emission from the antenna was integrated with an aim to obtain the total fluorescence yield.

Fig. 8
figure 8

Calculated time curves for excitation transfer for the three characteristic cases: open centers (blue lines), QA reduced centers (green lines) and membrane energized (QA + QB reduced, red lines). Initially, antenna was excited in all centers (AeQo = 1), double-exponentially declining lines show the decay of antenna excitation; exponentially increasing is integrated fluorescence—for fluorescence the ordinate unit is yield from the antenna (20% absolute). For open centers, the photochemical yield 0.66 is calculated as the accumulating AgQr (QA reduced) fraction. For open centers, ∆E was 0, but increased as shown for QA reduced (Ff fluorescence) and QA + QB reduced (membrane energized, Fm fluorescence) centers. For clarity panel B shows the initial 2 ns

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Navy blue curves in Fig. 8 indicate the open state. The fast-decaying dual-exponential curve shows how the excitation leaves the antenna. The rapidly increasing and then decaying curve, proceeding through the maximum of 0.25, shows population of the radical pair (initial 2 ns are enlarged in Fig. 8b). The upper curve saturating at 0.66 shows the time course of electron transfer to QA, but the lower curve saturating at 0.07 shows the fraction of excitations emitted as Fo fluorescence—in relation to the antenna yield of 0.2.

When the closed centers were calculated with ∆E = 0 as the open centers were done, the Ff/Fo ratio of 3.7 was not obtained, but ∆E = 0.02 V had to be assumed to reproduce the necessary Ff/Fo ratio (green curves). In this Ff state, excitation still rapidly equilibrates with the radical pair (initial fast decay of the antenna excitation), but the equilibrated state decays more slowly than with open centers. At its maximum, the radical pair state was populated in 0.25 of all PSII units.

To reach the Fm fluorescence yield, ∆E = 0.05 V had to be assumed with closed centers (red curves). The initial equilibration between the antenna and the radical pair was as fast as in the Ff state, but the maximum population of the radical pair was only 0.12. In this state, the fluorescence yield approached 0.5 of the antenna yield Fmax—meaning that in the Fm state, the radical pair still quenched a significant part of excitations. The bi-exponential character of antenna excitation decay was still pronounced in the Fm state, though the amplitude of the fastest component was smaller than in the Fo and Ff states.

Discussion

Nature of the electric field

We showed that during a low to high light induction transient in sunflower leaves, Chl fluorescence of closed PSII units initially adjusted on a Ff yield at Ff/Fo = 3.7, but later during the induction increased to the Fm yield at Fm/Fo = 6.7. The Ff fluorescence level is similar to the ST flash-induced fluorescence level, typically 0.5–0.7 Fm (Joliot and Joliot 1964, 1977, 1981; Neubauer and Schreiber 1987; Samson and Bruce 1996). Such variability of fluorescence in closed PII is explainable in the framework of the antenna-radical pair excitation equilibrium model, based on very fast excitation transfer through the antenna and fast primary charge separation in PSII center Chls (Schatz et al. 1988; Akhtar et al. 2017). In this model, the antenna/radical pair excitation equilibrium constant has been found to be dependent on the open or closed state of the center. The mechanistic background of this dependence has been suggested to be a conformational relaxation processes in the protein. Though structurally the cation may rapidly move only between two radical pair states—from the D1 accessory Chl to the PD1 Chl—four different radical pair (RP) states have been postulated, to best fit the multi-exponential fluorescence decay curves (Szczepaniak et al. 2009). In this work, we generalized the “conformational relaxations” under the term “electric field” exerting counter-pressure on separated charges—considering that the ultimate reason for any change in electron energy must be an electric field.

Molecular nature of changes in the electric field penetrating deeply into the PSII center may be complex. In the presence of the ionophore valinomycin, inhibiting specifically the formation of membrane voltages, the magnitude of the secondary, J–I phase of fluorescence induction, was clearly diminished or was fully suppressed. The field-induced variation of fluorescence yield resulted mainly from the rate constant of primary charge separation, and to a smaller extent from the rate constant of charge recombination. The authors concluded that the light-driven formation of the thylakoid-membrane voltage results in an increase of the chlorophyll excited-state lifetime, a phenomenon explainable by the electric-field-induced shift of the free-energy level of the primary radical pair (Dau and Sauer 1992; Pospíšil and Dau 2002). The term photoelectrochemical quenching of Chl fluorescence was introduced by Vredenberg et al. (2009) to characterize the slow induction of fluorescence in pea leaves and isolated chloroplasts under low light intensities. Properties of this retarded slow rise, mainly suppression by low concentration of protonophores and responsiveness to complementary single-turnover flash excitation, suggested that the fluorescence increase during a train of 60 flashes was caused by release of a photo-electrochemical type of quenching, controlled by the trans-thylakoid proton pump powered by the light-driven Q-cycle. This suggests that a significant component of the PSII internal field is the overlapping delocalized transmembrane field, generated by electrochemical activity of the Q-cycle and PSI (Junge and Witt 1968). This field is rapidly generated during the dark–light induction of photosynthesis, but decreases later as the field component of membrane energization is replaced by proton concentration difference (Cruz et al. 2001; Klughammer et al. 2013; Lyu and Lazár 2017a, 2017b).

According to this assumption, no high Fm/Fo ratio could be expected with isolated PSII particles unable to energize the membrane. The Ff/Fo ratio was only 3–4 indeed when QA was reduced in oxygen-evolving photosystem II particles from Synechococcus by sodium dithionite (Schatz et al. 1987). However, in similar experiments, but using DCMU instead of sodium dithionite, a high ratio Fm/Fo = 10 was obtained (Szczepaniak et al. 2009). Similarly, in untreated leaves the flash-induced fluorescence yield is normally about 0.6 Fm (Joliot and Joliot 1964, 1977, 1981; Neubauer and Schreiber 1987; Samson and Bruce 1996), but the flash-induced Ff closely approaches Fm in DCMU-treated leaves (Schreiber and Krieger 1996; Schansker et al. 2011; Laisk and Oja 2013). After being driven into the Fm state, when a sunflower, pea or tobacco leaf was exposed to darkness during a few seconds, the florescence yield declined to a value of 2Fo, but just one charge transfer was needed to return it to the Fm state again (Schansker et al. 2011; Laisk et al. 2015). This showed that while QA and QB both were reduced, QA could be oxidized in the dark, leaving QB occupied by PQH2. Illumination of the leaf in this state was equivalent to the illumination of a DCMU-treated leaf, but PQH2 occupying the QB site. As no membrane energization could be assumed in the PSII particles or DCMU-treated leaves, it suggests that the fluorescence yield of QA-reduced centers depends on the occupation of QB. The ST flash-induced fluorescence yield Ff is low when the flash is applied on open PSII—i.e. QA becomes reduced, though electron transport to QB is possible, but it did not occur yet. When electron transport from QA to QB is impossible—the QB site is occupied either by a plastoquinol or DCMU—then the transfer of just one electron is enough to reach the state close to Fm either in leaves (Schansker et al. 2011; Laisk and Oja 2013) or in PSII particles (Szczepaniak et al. 2009). Though the repulsive electric field is the ultimate intrinsic reason causing variations in the antenna/radical pair equilibrium, the field may be enhanced by the delocalized transmembrane field, or it may be reconfigured by the occupation of the QB-binding site—whether electron transfer from QA to QB is possible or is not possible (Prášil et al. 2018).

Interestingly, a stepwise increase of fluorescence in response to a train of ST flashes was recently detected in DCMU-inhibited PSII core complexes isolated from Thermosynechococcus vulcanus (Sipka et al. 2019). High Chl fluorescence with the maximum Fv/Fm parameter 0.85 could only be induced by a train of the flashes. As no PSI and Q-cycle activity was present in the isolated PSII core complexes, membrane energization did not occur—unless PSII itself was electrochemically active (Laisk et al. 2015). Or more likely, in the isolated complexes PQH2 could spread within a membrane volume before it significantly accumulated in the QB sites.

Amplitude of Fm/Fo

The model defines two extreme values of the fluorescence yield: the minimum is Fo, emitted by excitation in the antenna, reversibly equilibrated with the radical pair state while the latter is quenched by photochemical charge transfer and non-radiative recombination. The theoretical maximum is the antenna fluorescence Fmax—when the repulsive electric field is so strong that the radical pair practically cannot exist. Experimental cases may cover the span between these extremes. Our model placed the Fm fluorescence yield at a half-way between Fo and the antenna yield of 0.2, normalized to unity in Fig. 8.

The rate constants for our model were chosen by fitting the integral fluorescence yields Fo, Ff and Fm and considering the measured quantum yield of PSII photochemistry, as described in the Model section. Though the fluorescence decay curves were not available for our leaves, nevertheless our rate constants are close to those derived from time-resolved measurements for wild-type arabidopsis (Lambrev et al. 2012), though still somewhat faster—it was necessary to fit the low Fo yield. The position of Fm between Fo and Fmax was determined considering reported fluorescence lifetimes. A typical fluorescence lifetime in isolated light-harvesting antenna complexes is 3.5 ns (Pascal et al. 2005; Gruber et al. 2015). In leaves, the average lifetime in the Fm state does not exceed 2 ns (Belgio et al. 2012), reported to be 1.3 ns in Arabidopsis (Holzwarth et al. 2009), 0.9 ns in maize (Chukhutsina et al. 2019) or 0.7 ns in thylakoid membranes (Farooq et al. 1918). This quite clearly shows that in the Fm state, the radical pair is not completely gated for the entrance of excitation, but the Fm fluorescence is still significantly quenched by non-radiative recombination within the radical pair. The conclusion is confirmed by fluorescence decay curves. Our modelled decay curves were multi-exponential when the radical pair was populated, but termination of excitation in the antenna—the Fmax level—was described by a single rate constant, as experimentally confirmed in an individual LHCII (Gruber et al. 2015) and LHCII trimers (Pascal et al. 2005). In accordance with this, our model reproduced a single exponent for the Fmax state, but at the Fm state the modeled decay curves still remained bi-exponential.

Relationship between Chl fluorescence and photochemistry

Fluorescence has been found to be a convenient signal, proportional to light energy not used by photosynthesis. A wide-spread understanding of fluorescence is based on a simple model, assuming that several processes are simultaneously competing to terminate (quench) an excitation. The corresponding formula for fluorescence yield F is

$${F}_{\text{o}}=\frac{{k}_{\text{f}}}{\left({k}_{\text{f}}+{k}_{\text{d}}+{k}_{\text{p}}\right)}$$
(2)

where k are the competing rate constants with subscripts f for fluorescence emission, d for thermal dissipation and p for the photochemical process. Fluorescence yield is minimal, Fo, when all the competitive quenchers are active, but the yield is much higher, Fm, when photochemistry is blocked (kp = 0). Considering that the yield of photochemistry is expressed as

$${Y}_{\text{p}}=\frac{{k}_{\text{p}}}{\left({k}_{\text{f}}+{k}_{\text{d}}+{k}_{\text{p}}\right)},$$
(3)

the following equation relating the photochemical yield Yp to the measurable fluorescence yields was derived (Genty et al. 1989)

$${Y}_{\text{p}}=\frac{{F}_{m}-{F}_{\text{o}}}{{F}_{m}}.$$
(4)

Inserting the calculated Fo and Fm (Fig. 8) into Eq. (4) we obtain the photochemical yield Yp = 0.85, which is by far higher than the model/calculated yield 0.66. Using the flash-induced Ff instead of Fm in Eq. (4), the yield would be Yp = 0.72.

These yield calculations assume that the dissipative quenchers kd are constantly present, independent of the presence or absence of photochemistry, kp. Experimentally, the Fm yield is determined after all PSII centers are closed due to complete reduction of the whole electron transport chain under a strong “saturation” light pulse, but Fo is determined either in the dark or under very low light—generally, under conditions facilitating complete oxidation of the PSII electron acceptors, including QB. Our present results show that the photochemical act takes place in the state when fluorescence of closed centers is much lower than in the final Fm state. The flash-induced Ff is closer to the fluorescence of closed centers at the moment of electron transfer to QA, but even it may be somewhat overestimated: we needed to assume an additional membrane voltage of 0.02 V in order to model the measured Ff/Fo ratio. For this same reason, Eq. (4) resulted in the quantum yield of 0.72 when Ff was inserted, but not 0.66 as calculated from the model.

In leaves, the total quantum yield of photosynthesis has been reported to be 0.106 O2 evolved per photon absorbed (Ehleringer and Björkman 1977), but this does not characterize the PSII yield, as partitioning of excitation between PSII and PSI was not known. The usually assumed even partitioning would mean 0.212 O2 or 0.85 electrons transferred per PSII photon. A more detailed spectral study of the quantum yields of PSII and PSI together with excitation partitioning between the photosystems in sunflower leaves (Laisk et al. 2014) revealed the global yield of the two photosystems of 0.72 in the red part of spectrum. After the yields were partitioned, the PSI yield yI = 0.88, but unexpectedly this photosystem absorbed only about 1/3 of all quanta; consequently, about 2/3 of the quanta were absorbed by PSII, but processed with the low intrinsic yield yII = 0.63. Such a low PSII quantum yield was incompatible with the high (Fm – Fo)/Fm value in these same sunflower leaves, but is consistent with the present notion that excitation is additionally lost in the state of the Pheo−P680+ radical pair, which can be non-radiatively recombined before the electron is transferred to QA. In our model, the rate constants were chosen considering this relatively low-PSII photochemical yield.

Concluding this section, the common fluorescence-based calculations of the quantum yield of PSII photochemistry overestimate the PSII quantum yield for two reasons. First, excitation is competitively quenched not only in the antenna but also in the radical pair, not observable in fluorescence. Second, Fm is significantly overestimated when measured in the state of the maximum membrane voltage—just after the whole electron transport chain became reduced. Though not fully correct, but a better approximation would be to use the flash-induced Ff value instead of Fm, as the former is less overestimated than the latter.

General conclusions

The antenna/radical pair equilibrium theory predicts that fluorescence yield of a closed (acceptor reduced) photochemical center may vary dependent on energetic depth of the radical pair trap and on probability for non-radiative recombination of the radical pair. A spectacular example of the deep radical pair trap is photosystem I, where the trapped excitation returns to the antenna with a very low probability, even if further electron transport is blocked by a reduced acceptor (Croce et al. 2000; Gobets and van Grondelle 2001). For example, in sunflower leaves, the room-temperature 750 nm fluorescence yield from PSI was found to be 37% of Fo (Peterson et al. 2014), not variable over the whole induction trace, during which P700 transiently became oxidized and finally reduced again. This result is consistent with the model proposed by (Holzwarth et al. 2006), assuming the “accessory” Chl is the primary electron donor, but not P700.

In PSII the relaxed Pheo−P680+ radical pair is shallow, in open centers resulting in about double higher Fo than in PSI. In leaves, the entropic force of the large antenna contributes, resulting in even, 1:1 equilibration of excitation between the antenna and the radical pair. Thanks to the shallow trap, a low additional electric field of 0.05 V increases the fluorescence yield of closed reaction centers more than two times, efficiently converting the trap into a small bump.

The central notion from this work is the cooperative allosteric effect between PSII: after an electron has been carried through the membrane in a local PSII center, a delocalized cooperative force is generated, counteracting the presence of the primary radical pair in adjacent centers. As discussed above, the intrinsic nature of the force is electric field anyway, but its origin may be related just to reorganization of the PSII internal field dependent on the occupation of the QB site, or the effect may be more complex, involving a component exerted by delocalized transmembrane electric field—termed membrane energization (Bulychev and Vredenberg 1999). The high fluorescence of DCMU-poisoned samples speaks for the internal, protein conformation relaxation, but systematic studies (Dau and Sauer 1992; Pospíšil and Dau 2002; Vredenberg et al. 2009), emphasizing the role of membrane energization, cannot be ignored. The cooperative character of the delocalized transmembrane field is easily understandable. Plastoquinol also acts cooperatively, because PQH2 generated by still open centers may bind into the QB pockets of adjacent centers—particularly well if PQH2 has strong product-inhibitory affinity to the QB pocket (Laisk and Oja 2018). But the problem is, can an electron transfer from Pheo− to QA—what happens during a ST flash in a PSII center—allosterically influence the internal electric field within adjacent PSII centers?

Though the intrinsic mechanism may need elaboration, we have experimentally shown that fluorescence yield of closed PSII centers does increase during a low to high light induction—while the membrane gets energized and the plastoquinone pool gets reduced. During the very initial part of the induction, while electrons were transferred within the PSII, our data showed a constant fluorescence yield, similar to the post-flash fluorescence yield Ff. As our induction traces were started not from the dark but from a low light intensity (in order to randomize the S-states), the whole electron transport chain was already energized—to the extent necessary to support ATP synthesis at the low rate. Therefore, our data do not cover the completely de-energized state, comparable to the time-resolved fluorescence experiments. For understanding of the PSII electron transport process it would be necessary to know, is there a cooperative influence between PSII when electrons are moved only within the center? The term “protein conformational relaxation processes” (Szczepaniak et al. 2009) may have a wider content than temporal reorganization of protein conformation within a PSII center, proceeding simultaneously with Chl excitation decay.