Mathematical review of literature to assess alternative electron transports and interphotosystem excitation partitioning of steady-state C3 photosynthesis under limiting light


Xinyou Yin. Fax: +31 317 485572; e-mail:


Linear whole-chain electron (e) transport plays a dominant role in generating NADPH and ATP required for carbon fixation in chloroplasts. However, other e pathways may be present to contribute to the flexibility of e transport in meeting demands by various downstream metabolic processes. The estimation of the fluxes of these alternative pathways in vivo is difficult, as they are not amenable to direct experimental measurement. A recently developed model based on the generalized stoichiometry for the chloroplast e transport pathways makes it possible to indirectly but quantitatively assess the fractions of e that follow the alternative pathways. This model approach is used to review data from the literature on concurrent measurements of gas exchange and chlorophyll (Chl) fluorescence under steady-state, limiting light, non-photorespiratory conditions. The review suggests possible in vivo occurrence of cyclic e transport (CET) under such conditions. About 10% of e from the reduced ferredoxin follow the pseudocyclic mode, notably in support of nitrate reduction. The estimated fraction of e from the reduced plastoquinone that follows the Q-cycle ( fQ) depends on the number of protons required per ATP synthesis. Our model approach also allows the excitation partitioning to photosystem II (PSII) to be assessed quantitatively. Most important, the model helps assess the limit value to uncertain physiological parameters and answer the ‘what-if’ question with regard to the effect of non-measured processes or measurement uncertainties on the estimations of alternative e transports.


The thylakoid electron (e) transport chain in plant chloroplasts is pivotal in coordinating the fluctuating supply of absorbed light energy with the varying demands of the photosynthetic metabolism. Different metabolic processes have different requirements for ATP and reductant (either NADPH or reduced ferredoxin). Similarly, different e transport processes generate ATP and reductant in different ratios. To synthesize ATP and reductant at the correct rate and proportion, the thylakoid reaction must coordinate the activities of various e transport processes.

The classical ‘Z scheme’ for e transport (Hill & Bendall 1960) can accommodate linear, cyclic and pseudocyclic reactions (Fig. 1). Following Farquhar & von Caemmerer (1982), we refer to the linear e transport (LET) as the reaction chain from H2O to ferredoxin and then to NADP+ that generates NADPH and ATP for carbon reduction or photorespiration, and to the pseudocyclic e transport (PET) as all non-cyclic e fluxes supporting direct O2 reduction and quantitatively minor metabolic processes in the chloroplast and possibly the cytosol (i.e. other than carbon reduction or photorespiration). Both LET and PET require photosystem I (PSI) and photosystem II (PSII). In contrast, cyclic e transport (CET) only involves PSI. LET produces O2; PET may or may not produce O2, whereas CET does not involve any gas exchange.

Figure 1.

The ‘Z scheme’ for photosynthetic light reactions showing linear and alternative (i.e. cyclic and pseudocyclic) e transport along the chain. From reduced ferredoxin, a fraction of e follows the cyclic mode ( fcyc) around photosystem I (PSI). Another fraction of e that have passed PSI, either from PSI directly or from the reduced ferredoxin, follows the pseudocyclic mode ( fpseudo) for supporting the water-water cycle (WWC), or nitrate reduction, or other minor metabolic processes (see text). The remaining fraction (1 − fcyc − fpseudo), is transferred to NADP+– the end acceptor of the linear e transport (LET) for generating NADPH in support of CO2 reduction or photorespiration. The efficiency of ATP synthesis along the e transfer chain depends on the operation of the Q-cycle. The scheme assumes that a fraction of e from the reduced plastoquinone follows the Q-cycle ( fQ), and a remaining fraction (1 − fQ) is transferred directly towards the plastocyanin. ADP, adenosine diphosphate; Chl, chlorophyll; Chl*, the excited state of Chl; hv, light photon absorbed either by PSI or by photosystem II (PSII); Pi, inorganic phosphate.

CET is easily detected in isolated chloroplasts (Arnon 1959) or in vivo during the induction period (e.g. when dark-adapted leaves are first illuminated) (Holtgrefe et al. 2003; Joliot & Joliot 2005). Participation of CET in ATP synthesis in green algae, cyanobacteria and in C4 bundle sheath chloroplasts is well recognized. For C3 vascular plants, CET (if any) has been supposed to play a role under stress or at high light, as there is coincidence in the cyclic rate and the level of non-photochemical quenching (Johnson 2005; Miyake et al. 2005). During steady-state, non-stress conditions, CET has only infrequently been identified in C3 leaves (Harbinson & Foyer 1991). When quantum efficiencies of PSI and PSII are measured in leaves under steady-state conditions, they both change in parallel with varying irradiance or CO2 concentration (Genty & Harbinson 1996), supporting that CET either does not occur, or occurs at a fixed percentage of LET. Recent work using Arabidopsis mutants that appear to lack CET (Munekage et al. 2002, 2004) provides experimental evidence supporting its occurrence in vivo (Allen 2002, 2003; Johnson 2005).

Of the processes supported by PET, the most important ones in mature leaves are direct O2 reduction and nitrate or nitrite reduction (Fig. 1). The reduction of O2 by PSI is the start of the Mehler ascorbate–peroxidase pathway, which Asada (1999) called the water-water cycle (WWC). O2 can also be reduced by other components of the stroma, such as reduced thioredoxin or flavonoid groups, thus further feeding WWC (Robinson 1988). The complete WWC consumes NADPH but not ATP (Asada 1999; Ort & Baker 2002). The first step of nitrate reduction (i.e. from nitrate to nitrite) takes place in the cytosol; this step, however, may use reducing power that is generated in the chloroplast but exported to the cytosol (Gray & Cresswell 1984; Backhausen et al. 2000). Further reduction of nitrite occurs in the stroma, is driven by reduced ferredoxin and requires only small amounts of ATP for its inclusion into organic backbones (Noctor & Foyer 1998). In addition to O2 reduction and nitrate reduction, there are other minor alternative e acceptors (e.g. sulphate reductase and fatty acid biosynthesis). The reductant formed by the e transport chain can be exported to the cytosol via the malate–oxaloacetate shuttle, a process that uses NADPH but not ATP. Because of the lack of (or little) requirement for ATP, the proton (H+)-pumping activity associated with WWC, nitrate reduction and the malate–oxaloacetate shuttle will either result in a decreasing intrathylakoid pH (Genty & Harbinson 1996; Avenson et al. 2005) or will drive the synthesis of ATP for other processes. This feature has implications for the overall balance between the H+ and e fluxes of the thylakoid (Kramer & Crofts 1993; Avenson et al. 2005), and for this reason, the fluxes associated with these processes will be combined as PET. Whether PET is associated with net gas exchange or not depends on the processes that it supports. In case of WWC, there is no net gas exchange (Asada 1999). For nitrate reduction or other minor processes, PET results in some O2 evolution (Noctor & Foyer 1998).

All LET, PET and CET are likely at work in vivo to tune the ATP:NADPH ratio required by downstream metabolism (Allen 2003). The dominant metabolic processes are carboxylation or oxygenation of RuBP, which require similar amounts of ATP and NADPH. So, if the stoichiometries of H+ transfer per e, and of H+ required per ATP synthesized, are known, it should be easy to estimate to what extent LET can support carboxylation and oxygenation, and thus to what extent other e transport processes would be necessary. However, even this apparently simple question is fraught with difficulties, because of the following uncertainties.

One uncertainty related to the Z scheme is the efficiency of H+ transfer by the cytochrome b6 f complex, depending on whether the Q-cycle operates or not (Sacksteder et al. 2000). The Q-cycle refers to a mechanism for H+ translocation through the chloroplast cytochrome b6 f complex and its mitochondrial counterpart (the cytochrome bc1 complex) (Hauska, Schütz & Büttner 1996). The Q-cycle effectively doubles the stoichiometry of H+ transport through the cytochrome b6 f complex from 1H+ to 2H+ per e transferred from PSII to PSI (Kramer & Crofts 1993; Allen 2003). Another uncertainty is the number of H+ transported per ATP produced by the thylakoid ATPase [i.e. the H+ : ATP ratio (termed h hereafter)]. The two commonly used values for h are 3 and 4 (von Caemmerer 2000); smaller values have also been suggested (Bell 1985). Allen (2002, 2003) and Joliot & Joliot (2002) indicate that h is probably 14/3, on the basis of the structural data of Seelert et al. (2000) that the H+-driven turbine of the chloroplast ATPase has 14 subunits instead of the expected 12. If LET functions alone, high values for h (i.e. 4 or 14/3) require running the Q-cycle. However, one may question the necessity of the full operation of the Q-cycle for yielding the NADPH : ATP ratio required by photosynthetic metabolism if PET or CET occurs.

A problem for the occurrence of large alternative e fluxes is that the measured quantum efficiency of CO2 fixation (inline image) or O2 evolution (inline image) under non-photorespiratory conditions (e.g. Evans 1987) is close to the theoretical maximum of 0.125 (Genty & Harbinson 1996). This upper efficiency presumes that all absorbed quanta are used with 100% efficiency to drive only LET, and that no processes other than CO2 reduction occur. However, many leaves have non-photosynthetic blue-light absorbing pigments (McCree 1972; Inada 1976); the action spectra of PSI and PSII are different (Evans 1987); neither photosystem works with 100% quantum efficiency (Trissl & Lavergne 1995), and other metabolic sinks for reducing power are present. So, data in which inline image or inline image is below 0.125 may not indicate the occurrence of CET.

Some alternative pathways cannot be measured directly, because cyclic processes (CET or WWC), by their nature, do not involve a net flux (Johnson 2005). Identifying CET indirectly, on the basis of differences between PSI and PSII e fluxes, is also difficult. The biophysical techniques used to measure the quantum efficiencies of both photosystems have calibration problems which make it difficult to convert measured quantum efficiencies into absolute e transport rates (e.g. Trissl & Lavergne 1995; Kingston-Smith et al. 1997). Measurement of e fluxes to other alternative e sinks (e.g. nitrate) presents technical problems. Therefore, developing an approach based on a mathematical model to indirectly assess various photosynthetic e transport pathways is useful. It will highlight experimental deficiencies and allow the assessment of how certain assumptions would affect the operation of e transports.

The steady-state C3 photosynthesis model of Farquhar, von Caemmerer & Berry (1980) has been widely used to evaluate if there is any PET, using the data of combined measurements of gas exchange and chlorophyll (Chl) fluorescence (e.g. Ruuska et al. 2000; Makino, Miyake & Yokota 2002; Long & Bernacchi 2003). In this model, two forms of the equation for e transport-limited carboxylation coexist: C/(4C + 8Γ*) and C/(4.5C + 10.5Γ*) in mol CO2 per mol whole-chain e (where C is the chloroplast CO2 concentration, and Γ* is the CO2 compensation point in the absence of mitochondrial respiration). The estimated PET depends on which equation form is chosen, but the choice of the equation, so far, seems largely arbitrary. Moreover, the model ignores (1) any PSI-mediated CET and (2) a difference in e transport efficiency between PSI and PSII, as shown by many studies (e.g. Harbinson & Foyer 1991). Thus, the model is unable to straightforwardly assess the activities of alternative e flow pathways, CET in particular. The model also does not directly consider uncertainties with respect to the Q-cycle and the H+ : ATP ratio (fixing h at 3).

Recently, the model of Farquhar et al. (1980) for e transport-limited photosynthesis has been extended for a generalized stoichiometry, which considers LET, CET and PET, as well as the difference in PSI and PSII e transport efficiency and the uncertainty with regard to the Q-cycle activity (Yin, van Oijen & Schapendonk 2004; cf. Appendix for its basic equations). Here, this extended model is used as a reviewing tool to quantitatively assess fractions of CET, PET and the Q-cycle under limiting light. Because the operation of CET requires more quanta that are distributed to PSI relative to that in the absence of CET (Albertsson 2001), we also assess the excitation distribution between the two photosystems. All the analyses are based on combined data of gas exchange and PSII e transport efficiency derived from Chl fluorescence measurements obtained from literature. We will first discuss potential pitfalls in using such combined data in the physiological interpretation of photosynthesis studies.

Use of gas exchange and Chl fluorescence measurements at limiting light

As will be shown later, using the model of Yin et al. (2004) to assess alternative e fluxes under limiting light conditions requires combined information for maximum quantum efficiency of CO2 fixation (inline image) or O2 evolution (inline image), and maximum quantum efficiency of e transport for each of two photosystems.

Within the range of limiting irradiance (for a typical crop plant, this will be up to about 100 µmol m−2 s−1), the rate of photosynthetic assimilation increases linearly with increasing light intensity (e.g. Björkman & Demmig 1987; Evans 1987; Long, Postl & Bolhár-Nordenkampf 1993). The value of inline image or inline image can thus be determined as the slope of the plot of net gas exchange rate against absorbed-light intensity over the linear range, assuming that variation of mitochondrial respiration in the light, if any, does not occur over that range (i.e. no Kok effect) (Sharp, Matthews & Boyer 1984), and provided that there is no light absorption by non-photosynthetic pigments.

e transport efficiency of PSII has often been revealed by Chl fluorescence measurements. When the leaf sample is in the dark-adapted state, Fo (the minimum fluorescence when all PSII reaction centres are assumed open) and Fm (the maximum fluorescence in saturating excitation light when closure of PSII reaction centres is maximal) are determined. The quantity (1 − Fo/Fm) is a measure of the relative maximum PSII quantum efficiency of a given sample (Butler 1978). A similar quantity for the light-adapted samples – known as the Genty method, gives a measure of the relative PSII quantum efficiency at a given light level (Genty, Briantais & Baker 1989). However, these measurements need to be used with care. Firstly, the term ‘relative’ is emphasized because the measure of quantum efficiency of PSII obtained from fluorescence measurements does not give the real PSII quantum yield. We will use inline image to denote the PSII quantum efficiency estimated via the Genty method and inline image to denote the real efficiency of PSII. Secondly, when measured over a wide range of irradiances, the relationship between inline image and inline image or inline image can be non-linear (Seaton & Walker 1990; Schreiber et al. 1995), in contrast with the linear correlation between inline image and inline image measured using mass spectrophotometric techniques (Genty et al. 1992). Thirdly, the inline image obtained from a dark-adapted leaf (i.e. 1 − Fo/Fm) – which we denote as inline image, may be higher than the inline image measured under strictly limiting light –inline image (Harbinson, Genty & Baker 1989).

Similar arguments apply to assessing the real PSI quantum efficiency (inline image). Biophysical measurement using the 820 nm technique (inline image) yields only a relative measure of inline image. inline image is sometimes observed to decrease non-linearly with inline image or inline image, especially at low irradiances (Harbinson et al. 1989; Harbinson, Genty & Baker 1990). Further, the inline image under limiting light may not be the same as the dark-adapted inline image.

When data of gas exchange and biophysical measurements (typically Chl fluorescence) are combined, the analyses implicitly assume that the chloroplasts that are subsampled by fluorescence are quantitatively representative of those functioning to produce CO2 fixation. This assumption may not be correct in all cases, because the measuring beam that is used to excite Chl fluorescence may quantitatively be exciting a population of chloroplasts different from that excited by the actinic light used to drive CO2 fixation or O2 evolution. These differences will occur with depth in the leaf (Kingston-Smith et al. 1997). They could also be significant if fluorescence is being measured from only a small part of a leaf with laterally heterogeneous gas exchange.

In spite of these problems, combined measurements of gas exchange and Chl fluorescence have been used routinely (Long & Bernacchi 2003), for example, to estimate the CO2/O2 specificity of Rubisco (Peterson 1989), the mesophyll diffusion conductance to CO2 (Evans & von Caemmerer 1996; Bernacchi et al. 2002) or for estimation of e flow to alternative e sinks (Laisk & Loreto 1996; Makino et al. 2002). The combined data of this kind, if carefully measured and with awareness of the assumptions and pitfalls, can be valuable in analyzing the operation and regulation of photosynthesis. Some non-linear correlations between inline image and other parameters should not be used to cast doubt upon the general validity of the Genty equation.


Estimating the fractions of cyclic and pseudocyclic e pathways

Following a common assumption (e.g. Laisk et al. 2002) that WWC is negligible under limiting light, we will initially presume that nitrate reduction is the major PET-mediated pathway for this condition. Because the assimilation of nitrate in many species occurs predominately in the leaves, this process will often take place simultaneously with CO2 fixation in photosynthetic cells (Bell 1985; Noctor & Foyer 1998). If plants are deprived of CO2, N assimilation ceases (Kaiser & Förster 1989), indicating a tight coordination of carbon and N assimilation.

Overall, reduction of 1 mol nitrate to glutamate requires 10 and 1 mol e and ATP, respectively (Noctor & Foyer 1998), thus, 2.5 times as many e but only 0.33 times as much ATP as the reduction of 1 mol CO2 requires. Assuming that (1) the first step of nitrate reduction (i.e. the conversion from nitrate to nitrite in the cytosol) consumes reducing power generated in the chloroplast and (2) the small ATP requirement by nitrate reduction can be met by other processes such as mitochondrial respiration, the partitioning of e to support nitrate reduction and CO2 fixation must meet the relation

fpseudo/(1 − fcyc − fpseudo) = 2.5x(1)

where x is the ratio of the rate of nitrate assimilation to the rate of CO2 carboxylation (including photorespiration), fcyc and fpseudo are the fractions of e at ferredoxin that follow the cyclic and pseudocyclic mode, respectively, and 1 − fcyc − fpseudo is therefore the fraction of e that goes to NADP+ to produce the NADPH utilized by the Benson–Calvin cycle and photorespiration (Fig. 1).

From Eqns A1, A3 and A4 of the model in Appendix, the maximum quantum efficiency for CO2 assimilation under limiting light can be derived as


where inline image and inline image are the real quantum efficiencies of e transport of PSI and of PSII, respectively, under limiting light, on the basis of light absorbed by each photosystem alone. An implication of Eqn 2 is that if inline image does not vary proportionally with inline image, the relationship between inline image and inline image is not entirely linear, as shown by the curve in Fig. 2 for the case in which there is neither photorespiration nor alternative e transport. When C and Γ* are known, fcyc and fpseudo can be solved simultaneously from Eqns 1 and 2 as

Figure 2.

The relationships between maximum photosynthetic quantum efficiency and the efficiency of photosystem II (PSII) e transport under limiting light (indicated by the Genty method for dark-adapted leaves –inline image), as predicted by Eqn 2 (assuming inline image = inline image) in the absence of photorespiration and alternative e transport (curve), or measured for 11 species tested by Long, Postl & Bolhár-Nordenkampf (1993) in which photosynthetic quantum efficiency is given in terms of CO2 uptake –inline image (closed circles), or measured for 37 species by Björkman & Demmig (1987) in which photosynthetic quantum efficiency is given in O2 evolution –inline image (open circles). The dotted lines indicate the position at the average inline image, at which the predicted inline image is about 0.114. The theoretical inline image or inline image in the absence of both photorespiration and alternative e transport can be predicted as 0.125 if inline image has an absolute efficiency of 1. Only 10 points are visible for the data of Long et al. (1993), because measured inline image and inline image were the same for two species (also for Figs 3 & 4).


We will first use these equations to review the data of Long et al. (1993) for 11 species of C3 vascular plants of diverse taxa, habitat and form, obtained under non-photorespiratory condition ([O2] = 10 mmol mol−1), for which Γ- can be considered to equal 0. We will employ the widely used assumption that inline image = inline image. Values of inline image (assessed at 695 nm) in the data set of Long et al. (1993) had a quite stable value among the species – about 0.838 (Fig. 2), reflecting a fundamental similarity between different species in the basic organization and operation of the PSII primary processes. The PSI efficiency was not measured by Long et al. (1993), but the efficiency of charge separation by PSI is very high, and thus inline image is believed to be at least 0.95 (Trissl & Wilhelm 1993). In our analysis, inline image is provisionally set to 1. With this inline image, Eqn 2 predicts that the inline image in the absence of both CET and PET is 0.838/[4 × (0.838/1 + 1)] = 0.114 under non-photorespiratory conditions (Fig. 2). Note that this value is lower than 0.125 – the theoretical upper limit in the absence of both CET and PET if both PSI and PSII had an absolute efficiency of 1. The mean inline image measured by Long et al. (1993) was 0.093 – about 18% lower than our estimate at 0.114.

The value of x is not certain (possibly depending on species, nutrient supply and growth stage) but is typically about 0.05–0.10 in higher plants (Bell 1985; Noctor & Foyer 1998). Assuming x = 0.05, the calculated fcyc using Eqn 3 for the 11 species of Long et al. (1993) varied from 0.080 to 0.229, with a mean of 0.154. Because inline image was very stable, the estimated fcyc was almost exclusively dependent on inline image (Fig. 3). Given the fixed x (0.05), the estimated fpseudo using Eqn 4 varied much less, from 0.086 to 0.102 with a mean of 0.094 (Fig. 3); this is not surprising as at this point, the model limits fpseudo to the flux that supports nitrate reduction.

Figure 3.

Fractions of e transport at ferredoxin that follow the cyclic ( fcyc, open circles) and pseudocyclic ( fpseudo, open squares) modes estimated by Eqns 3 and 4, respectively, assuming the ratio of N to carbon assimilation is 0.05, and the 10 mol e required per mol N reduction all come from the light reaction in the chloroplast (see text), plotted against quantum efficiency of CO2 assimilation (inline image) in the 11 species tested by Long, Postl & Bolhár-Nordenkampf (1993). The filled squares represent the estimated fpseudo by solving Eqn 2 assuming the absence of cyclic flow. The curves were drawn according to the model, assuming that the efficiency of PSII e transport under limiting light (represented by the Genty method for dark-adapted leaves –inline image) is equal to the average value of the 11 species. Because inline image was conservative across the species, points for calculated fcyc and fpseudo are very close to the corresponding curves, indicating that calculated fractions of alternative e flows were almost exclusively dependent on the value of inline image.

If x is set to 0.10, the calculated fcyc had a negative value in 9 out of the 11 species (results not shown), indicating that x cannot be as high as 0.10. A negative CET is a physiological impossibility, but its occurrence as a mathematical solution implies that e transport is not sufficient to account for the rate of CO2 fixation combined with the demand for a reductant to support nitrate reduction. This is because if x is fixed ( fpseudo is also largely fixed), only CET will function as a ‘brake’ for LET, so a deficit of reducing power will result in a ‘negative brake’. Assuming an absence of CET (fcyc = 0), the maximum fpseudo (allowing in this case the rate of PET in support of nitrate reduction to increase to accommodate the imbalance between LET and the demands of CO2 fixation) can then be solved from Eqn 2, and its estimated value varied from 0.145 to 0.217 with a mean of 0.180 (Fig. 3). The resultant x in this case, estimated from Eqn 1, ranged from 0.068 to 0.111 with a mean of 0.087. Although physiologically, the increase in fpseudo is unlikely to be accounted for by an increase in nitrate reduction alone, these estimated fpseudo for nitrate reduction and x agree well with the expected range, casting doubt on the necessity of CET at limiting light.

In a second analysis, we reviewed the comprehensive data of Björkman & Demmig (1987) for 37 C3 species, where the maximum photosynthetic quantum efficiency was measured in inline image. Measurements were made in an air of 5% CO2 that effectively prevented photorespiration, and with the quartz-iodide light source – the same as used by Long et al. (1993) so that any influence of light wavelength on quantum efficiency (Evans 1987) is not relevant in our comparative analysis of the two data sets. The measured mean inline image (assessed at 692 nm) was 0.832, very similar to 0.838 – the mean inline image for the 11 species tested by Long et al. (1993). However, the mean inline image that was measured by Björkman & Demmig (1987) was 0.106, approximately 12% higher than the mean inline image (0.093) that was determined by Long et al. (1993) (Fig. 2). Because the two studies used different species, the possibility of taxonomic differences cannot be ruled out, but this seems unlikely, given the broad diversity of taxa used in the two studies. Long et al. (1993) showed that measured inline image and inline image was significantly different (P < 0.01). A higher inline image than inline image suggests the PET fluxes in support of processes rather than WWC, as both LET and non-WWC-mediated PET lead to O2 evolution. The equation for fcyc for this case can be derived from Eqn 2 by replacing inline image by inline image and setting fpseudo at 0 as if non-WWC PET fluxes were also transferred in support of CO2 carboxylation, that is,


The value for fcyc can then be solved as an equation equivalent to Eqn 3 with x = 0:


Again assuming that inline image = inline image and inline image = 1, the calculated fcyc with Eqn 6 was almost exclusively dependent on inline image (results not shown). Among the 37 species, four had a negative small fcyc (corresponding to those four points above the theoretical curve in Fig. 2). For the other 33 species, estimated fcyc ranged evenly from 0.04 to 0.31. The mean fcyc for all 37 species was 0.131, close to 0.154 – the mean fcyc earlier estimated from the data of Long et al. (1993) assuming x = 0.05. Given the calculated fcyc, fpseudo can be solved from Eqn 1, again assuming that nitrate reduction was the only sink of PET. The estimated fpseudo assuming x = 0.05 ranged evenly from 0.077 to 0.118, with a mean of 0.097. This estimate is again very close to 0.094 – the mean fpseudo earlier estimated from the data of Long et al. (1993).

Our analysis was based on the assumptions that nitrate reduction is the major sink of PET and that all 10 mol e required for reduction of 1 mol nitrate to glutamate (Noctor & Foyer 1998) come from the chloroplast light reaction. When conversion of nitrate to nitrite in the cytosol utilizes NADH generated during respiratory carbon metabolism, our approach can still be applied, but the coefficient 2.5 in Eqns 1, 3 and 4 needs to be adjusted to 2. Reduction of nitrate to other products (such as glutamine, alanine, aspartate) or participation of other processes (such as fatty acid biosynthesis, etc.) may slightly change the estimates for both fpseudo and fcyc, again via an adjustment of the coefficient 2.5 in Eqn 1 on the basis of integrated information on cellular reductant utilization. However, participation of these processes was not considered in our review, mainly either because the relative importance of these processes is small (e.g. sulphate:CO2 assimilation ratio < 0.01, Bell 1985) or because their e consumption is not known quantitatively. If our understanding or procedural solutions allow the quantification of these fluxes, then the model could be easily extended to accommodate them.

Combining CO2 fixation and O2 evolution data to assess alternative e flow

We combine inline image and inline image data from Long et al. (1993) and Björkman & Demmig (1987), respectively, for a joint analysis. For such, the mean fcyc can be set to be the same (= 0.131; see paragraph after Eqn 6) for the two studies. The mean fpseudo can then be estimated from inline image using an equation that is derived from Eqn 2:


or more simply, based on the equation resulting from dividing Eqn 2 by Eqn 5:


Using the mean values of inline image from the data of Long et al. (1993) and again assuming that inline image = inline image and inline image = 1, both equations give 0.107 for the mean fpseudo. The resultant value for parameter x, estimated from Eqn 1, would be 0.056, assuming that nitrate reduction is the major e sink of PET.

The estimate for the mean fpseudo (0.107) accords with the reported fpseudo supporting nitrate reduction (Foyer, Ferrario-Mery & Noctor 2001). Our estimate was based on the fact that mean inline image measured by Björkman & Demmig (1987) was about 12% higher than mean inline image measured by Long et al. (1993) (Fig. 2). Concurrent measurement of CO2 exchange, O2 evolution and Chl fluorescence on the same leaves (e.g. Maxwell, Badger & Osmond 1998) would provide solid data sets for such an analysis. With such combined data, our approach will not require the assumption that nitrate reduction is the major sink of O2-evolving PET under limiting light. Further, the estimate for fpseudo and fcyc becomes insensitive to the uncertainty for the coefficient of 2.5 in Eqn 1, because fcyc can then be estimated directly from Eqn 6, and fpseudo can be obtained from Eqn 7 or 8. A usually slightly higher net O2 exchange than CO2 uptake, measured simultaneously (e.g. Ruuska et al. 2000), suggests some ‘basal’ PET, in addition to the PET supporting the WWC (which is most likely induced by high light and other stresses). To this end, for the model of Farquhar et al. (1980), the form C/(4.5C + 10.5Γ*) is more appropriate than the more used one C/(4C + 8Γ*), because the former implies a fraction of PET as 1 − (4C + 8Γ*)/(4.5C + 10.5Γ*) (Yin et al. 2004). This predicts 0.11 for fpseudo under the non-photorespiratory condition, very close to our estimate for the ‘basal’fpseudo. Some reports showed little difference between inline image and inline image (e.g. Evans 1987), probably because nitrate reduction occurs mainly in roots in some species or under certain conditions. For such species or conditions, the basal fpseudo should be smaller.

Interphotosystem excitation partitioning in relation to CET

In existing studies on CET, typically PSI and PSII e transport rates are measured as the product of absorbed light level and inline image and inline image, respectively, and the ratio of PSI e transport rate to the PSII rate compared over a range of steady-state conditions (e.g. Harbinson & Foyer 1991; Makino et al. 2002; Holtgrefe et al. 2003; Miyake et al. 2005). If this ratio varies in favour of PSI, CET is considered to occur. However, if CET remains constant as a portion of total e transport, it could not be detected in this way. Furthermore, this approach implies a fixed factor (typically 0.5) for the excitation partitioning of absorbed light between PSI and PSII. When excitation partitioning varies, there will be no guarantee that a change in the ratio of PSI to PSII e transport efficiencies results from the operation of CET. As shown in our review, using gas exchange data as additional information, our approach does not have this problem. For the limiting light, CET is estimated using an absolute inline image of 1. The factor of energy partitioning between PSI and PSII can then be estimated in a mathematically and biologically consistent manner, as shown next.

Let ρ2 be the fraction of the absorbed light partitioned to PSII. Assuming a negligible quantum absorption by non-photosynthetic pigments, ρ2 can be defined as


where I2 is the absorbed light partitioned to PSII; J2 is rate of e transport through PSII, and inline image is the efficiency of PSII e transport on the basis of light absorbed by both photosystems. The partitioning fraction for PSI can then be simply set at (1 − ρ2). Equation 9 is the mathematical expression equivalent to the graphical procedure of Laisk et al. (2002) that estimates the relative optical cross section of PSII antenna for the case where LET functions alone. For limiting light conditions, substituting Eqn A4 with Eqn 9 gives an expression for ρ2 in the presence of CET:


Equation 10 is in line with a qualitative statement of Albertsson (2001) that additional quanta for carrying out CET are required to be distributed to PSI. If inline image = inline image (0.83) and inline image, Eqn 10 predicts that in the absence of CET, the required ρ2 to keep equal velocity in photochemistry of PSI and PSII would be about 0.55 (instead of the intuitively assumed 0.5). If CET is active, a lower ρ2 is required. With the earlier estimated fcyc, the estimated ρ2 using Eqn 10 varies from 0.480 to 0.521, with a mean of 0.503 for the 11 species tested by Long et al. (1993), and varies from 0.457 to 0.559, with a mean of 0.511 for the 37 species of Björkman & Demmig (1987).

The photosynthetic quantum requirement is commonly assessed on the basis of absorbed light as a whole. When ρ2 is known, the quantum requirement for each photosystem can be specifically estimated. The ratio of ρ2 to inline image or to inline image gives the PSII quantum requirement per mole O2 evolution or CO2 assimilation, respectively. For O2 evolution, this can be illustrated by dividing Eqn 10 by Eqn 5:


Equation 11 means that the PSII quantum requirement for O2 evolution in the absence of photorespiration is inline image, which, whenever inline image is used for inline image, equals 4.81 for the average of the 37 species tested by Björkman & Demmig (1987). This value is higher than 4 – the theoretical lower limit, because inline image is lower than the absolute efficiency of 1. A similar equation for CO2 assimilation can be obtained from dividing Eqn 10 by Eqn 2:


The estimated average PSII quantum requirement for CO2 assimilation in the absence of photorespiration was 5.37 for the data set of Long et al. (1993) – higher than that for O2 evolution, reflecting additional loss because of the fact that part of PSII e fluxes followed PET for supporting processes such as nitrate reduction.

Estimating the fraction of e following the Q-cycle (fQ)

Given the estimated fcyc and fpseudo, fQ can be solved from Eqn A2– the relation for tuning the ATP:NADPH ratio as required by Rubisco-catalysed metabolisms. While we first estimated fcyc and fpseudo, and then fQ, it is also possible to calculate fcyc and fQ first, followed by estimating fpseudo, but the results are the same, because the values obtained by either approach are the simultaneous solution for fcyc, fpseudo and fQ, from Eqns 1, 2 and A2.

Three different H+ : ATP ratios (i.e. h = 3, or 4 or 14/3) are considered. Estimated values for fQ decrease linearly with the estimated fcyc (Fig. 4). If h = 3, the estimated fQ values were negative in all 11 species tested by Long et al. (1993) and in 33 (the same 33 mentioned earlier having a positive fcyc) out of 37 species tested by Björkman & Demmig (1987). This indicates that if h = 3 (as used in the model of Farquhar et al. 1980), there is basically no need to run the Q-cycle; instead, there are some extra ATP which could be used for processes other than carbon reduction and photorespiration. Alternatively, actual ATP synthesis could be reduced because of a basal H+ leakage through the thylakoid membrane (Albertsson 2001); the basal H+ leakage prevents excessive net H+ accumulation in the thylakoid lumen that otherwise would arrest LET via a decrease in the intrathylakoid pH (Tikhonov, Khomutov & Ruuge 1984). The model of Farquhar et al. (1980), assuming that there is no CET, implies a deficiency of ATP relative to the NADPH supply from the photosynthetic e transport chain even in the absence of H+ leakage (Farquhar & von Caemmerer 1982). Our analysis based on a more complete model that incorporates CET shows an overproduction of ATP in most cases if h = 3.

Figure 4.

The plot of estimated fraction of e that follow the Q-cycle (fQ) against estimated fraction of cyclic e flows at ferredoxin (fcyc), assuming parameter h– the number of protons required to synthesize one ATP – is 3 (circles), or 4 (squares) or 14/3 (triangles), for the 11 species tested by Long, Postl & Bolhár-Nordenkampf (1993) (closed symbols) and the 37 species tested by Björkman & Demmig (1987) (open symbols).

If h = 4, the estimated fQ varied from 0.284 to 0.533 for the data set of Long et al. (1993), and from 0.157 to 0.772 for the data set of Björkman & Demmig (1987). If a basal H+ leakage occurs in intact leaves, fQ would be somewhat higher. Therefore, if h = 4, at least a partial engagement of the Q-cycle is required.

If h = 14/3, the estimated fQ varied from 0.627 to 0.942 for the data set of Long et al. (1993), and from 0.466 to 1.245 for the data set of Björkman & Demmig (1987). The estimated fQ was above 1 in those seven species tested by Björkman & Demmig (1987), which had a low or negative estimated fcyc. A small negative fcyc, or a value of fQ slightly above 1, may simply be due to measurement noise. However, an fQ above 1 also indicates that there is an overall shortfall of ATP supply from photosynthetic e transport; this shortfall could be met from non-photosynthetic processes such as oxidative phosphorylation. Nevertheless, such a high value of h requires little or no H+ leakage and a high degree of obligatory involvement of the Q-cycle for supplying the ATP needed for photosynthetic metabolic reactions.

Apparently, if there is no basal H+ leakage for ATP synthesis, the assumption h = 4 always yields a sensible estimate of fQ, ranging between 0 and 1. The assumption of h = 4, combined with full operation of the Q-cycle (i.e. fQ = 1), also results in the exact overall ratio of ATP : NADPH required for the Benson–Calvin cycle in C3 photosynthesis in the absence of CET, PET and photorespiration (Allen 2003; also cf. Eqn A2). However, given the occurrence of photorespiration, possible basal H+ leakage through the thylakoid membrane (Albertsson 2001) and tight linkage of photosynthesis with other processes (Noctor & Foyer 1998) in intact leaves, it is difficult to confidently make a conclusion about the value of h.

Uncertainty analysis

Our review has involved an uncertainty analysis for some parameters (such as x and h). The review has also made use of additional assumptions, some of which have already been alluded to. Firstly, it is assumed in our analysis that the quantum absorption by non-photosynthetic pigments is negligible. Leaves of many plants have sufficient blue-light absorbing non-photosynthetic pigments (McCree 1972; Inada 1976). Uncertainties (if any) concerning the amount of light absorbed by photosynthetic pigments when non-photosynthetic pigments are present will affect the accuracy of the analyses. The second uncertainty is the effect of light wavelength on photosynthetic quantum efficiency, as shown by Evans’s (1987) report that maximum quantum efficiency was achieved at 600 nm. Most reports, including Long et al. (1993) and Björkman & Demmig (1987), used broadband (white) light in measuring quantum efficiency. Evans (1987) explained the variability of the quantum efficiency in wavelength-dependent changes in the partitioning of excitation energy between the photosystems. An unbalanced excitation of the photosystems would result in a loss of quantum efficiency of one photosystem relative to the other and an increase in energy loss via thermal dissipation from PSI or PSII. In PSII, it would result in inline image < inline image (Harbinson et al. 1989). The third uncertain element has been stated earlier – that is, inline image is not an accurate measure of inline image. Although most physiological applications of Chl fluorescence have taken the accuracy of inline image for granted, Genty, Wonders & Baker (1990) and Lavergne & Trissl (1995) pointed out that inline image tends to underestimate inline image. Finally, our analysis assumes that WWC does not take place under strictly limiting light.

Considering these uncertainties, we will attempt to show what the consequences would be if some of the assumptions were incorrect. Our model approach is valuable in developing ‘what-if’ scenarios based upon likely physiology for most non-measured processes. For the effect of irradiance wavelength, we used data of Evans (1987) and calculated (assuming inline image = 1 and inline image = 0.835) that fcyc, if measured with the 600 nm light, is small: 0.12 for pea (Pisum sativum) and 0.03 for spinach (Spinacia oleracea), suggesting that at least for the 600 nm light, alternative e transport is a minor route. Further, we examined the extent to which the estimated alternative e fractions vary if light absorptance by non-photosynthetic pigments exists (Fig. 5a) or if the inline image : inline image ratio is not equal to 1 (Fig. 5b). Occurrence of negative fcyc in Fig. 5a means that absorptance by non-photosynthetic pigments cannot be higher than approximately 7% if other parameters are measured with sufficient accuracy. Figure 5 shows that (1) the direction of the response of fpseudo, relative to that of fcyc, is in line with that shown in Fig. 3, and (2) fcyc is more responsive to these uncertain parameters than fpseudo is. A high fcyc was obtained because when inline image and inline image are fixed, the basal fpseudo is also largely fixed (as shown in Fig. 5), meaning that only CET will function as brake for LET to match the PSII efficiency with the rate of CO2 fixation. If the WWC also functions as a brake, the required CET would be lower, which can be seen from an equation for fcyc derived from Eqn 2 where inline image is replaced by inline image, and fpseudo refers to the fraction of PET in support of WWC ( fpseudo,wwc), that is,

Figure 5.

Estimated fraction of e transport at ferredoxin that follow the cyclic (fcyc) and pseudocyclic (fpseudo) modes in response to the fraction of light absorbed by non-photosynthetic pigments in the leaves (a), and in response to the ratio of real maximum photosystem II (PSII) efficiency (inline image) to the value given by (1 −Fo/Fm) (b). In the calculation illustrated in (a) and (b), the average values of relevant parameters in the paper were used [i.e. 1 for inline image, 0.835 as the value for (1 − Fo/Fm), and 0.093 and 0.106 for inline image and inline image, respectively, both on the basis of leaf absorbed light]. Fo, the minimum fluorescence when all PSII reaction centres are assumed open; Fm, maximum fluorescence in saturating excitation light when closure of PSII reaction centres is maximal.


The fraction of PET supporting the non-WWC processes can then still be calculated by Eqn 7 or 8. Using the default values as set in Fig. 5, Eqn 13 predicts that the maximum fpseudo,wwc is 0.068, at which fcyc = 0. Figure 6 shows the calculated fcyc and fpseudo for non-WWC processes under various hypothetical fpseudo,wwc values, as a function of the inline image : inline image ratio. The occurrence of negative fcyc indicates that WWC can never consume more than 15% of total e fluxes under limiting light.

Figure 6.

Estimated fraction of e transport at ferredoxin that follow the cyclic ( fcyc, curves 1–4) and the basal pseudocyclic ( fpseudo, curves 5–8) modes in response to the ratio of real maximum photosystem II (PSII) efficiency (inline image) to the value given by (1 − Fo/Fm), under different scenarios for the fraction of the pseudocyclic e transport (PET) supporting the water-water cycle (WWC) ( fpseudo,wwc, with curves 1 and 5 for fpseudo,wwc = 0.00, curves 2 and 6 for fpseudo,wwc = 0.05, curves 3 and 7 for fpseudo,wwc = 0.10, and curves 4 and 8 for fpseudo,wwc = 0.15). In this calculation, the average values of parameters in the paper were used [i.e. 1 for inline image, 0.835 as the value for (1 − Fo/Fm), 0.093 and 0.106 for inline image and inline image, respectively, both on the basis of absorbed light]. Fo, the minimum fluorescence when all PSII reaction centres are assumed open; Fm, maximum fluorescence in saturating excitation light when closure of PSII reaction centres is maximal.


The recent work of Munekage et al. (2002, 2004) put the old idea of PSI-mediated CET back on the agenda. Allen (2002, 2003) indicated qualitatively that CET and PET are at work in vivo and interplay with LET to tune the output of ATP and NADPH. Here we have reviewed how a recent model for e transport-limited C3 photosynthesis (Yin et al. 2004) can be used to quantitatively examine the extent to which CET and PET operate under steady-state, limiting light, non-photorespiratory conditions, using literature data of combined gas exchange and Chl fluorescence measurements. If these combined data are measured accurately using advanced equipment, our approach provides a tool for in vivo assessment of fcyc, fpseudo, fQ and ρ2 in C3 photosynthesis. Other parameters could also be explored. For example, given the estimates of fcyc and fpseudo, the ratio x in nitrate reduction to carboxylation can be assessed from Eqn 1, if nitrate reduction is the predominant process driving PET under limiting light. Most important, the model helps to answer ‘what-if’ questions for uncertain parameters, non-measured processes or measurement uncertainties.

This review is an important basis for assessing underlying limitations to photosynthesis for more general situations (i.e. at non-limiting lights and under photorespiratory conditions). For the photorespiratory conditions, the CO2/O2 specificity of Rubisco (for quantifying parameter Γ*) and mesophyll conductance (for estimating C– chloroplast CO2 concentration) need to be adequately estimated. At high light levels, especially combined with other stresses, the WWC and energy dissipation as heat play the major photoprotective role. The quantitative assessment of these photosynthesis parameters merits further model investigations.


The extended model of e transport-limited C3 photosynthesis

The model of Farquhar et al. (1980) is based on LET, assuming the stoichiometry of 2 as the H+ : e ratio – the number of H+ pumped across the thylakoid membrane per e, and 3 as the H+ : ATP ratio (termed h) – the number of H+ required to synthesize one ATP. In fact, there are uncertainties for the H+ : e ratio of LET (being 3 if the Q-cycle fully operates or 2 if not at all). In addition, parameter h is not certain, being either 3 or 4 (von Caemmerer 2000). More recently, Joliot & Joliot (2002) and Allen (2002, 2003) inferred an h of 14/3, based on structural data of Seelert et al. (2000).

It has been proposed that CET and PET may function in vivo to tune the ATP : NADPH ratio as required by stromal metabolisms (Allen 2003). With this assertion and also in view of the uncertainties with regard to the H+ : e and H+ : ATP ratios and possible partial engagement of the Q-cycle, Yin et al. (2004) developed a generalized algorithm for describing e transport-limited gross CO2 assimilation rate (AGj) as


where J2 is the rate of e transport through PSII; C is chloroplast CO2 concentration, and Γ* is the CO2 compensation point in the absence of mitochondrial respiration. Fraction of the Q-cycle (fQ), fraction of cyclic e transport (fcyc) and fraction of pseudocyclic pathway (fpseudo) (cf. Fig. 1) need to satisfy the following relation for the balanced ATP : NADPH ratio as required by the Rubisco-catalysed metabolisms:


As CET uses all of the machinery of LET with exception of PSII (Fig. 1), Eqn A2 implicitly assumes that the Q-cycle, once active, is impartial for electrons of LET and of CET. In Fig. 1, the CET is shown on the main, ferredoxin-dependent pathway, proposed by Arnon (1959). CET could also be NAD(P)H-dehydrogenase dependent (Ogawa 1991; Munekage et al. 2004). Our model remains valid, because CET is coupled to ATP synthesis via an H+ gradient formed by either pathway (Albertsson 2001).

In analogy to the model of Farquhar & Wong (1984), the dependence of J2 in Eqn A1 on absorbed irradiance (I ) is described by


where θ is the curvature factor of the nonrectangular response; Jmax is the maximum rate of e transport through PSII under saturating illumination, and inline image is the efficiency of e transport of PSII, under strictly limiting light, on the basis of light absorbed by both photosystems. Following Yin et al. (2004), inline image is determined by


where inline image and inline image are the efficiency of e transport of PSI and of PSII, respectively, under limiting light, on the basis of light absorbed by each photosystem alone. Instead of using an equal efficiency as assumed in the model of Farquhar et al. (1980), Eqn A4 allows the difference in e transport efficiency between PSI and PSII.