A Mathematical Model of Photosynthetic Electron Transport in Response to the Light Spectrum Based on Excitation Energy Distributed to Photosystems

A Mathematical Model of Photosynthetic Electron Transport in Response to the Light Spectrum Based... Abstract To enable us to analyze more systematically the effects of the spectral distribution of light (i.e. light quality) on photosynthetic electron transport, we propose a simple mathematical model which describes electron transport reactions under light-limited conditions based on the excitation energy distributed to the photosystems. The model assumes that the rate-limiting photosystem performs the photochemical reaction at its maximum yield, while the yield in the other photosystem is passively down-regulated to equalize the rates of linear electron transport through the photosystems. Using intact cucumber leaves, we tested the model by comparing actual and estimated photosynthetic parameters under several combinations of photon flux densities of red and far-red lights (R and FR, respectively). Simultaneously provided R and FR yielded greater gross photosynthetic rates than the sums of the rates under only R and only FR, which is known as the ‘enhancement effect’. The present model reproduced these non-additive increases in the gross photosynthetic rates in response to supplemental FR to R and provided more accurate estimates than an existing method that did not take the enhancement effect into account (root mean square errors: 0.11 and 0.21 μmol m-2 s-1, respectively). Using the present model, the photon flux density of the supplemental FR which gives the changing point of rate-limiting photosystem and the photochemical yields of the non-rate-limiting photosystems were estimated reasonably well. The present study has therefore formulated a simplified quantitative electron transport model in response to the light spectrum based on generally accepted concepts and demonstrated its validity experimentally. Introduction Photosynthetic electron transport and CO2 fixation rates and their quantum yields under light-limited conditions are essential indices for understanding the acclimation responses of a leaf to its environment and for regulating the light environment in horticulture. The number of fixed CO2 molecules per electron transported to NADP+ has been described by the C3 photosynthesis model (Farquhar et al. 1980, Farquhar and von Caemmerer 1982, Sharkey 1985). As long as the relative spectral distribution of light (i.e. light quality) is constant, the photosynthetic electron transport rate (ETR) is generally expressed as an empirical function of the incident photosynthetically active photon flux density (PFD), a curvature factor which indicates how abruptly the light curve saturates, maximum ETR and the maximum quantum yield of ETR (Farquhar and Wong 1984). Among these parameters, the maximum quantum yield is known to depend on the wavelength and the light spectrum of the incident light (e.g. Emerson and Lewis 1943). Therefore, the gross photosynthetic rate (Pg) also depends on the light spectrum. Under strictly light-limited conditions (i.e. ETR is in proportion to the incident PFD), Pg under light with a given spectral distribution can be calculated from the photosynthetic action spectrum (e.g. McCree 1972b, McCree 1972a, Inada 1976) as follows:   Pg≃∑λ{PFDλ×αλ×YCO2,λ }, (1) where PFDλ is the PFD of incident light, αλ is the leaf absorptance and YCO2,λ, the photosynthetic quantum yield (i.e. Pg/flux density of an absorbed photon) at a wavelength of λ. However, this integration method is expected to underestimate Pg because it does not consider the ‘enhancement effect’ (Emerson et al. 1957; described below). In organisms performing oxygenic photosynthesis, the photosynthetic electron transport chain (i.e. the Z-scheme) is anchored by photochemical reactions that occur in PSII and PSI. The excitation energy derived from absorbed photons and transferred to the reaction centers of the photosystems is consumed by serial photochemical reactions. It has been reported that excitation energy distribution between the photosystems depends on the wavelength of light (Evans 1986, Evans 1987, Evans and Anderson 1987, Hogewoning et al. 2012, Wientjes et al. 2013, Laisk et al. 2014, Murakami et al. 2018) and thus on the light spectrum. Under light whose excitation energy is preferentially distributed to PSII (PSII-light), a part of the energy distributed to PSII is not used for electron transport because the photochemical reaction in PSI limits the whole-chain ETR. Likewise, if the excitation energy is preferentially distributed to PSI (PSI-light), some of the energy distributed to PSI is accordingly dissipated. In other words, the photochemical reaction in the non-rate-limiting photosystem is passively down-regulated by the reaction in the other photosystem. When these PSII- and PSI-lights are simultaneously provided, the energy distributed to the photosystems is somewhat counterbalanced, and thus the resultant ETR will be greater than the sum of ETRs under PSII- and PSI-lights that are provided individually. Apparently, Equation 1 holds true only if the effects of PFDs at different wavelengths on the Pg are independent and additive. The simply integrated estimates from the light spectrum were indeed smaller than those actually measured in some studies, due to the enhancement effect (e.g. Inada 1978, Hogewoning et al. 2012). The spectrum of incident light on a leaf changes with physical (e.g. solar zenith angle, cloudiness and atmospheric composition; Campbell and Norman 1998), biological (e.g. canopy structure; Smith 1982) and agricultural factors (e.g. use of artificial light sources and wavelength-selective covering materials). Quantitative models of the effect of the light spectrum on the photosynthetic electron transport must be useful to analyze these factors systematically. As mentioned above, it has generally been accepted that excitation energy distribution between PSII and PSI is the major determinant of the ETR under light-limited conditions. Because some methods for the estimation of the excitation energy distribution at a given wavelength are available (Evans 1986, Evans 1987, Evans and Anderson 1987, Hogewoning et al. 2012, Wientjes et al. 2013, Laisk et al. 2014), energy distributed to PSII and PSI can be calculated from the spectral distribution of the light. However, little work on quantitative modeling of the light spectrum effects on the electron transport has been done, and there is no method to estimate ETR based on the excitation energy distributed to the respective photosystems. The aim of this study was to develop a quantitative model describing the electron transport under light-limited conditions based on the excitation energy distributed to the photosystems and taking the enhancement effects into account. Here, we formulated a simple mathematical model of the electron transport and tested its validity under conditions where the enhancement occurred. The ETR and photochemical yields of the photosystems (YII and YI) under simultaneously provided red light (R) and far-red light (FR)—typical PSII- and PSI-light, respectively—were estimated using the model and compared with those actually measured. The ETR estimated by the present model was also compared with the ETR obtained using the integration method that did not incorporate the enhancement effect (i.e. Equation 1). We also evaluated the redox state of the photosynthetic intermediate between the photosystems and the quantum yields of non-photochemical energy dissipation in PSI to analyze rate-limiting factors of the electron transport from PSII to PSI under conditions where the enhancement occurred. Results The present model estimates the whole-chain ETR, YII and YI based on the excitation energy distribution between the photosystems (Fig. 1a; see also the Materials and Methods). To determine the excitation energy distribution under simultaneously provided R and FR, the fractions of energy distributed to PSII for R and FR (fR and fFR) were determined using a curve-fitting method without measuring gas exchange rates (Fig. 1b; see also Murakami et al. 2018). The mean values of fR and fFR in the three replicated experiments were 0.54 and 0.16 (replicate 1), 0.55 and 0.15 (replicate 2), and 0.56 and 0.18 (replicate 3), respectively. Supplemental FR to R increased Pg (Fig. 2) and YII (Fig. 3a), while it decreased YI (Fig. 3b). The actual values of Pg under R + FR were always greater than those estimated using the integration method (i.e. the sum of Pg values under only R and only FR) (Fig. 2). These differences were presumably caused by the enhancement effect. The maximum extent of the enhancement effect ranged from 6.1 to 7.5% in the three replicates. In the present model, the estimates based on the excitation energy distributed to the photosystems reduced these differences (Fig. 2). The YII and YI under R + FR were estimated using Equations 5 and 6 (Fig. 3). The horizontal parts of the lines indicate the measured maximum yields (Ymax,II and Ymax,I) under individually provided FR and R, respectively. The model closely reproduced the decrease in YI in response to the increase in the PFD of supplemental FR (Fig. 3b). The estimates of YII also reproduced the measured trends, although the estimated values tended to be greater than the measured values (Fig. 3a). Fig. 1 View largeDownload slide (a) A schematic diagram of the present electron transport model. (1) Potential electron transport rates through the photosystems (pETRII and pETRI) are calculated from their maximum yields (Ymax,II and Ymax,I) and the excitation energy (EII and EI), (2) the whole-chain ETR is given as the minimum of the pETRs and (3) the photochemical yield of the non-rate-limiting photosystem was passively down-regulated so as to equalize the ETRs through the photosystems. The diagram shows the electron transport under a PSII-limited condition. See text for details. (b) An irradiation scheme adopted to determine the excitation energy distributions for red (R) and far-red light (FR) (adapted from Murakami et al. 2018 with modifications). An electron transport model was fitted to YII/YI values measured under several combinations of flux densities of absorbed R and FR photons (ABSR and ABSFR) to estimate the fractions of excitation energy distributed to PSII (fR and fFR). Fig. 1 View largeDownload slide (a) A schematic diagram of the present electron transport model. (1) Potential electron transport rates through the photosystems (pETRII and pETRI) are calculated from their maximum yields (Ymax,II and Ymax,I) and the excitation energy (EII and EI), (2) the whole-chain ETR is given as the minimum of the pETRs and (3) the photochemical yield of the non-rate-limiting photosystem was passively down-regulated so as to equalize the ETRs through the photosystems. The diagram shows the electron transport under a PSII-limited condition. See text for details. (b) An irradiation scheme adopted to determine the excitation energy distributions for red (R) and far-red light (FR) (adapted from Murakami et al. 2018 with modifications). An electron transport model was fitted to YII/YI values measured under several combinations of flux densities of absorbed R and FR photons (ABSR and ABSFR) to estimate the fractions of excitation energy distributed to PSII (fR and fFR). Fig. 2 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (open symbols) and values estimated using the integration method (filled symbols) and the model based on the distribution of excitation energy (lines) are shown. Pg values estimated using the model were limited by the potential electron transport, either in PSII (dotted lines and their extensions) or in PSI (dashed lines and their extensions). Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. Fig. 2 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (open symbols) and values estimated using the integration method (filled symbols) and the model based on the distribution of excitation energy (lines) are shown. Pg values estimated using the model were limited by the potential electron transport, either in PSII (dotted lines and their extensions) or in PSI (dashed lines and their extensions). Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. Fig. 3 View largeDownload slide Photochemical quantum yields of (a) PSII (YII) and (b) PSI (YI) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (symbols) and values estimated using the model based on the excitation energy distribution (lines) are shown. Means ± SDs from values of 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. Fig. 3 View largeDownload slide Photochemical quantum yields of (a) PSII (YII) and (b) PSI (YI) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (symbols) and values estimated using the model based on the excitation energy distribution (lines) are shown. Means ± SDs from values of 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. The broken points of the estimated lines by the present method (Figs. 2, 3) were the changing points of the ETR limitation. To the left of these points, the estimated potential ETR at PSI (i.e. pETRI) was smaller than that at PSII (i.e. pETRII) and limited the whole-chain ETR. As the PFD of the supplemental FR increased, the excitation energy distribution reached equilibrium (i.e. pETRII = pETRI), where both PSII and PSI were assumed to achieve their maximum quantum yields. An increase in the PFD of the supplemental FR beyond the equilibrium values intensified PSI overexcitation and reduced YI (Fig. 3b). The estimated FR PFDs giving the broken points in the model lines were higher in replicates 1 and 3 than in replicate 2 (see also Supplementary Fig. S1). The higher FR PFDs in replicate 1 than in replicate 2 resulted from a slightly higher (∼5 µmol m−2 s−1) R PFD. The higher FR PFDs in replicate 3 than in replicate 2 resulted from the higher fR and fFR values. The supplemental FR on top of R slightly decreased 1 − qL values or oxidized the plastoquinone pool (Fig. 4a), suggesting that the electron transport from the pool to PSI was promoted by overexciting PSI. The limiting factor of photochemical reactions in PSI was shifted from the acceptor side (YNA) to the donor side (YND) by the supplemental FR (Fig. 4b, c). These data also confirm that the supplemental FR excited PSI more than PSII. Fig. 4 View largeDownload slide (a) The fraction of closed PSII reaction centers (1 − qL), the quantum yields of non-photochemical energy dissipation in PSI due to (b) the acceptor-side limitation (YNA) and (c) the donor-side limitation (YND) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. Fig. 4 View largeDownload slide (a) The fraction of closed PSII reaction centers (1 − qL), the quantum yields of non-photochemical energy dissipation in PSI due to (b) the acceptor-side limitation (YNA) and (c) the donor-side limitation (YND) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. Our model incorporated the enhancement effect and provided more accurate estimates of Pg (root mean square error: 0.11 µmol m−2 s−1) than those obtained using the integration method (root mean square error: 0.21 µmol m−2 s−1) (Fig. 5), suggesting an increased accuracy of ETR estimates. The present model tended to overestimate the Pg, especially in the high-value range (i.e. when the PFD of the supplemental FR increased; Fig. 5). Fig. 5 View largeDownload slide The relationship between the actual and estimated values of gross photosynthetic rates (Pg) of cucumber leaves. Estimates obtained using the integration method (filled symbols) and the model based on the distribution of excitation energy (open symbols) were compared. Symbols indicate means of values from 2–4 leaves. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 5 View largeDownload slide The relationship between the actual and estimated values of gross photosynthetic rates (Pg) of cucumber leaves. Estimates obtained using the integration method (filled symbols) and the model based on the distribution of excitation energy (open symbols) were compared. Symbols indicate means of values from 2–4 leaves. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Under individually provided R and FR, Pg was in proportion to the incident PFDs (Fig. 6). YII was slightly higher under FR than under R (Fig. 7a, b). YI was substantially smaller under FR than under R (Fig. 7c, d). The observed maximum yields of the photosystems (i.e. YII under FR and YI under R) were used as model inputs (Ymax,II and Ymax,I in Equations 2 and 4–6). YI remained almost constant under different PFDs of R, while it decreased with the increase in the PFD of the FR (P = 0.0029). Fig. 6 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves under (a) red LED light (R) and (b) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 6 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves under (a) red LED light (R) and (b) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 7 View largeDownload slide Photochemical quantum yields of (a, b) PSII (YII) and (c, d) PSI (YI) of cucumber leaves under (a, c) red LED light (R) and (b, d) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 7 View largeDownload slide Photochemical quantum yields of (a, b) PSII (YII) and (c, d) PSI (YI) of cucumber leaves under (a, c) red LED light (R) and (b, d) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Discussion In this study, photosynthetic electron transport was illustrated using a mathematical model based on the excitation energy distribution between the photosystems (Fig. 1a). Good agreement between the actual and estimated values of Pg, YII and YI under R + FR (Figs. 2, 3, 5) supports the reliability of the proposed model. The essential assumptions of the proposed model are as follows: (i) the whole-chain ETR is given as the minimum of potential ETR at either PSII or PSI; (ii) the rate-limiting photosystem performs the photochemical reaction at its maximum quantum yield; and (iii) the photochemical yield of the non-rate-limiting photosystem is determined so as to equalize the actual ETR in the two photosystems. In other words, the yield of the non-rate-limiting photosystem was assumed to be passively down-regulated. The present study experimentally tested these qualitatively accepted assumptions and demonstrated their plausibility, at least under the strictly light-limited conditions. Note that the model will not hold under high light conditions because energy-dissipating mechanisms are activated under high light conditions (Niyogi 1999) and the rate-limiting photosystem does not perform to its maximum yield. Our model and the adopted approach might be useful for separating decreases in the photosynthetic yield into actively and passively regulated fractions. In addition, depending on the redox state of the electron transport under prolonged irradiation with different light spectra, leaf properties involved in the excitation energy distribution are adjusted by several acclimatory responses (e.g. Chow et al. 1990a, Chow et al. 1990b, Melis 1991, Kim et al. 1993, Walters and Horton 1994, Walters and Horton 1995, Pfannschmidt et al. 1999, Wagner et al. 2008, Hogewoning et al. 2012, Murakami et al. 2016, Murakami et al. 2018). These acclimatory responses include the dynamic reallocation of the light-harvesting antenna complex (i.e. state transitions; Goldschmidt-Clermont and Bassi 2015) and the long-term adjustment of the photosystem stoichiometry (Anderson et al. 1995). Analyzing the changes in the excitation energy distribution due to these responses and simulating their effects on the ETR under various environmental conditions (e.g. fluctuating light spectrum in the understorey) by using the model proposed here may be useful to understand the physiological roles and in situ contributions of these responses. The model corrected the gap between the measured Pg values and estimated values from the integration method (Figs. 2, 5) because this model accounts for the ‘enhancement effect’ ignored in the integration method (see also the Introduction). In higher plants, at most 16% (Inada 1978) and 21% (Hogewoning et al. 2012) enhancements in Pg have been experimentally demonstrated, while some experiments have found no enhancement (McCree 1972b, McCree 1972a). In the present study, we observed enhancement at an intermediate extent of at most 7.5%. The difference among the extents could be caused by several factors affecting the excitation energy distribution between the photosystems, such as the spectral distribution of growth light (e.g. Chow et al. 1990a, Chow et al. 1990b, Melis 1991, Kim et al. 1993, Walters and Horton 1994, Walters and Horton 1995, Pfannschmidt et al. 1999, Wagner et al. 2008, Hogewoning et al. 2012, Murakami et al. 2016, Murakami et al. 2018) and the spectral distributions of simultaneously provided lights (e.g. Evans 1986, Evans 1987, Evans and Anderson 1987, Hogewoning et al. 2012, Wientjes et al. 2013, Laisk et al. 2014). Zhen and van Iersel (2017) also showed significant non-additive enhancements in net photosynthetic rates by adding several PFDs of supplemental FR to white and blue + red LED light. The model did not completely explain the electron transport under R or FR light provided individually. When acclimatory responses (i.e. state transitions and adjustments of photosystem stoichiometry) do not occur and leaf properties involved in the excitation energy distribution are not changed, the excitation balance (i.e. EII/EI) is likely to depend only on the light spectrum and not on the PFD. Since this study was designed to minimize these changes in the leaf properties, the present model expected constant YII and YI irrespective of the PFD of individually provided R or FR (Equations 5 and 6). However, YI decreased in response to the PFD of individually provided FR (Fig. 7d). As the Pg measured under these conditions was in proportion to the incident PFD (Fig. 6b), YCO2 should be constant in spite of the gradual decrease in the measured YI. Similar decreases in YII without a decrease in YCO2 have been observed in cucumber (Hogewoning et al. 2012) and lettuce (data not shown) under low PFDs of PSII-light (narrow-waveband blue and red LED light). The decrease in the photochemical yields without an accompanying reduction in YCO2 might be related to the activities of alternative electron flows, as Hogewoning et al. (2012) suggested. That is, fluxes to alternative electron pathways were present even under extremely low PFDs; they decreased with an increase in the PFDs. As fluxes to some alternative electron pathways do not affect the linear electron flow to ferredoxin, their reduction decreases YII or YI without reducing the YCO2. These pathways may include electron transport to O2 in PSII (Vass 2011) or to plastid terminal oxidase from plastoquinone (Nawrocki et al. 2015), cyclic electron flow around PSI (Shikanai 2007) and putative cyclic electron flow around PSII (e.g. Laisk et al. 2015). The lower YII under PSI-limited conditions (i.e. high supplemental FR conditions) than the Ymax,II, which was measured under only FR provided, might result from the regulation of these flows (Fig. 3a). Slight increases in 1 − qL (i.e. reduction of the plastoquinone pool) and YND in response to an increase in PFD of FR (Supplementary Fig. S2b, f) might result from ‘photosynthetic control’ initiated by the cyclic electron flow around PSI (e.g. Kono and Terashima 2014). On the other hand, it is also possible that the decreases in YII and YI reflected the decrease in the actual YCO2. In this case, the reduced actual YCO2may be compensated for by electron influxes from other electron donors to maintain the constant apparent YCO2. These pathways may include electron transport from the NADH dehydrogenase-like complex to the plastoquinone pool (Shikanai 2016) and malate–oxaloacetate shuttles (Scheibe 2004). Although either or both of these regulations in the alternative electron flows might operate in vivo, their contribution to the electron transport should be small because the estimated Pg, YII and YI (Figs. 2, 3, 5) were in good agreement with the measured values in the present experimental conditions. The regulation of these alternative electron pathways, in particular cyclic electron flow around PSI, might play key roles in fluctuating and unfavorable (e.g. drought, extreme temperatures and high salinity) environments (for a review, see Yamori and Shikanai 2016) compared with the steady and moderate environment adopted in this study. Incorporating activities of the alternative electron pathways into the model must be a promising step to understanding in situ roles of these pathways. Because the present model estimates the ETR from the distributed excitation energy to PSII and PSI, estimating EII and EI from the light spectrum may result in a deeper understanding of the ETR response to the light spectrum. Recent measurements of leaf photosynthetic rates are usually performed using commercially available blue and red LED light, but what needs to be known are not the rates under light in most cases. This discrepancy between the measuring light spectra causes systematic biases in measured rates and other parameters (e.g. Chl fluorescence parameters), as some studies have pointed out (Walters 2005, Murakami et al. 2016, Murakami et al. 2017). Inferring the rates under sunlight from the rates measured under an artificial light source is necessary to remove biases and to analyze the in situ photosynthetic responses. In addition, a number of horticultural researchers have investigated the effect of the light spectrum on plant growth to enhance productivity by providing artificial light (e.g. Matsuda et al. 2004, Hogewoning et al. 2010). Owing to the lighting technique, in particular to LEDs, we can design and select the light spectrum from a wide variety of options. Preliminary estimation of the photosynthetic rates from the spectrum will be decisively important for optimization of the growth light spectrum. Materials and Methods Electron transport model The consumption of distributed excitation energy in PSII and PSI was illustrated using a simple mathematical model. This model was developed by extending an electron transport model described in our previous study (Murakami et al. 2018). Not all excitation energy distributed to the photosystems is consumed in the photosynthetic electron transport, even in the photosystem which limits the whole-chain ETR. For instance, the maximum photochemical quantum yield of PSII is not greater than approximately 0.8 even under FR light (i.e. PSI-light) at a low PFD (e.g. Hogewoning et al. 2012). The products of the maximum yields (Ymax,II and Ymax,I) and the distributed excitation energy (EII and EI, mol m−2 s−1) were presumed to determine the potential ETR through PSII and PSI (pETRII and pETRI, mol m−2 s−1). The whole-chain ETR was assumed to be limited by the smaller potential ETR at either PSII or PSI, as follows:   ETR=min{pETRII,pETRI}=min{EII×Ymax, II,EI×Ymax, I}. (2) The rate-limiting photosystem performs the photochemical reaction at its maximum quantum yield in this model. The photochemical yield of the other photosystem—the non-rate-limiting photosystem—is passively down-regulated so that the ETRs through PSII and PSI balance. The maximum yields of the photosystems of a leaf should be constant in the short term, at least over a period of a few minutes. The excitation energy derived from simultaneously provided lights with different spectra may be additive as long as the leaf properties related to the distribution of excitation energy are unchanged. Thus, EII and EI under two simultaneously provided lights (light1 and light2) can be calculated as follows:   EII=EII, light1 + EII, light2=ABSlight1×flight1 + ABSlight2×flight2,EI=EI, light1+ EI, light2=ABSlight1×(1−flight1) + ABSlight2×(1−flight2), (3) where ABSlight1 and ABSlight2 are photons of light1 and light2 absorbed by the leaf (i.e. incident PFD×absorptance; mol m−2 s−1), and flight1 and flight2 are fractions of the excitation energy from light1 and light2 distributed to PSII, respectively. Note that the photons absorbed by the leaf are distributed not only to the photosystems but also to other substrates (e.g. non-photosynthetic pigments) although the latter was not considered in Equation 3. This factor may be negligible in the present study because the R and FR lights used in this study are minimally absorbed by non-photosynthetic pigments. By substituting Equation 3 into Equation 2, ETR under light1 + light2 is estimated as follows:   ETR=min{(ABSlight1×flight1 + ABSlight2×flight2)×Ymax, II,{ABSlight1×(1−flight1) + ABSlight2×(1−flight2)}×Ymax, I}. (4) The simulated effects of the parameters on the estimated ETR are shown in Supplementary Fig. S1. According to this model, YII and YI can also be estimated from Equations 3 and 4 as follows:   YII=ETREII=min{Ymax, II,EI×Ymax, IEII}=min{Ymax, II,ABSlight1×(1−flight1) + ABSlight2×(1−flight2)ABSlight1×flight1 + ABSlight2×flight2×Ymax, I},. (5) and   YI=ETREI=min{EII×Ymax, IIEI,Ymax, I}=min{ABSlight1×flight1 + ABSlight2×flight2ABSlight1×(1−flight1) + ABSlight2×(1−flight2)×Ymax, II,Ymax, I}.. (6) Plant material and growth conditions Cucumis sativus L. (cv. Hokushin) were hydroponically grown as described by Murakami et al. (2018). In brief, the plants were grown under white LED (NSPW310DS; Nichia Chemical Industries Ltd.) light at a photosynthetic PFD of 300 µmol m−2 s−1 for 14–16 d and were then subjected to the following measurements. Gas exchange, Chl fluorescence and 830 nm absorbance measurements Gas exchange, Chl fluorescence and 830 nm absorbance parameters of the first true leaves were simultaneously measured in a dark room using a portable gas exchange measurement system (LI-6400XT; LI-COR Inc.) and a fiber-type P700 and Chl fluorescence measuring system (DUAL-PAM/F; Heinz Walz GmbH). Red LED (SRK3-3A80-LE; Toricon) light (peak wavelength of 660 nm) and far-red LED (L735-36 AU; Epitex Inc.) light (peak wavelength of 735 nm) were used as actinic lights in the experiments (refer to fig. 2 in Murakami et al. 2018 for the spectra of the LED lights). All measurements were made under a low PFD (PFDR ∼60 µmol m−2 s−1) and a high intercellular CO2 concentration (∼100 Pa) to evaluate gas exchange rates and photochemical yields under strictly light-limited conditions (Supplementary Table S1; Fig. S3). The respiration rate (Rd) and steady-state Chl fluorescence in dark-treated (> 60 min) leaves (Fo) were measured in the dark. The maximum level of the P700 signal (P700 fully oxidized) in the dark (Pm) was determined by applying a saturation pulse in the presence of FR light at the peak wavelength of 720 nm. The zero P700 signal (P0) was determined when complete reduction of P700 was induced after the saturating pulse in the absence of FR light. The steady-state net photosynthetic rate (Pn), YII, YI, a parameter estimating the fraction of PSII centers in open states (qL; Kramer et al. 2004) and the quantum yields of non-photochemical energy dissipation in PSI due to the acceptor- and the donor-side limitations (YNA and YND; Klughammer and Schreiber 1994) of the leaves were measured under R. These parameters under FR and R + FR were then logged 60 s after the light transitions (i.e. R to FR and R + FR) to minimize potential changes in fR and fFR caused by the state transitions (Goldschmidt-Clermont and Bassi 2015). The leaf photosynthesis was presumed to reach the steady state immediately after the transitions because of the small differences in Pn due to the light transitions. Considering the gas flow rate (500 µmol s−1 or 11.2 cm3 s−1) and the path volume of the gas exchange measurement system (56.4 cm3), the difference in the gas concentrations between the inlet and outlet should reach 99% of its steady state within 23 s (Weiss et al. 2009). Quantification of the excitation energy distributions The fR and fFR of the leaves were evaluated on the same day as the gas exchange, Chl fluorescence and 830 nm absorbance. The fR and fFR of leaves pre-irradiated with R for 10 min were quantified by curve fitting as described by Murakami et al. (2018). In brief, we estimated f values by measuring ratios of photochemical yields under several PFD combinations of R and FR. The yield ratio was formulated as a function of ABSR, ABSFR, fR and fFR, assuming the same ETR through PSII and PSI. The f values were quantified by fitting this formula to measured sets of values (i.e. YII, YI, ABSR and ABSFR). The measurements were made under two different levels of ABSR supplemented with several levels of ABSFR. Note that the f values were quantified without gas exchange parameters. ABSR and ABSFR were calculated from the spectral distributions of leaf absorptance (Fig. 8) and actinic lights. Fig. 8 View largeDownload slide A spectral distribution of absorptance of cucumber leaves. The ranges between mean values + SEs and mean values − SEs for means from three independent experiments are shown. Absorptance at a given wavelength was calculated from reflectance and transmittance measured with integrating spheres (ISP-REF and FOIS-1; Ocean Optics Inc.) connected to a spectroradiometer (HR-2000, Ocean Optics). Fig. 8 View largeDownload slide A spectral distribution of absorptance of cucumber leaves. The ranges between mean values + SEs and mean values − SEs for means from three independent experiments are shown. Absorptance at a given wavelength was calculated from reflectance and transmittance measured with integrating spheres (ISP-REF and FOIS-1; Ocean Optics Inc.) connected to a spectroradiometer (HR-2000, Ocean Optics). Comparison of actual and estimated gross photosynthetic rates Because direct ETR measurement was not possible, the actual and estimated values of Pg were compared. The actual Pg was obtained by adding Rd and Pn measured under several combinations of ABSR and ABSFR. The estimated Pg was assumed to be in proportion to the estimated ETR, as in the following equation:   Pg=k×ETR, (7) where k is the coefficient representing the number of fixed CO2 molecules per electron transported from PSI to ferredoxin. The k value for each leaf was calculated from the actual Pg and estimated ETRII (i.e. ABS×f×YII) under R, and was assumed to be constant irrespective of the PFD of the supplemental FR. The mean k values ranged from 0.16 to 0.19 in the three replicated experiments. Changes in the operating efficiency of the Calvin cycle and in the activities of several alternative electron flows potentially affect the k value. As the measurements were made under constant high CO2 partial pressures, the efficiency of the Calvin cycle was presumed to be constant. Several alternative flows derived from the electron carriers after P700, i.e. cyclic electron flow around PSI (Shikanai 2007), the water–water cycle initiated by the Mehler reaction (Mehler 1951, Asada 1999), malate–oxaloacetate shuttles (Scheibe 2004) and metabolic pathways (e.g. nitrogen and sulfur reduction), were presumed to consume constant fractions of the whole-chain ETR, and thus not to affect k. These assumptions are likely to be valid because the major alternative electron flows—cyclic electron flow and the water–water cycle—are likely to be regulated under excess light conditions to protect the photosynthetic apparatus. Although recent work has suggested that the activity of the NADH dehydrogenase-like complex-dependent cyclic electron transfer pathway is regulated by PFD in rice (Yamori et al. 2015), its effect on the k value was ignored because of the minor contribution of this pathway to total PSI cyclic electron transport activity (Shikanai 2016) and the small range of PFD in the present measurements. The Pg was also estimated using the integration method (Equation 1). The extent of the enhancement effect was calculated as Pg under R + FR/(Pg under R + Pg under FR) − 1. Statistical analysis All statistical analyses were performed with the R program (R Core Team 2016). Means of values from 2–4 leaves from different plants were used for the analyses. The measurements were replicated three times. Supplementary Data Supplementary data are available at PCP online. Funding This work was supported by the Japan Society for the Promotion of Science (JSPS) [KAKENHI grant No. 26·9372 to K.M.]. Acknowledgments The authors are grateful to Professor Ichiro Terashima (Graduate School of Science, The University of Tokyo) for helpful suggestions. Disclosures The authors have no conflicts of interest to declare. References Anderson J.M., Chow W.S., Park Y.-I. ( 1995) The grand design of photosynthesis: acclimation of the photosynthetic apparatus to environmental cues. Photosynth. Res . 46: 129– 139. Google Scholar CrossRef Search ADS PubMed  Asada K. ( 1999) The water–water cycle in chloroplast: scavenging of active oxygens and dissipation of excess photons. Annu. Rev. Plant Physiol. Plant Mol. Biol.  50: 601– 639. Google Scholar CrossRef Search ADS PubMed  Campbell G.S., Norman J.M. ( 1998) Radiation basics. In An Introduction to Environmental Biophysics , 2nd edn. pp. 147– 165. Springer Verlag, New York. Google Scholar CrossRef Search ADS   Chow W.S., Goodchild D.J., Miller C., Anderson J.M. ( 1990a) The influence of high levels of brief or prolonged supplementary far-red illumination during growth on the photosynthetic characteristics, composition and morphology of Pisum sativum chloroplasts. Plant Cell Environ.  13: 135– 145. Google Scholar CrossRef Search ADS   Chow W.S., Melis A., Anderson J.M. ( 1990b) Adjustments of photosystem stoichiometry in chloroplasts improve the quantum efficiency of photosynthesis. Proc. Natl. Acad. Sci. USA  87: 7502– 7506. Google Scholar CrossRef Search ADS   Emerson R., Chalmers R., Cederstrand C. ( 1957) Some factors influencing the long-wave limit of photosynthesis. Proc. Natl. Acad. Sci. USA  43: 133– 143. Google Scholar CrossRef Search ADS   Emerson R., Lewis C.M. ( 1943) The dependence of the quantum yield of chlorella photosynthesis on wave length of light. Amer. J. Bot . 30: 165– 178. Google Scholar CrossRef Search ADS   Evans J.R. ( 1986) Quantitative analysis of light distribution between the two photosystems, considering variation in both the relative amounts of the chlorophyll–protein complexes and the spectral quality of light. Photobiochem. Photobiophys . 10: 135– 148. Evans J.R. ( 1987) The dependence of quantum yield on wavelength and growth irradiance. Aust. J. Plant Physiol.  14: 69– 79. Google Scholar CrossRef Search ADS   Evans J.R., Anderson J.M. ( 1987) Absolute absorption and relative fluorescence excitation spectra of the five major chlorophyll–protein complexes from spinach thylakoid membranes. Biochim. Biophys. Acta  892: 75– 82. Google Scholar CrossRef Search ADS   Farquhar G., von Caemmerer S. ( 1982) Modelling of photosynthetic response to environmental conditions. In Physiological Plant Ecology II . Edited by Lange O.L., Nobel P.S., Osmond C.B., Ziegler H. pp. 549– 587. Springer-Verlag, Berlin. Google Scholar CrossRef Search ADS   Farquhar G., von Caemmerer S., Berry J. ( 1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta  149: 78– 90. Google Scholar CrossRef Search ADS PubMed  Farquhar G., Wong S. ( 1984) An empirical model of stomatal conductance. Aust. J. Plant Physiol.  11: 191– 210. Google Scholar CrossRef Search ADS   Goldschmidt-Clermont M., Bassi R. ( 2015) Sharing light between two photosystems: mechanism of state transitions. Curr. Opin. Plant Biol . 25: 71– 78. Google Scholar CrossRef Search ADS PubMed  Hogewoning S.W., Douwstra P., Trouwborst G., van Ieperen W., Harbinson J. ( 2010) An artificial solar spectrum substantially alters plant development compared with usual climate room irradiance spectra. J. Exp. Bot . 61: 1267– 1276. Google Scholar CrossRef Search ADS PubMed  Hogewoning S.W., Wientjes E., Douwstra P., Trouwborst G., van Ieperen W., Croce R. ( 2012) Photosynthetic quantum yield dynamics: from photosystems to leaves. Plant Cell  24: 1921– 1935. Google Scholar CrossRef Search ADS PubMed  Inada K. ( 1976) Action spectra for photosynthesis in higher plants. Plant Cell Physiol . 17: 355– 365. Inada K. ( 1978) Photosynthetic enhancement spectra in higher plants. Plant Cell Physiol . 19: 1007– 1017. Google Scholar CrossRef Search ADS   Kim J.H., Glick R.E., Melis A. ( 1993) Dynamics of photosystem stoichiometry adjustment by light quality in chloroplasts. Plant Physiol.  102: 181– 190. Google Scholar CrossRef Search ADS PubMed  Klughammer C., Schreiber U. ( 1994) An improved method, using saturating light pulses, for the determination of photosystem I quantum yield via P700+-absorbance changes at 830 nm. Planta  192: 261– 268. Google Scholar CrossRef Search ADS   Kono M., Terashima I. ( 2014) Long-term and short-term responses of the photosynthetic electron transport to fluctuating light. J. Photochem. Photobiol . 137: 89– 99. Google Scholar CrossRef Search ADS   Kramer D.M., Johnson G., Kiirats O., Edwards G.E. ( 2004) New fluorescence parameters for the determination of QA redox state and excitation energy fluxes. Photosynth. Res . 79: 209– 218. Google Scholar CrossRef Search ADS PubMed  Laisk A., Eichelmann H., Oja V. ( 2015) Oxidation of plastohydroquinone by photosystem II and by dioxygen in leaves. Biochim. Biophys. Acta  1847: 565– 575. Google Scholar CrossRef Search ADS PubMed  Laisk A., Oja V., Eichelmann H., Dall’Osto L. ( 2014) Action spectra of photosystems II and I and quantum yield of photosynthesis in leaves in State 1. Biochim. Biophys. Acta  1837: 315– 325. Google Scholar CrossRef Search ADS PubMed  Matsuda R., Ohashi-Kaneko K., Fujiwara K., Goto E., Kurata K. ( 2004) Photosynthetic characteristics of rice leaves grown under red light with or without supplemental blue light. Plant Cell Physiol.  45: 1870– 1874. Google Scholar CrossRef Search ADS PubMed  McCree K.J. ( 1972a) The action spectrum, absorptance and quantum yield of photosynthesis in crop plants. Agric. Meteorol . 9: 191– 216. Google Scholar CrossRef Search ADS   McCree K.J. ( 1972b) Significance of enhancement for calculations based on the action spectrum for photosynthesis. Plant Physiol . 49: 704– 706. Google Scholar CrossRef Search ADS   Mehler A.H. ( 1951) Studies on reactions of illuminated chloroplasts: I. Mechanism of the reduction of oxygen and other hill reagents. Arch. Biochem. Biophys.  33: 65– 77. Google Scholar CrossRef Search ADS PubMed  Melis A. ( 1991) Dynamics of photosynthetic membrane composition and function. Biochim. Biophys. Acta  1058: 87– 106. Google Scholar CrossRef Search ADS   Murakami K., Matsuda R., Fujiwara K. ( 2016) Interaction between the spectral photon flux density distributions of light during growth and for measurements in net photosynthetic rates of cucumber leaves. Physiol. Plant.  158: 213– 224. Google Scholar CrossRef Search ADS PubMed  Murakami K., Matsuda R., Fujiwara K. ( 2017) A basis for selecting light spectral distribution for evaluating leaf photosynthetic rates of plants grown under different light spectral distributions. Environ. Control Biol.  55: 1– 6. Google Scholar CrossRef Search ADS   Murakami K., Matsuda R., Fujiwara K. ( 2018) Quantification of excitation energy distribution between photosystems based on a mechanistic model of photosynthetic electron transport. Plant Cell Environ.  41: 148– 159. Google Scholar CrossRef Search ADS PubMed  Nawrocki W.J., Tourasse N.J., Taly A., Rappaport F., Wollman F.-A. ( 2015) The plastid terminal oxidase: its elusive function points to multiple contributions to plastid physiology. Annu. Rev. Plant Biol.  66: 49– 74. Google Scholar CrossRef Search ADS PubMed  Niyogi K.K. ( 1999) Photoprotection revisited: genetic and molecular approaches. Annu. Rev. Plant Physiol. Plant Mol. Biol.  50: 333– 359. Google Scholar CrossRef Search ADS PubMed  Pfannschmidt T., Nilsson A., Allen J.F. ( 1999) Photosynthetic control of chloroplast gene expression. Nature  397: 625– 628. Google Scholar CrossRef Search ADS   R Core Team ( 2016) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Scheibe R. ( 2004) Malate valves to balance cellular energy supply. Physiol. Plant.  120: 21– 26. Google Scholar CrossRef Search ADS PubMed  Sharkey T.D. ( 1985) Photosynthesis in intact leaves of C3 plants: physics, physiology and rate limitations. Bot. Rev.  51: 53– 105. Google Scholar CrossRef Search ADS   Shikanai T. ( 2007) Cyclic electron transport around photosystem I: genetic approaches. Annu. Rev. Plant Biol.  58: 199– 217. Google Scholar CrossRef Search ADS PubMed  Shikanai T. ( 2016) Chloroplast NDH: a different enzyme with a structure similar to that of respiratory NADH dehydrogenase. Biochim. Biophys. Acta  1857: 1015– 1022. Google Scholar CrossRef Search ADS PubMed  Smith H. ( 1982) Light quality, photoperception, and plant strategy. Annu. Rev. Plant Physiol.  33: 481– 518. Google Scholar CrossRef Search ADS   Vass I. ( 2011) Role of charge recombination processes in photodamage and photoprotection of the photosystem II complex. Physiol. Plant.  142: 6– 16. Google Scholar CrossRef Search ADS PubMed  Wagner R., Dietzel L., Bräutigam K., Fischer W., Pfannschmidt T. ( 2008) The long-term response to fluctuating light quality is an important and distinct light acclimation mechanism that supports survival of Arabidopsis thaliana under low light conditions. Planta  228: 573– 587. Google Scholar CrossRef Search ADS PubMed  Walters R.G. ( 2005) Towards an understanding of photosynthetic acclimation. J. Exp. Bot.  56: 435– 447. Google Scholar CrossRef Search ADS PubMed  Walters R.G., Horton P. ( 1994) Acclimation of Arabidopsis thaliana to the light environment: changes in composition of the photosynthetic apparatus. Planta  195: 248– 256. Google Scholar CrossRef Search ADS   Walters R.G., Horton P. ( 1995) Acclimation of Arabidopsis thaliana to the light environment: changes in photosynthetic function. Planta  197: 306– 312. Google Scholar PubMed  Weiss I., Mizrahi Y., Raveh E. ( 2009) Chamber response time: a neglected issue in gas exchange measurements. Photosynthetica  47: 121– 124. Google Scholar CrossRef Search ADS   Wientjes E., van Amerongen H., Croce R. ( 2013) LHCII is an antenna of both photosystems after long-term acclimation. Biochim. Biophys. Acta  1827: 420– 426. Google Scholar CrossRef Search ADS PubMed  Yamori W., Shikanai T. ( 2016) Physiological functions of cyclic electron transport around photosystem I in sustaining photosynthesis and plant growth. Annu. Rev. Plant Biol.  67: 81– 106. Google Scholar CrossRef Search ADS PubMed  Yamori W., Shikanai T., Makino A. ( 2015) Photosystem I cyclic electron flow via chloroplast NADH dehydrogenase-like complex performs a physiological role for photosynthesis at low light. Sci. Rep.  5: 1– 9. Zhen S., van Iersel M.W. ( 2017) Far-red light is needed for efficient photochemistry and photosynthesis. J. Plant Physiol.  209: 115– 122. Google Scholar CrossRef Search ADS PubMed  Abbreviations Abbreviations ABS flux density of absorbed photons EI and EII excitation energy distributed to PSI and PSII ETR electron transport rate f fraction of excitation energy distributed to PSII FR far-red LED light LED light-emitting diode pETRII and pETRI potential electron transport rates at PSII and PSI Pg gross photosynthetic rate Pn net photosynthetic rate PFD photon flux density qL a parameter estimating the fraction of PSII centers in open states R red LED light Rd dark respiration rate YCO2 quantum yields of gross photosynthetic rate YII and YI quantum yields of photochemical reactions at PSII and PSI Ymax;II and Ymax;I maximum quantum yields of photochemical reactions at PSII and PSI YNA and YND quantum yields of the non-photochemical energy dissipation due to the acceptor- and donor-side limitations of PSI © The Author(s) 2018. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices) http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Plant and Cell Physiology Oxford University Press

A Mathematical Model of Photosynthetic Electron Transport in Response to the Light Spectrum Based on Excitation Energy Distributed to Photosystems

Loading next page...
 
/lp/ou_press/a-mathematical-model-of-photosynthetic-electron-transport-in-response-mZQEEbpCva
Publisher
Oxford University Press
Copyright
© The Author(s) 2018. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: journals.permissions@oup.com
ISSN
0032-0781
eISSN
1471-9053
D.O.I.
10.1093/pcp/pcy085
Publisher site
See Article on Publisher Site

Abstract

Abstract To enable us to analyze more systematically the effects of the spectral distribution of light (i.e. light quality) on photosynthetic electron transport, we propose a simple mathematical model which describes electron transport reactions under light-limited conditions based on the excitation energy distributed to the photosystems. The model assumes that the rate-limiting photosystem performs the photochemical reaction at its maximum yield, while the yield in the other photosystem is passively down-regulated to equalize the rates of linear electron transport through the photosystems. Using intact cucumber leaves, we tested the model by comparing actual and estimated photosynthetic parameters under several combinations of photon flux densities of red and far-red lights (R and FR, respectively). Simultaneously provided R and FR yielded greater gross photosynthetic rates than the sums of the rates under only R and only FR, which is known as the ‘enhancement effect’. The present model reproduced these non-additive increases in the gross photosynthetic rates in response to supplemental FR to R and provided more accurate estimates than an existing method that did not take the enhancement effect into account (root mean square errors: 0.11 and 0.21 μmol m-2 s-1, respectively). Using the present model, the photon flux density of the supplemental FR which gives the changing point of rate-limiting photosystem and the photochemical yields of the non-rate-limiting photosystems were estimated reasonably well. The present study has therefore formulated a simplified quantitative electron transport model in response to the light spectrum based on generally accepted concepts and demonstrated its validity experimentally. Introduction Photosynthetic electron transport and CO2 fixation rates and their quantum yields under light-limited conditions are essential indices for understanding the acclimation responses of a leaf to its environment and for regulating the light environment in horticulture. The number of fixed CO2 molecules per electron transported to NADP+ has been described by the C3 photosynthesis model (Farquhar et al. 1980, Farquhar and von Caemmerer 1982, Sharkey 1985). As long as the relative spectral distribution of light (i.e. light quality) is constant, the photosynthetic electron transport rate (ETR) is generally expressed as an empirical function of the incident photosynthetically active photon flux density (PFD), a curvature factor which indicates how abruptly the light curve saturates, maximum ETR and the maximum quantum yield of ETR (Farquhar and Wong 1984). Among these parameters, the maximum quantum yield is known to depend on the wavelength and the light spectrum of the incident light (e.g. Emerson and Lewis 1943). Therefore, the gross photosynthetic rate (Pg) also depends on the light spectrum. Under strictly light-limited conditions (i.e. ETR is in proportion to the incident PFD), Pg under light with a given spectral distribution can be calculated from the photosynthetic action spectrum (e.g. McCree 1972b, McCree 1972a, Inada 1976) as follows:   Pg≃∑λ{PFDλ×αλ×YCO2,λ }, (1) where PFDλ is the PFD of incident light, αλ is the leaf absorptance and YCO2,λ, the photosynthetic quantum yield (i.e. Pg/flux density of an absorbed photon) at a wavelength of λ. However, this integration method is expected to underestimate Pg because it does not consider the ‘enhancement effect’ (Emerson et al. 1957; described below). In organisms performing oxygenic photosynthesis, the photosynthetic electron transport chain (i.e. the Z-scheme) is anchored by photochemical reactions that occur in PSII and PSI. The excitation energy derived from absorbed photons and transferred to the reaction centers of the photosystems is consumed by serial photochemical reactions. It has been reported that excitation energy distribution between the photosystems depends on the wavelength of light (Evans 1986, Evans 1987, Evans and Anderson 1987, Hogewoning et al. 2012, Wientjes et al. 2013, Laisk et al. 2014, Murakami et al. 2018) and thus on the light spectrum. Under light whose excitation energy is preferentially distributed to PSII (PSII-light), a part of the energy distributed to PSII is not used for electron transport because the photochemical reaction in PSI limits the whole-chain ETR. Likewise, if the excitation energy is preferentially distributed to PSI (PSI-light), some of the energy distributed to PSI is accordingly dissipated. In other words, the photochemical reaction in the non-rate-limiting photosystem is passively down-regulated by the reaction in the other photosystem. When these PSII- and PSI-lights are simultaneously provided, the energy distributed to the photosystems is somewhat counterbalanced, and thus the resultant ETR will be greater than the sum of ETRs under PSII- and PSI-lights that are provided individually. Apparently, Equation 1 holds true only if the effects of PFDs at different wavelengths on the Pg are independent and additive. The simply integrated estimates from the light spectrum were indeed smaller than those actually measured in some studies, due to the enhancement effect (e.g. Inada 1978, Hogewoning et al. 2012). The spectrum of incident light on a leaf changes with physical (e.g. solar zenith angle, cloudiness and atmospheric composition; Campbell and Norman 1998), biological (e.g. canopy structure; Smith 1982) and agricultural factors (e.g. use of artificial light sources and wavelength-selective covering materials). Quantitative models of the effect of the light spectrum on the photosynthetic electron transport must be useful to analyze these factors systematically. As mentioned above, it has generally been accepted that excitation energy distribution between PSII and PSI is the major determinant of the ETR under light-limited conditions. Because some methods for the estimation of the excitation energy distribution at a given wavelength are available (Evans 1986, Evans 1987, Evans and Anderson 1987, Hogewoning et al. 2012, Wientjes et al. 2013, Laisk et al. 2014), energy distributed to PSII and PSI can be calculated from the spectral distribution of the light. However, little work on quantitative modeling of the light spectrum effects on the electron transport has been done, and there is no method to estimate ETR based on the excitation energy distributed to the respective photosystems. The aim of this study was to develop a quantitative model describing the electron transport under light-limited conditions based on the excitation energy distributed to the photosystems and taking the enhancement effects into account. Here, we formulated a simple mathematical model of the electron transport and tested its validity under conditions where the enhancement occurred. The ETR and photochemical yields of the photosystems (YII and YI) under simultaneously provided red light (R) and far-red light (FR)—typical PSII- and PSI-light, respectively—were estimated using the model and compared with those actually measured. The ETR estimated by the present model was also compared with the ETR obtained using the integration method that did not incorporate the enhancement effect (i.e. Equation 1). We also evaluated the redox state of the photosynthetic intermediate between the photosystems and the quantum yields of non-photochemical energy dissipation in PSI to analyze rate-limiting factors of the electron transport from PSII to PSI under conditions where the enhancement occurred. Results The present model estimates the whole-chain ETR, YII and YI based on the excitation energy distribution between the photosystems (Fig. 1a; see also the Materials and Methods). To determine the excitation energy distribution under simultaneously provided R and FR, the fractions of energy distributed to PSII for R and FR (fR and fFR) were determined using a curve-fitting method without measuring gas exchange rates (Fig. 1b; see also Murakami et al. 2018). The mean values of fR and fFR in the three replicated experiments were 0.54 and 0.16 (replicate 1), 0.55 and 0.15 (replicate 2), and 0.56 and 0.18 (replicate 3), respectively. Supplemental FR to R increased Pg (Fig. 2) and YII (Fig. 3a), while it decreased YI (Fig. 3b). The actual values of Pg under R + FR were always greater than those estimated using the integration method (i.e. the sum of Pg values under only R and only FR) (Fig. 2). These differences were presumably caused by the enhancement effect. The maximum extent of the enhancement effect ranged from 6.1 to 7.5% in the three replicates. In the present model, the estimates based on the excitation energy distributed to the photosystems reduced these differences (Fig. 2). The YII and YI under R + FR were estimated using Equations 5 and 6 (Fig. 3). The horizontal parts of the lines indicate the measured maximum yields (Ymax,II and Ymax,I) under individually provided FR and R, respectively. The model closely reproduced the decrease in YI in response to the increase in the PFD of supplemental FR (Fig. 3b). The estimates of YII also reproduced the measured trends, although the estimated values tended to be greater than the measured values (Fig. 3a). Fig. 1 View largeDownload slide (a) A schematic diagram of the present electron transport model. (1) Potential electron transport rates through the photosystems (pETRII and pETRI) are calculated from their maximum yields (Ymax,II and Ymax,I) and the excitation energy (EII and EI), (2) the whole-chain ETR is given as the minimum of the pETRs and (3) the photochemical yield of the non-rate-limiting photosystem was passively down-regulated so as to equalize the ETRs through the photosystems. The diagram shows the electron transport under a PSII-limited condition. See text for details. (b) An irradiation scheme adopted to determine the excitation energy distributions for red (R) and far-red light (FR) (adapted from Murakami et al. 2018 with modifications). An electron transport model was fitted to YII/YI values measured under several combinations of flux densities of absorbed R and FR photons (ABSR and ABSFR) to estimate the fractions of excitation energy distributed to PSII (fR and fFR). Fig. 1 View largeDownload slide (a) A schematic diagram of the present electron transport model. (1) Potential electron transport rates through the photosystems (pETRII and pETRI) are calculated from their maximum yields (Ymax,II and Ymax,I) and the excitation energy (EII and EI), (2) the whole-chain ETR is given as the minimum of the pETRs and (3) the photochemical yield of the non-rate-limiting photosystem was passively down-regulated so as to equalize the ETRs through the photosystems. The diagram shows the electron transport under a PSII-limited condition. See text for details. (b) An irradiation scheme adopted to determine the excitation energy distributions for red (R) and far-red light (FR) (adapted from Murakami et al. 2018 with modifications). An electron transport model was fitted to YII/YI values measured under several combinations of flux densities of absorbed R and FR photons (ABSR and ABSFR) to estimate the fractions of excitation energy distributed to PSII (fR and fFR). Fig. 2 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (open symbols) and values estimated using the integration method (filled symbols) and the model based on the distribution of excitation energy (lines) are shown. Pg values estimated using the model were limited by the potential electron transport, either in PSII (dotted lines and their extensions) or in PSI (dashed lines and their extensions). Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. Fig. 2 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (open symbols) and values estimated using the integration method (filled symbols) and the model based on the distribution of excitation energy (lines) are shown. Pg values estimated using the model were limited by the potential electron transport, either in PSII (dotted lines and their extensions) or in PSI (dashed lines and their extensions). Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. Fig. 3 View largeDownload slide Photochemical quantum yields of (a) PSII (YII) and (b) PSI (YI) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (symbols) and values estimated using the model based on the excitation energy distribution (lines) are shown. Means ± SDs from values of 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. Fig. 3 View largeDownload slide Photochemical quantum yields of (a) PSII (YII) and (b) PSI (YI) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Actual values (symbols) and values estimated using the model based on the excitation energy distribution (lines) are shown. Means ± SDs from values of 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. The model inputs are listed in Supplementary Table S1. The broken points of the estimated lines by the present method (Figs. 2, 3) were the changing points of the ETR limitation. To the left of these points, the estimated potential ETR at PSI (i.e. pETRI) was smaller than that at PSII (i.e. pETRII) and limited the whole-chain ETR. As the PFD of the supplemental FR increased, the excitation energy distribution reached equilibrium (i.e. pETRII = pETRI), where both PSII and PSI were assumed to achieve their maximum quantum yields. An increase in the PFD of the supplemental FR beyond the equilibrium values intensified PSI overexcitation and reduced YI (Fig. 3b). The estimated FR PFDs giving the broken points in the model lines were higher in replicates 1 and 3 than in replicate 2 (see also Supplementary Fig. S1). The higher FR PFDs in replicate 1 than in replicate 2 resulted from a slightly higher (∼5 µmol m−2 s−1) R PFD. The higher FR PFDs in replicate 3 than in replicate 2 resulted from the higher fR and fFR values. The supplemental FR on top of R slightly decreased 1 − qL values or oxidized the plastoquinone pool (Fig. 4a), suggesting that the electron transport from the pool to PSI was promoted by overexciting PSI. The limiting factor of photochemical reactions in PSI was shifted from the acceptor side (YNA) to the donor side (YND) by the supplemental FR (Fig. 4b, c). These data also confirm that the supplemental FR excited PSI more than PSII. Fig. 4 View largeDownload slide (a) The fraction of closed PSII reaction centers (1 − qL), the quantum yields of non-photochemical energy dissipation in PSI due to (b) the acceptor-side limitation (YNA) and (c) the donor-side limitation (YND) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. Fig. 4 View largeDownload slide (a) The fraction of closed PSII reaction centers (1 − qL), the quantum yields of non-photochemical energy dissipation in PSI due to (b) the acceptor-side limitation (YNA) and (c) the donor-side limitation (YND) of cucumber leaves in response to photon flux density of supplemental far-red LED light (FR) to red LED light. Means ± SDs of values from 2–4 leaves are shown. Photon flux densities of red light were 60.2, 55.4 and 55.4 µmol m−2 s−1 in the three replicates, respectively. Our model incorporated the enhancement effect and provided more accurate estimates of Pg (root mean square error: 0.11 µmol m−2 s−1) than those obtained using the integration method (root mean square error: 0.21 µmol m−2 s−1) (Fig. 5), suggesting an increased accuracy of ETR estimates. The present model tended to overestimate the Pg, especially in the high-value range (i.e. when the PFD of the supplemental FR increased; Fig. 5). Fig. 5 View largeDownload slide The relationship between the actual and estimated values of gross photosynthetic rates (Pg) of cucumber leaves. Estimates obtained using the integration method (filled symbols) and the model based on the distribution of excitation energy (open symbols) were compared. Symbols indicate means of values from 2–4 leaves. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 5 View largeDownload slide The relationship between the actual and estimated values of gross photosynthetic rates (Pg) of cucumber leaves. Estimates obtained using the integration method (filled symbols) and the model based on the distribution of excitation energy (open symbols) were compared. Symbols indicate means of values from 2–4 leaves. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Under individually provided R and FR, Pg was in proportion to the incident PFDs (Fig. 6). YII was slightly higher under FR than under R (Fig. 7a, b). YI was substantially smaller under FR than under R (Fig. 7c, d). The observed maximum yields of the photosystems (i.e. YII under FR and YI under R) were used as model inputs (Ymax,II and Ymax,I in Equations 2 and 4–6). YI remained almost constant under different PFDs of R, while it decreased with the increase in the PFD of the FR (P = 0.0029). Fig. 6 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves under (a) red LED light (R) and (b) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 6 View largeDownload slide Gross photosynthetic rates (Pg) of cucumber leaves under (a) red LED light (R) and (b) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 7 View largeDownload slide Photochemical quantum yields of (a, b) PSII (YII) and (c, d) PSI (YI) of cucumber leaves under (a, c) red LED light (R) and (b, d) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Fig. 7 View largeDownload slide Photochemical quantum yields of (a, b) PSII (YII) and (c, d) PSI (YI) of cucumber leaves under (a, c) red LED light (R) and (b, d) far-red LED light (FR). Means ± SDs of values from 2–4 leaves are shown. Data from the three replicates are indicated by different symbols. Regression lines and 95% confidence intervals (gray shadings) are shown. Discussion In this study, photosynthetic electron transport was illustrated using a mathematical model based on the excitation energy distribution between the photosystems (Fig. 1a). Good agreement between the actual and estimated values of Pg, YII and YI under R + FR (Figs. 2, 3, 5) supports the reliability of the proposed model. The essential assumptions of the proposed model are as follows: (i) the whole-chain ETR is given as the minimum of potential ETR at either PSII or PSI; (ii) the rate-limiting photosystem performs the photochemical reaction at its maximum quantum yield; and (iii) the photochemical yield of the non-rate-limiting photosystem is determined so as to equalize the actual ETR in the two photosystems. In other words, the yield of the non-rate-limiting photosystem was assumed to be passively down-regulated. The present study experimentally tested these qualitatively accepted assumptions and demonstrated their plausibility, at least under the strictly light-limited conditions. Note that the model will not hold under high light conditions because energy-dissipating mechanisms are activated under high light conditions (Niyogi 1999) and the rate-limiting photosystem does not perform to its maximum yield. Our model and the adopted approach might be useful for separating decreases in the photosynthetic yield into actively and passively regulated fractions. In addition, depending on the redox state of the electron transport under prolonged irradiation with different light spectra, leaf properties involved in the excitation energy distribution are adjusted by several acclimatory responses (e.g. Chow et al. 1990a, Chow et al. 1990b, Melis 1991, Kim et al. 1993, Walters and Horton 1994, Walters and Horton 1995, Pfannschmidt et al. 1999, Wagner et al. 2008, Hogewoning et al. 2012, Murakami et al. 2016, Murakami et al. 2018). These acclimatory responses include the dynamic reallocation of the light-harvesting antenna complex (i.e. state transitions; Goldschmidt-Clermont and Bassi 2015) and the long-term adjustment of the photosystem stoichiometry (Anderson et al. 1995). Analyzing the changes in the excitation energy distribution due to these responses and simulating their effects on the ETR under various environmental conditions (e.g. fluctuating light spectrum in the understorey) by using the model proposed here may be useful to understand the physiological roles and in situ contributions of these responses. The model corrected the gap between the measured Pg values and estimated values from the integration method (Figs. 2, 5) because this model accounts for the ‘enhancement effect’ ignored in the integration method (see also the Introduction). In higher plants, at most 16% (Inada 1978) and 21% (Hogewoning et al. 2012) enhancements in Pg have been experimentally demonstrated, while some experiments have found no enhancement (McCree 1972b, McCree 1972a). In the present study, we observed enhancement at an intermediate extent of at most 7.5%. The difference among the extents could be caused by several factors affecting the excitation energy distribution between the photosystems, such as the spectral distribution of growth light (e.g. Chow et al. 1990a, Chow et al. 1990b, Melis 1991, Kim et al. 1993, Walters and Horton 1994, Walters and Horton 1995, Pfannschmidt et al. 1999, Wagner et al. 2008, Hogewoning et al. 2012, Murakami et al. 2016, Murakami et al. 2018) and the spectral distributions of simultaneously provided lights (e.g. Evans 1986, Evans 1987, Evans and Anderson 1987, Hogewoning et al. 2012, Wientjes et al. 2013, Laisk et al. 2014). Zhen and van Iersel (2017) also showed significant non-additive enhancements in net photosynthetic rates by adding several PFDs of supplemental FR to white and blue + red LED light. The model did not completely explain the electron transport under R or FR light provided individually. When acclimatory responses (i.e. state transitions and adjustments of photosystem stoichiometry) do not occur and leaf properties involved in the excitation energy distribution are not changed, the excitation balance (i.e. EII/EI) is likely to depend only on the light spectrum and not on the PFD. Since this study was designed to minimize these changes in the leaf properties, the present model expected constant YII and YI irrespective of the PFD of individually provided R or FR (Equations 5 and 6). However, YI decreased in response to the PFD of individually provided FR (Fig. 7d). As the Pg measured under these conditions was in proportion to the incident PFD (Fig. 6b), YCO2 should be constant in spite of the gradual decrease in the measured YI. Similar decreases in YII without a decrease in YCO2 have been observed in cucumber (Hogewoning et al. 2012) and lettuce (data not shown) under low PFDs of PSII-light (narrow-waveband blue and red LED light). The decrease in the photochemical yields without an accompanying reduction in YCO2 might be related to the activities of alternative electron flows, as Hogewoning et al. (2012) suggested. That is, fluxes to alternative electron pathways were present even under extremely low PFDs; they decreased with an increase in the PFDs. As fluxes to some alternative electron pathways do not affect the linear electron flow to ferredoxin, their reduction decreases YII or YI without reducing the YCO2. These pathways may include electron transport to O2 in PSII (Vass 2011) or to plastid terminal oxidase from plastoquinone (Nawrocki et al. 2015), cyclic electron flow around PSI (Shikanai 2007) and putative cyclic electron flow around PSII (e.g. Laisk et al. 2015). The lower YII under PSI-limited conditions (i.e. high supplemental FR conditions) than the Ymax,II, which was measured under only FR provided, might result from the regulation of these flows (Fig. 3a). Slight increases in 1 − qL (i.e. reduction of the plastoquinone pool) and YND in response to an increase in PFD of FR (Supplementary Fig. S2b, f) might result from ‘photosynthetic control’ initiated by the cyclic electron flow around PSI (e.g. Kono and Terashima 2014). On the other hand, it is also possible that the decreases in YII and YI reflected the decrease in the actual YCO2. In this case, the reduced actual YCO2may be compensated for by electron influxes from other electron donors to maintain the constant apparent YCO2. These pathways may include electron transport from the NADH dehydrogenase-like complex to the plastoquinone pool (Shikanai 2016) and malate–oxaloacetate shuttles (Scheibe 2004). Although either or both of these regulations in the alternative electron flows might operate in vivo, their contribution to the electron transport should be small because the estimated Pg, YII and YI (Figs. 2, 3, 5) were in good agreement with the measured values in the present experimental conditions. The regulation of these alternative electron pathways, in particular cyclic electron flow around PSI, might play key roles in fluctuating and unfavorable (e.g. drought, extreme temperatures and high salinity) environments (for a review, see Yamori and Shikanai 2016) compared with the steady and moderate environment adopted in this study. Incorporating activities of the alternative electron pathways into the model must be a promising step to understanding in situ roles of these pathways. Because the present model estimates the ETR from the distributed excitation energy to PSII and PSI, estimating EII and EI from the light spectrum may result in a deeper understanding of the ETR response to the light spectrum. Recent measurements of leaf photosynthetic rates are usually performed using commercially available blue and red LED light, but what needs to be known are not the rates under light in most cases. This discrepancy between the measuring light spectra causes systematic biases in measured rates and other parameters (e.g. Chl fluorescence parameters), as some studies have pointed out (Walters 2005, Murakami et al. 2016, Murakami et al. 2017). Inferring the rates under sunlight from the rates measured under an artificial light source is necessary to remove biases and to analyze the in situ photosynthetic responses. In addition, a number of horticultural researchers have investigated the effect of the light spectrum on plant growth to enhance productivity by providing artificial light (e.g. Matsuda et al. 2004, Hogewoning et al. 2010). Owing to the lighting technique, in particular to LEDs, we can design and select the light spectrum from a wide variety of options. Preliminary estimation of the photosynthetic rates from the spectrum will be decisively important for optimization of the growth light spectrum. Materials and Methods Electron transport model The consumption of distributed excitation energy in PSII and PSI was illustrated using a simple mathematical model. This model was developed by extending an electron transport model described in our previous study (Murakami et al. 2018). Not all excitation energy distributed to the photosystems is consumed in the photosynthetic electron transport, even in the photosystem which limits the whole-chain ETR. For instance, the maximum photochemical quantum yield of PSII is not greater than approximately 0.8 even under FR light (i.e. PSI-light) at a low PFD (e.g. Hogewoning et al. 2012). The products of the maximum yields (Ymax,II and Ymax,I) and the distributed excitation energy (EII and EI, mol m−2 s−1) were presumed to determine the potential ETR through PSII and PSI (pETRII and pETRI, mol m−2 s−1). The whole-chain ETR was assumed to be limited by the smaller potential ETR at either PSII or PSI, as follows:   ETR=min{pETRII,pETRI}=min{EII×Ymax, II,EI×Ymax, I}. (2) The rate-limiting photosystem performs the photochemical reaction at its maximum quantum yield in this model. The photochemical yield of the other photosystem—the non-rate-limiting photosystem—is passively down-regulated so that the ETRs through PSII and PSI balance. The maximum yields of the photosystems of a leaf should be constant in the short term, at least over a period of a few minutes. The excitation energy derived from simultaneously provided lights with different spectra may be additive as long as the leaf properties related to the distribution of excitation energy are unchanged. Thus, EII and EI under two simultaneously provided lights (light1 and light2) can be calculated as follows:   EII=EII, light1 + EII, light2=ABSlight1×flight1 + ABSlight2×flight2,EI=EI, light1+ EI, light2=ABSlight1×(1−flight1) + ABSlight2×(1−flight2), (3) where ABSlight1 and ABSlight2 are photons of light1 and light2 absorbed by the leaf (i.e. incident PFD×absorptance; mol m−2 s−1), and flight1 and flight2 are fractions of the excitation energy from light1 and light2 distributed to PSII, respectively. Note that the photons absorbed by the leaf are distributed not only to the photosystems but also to other substrates (e.g. non-photosynthetic pigments) although the latter was not considered in Equation 3. This factor may be negligible in the present study because the R and FR lights used in this study are minimally absorbed by non-photosynthetic pigments. By substituting Equation 3 into Equation 2, ETR under light1 + light2 is estimated as follows:   ETR=min{(ABSlight1×flight1 + ABSlight2×flight2)×Ymax, II,{ABSlight1×(1−flight1) + ABSlight2×(1−flight2)}×Ymax, I}. (4) The simulated effects of the parameters on the estimated ETR are shown in Supplementary Fig. S1. According to this model, YII and YI can also be estimated from Equations 3 and 4 as follows:   YII=ETREII=min{Ymax, II,EI×Ymax, IEII}=min{Ymax, II,ABSlight1×(1−flight1) + ABSlight2×(1−flight2)ABSlight1×flight1 + ABSlight2×flight2×Ymax, I},. (5) and   YI=ETREI=min{EII×Ymax, IIEI,Ymax, I}=min{ABSlight1×flight1 + ABSlight2×flight2ABSlight1×(1−flight1) + ABSlight2×(1−flight2)×Ymax, II,Ymax, I}.. (6) Plant material and growth conditions Cucumis sativus L. (cv. Hokushin) were hydroponically grown as described by Murakami et al. (2018). In brief, the plants were grown under white LED (NSPW310DS; Nichia Chemical Industries Ltd.) light at a photosynthetic PFD of 300 µmol m−2 s−1 for 14–16 d and were then subjected to the following measurements. Gas exchange, Chl fluorescence and 830 nm absorbance measurements Gas exchange, Chl fluorescence and 830 nm absorbance parameters of the first true leaves were simultaneously measured in a dark room using a portable gas exchange measurement system (LI-6400XT; LI-COR Inc.) and a fiber-type P700 and Chl fluorescence measuring system (DUAL-PAM/F; Heinz Walz GmbH). Red LED (SRK3-3A80-LE; Toricon) light (peak wavelength of 660 nm) and far-red LED (L735-36 AU; Epitex Inc.) light (peak wavelength of 735 nm) were used as actinic lights in the experiments (refer to fig. 2 in Murakami et al. 2018 for the spectra of the LED lights). All measurements were made under a low PFD (PFDR ∼60 µmol m−2 s−1) and a high intercellular CO2 concentration (∼100 Pa) to evaluate gas exchange rates and photochemical yields under strictly light-limited conditions (Supplementary Table S1; Fig. S3). The respiration rate (Rd) and steady-state Chl fluorescence in dark-treated (> 60 min) leaves (Fo) were measured in the dark. The maximum level of the P700 signal (P700 fully oxidized) in the dark (Pm) was determined by applying a saturation pulse in the presence of FR light at the peak wavelength of 720 nm. The zero P700 signal (P0) was determined when complete reduction of P700 was induced after the saturating pulse in the absence of FR light. The steady-state net photosynthetic rate (Pn), YII, YI, a parameter estimating the fraction of PSII centers in open states (qL; Kramer et al. 2004) and the quantum yields of non-photochemical energy dissipation in PSI due to the acceptor- and the donor-side limitations (YNA and YND; Klughammer and Schreiber 1994) of the leaves were measured under R. These parameters under FR and R + FR were then logged 60 s after the light transitions (i.e. R to FR and R + FR) to minimize potential changes in fR and fFR caused by the state transitions (Goldschmidt-Clermont and Bassi 2015). The leaf photosynthesis was presumed to reach the steady state immediately after the transitions because of the small differences in Pn due to the light transitions. Considering the gas flow rate (500 µmol s−1 or 11.2 cm3 s−1) and the path volume of the gas exchange measurement system (56.4 cm3), the difference in the gas concentrations between the inlet and outlet should reach 99% of its steady state within 23 s (Weiss et al. 2009). Quantification of the excitation energy distributions The fR and fFR of the leaves were evaluated on the same day as the gas exchange, Chl fluorescence and 830 nm absorbance. The fR and fFR of leaves pre-irradiated with R for 10 min were quantified by curve fitting as described by Murakami et al. (2018). In brief, we estimated f values by measuring ratios of photochemical yields under several PFD combinations of R and FR. The yield ratio was formulated as a function of ABSR, ABSFR, fR and fFR, assuming the same ETR through PSII and PSI. The f values were quantified by fitting this formula to measured sets of values (i.e. YII, YI, ABSR and ABSFR). The measurements were made under two different levels of ABSR supplemented with several levels of ABSFR. Note that the f values were quantified without gas exchange parameters. ABSR and ABSFR were calculated from the spectral distributions of leaf absorptance (Fig. 8) and actinic lights. Fig. 8 View largeDownload slide A spectral distribution of absorptance of cucumber leaves. The ranges between mean values + SEs and mean values − SEs for means from three independent experiments are shown. Absorptance at a given wavelength was calculated from reflectance and transmittance measured with integrating spheres (ISP-REF and FOIS-1; Ocean Optics Inc.) connected to a spectroradiometer (HR-2000, Ocean Optics). Fig. 8 View largeDownload slide A spectral distribution of absorptance of cucumber leaves. The ranges between mean values + SEs and mean values − SEs for means from three independent experiments are shown. Absorptance at a given wavelength was calculated from reflectance and transmittance measured with integrating spheres (ISP-REF and FOIS-1; Ocean Optics Inc.) connected to a spectroradiometer (HR-2000, Ocean Optics). Comparison of actual and estimated gross photosynthetic rates Because direct ETR measurement was not possible, the actual and estimated values of Pg were compared. The actual Pg was obtained by adding Rd and Pn measured under several combinations of ABSR and ABSFR. The estimated Pg was assumed to be in proportion to the estimated ETR, as in the following equation:   Pg=k×ETR, (7) where k is the coefficient representing the number of fixed CO2 molecules per electron transported from PSI to ferredoxin. The k value for each leaf was calculated from the actual Pg and estimated ETRII (i.e. ABS×f×YII) under R, and was assumed to be constant irrespective of the PFD of the supplemental FR. The mean k values ranged from 0.16 to 0.19 in the three replicated experiments. Changes in the operating efficiency of the Calvin cycle and in the activities of several alternative electron flows potentially affect the k value. As the measurements were made under constant high CO2 partial pressures, the efficiency of the Calvin cycle was presumed to be constant. Several alternative flows derived from the electron carriers after P700, i.e. cyclic electron flow around PSI (Shikanai 2007), the water–water cycle initiated by the Mehler reaction (Mehler 1951, Asada 1999), malate–oxaloacetate shuttles (Scheibe 2004) and metabolic pathways (e.g. nitrogen and sulfur reduction), were presumed to consume constant fractions of the whole-chain ETR, and thus not to affect k. These assumptions are likely to be valid because the major alternative electron flows—cyclic electron flow and the water–water cycle—are likely to be regulated under excess light conditions to protect the photosynthetic apparatus. Although recent work has suggested that the activity of the NADH dehydrogenase-like complex-dependent cyclic electron transfer pathway is regulated by PFD in rice (Yamori et al. 2015), its effect on the k value was ignored because of the minor contribution of this pathway to total PSI cyclic electron transport activity (Shikanai 2016) and the small range of PFD in the present measurements. The Pg was also estimated using the integration method (Equation 1). The extent of the enhancement effect was calculated as Pg under R + FR/(Pg under R + Pg under FR) − 1. Statistical analysis All statistical analyses were performed with the R program (R Core Team 2016). Means of values from 2–4 leaves from different plants were used for the analyses. The measurements were replicated three times. Supplementary Data Supplementary data are available at PCP online. Funding This work was supported by the Japan Society for the Promotion of Science (JSPS) [KAKENHI grant No. 26·9372 to K.M.]. Acknowledgments The authors are grateful to Professor Ichiro Terashima (Graduate School of Science, The University of Tokyo) for helpful suggestions. Disclosures The authors have no conflicts of interest to declare. References Anderson J.M., Chow W.S., Park Y.-I. ( 1995) The grand design of photosynthesis: acclimation of the photosynthetic apparatus to environmental cues. Photosynth. Res . 46: 129– 139. Google Scholar CrossRef Search ADS PubMed  Asada K. ( 1999) The water–water cycle in chloroplast: scavenging of active oxygens and dissipation of excess photons. Annu. Rev. Plant Physiol. Plant Mol. Biol.  50: 601– 639. Google Scholar CrossRef Search ADS PubMed  Campbell G.S., Norman J.M. ( 1998) Radiation basics. In An Introduction to Environmental Biophysics , 2nd edn. pp. 147– 165. Springer Verlag, New York. Google Scholar CrossRef Search ADS   Chow W.S., Goodchild D.J., Miller C., Anderson J.M. ( 1990a) The influence of high levels of brief or prolonged supplementary far-red illumination during growth on the photosynthetic characteristics, composition and morphology of Pisum sativum chloroplasts. Plant Cell Environ.  13: 135– 145. Google Scholar CrossRef Search ADS   Chow W.S., Melis A., Anderson J.M. ( 1990b) Adjustments of photosystem stoichiometry in chloroplasts improve the quantum efficiency of photosynthesis. Proc. Natl. Acad. Sci. USA  87: 7502– 7506. Google Scholar CrossRef Search ADS   Emerson R., Chalmers R., Cederstrand C. ( 1957) Some factors influencing the long-wave limit of photosynthesis. Proc. Natl. Acad. Sci. USA  43: 133– 143. Google Scholar CrossRef Search ADS   Emerson R., Lewis C.M. ( 1943) The dependence of the quantum yield of chlorella photosynthesis on wave length of light. Amer. J. Bot . 30: 165– 178. Google Scholar CrossRef Search ADS   Evans J.R. ( 1986) Quantitative analysis of light distribution between the two photosystems, considering variation in both the relative amounts of the chlorophyll–protein complexes and the spectral quality of light. Photobiochem. Photobiophys . 10: 135– 148. Evans J.R. ( 1987) The dependence of quantum yield on wavelength and growth irradiance. Aust. J. Plant Physiol.  14: 69– 79. Google Scholar CrossRef Search ADS   Evans J.R., Anderson J.M. ( 1987) Absolute absorption and relative fluorescence excitation spectra of the five major chlorophyll–protein complexes from spinach thylakoid membranes. Biochim. Biophys. Acta  892: 75– 82. Google Scholar CrossRef Search ADS   Farquhar G., von Caemmerer S. ( 1982) Modelling of photosynthetic response to environmental conditions. In Physiological Plant Ecology II . Edited by Lange O.L., Nobel P.S., Osmond C.B., Ziegler H. pp. 549– 587. Springer-Verlag, Berlin. Google Scholar CrossRef Search ADS   Farquhar G., von Caemmerer S., Berry J. ( 1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta  149: 78– 90. Google Scholar CrossRef Search ADS PubMed  Farquhar G., Wong S. ( 1984) An empirical model of stomatal conductance. Aust. J. Plant Physiol.  11: 191– 210. Google Scholar CrossRef Search ADS   Goldschmidt-Clermont M., Bassi R. ( 2015) Sharing light between two photosystems: mechanism of state transitions. Curr. Opin. Plant Biol . 25: 71– 78. Google Scholar CrossRef Search ADS PubMed  Hogewoning S.W., Douwstra P., Trouwborst G., van Ieperen W., Harbinson J. ( 2010) An artificial solar spectrum substantially alters plant development compared with usual climate room irradiance spectra. J. Exp. Bot . 61: 1267– 1276. Google Scholar CrossRef Search ADS PubMed  Hogewoning S.W., Wientjes E., Douwstra P., Trouwborst G., van Ieperen W., Croce R. ( 2012) Photosynthetic quantum yield dynamics: from photosystems to leaves. Plant Cell  24: 1921– 1935. Google Scholar CrossRef Search ADS PubMed  Inada K. ( 1976) Action spectra for photosynthesis in higher plants. Plant Cell Physiol . 17: 355– 365. Inada K. ( 1978) Photosynthetic enhancement spectra in higher plants. Plant Cell Physiol . 19: 1007– 1017. Google Scholar CrossRef Search ADS   Kim J.H., Glick R.E., Melis A. ( 1993) Dynamics of photosystem stoichiometry adjustment by light quality in chloroplasts. Plant Physiol.  102: 181– 190. Google Scholar CrossRef Search ADS PubMed  Klughammer C., Schreiber U. ( 1994) An improved method, using saturating light pulses, for the determination of photosystem I quantum yield via P700+-absorbance changes at 830 nm. Planta  192: 261– 268. Google Scholar CrossRef Search ADS   Kono M., Terashima I. ( 2014) Long-term and short-term responses of the photosynthetic electron transport to fluctuating light. J. Photochem. Photobiol . 137: 89– 99. Google Scholar CrossRef Search ADS   Kramer D.M., Johnson G., Kiirats O., Edwards G.E. ( 2004) New fluorescence parameters for the determination of QA redox state and excitation energy fluxes. Photosynth. Res . 79: 209– 218. Google Scholar CrossRef Search ADS PubMed  Laisk A., Eichelmann H., Oja V. ( 2015) Oxidation of plastohydroquinone by photosystem II and by dioxygen in leaves. Biochim. Biophys. Acta  1847: 565– 575. Google Scholar CrossRef Search ADS PubMed  Laisk A., Oja V., Eichelmann H., Dall’Osto L. ( 2014) Action spectra of photosystems II and I and quantum yield of photosynthesis in leaves in State 1. Biochim. Biophys. Acta  1837: 315– 325. Google Scholar CrossRef Search ADS PubMed  Matsuda R., Ohashi-Kaneko K., Fujiwara K., Goto E., Kurata K. ( 2004) Photosynthetic characteristics of rice leaves grown under red light with or without supplemental blue light. Plant Cell Physiol.  45: 1870– 1874. Google Scholar CrossRef Search ADS PubMed  McCree K.J. ( 1972a) The action spectrum, absorptance and quantum yield of photosynthesis in crop plants. Agric. Meteorol . 9: 191– 216. Google Scholar CrossRef Search ADS   McCree K.J. ( 1972b) Significance of enhancement for calculations based on the action spectrum for photosynthesis. Plant Physiol . 49: 704– 706. Google Scholar CrossRef Search ADS   Mehler A.H. ( 1951) Studies on reactions of illuminated chloroplasts: I. Mechanism of the reduction of oxygen and other hill reagents. Arch. Biochem. Biophys.  33: 65– 77. Google Scholar CrossRef Search ADS PubMed  Melis A. ( 1991) Dynamics of photosynthetic membrane composition and function. Biochim. Biophys. Acta  1058: 87– 106. Google Scholar CrossRef Search ADS   Murakami K., Matsuda R., Fujiwara K. ( 2016) Interaction between the spectral photon flux density distributions of light during growth and for measurements in net photosynthetic rates of cucumber leaves. Physiol. Plant.  158: 213– 224. Google Scholar CrossRef Search ADS PubMed  Murakami K., Matsuda R., Fujiwara K. ( 2017) A basis for selecting light spectral distribution for evaluating leaf photosynthetic rates of plants grown under different light spectral distributions. Environ. Control Biol.  55: 1– 6. Google Scholar CrossRef Search ADS   Murakami K., Matsuda R., Fujiwara K. ( 2018) Quantification of excitation energy distribution between photosystems based on a mechanistic model of photosynthetic electron transport. Plant Cell Environ.  41: 148– 159. Google Scholar CrossRef Search ADS PubMed  Nawrocki W.J., Tourasse N.J., Taly A., Rappaport F., Wollman F.-A. ( 2015) The plastid terminal oxidase: its elusive function points to multiple contributions to plastid physiology. Annu. Rev. Plant Biol.  66: 49– 74. Google Scholar CrossRef Search ADS PubMed  Niyogi K.K. ( 1999) Photoprotection revisited: genetic and molecular approaches. Annu. Rev. Plant Physiol. Plant Mol. Biol.  50: 333– 359. Google Scholar CrossRef Search ADS PubMed  Pfannschmidt T., Nilsson A., Allen J.F. ( 1999) Photosynthetic control of chloroplast gene expression. Nature  397: 625– 628. Google Scholar CrossRef Search ADS   R Core Team ( 2016) R: A Language and Environment for Statistical Computing. R Foundation for Statistical Computing, Vienna, Austria. Scheibe R. ( 2004) Malate valves to balance cellular energy supply. Physiol. Plant.  120: 21– 26. Google Scholar CrossRef Search ADS PubMed  Sharkey T.D. ( 1985) Photosynthesis in intact leaves of C3 plants: physics, physiology and rate limitations. Bot. Rev.  51: 53– 105. Google Scholar CrossRef Search ADS   Shikanai T. ( 2007) Cyclic electron transport around photosystem I: genetic approaches. Annu. Rev. Plant Biol.  58: 199– 217. Google Scholar CrossRef Search ADS PubMed  Shikanai T. ( 2016) Chloroplast NDH: a different enzyme with a structure similar to that of respiratory NADH dehydrogenase. Biochim. Biophys. Acta  1857: 1015– 1022. Google Scholar CrossRef Search ADS PubMed  Smith H. ( 1982) Light quality, photoperception, and plant strategy. Annu. Rev. Plant Physiol.  33: 481– 518. Google Scholar CrossRef Search ADS   Vass I. ( 2011) Role of charge recombination processes in photodamage and photoprotection of the photosystem II complex. Physiol. Plant.  142: 6– 16. Google Scholar CrossRef Search ADS PubMed  Wagner R., Dietzel L., Bräutigam K., Fischer W., Pfannschmidt T. ( 2008) The long-term response to fluctuating light quality is an important and distinct light acclimation mechanism that supports survival of Arabidopsis thaliana under low light conditions. Planta  228: 573– 587. Google Scholar CrossRef Search ADS PubMed  Walters R.G. ( 2005) Towards an understanding of photosynthetic acclimation. J. Exp. Bot.  56: 435– 447. Google Scholar CrossRef Search ADS PubMed  Walters R.G., Horton P. ( 1994) Acclimation of Arabidopsis thaliana to the light environment: changes in composition of the photosynthetic apparatus. Planta  195: 248– 256. Google Scholar CrossRef Search ADS   Walters R.G., Horton P. ( 1995) Acclimation of Arabidopsis thaliana to the light environment: changes in photosynthetic function. Planta  197: 306– 312. Google Scholar PubMed  Weiss I., Mizrahi Y., Raveh E. ( 2009) Chamber response time: a neglected issue in gas exchange measurements. Photosynthetica  47: 121– 124. Google Scholar CrossRef Search ADS   Wientjes E., van Amerongen H., Croce R. ( 2013) LHCII is an antenna of both photosystems after long-term acclimation. Biochim. Biophys. Acta  1827: 420– 426. Google Scholar CrossRef Search ADS PubMed  Yamori W., Shikanai T. ( 2016) Physiological functions of cyclic electron transport around photosystem I in sustaining photosynthesis and plant growth. Annu. Rev. Plant Biol.  67: 81– 106. Google Scholar CrossRef Search ADS PubMed  Yamori W., Shikanai T., Makino A. ( 2015) Photosystem I cyclic electron flow via chloroplast NADH dehydrogenase-like complex performs a physiological role for photosynthesis at low light. Sci. Rep.  5: 1– 9. Zhen S., van Iersel M.W. ( 2017) Far-red light is needed for efficient photochemistry and photosynthesis. J. Plant Physiol.  209: 115– 122. Google Scholar CrossRef Search ADS PubMed  Abbreviations Abbreviations ABS flux density of absorbed photons EI and EII excitation energy distributed to PSI and PSII ETR electron transport rate f fraction of excitation energy distributed to PSII FR far-red LED light LED light-emitting diode pETRII and pETRI potential electron transport rates at PSII and PSI Pg gross photosynthetic rate Pn net photosynthetic rate PFD photon flux density qL a parameter estimating the fraction of PSII centers in open states R red LED light Rd dark respiration rate YCO2 quantum yields of gross photosynthetic rate YII and YI quantum yields of photochemical reactions at PSII and PSI Ymax;II and Ymax;I maximum quantum yields of photochemical reactions at PSII and PSI YNA and YND quantum yields of the non-photochemical energy dissipation due to the acceptor- and donor-side limitations of PSI © The Author(s) 2018. Published by Oxford University Press on behalf of Japanese Society of Plant Physiologists. All rights reserved. For permissions, please email: journals.permissions@oup.com This article is published and distributed under the terms of the Oxford University Press, Standard Journals Publication Model (https://academic.oup.com/journals/pages/about_us/legal/notices)

Journal

Plant and Cell PhysiologyOxford University Press

Published: Apr 25, 2018

There are no references for this article.

You’re reading a free preview. Subscribe to read the entire article.


DeepDyve is your
personal research library

It’s your single place to instantly
discover and read the research
that matters to you.

Enjoy affordable access to
over 18 million articles from more than
15,000 peer-reviewed journals.

All for just $49/month

Explore the DeepDyve Library

Search

Query the DeepDyve database, plus search all of PubMed and Google Scholar seamlessly

Organize

Save any article or search result from DeepDyve, PubMed, and Google Scholar... all in one place.

Access

Get unlimited, online access to over 18 million full-text articles from more than 15,000 scientific journals.

Your journals are on DeepDyve

Read from thousands of the leading scholarly journals from SpringerNature, Elsevier, Wiley-Blackwell, Oxford University Press and more.

All the latest content is available, no embargo periods.

See the journals in your area

DeepDyve

Freelancer

DeepDyve

Pro

Price

FREE

$49/month
$360/year

Save searches from
Google Scholar,
PubMed

Create lists to
organize your research

Export lists, citations

Read DeepDyve articles

Abstract access only

Unlimited access to over
18 million full-text articles

Print

20 pages / month

PDF Discount

20% off