A mechanistic model for the photosynthesis–light response based on the photosynthetic electron transport of photosystem II in C3 and C4 species

Authors


Author for correspondence:

Zi-Piao Ye

Tel: +86 796 8100493

Email: yezp@jgsu.edu.cn

Summary

  • A new mechanistic model of the photosynthesis–light response is developed based on photosynthetic electron transport via photosystem II (PSII) to specifically describe light-harvesting characteristics and associated biophysical parameters of photosynthetic pigment molecules. This model parameterizes ‘core’ characteristics not only of the light response but also of difficult to measure physical parameters of photosynthetic pigment molecules in plants.
  • Application of the model to two C3 and two C4 species grown under the same conditions demonstrated that the model reproduced extremely well (r2 > 0.992) the light response trends of both electron transport and CO2 uptake.
  • In all cases, the effective absorption cross-section of photosynthetic pigment molecules decreased with increasing light intensity, demonstrating novel operation of a key mechanism for plants to avoid high light damage.
  • In parameterizing these previously difficult to measure characteristics of light harvesting in higher plants, the model provides a new means to understand the mechanistic processes underpinning variability of CO2 uptake, for example, photosynthetic down-regulation or reversible photoinhibition induced by high light and photoprotection. However, an important next step is validating this parameterization, possibly through application to less structurally complex organisms such as single-celled algae.

Introduction

Photosynthesis (the net CO2 assimilation rate (Pn)) in plants is composed of biophysical processes, such as light absorption and energy transfer to the water-splitting reaction centers, coupled to biochemical processes, such as the formation of ATP and NADPH. Consequently, both processes are strongly affected by environmental factors (e.g. light, CO2 concentration and temperature), adding complexity to predicting how environmental factors modify photosynthesis. Dissection of the various biophysical and biochemical factors, alongside calculation of parameters characterizing photosynthesis, is particularly important for predicting the net outcome of environmental change upon the harvesting and subsequent utilization of light by leaves (Sharkey et al., 2007). Thus, it is essential that the mechanistic quantification of leaf photosynthesis is better understood, in particular for dynamic simulation growth models and in parameterization of the light-harvesting properties of photosynthetic pigment molecules, that is, chlorophyll and carotenoid molecules (Ye et al., 2013).

Models of photosynthesis of varying complexity have been used to predict photosynthesis to highlight processes and pathways that are not well understood (Farazdaghi & Edwards, 1988). A number of mechanistic and empirical models have been developed for photosynthesis in C3 plants; however, the most frequently used for understanding the photosynthetic response to CO2 is the biochemical model of Farquhar et al. (1980), or its various refined forms (e.g. von Caemmerer, 2000; Sharkey et al., 2007), which parameterizes key kinetic variables, for example, the maximum rates of RuBP carboxylase/oxygenase carboxylation (Vcmax; see Table 1 for the list of abbreviations), the maximum rate of electron transport (Jmax), and triose-phosphate utilization (VTPU). Such biochemical models provide a tried and tested means of quantitatively partitioning biochemical versus stomatal limitation on the CO2 response of photosynthesis (Long & Bernacchi, 2003; Dubois et al., 2007).

Table 1. Definitions of the abbreviations
AbbreviationDefinitionUnits
J Electron transport rateμmol electrons m−2 s−1
J-I Light response curve of photosynthetic electron transport rate 
J max Maximum photosynthetic electron transport rateμmol electrons m−2 s−1
g i Degeneration of energy level of photosynthetic pigment molecules in the ground state iDimensionless
g k Degeneration of energy level of photosynthetic pigment molecules in the excited state kDimensionless
I Light intensityμmol photons m−2 s−1
I c Light compensation pointμmol photons m−2 s−1
I sat Saturation light intensity corresponding to maximum net photosynthetic rateμmol photons m−2 s−1
N k Total photosynthetic pigment molecules in the excited state k 
N 0 Total photosynthetic pigment molecules 
PARsatSaturation light intensity corresponding to maximum electron transport rateμmol photons m−2 s−1
P max Maximum gross photosynthetic rateμmol COm−2 s−1
P nmax Maximum net photosynthetic rateμmol COm−2 s−1
P n Net photosynthetic rateμmol COm−2 s−1
P n -I Light response curve of photosynthesis 
PSIPhotosystem I 
PSIIPhotosystem II 
R dark Mitochondrial CO2 release in the darkμmol COm−2 s−1
R light Nonphotorespiratory mitochondrial CO2 release in lightμmol COm−2 s−1
R p Photorespiration rateμmol COm−2 s−1
R 1 Rate of pigment molecules from the excited state k to the ground state i as a result of photochemical reactions−1
R 2 Rate of pigment molecules from the excited state k to the ground state i as a result of nonradiation heat dissipations−1
RuBPRibulose biphosphate 
V cmax Maximum rates of RuBP carboxylase/oxygenase carboxylationμmol COm−2 s−1
V TPU Triose-phosphate utilizationμmol COm−2 s−1
αeInitial slope of light response curve of photosynthetic electron transport rateμmol electron (μmol photon)−1
αpInitial slope of light response curve of photosynthesisμmol CO2 (μmol photon)−1
α'Fraction of light absorbed by PSIIdimensionless
β′Leaf absorptancedimensionless
βeCoefficientm2 s (μmol photons)−1
βpCoefficientm2 s (μmol photons)−1
γeCoefficientm2 s (μmol photons)−1
γpCoefficientm2 s (μmol photons)−1
ξ1Occupation probability of photochemistryDimensionless
ξ2Occupation probability of nonradiation heat dissipationDimensionless
ξ3Occupation probability of fluorescenceDimensionless
σikEigen-absorption cross-section of photosynthetic pigment molecule from ground state i to excited state k as a result of light illuminationm2
σ'ikEffective optical absorption cross-section of photosynthetic pigment molecule from ground state i to excited state k as a result of light illuminationm2
θPhotosynthetic electron use efficiency via PSIIμmol CO2 (μmol electron)−1
φUse efficiency of exciton transport reaction center PSII to cause charge separation of P680μmol electrons (μmol photon)−1
τAverage lifetime of the photosynthetic pigment molecules in the excited state ks
τminMinimum average lifetime of photosynthetic pigment molecules in the excited states

A variety of models describing the light response of photosynthetic CO2 uptake (Pn-I) have also been established for plants, for example, nonrectangular hyperbola (von Caemmerer, 2000), rectangular hyperbola (Thornley, 1998), and exponential-based functions (Leakey et al., 2006). However, most of these Pn-I models arguably lack widespread applicability as they have been established empirically without considering the underlying biophysical and biochemical processes of photosynthesis. For example, photosynthetic parameters currently returned from Pn-I models, such as the initial slope (αp) and the maximum net CO2 assimilation rate (Pnmax) (see Table 1), are difficult to link to the underlying biophysical processes of light harvesting (e.g. the average lifetime of the pigment molecules in the excited state; Table 1) and subsequent biochemical processes of light utilization (e.g. photosynthetic electron use efficiency via photosystem II (PSII)). Both processes can be inherently different among species and environmental conditions and it is therefore perhaps unsurprising that empirical models often fail to describe well-known photoacclimation responses (Porter et al., 1984; Liu & He, 2005), reversible photoinhibition (Galle et al., 2011; Reynolds et al., 2012), high light-induced down-regulation of PSII (White & Critchley, 1999; Ralph & Gademann, 2005; Barron-Gafford et al., 2012) and photoprotection (Murchie & Niyogi, 2011; Reynolds et al., 2012).

Existing Pn-I models fail to consider the fundamental interconnection of light absorption and energy transfer to the reaction centers (including the physical properties of the light-harvesting chlorophyll and carotenoid molecules in the pigment bed), primary charge separation of P680, and subsequent electron transport rate in leaves. However, such information (on difficult to measure variables) can potentially yield important new insight as to how species acclimate and adapt to their changing environmental conditions. Therefore, the objectives of our present study were (1) to develop a mechanistic model of Pn-I based on a recently described mechanistic model of the light response curve of photosynthetic electron transport rate (J-I) (Ye et al., 2013); (2) to measure simultaneously gas exchange and chlorophyll fluorescence to yield comparative Pn-I and J-I curves for two C3 species (Koelreuteria paniculata Laxm. and Capsicum annuum L.) and two C4 species (Zea mays L. and Sorghum bicolor L.); (3) to apply these data to calculate photosynthesis parameters (e.g. for J-I curves: αe, Jmax and PARsat; for Pn-I curves: αp, Pmax, Isat, Ic and Rdark) and photosynthetic electron use efficiency (θ); and in doing so (4) to produce a novel approach to investigate high light-induced photosynthetic down-regulation (reversible photoinhibition and photoprotection).

Description

The fundamental coupling between light absorption by the light-harvesting antenna, transfer of excitation energy to the reaction centers, electron transport (to drive ATP and NADP(H) formation) and net CO2 uptake forms the basis of the mechanistic model for Pn-I (via the mechanistic model of J-I; Ye et al., 2013) presented here.

Photosynthetic pigment molecule effective cross section and their total number in the excited state

The effective light absorption cross-section of photosynthetic pigment molecules, based on uniform light absorption in leaves (inline image), and the total number of photosynthetic pigment molecules in the excited state can be described as follows (see Ye, 2012); note that the term ‘photosynthetic pigment molecules’ hereafter refers to the entire pool of chlorophyll a, accessory chlorophyll and carotenoids (including the reversible xanthophylls).

display math(Eqn 1)

inline image increases with R1, R2, ξ1, ξ2 and ξ3 but will decrease with increasing I. inline image = σik when = 0 in (Eqn 1). As such, the light absorption cross-section is not a constant under any given light intensity (excluding = 0). The total number of photosynthetic pigment molecules in the excited state is expressed as

display math(Eqn 2)

In (Eqn 2), Nk is an asymptote function, which increases with I to its maximum value (= N0/(1 + gi/gk)), assuming that environmental factors (e.g. CO2 concentration and temperature) remain constant throughout for any given species. More detailed derivation of Eqns 12 is given in Ye (2012).

Photosynthetic electron transport rate via PSII

The photosynthetic electron transport rate via PSII, the eigen-absorption cross-section of photosynthetic pigment molecules and the minimum average lifetime of photosynthetic pigment molecules in the excited state can be described via the photosynthetic electron transport rate ( J ) of PSII (see Ye et al., 2013),

display math(Eqn 3)

(N0, the total number of photosynthetic pigment molecules of the measured leaf; S, the area of the measured leaf.) (Eqn 3) demonstrates that J is dependent on α′, β′, N0, σik, τ, φ, S, R1, R2, gi, gk, ξ1, ξ2, ξ3 and I. Furthermore, it demonstrates that J increases with I where < PARsat but decreases with increasing I where > PARsat. In addition, αe depends on α′, β′, N0, σik, φ, and S. Values for σik, τ, ξ1, ξ2, ξ3, gi, gk, R1 and R2 within (Eqn 3) will be inherently specific to both species and the environmental growth conditions (light, temperature, CO2 concentration and relative humidity). Therefore, we can assume inline image (μmol electrons (μmol photons)−1),inline image (m2 s (μmol photons)−1), inline image (m2 s (μmol photons)−1), so that (Eqn 3) can be simplified as

display math(Eqn 4)

PARsat is calculated from (Eqn 5) as

display math(Eqn 5)

Thus, PARsat depends on σik, τ, R1, R2, gi, gk, ξ1, ξ2 and ξ3, but it is independent of N0.

The maximum value for J (Jmax) = inline image and can be simplified as

display math(Eqn 6)

Using inline image and inline image, gi/gk is calculated as

display math(Eqn 7)

The eigen-absorption cross-section of photosynthetic pigment molecules (σik) is calculated from (Eqn 8) as

display math(Eqn 8)

Finally, the average lifetime of photosynthetic pigment molecules in the excited state (τ) is calculated from (Eqn 9) as

display math(Eqn 9)

(Eqn 9) where the unit for γe in (Eqn 9) is in m2 s per photosynthetic pigment molecule. For live plants, the maximum fluorescence yield in the photosynthetic apparatus is c. 3–5% (Krause & Weis, 1991). Thus, by using this minimum value (and hence ξ3 of 3%) the minimum average lifetime of photosynthetic pigment molecules in the excited state (τmin) is further calculated from (Eqn 10) as

display math(Eqn 10)

Net CO2 assimilation rate

Theoretically, a minimum of four electrons are needed to fix one CO2 molecule (Long & Bernacchi, 2003); these electrons transported via PSII are mainly used to generate energy (ATP) and reducing power (NADPH) for photosynthetic carbon reduction, photorespiratory carbon oxidation and other electron-consuming processes (Asada, 1999; Ort & Baker, 2002; Eichelmann et al., 2011). The use efficiency of an electron can be considered as θ (where 0 ≤ θ ≤1, in units of μmol CO2 (μmol electron)−1, as not all electrons transported via PSII are used to produce the assimilatory power for CO2 uptake). As such, the gross photosynthetic rate (termed P) is calculated from (Eqn 11) as

display math(Eqn 11)

Combining Eqns 3 and 11, P is rewritten as

display math(Eqn 12)

P diverges from Pn (measured by the Li-6400; Li-Cor Inc., NE, USA) as a function of respiration. To simplify the calculation of Pn, we do not consider photorespiration (RP), which is negligible for C4 species but can vary with light intensity for C3 species (Tolbert & Essner, 1981); in this case, Pn will be equal to the gross photosynthesis (P) minus nonphotorespiratory mitochondrial CO2 release in the light (Rlight) (Crous et al., 2012), which itself is also influenced by the light intensity (Atkin et al., 2000). Unfortunately, the Li-6400 only yields measurements of Pn and hence strictly only mitochondrial CO2 release in the dark (Rdark). Also, conventional Pn-I models consider Rlight synonymously with Rdark; however, Rdark will not always equal Rlight (e.g. because of temperature changes; Atkin et al., 2000; Shapiro et al., 2004; Crous et al., 2012) and is the focus of on-going modeling efforts. Net photosynthesis is therefore calculated as

display math(Eqn 13)

According to (Eqn 13), Pn is dependent on α′, β′, N0, σik, τ, φ, S, R1, R2, gi, gk, ξ1, ξ2, ξ3, θ and I. Again, because α′, β′, N0, σik, τ, φ, S, R1, R2, gi, gk, ξ1, ξ2, ξ3 and θ ((Eqn 13)) will inherently have specific but different values among species/environments, we can assume inline image (μmol CO2 (μmol photons)−1),inline image (m2 s (μmol photons)−1) and inline image (m2 s (μmol photons)−1), and (Eqn 13) may be simplified as

display math(Eqn 14)

To simplify the calculation of the saturation light intensity (Isat), we assume here that Rlight (as with Rp) will be constant, such that Isat corresponds to both the maximum gross photosynthetic rate (Pmax) and the maximum net photosynthetic rate (Pnmax), and can be calculated from (Eqn 15) as

display math(Eqn 15)

Similarly, (Eqn 15) is independent of N0 and φ, but it depends on σik, τ, R1, R2, gi, gk, ξ1, ξ2, ξ3 and environmental conditions (e.g. temperature and CO2 concentration). Thus, Pnmax is calculated as

display math(Eqn 16)

The maximum gross photosynthetic rate (Pmax) = Pnmax+ Rlight (Crous et al., 2012).

According to Eqns 13 and 14, Pn increases with I where < Isat but decreases with increasing I where Isat via high light-induced photosynthetic down-regulation or photoinhibition.

Study site and plants

The study was conducted at the Botanical Garden of Wenzhou Vocational & Technical College, where growth conditions are considered subtropical with an annual mean temperature of 16.1–18.2°C and average precipitation of 1500–1900 mm. Approximately 70% of annual precipitation occurs between March and August. The soil is classified as clay with a pH of 7.2.

In March 2008, 1-yr-old seedlings of Koelreuteria paniculata Laxm. were transplanted from the Baiyuan germchit factory (Taishun, Wenzhou) to outdoor cultivation at the Botanical Garden of Wenzhou Vocational & Technical College. In March 2010, K. paniculata, Capsicum annuum L. cv ‘No.1 Dujiao’, maize (Zea mays L., cv NO.1Jinyutian) and sweet sorghum (Sorghum bicolor L., Moench subsp. bicolor) were subsequently sowed in fields at Wenzhou Vocational & Technical College. Depending on precipitation, C. annuum, Z. mays and S. bicolor were irrigated only at sowing. Koelreuteria paniculata was not irrigated during the growth stage. Herbicides and insecticides were not used throughout; however, nitrogen (N), phosphorus (P), and potassium (K) were applied as an inorganic compound chemical fertilizer containing N (urea), P (P2O5) and K (K2O) in a ratio of 12: 19: 13, and applied at 116 kg N ha−1, 178 kg P ha−1 and 122 kg K ha−1, respectively. Experiments were conducted in June 2010 (and in August 2010 for K. paniculata). Maximum local solar noon light intensities during growth were c. 2020 ± 5 μmol photons m−2 s−1 (= 4; n is the number of replications), measured with a PAR sensor (Captor LI-190; Li-Cor Inc.) on clear days in June 2010. Plants were selected for experimentation based on uniformity, where only the youngest fully expanded leaves (the fifth compound leaves from the top for K. paniculata or the third leaf from the top for C. annuum, Z. mays and S. bicolor) were used for gas exchange and fluorescence measurements (Kang et al., 2011; Ye et al., 2012).

Gas exchange and fluorescence measurements

The leaf gas exchange (including net photosynthetic rate (Pn), stomatal conductance (gs), and intercellular CO2 concentration (Ci)) and chlorophyll a fluorescence measurements were performed simultaneously from 09:00 to 11:30 h and from 14:30 to 17:00 h, respectively, using the portable photosynthesis open system Li-6400-40 (Li-Cor) equipped with a leaf chamber fluorometer. Leaf temperature was maintained at 35 ± 0.1°C (30 ± 0.1°C for K. paniculata) at a relative humidity of c. 60% in the leaf chamber. Before measurements, each leaf was placed in the cuvette for 60 min to achieve steady-state CO2 exchange at a photosynthetically active radiation (PAR) of 1600 μmol photons m−2 s−1 for K. paniculata, and 2000 μmol photons m−2 s−1 for C. annuum, Z. mays and S. bicolor. The CO2 concentration in the cuvette was maintained at 380 μmol mol−1 with a CO2 mixer.

Light response measurements of gas exchange and chlorophyll a fluorescence parameters were made in descending order of intensity (Nippert & Marshall, 2003; Bernacchi et al., 2005): 2000, 1800, 1600, 1400, 1200, 1000, 800, 600, 400, 200, 100, 50, and 0 μmol photons m−2 s−1 at the leaf surface level. We acknowledge that operating in descending intensities can potentially introduce artifacts to the light curve, such as a lag to the initiation of O2 evolution (CO2 uptake); we therefore assume that any potential artifacts operated consistently across species. At each PAR, CO2 assimilation and steady-state fluorescence (Fs) were monitored to ensure that they reached steady state (3–5 min) before each reading. Maximum fluorescence under light exposure (inline image) was obtained using a saturating light pulse (≤ 1 s duration; > 8000 μmol photons m−2 s−1). Jmax (Pnmax) was determined from the plateau in the J-I (Pn-I) curves but also from the model outputs for Jmax (Pnmax) from Eqns 6 and 16. Measurements of mitochondrial CO2 release in the dark (Rdark) were determined at 380 μmol mol−1 when irradiance was 0 μmol photons m−2 s−1.

All data were fitted using spss 11.5 (SPSS Inc., Chicago, IL, USA) using nonlinear, least-squares fitting based upon the Levenberg–Marquardt algorithm.

Results

J-I curves

As expected, all species exhibited a characteristic initial increase of J with light intensity to saturation (Fig. 1); this initial increase is described by αe ((Eqn 4)) and was the same value of c. 0.3 μmol electrons (μmol photons)−1 for all species (Table 2). The light intensity at which J was maximum (Jmax) is described by PARsat and was lowest for K. bipinnata and S. bicolor (1350–1600 μmol photons m−2 s−1) and highest for C. annuum (c. 2200 μmol photons m−2 s−1) with intermediate values for Z. mays; it should be noted that J for C. annuum did not reach saturation within the values of I applied for the J-I curve and hence values for PARsat (and Jmax) are an extrapolation. Values for Jmax followed a similar pattern as for PARsat given the relative constancy for αe. Beyond PARsat, values for J exhibited little decline with increasing I for K. paniculata and Z. mays (Figs 1b,c); however, some decline was observed for S. bicolor J, suggesting dynamic down-regulation of PSII or photoinhibition (Fig. 1d).

Table 2. Fitted results of photosynthetic electron transport rate (J) versus light intensity (I) (J-I) curves for Koelreuteria paniculata, Capsicum annuum, maize (Zea mays) and sorghum (Sorghum bicolor) using (Eqn 3)
 J-I modelMeasured valuesJ-I modelMeasured valuesJ-I modelMeasured valuesJ-I modelMeasured values
  1. All values are the mean ± SE except for the determination coefficient and measured values (n = 4; n is the number of replications). See Table 1 for definitions of abbreviations.

Photosynthesis parameters K. bipinnata K. bipinnata C. annuum C. annuum Z. mays Z. mays S. bicolor S. bicolor
αe (μmol electrons (μmol photons)−1)0.33 ± 0.000.30 ± 0.000.29 ± 0.000.31 ± 0.01
PARsat (μmol photons m−2 s−1)1 350.57 ± 42.32≈ 14002199.52 ± 87. 23> 20001 854.53 ± 55.67≈ 18001 591.27 ± 42.57≈ 1600
Jmax (μmol electrons m−2 s−1)147.76 ± 3.06≈ 146319.68 ± 5.42≈ 26264.29 ± 2.72≈ 263.59237.45 ± 2.16≈ 237.94
Determination coefficient (r2)0.9990.9990.9990.998
Figure 1.

Photosynthetic electron transport rate (J) versus light intensity (I) via photosystem II (PSII) for Capsicum annuum (a), Koelreuteria paniculata (b), Zea mays (c) and Sorghum bicolor (d). Open symbols indicate measured points; the straight line denotes the fit obtained using 3 or 4 (mean ± SE;= 4).

Pn-I curves

The light response of net CO2 uptake (Pn-I) also exhibited the generally expected trend, but notable differences were again observed among species. The lowest values of the initial light-dependent increase of Pn with I (i.e. αp; 13 or 14) of c. 0.055 μmol CO2 (μmol photons) −1 (Fig. 2, Table 3) were observed for K. bipinnata and S. bicolor. However, maximum values of Pn, that is, Pnmax (and hence Isat; (Eqn 15)), were much greater for S. bicolor (Pnmax = 39 μmol CO2 m−2 s−1; Isat = 1500 μmol photons m−2 s−1) than for K. bipinnata (Pnmax = 10 μmol CO2 m−2 s−1; Isat = 1250 μmol photons m−2 s−1) (Table 3). Values for αp were higher for C. annum and Z. mays (c. 0.075 μmol CO2 (μmol photons)−1) than for the other two species. However, values for Pnmax were relatively low and Isat relatively high for C. annuum (Pnmax = 29 μmol COm−2 s−1; Isat = 2500 μmol photons m−2 s−1) compared with Z. mays (Pnmax = 43 μmol COm−2 s−1; Isat = 1850 μmol photons m−2 s−1), the Isat  of which was more similar in magnitude to S. bicolor (Fig. 2, Table 3). As with the J-I curves, the Pn-I curves did not strictly reach saturation within the maximum light intensity employed (Fig. 2). Furthermore, S. bicolor appeared to exhibit a decline of Pn beyond Isat, indicating dynamic down-regulation/photoinhibition (Fig. 2d).

Table 3. Fitted results of net photosynthetic rate (Pn) versus light intensity (I) (Pn-I) curves for Koelreuteria paniculata, Capsicum annuum, maize (Zea mays) and sorghum (Sorghum. bicolor) using (Eqn 13)
 P n-I modelMeasured valuesP n-I modelMeasured valuesP n-I modelMeasured valuesP n-I modelMeasured values
  1. All values are the mean ± SE except for the determination coefficient and measured values (= 4).

  2. a

    Measurements of mitochondrial CO2 release in the dark (Rdark) were determined at 380 μmol mol−1 when irradiance was 0 μmol photons m−2 s−1. See Table 1 for definitions of abbreviations.

Photosynthesis parameters K. bipinnata K. bipinnata C. annuum C. annuum Z. mays Z. mays S. bicolor S. bicolor
αp (μmol CO2 (μmol electrons)−1)0.055 ± 0.0070.0758 ± 0.0040.074 ± 0.0050.057 ± 0.003
Pnmax (μmol CO2 m−2 s−1)10.36 ± 0.70≈ 1028.67 ± 0.83≈ 2842.81 ± 0.59≈ 43.1738.71 ± 0.64≈ 38.02
Isat (μmol photons m−2 s−1)1235.45 ± 57.05≈ 12002493.23 ± 120.53> 20001840.39 ± 37.95≈ 18001492.05 ± 49.45≈ 1500
Ic (μmol photons m−2 s−1)43.14 ± 3.51≈ 4374.63 ± 5.42≈ 7078.61 ± 4.89≈ 8061.93 ± 4.05≈ 60
Rdarka (μmol CO2 m−2 s−1)2.20 ± 0.14≈ 2.125.08 ± 0.35≈ 5.065.560 ± 0.53≈ 5.64.510 ± 0.41≈ 4.5
θ (μmol CO2 (μmol electrons)−1)0.1690.2520.2520.186
g i /g k 0.902 ± 0.0580.895 ± 0.0560.234 ± 0.0120.252 ± 0.014
Determination coefficient (r2)0.992 30.9990.9980.999
Figure 2.

Net photosynthetic rate (Pn) versus light intensity (I) for Capsicum annuum (a), Koelreuteria paniculata (b), Zea mays (c) and Sorghum bicolor (d). Open symbols indicate measured points; the straight line denotes the fit obtained using (Eqn 13) or (Eqn 14) (mean ± SE;= 4).

Eqns 13 and 14 were also used to examine differences in respiration between species. Overall leaf respiration (Rdark; μmol COm−2 s−1) was lowest for K. bipinnata (c. 2 μmol CO2 m−2 s−1) and highest (and of similar magnitude) for the other three species (c. 4.5–5.5 μmol COm−2 s−1) (Table 3).

Values for J were further considered alongside those of Pn to evaluate θ (Eqn 11), where higher values for θ indicate higher electron use efficiency. Values of θ were lowest for K. bipinnata (0.169 μmol CO2 (μmol electron)−1) and highest (c. 0.252 μmol CO2 (μmol electron)−1) for C. annuum and Z. mays, with intermediate values for S. bicolor (0.186 μmol CO2 (μmol electron)−1) (Table 3), indicating that C. annuum and Z. mays use electrons to produce the assimilatory power for CO2 uptake most efficiently. Overall Pn covaried with J linearly for S. bicolor and Z. mays where < 250 μmol electrons m−2 s−1 (Fig. 3c,d); by contrast, Pn covaried nonlinearly with J for Kbipinnata and C. annuum (Fig. 3a,b), indicating that electron use efficiency is a function of light intensity.

Figure 3.

Gross photosynthetic rate (P) versus photosynthetic electron transport rate (J) via photosystem II (PSII) for Capsicum annuum (a), Koelreuteria paniculata (b), Zea mays (c) and Sorghum bicolor (d). Open and closed symbols indicate the measured points. Note that the deviation of the data from 1 : 1 indicates the number (mol) of electrons required to fix each mol of CO2, while the deviation from linearity denotes differences in the light response characteristics (and hence physiological pathways) for generation of electrons versus uptake of CO2 (mean ± SE;= 4).

The effective absorption cross-section of photosynthetic pigment molecules

Light-driven changes in the effective absorption cross-sections of the photosynthetic pigment molecules (inline image) were determined via (Eqn 1) (as values for βp and γp were returned via (Eqn 14) when determining the photosynthesis light response parameters) for each species (Fig. 4). inline image consistently decreased with increasing I (Fig. 4). The most rapid decreases of inline image with increased I were observed for K. paniculata, which incidentally exhibited the lowest values for Jmax and Pnmax, and to a lesser extent C. annuum. In the latter case, values for inline image at the highest actinic irradiance (c. 2000 μmol photons m−2 s−1) remained relatively high and corresponded with a lack of saturation for Jmax (Pnmax; see Figs 1, 2). The rate of inline image decline with increasing I was similar for S. bicolor and Z. mays, reflecting their similar trends of Jmax and Pnmax versus I, but was less than for the other two species. Final values of inline image at the highest intensities were higher for S. bicolor and Z. mays than for K. paniculata, corresponding to the apparent onset of dynamic down-regulation/photoinhibition for Jmax (Pnmax).

Figure 4.

Ratio (inline imageik) of effective absorption cross-section (inline image) to eigen-absorption cross-section (σik) of photosynthetic pigment molecules versus light intensity (I) for Capsicum annuum (a), Koelreuteria paniculata (b), Zea mays (c) and Sorghum bicolor (d). Open and closed symbols denote points calculated using (Eqn 1) (mean ± SE;= 4) .

Discussion

Pn-I and J-I curves

Our model of Pn-I not only described well various light response curve shapes (r2 > 0.992), regardless of any decline in net CO2 assimilation beyond the saturation irradiance (i.e. photoinhibition), but also returned values for αp, Pmax, Isat, Ic and Rdark that were in very close agreement with the measured values. Previous comparisons of parameters returned from different Pn-I models (Thornley, 1998; von Caemmerer, 2000) and hence mathematical functions, that is, rectangular hyperbola, nonrectangular hyperbola and exponential function, showed different fits (Frenette et al., 1993; Rubio et al., 2003) and consequently different degrees of confidence in their parameterizations. However, these models/studies did not describe well photosynthetic down-regulation/photoinhibition induced by high light (often overestimating Pnmax), in particular in the case of nonrectangular and rectangular hyperbola models (Leakey et al., 2006; Lombardini et al., 2009). A model (and in turn the accuracy of the fit) of course depends on the quality of the measured data. However, a major advantage of our model, aside from the additional wealth of mechanistic information that can be returned, is that it can be employed in fitting various light response curves over a wide range of light intensities from below the compensation point to well above the saturation light intensities.

The approach presented here also demonstrated that integrating the model for Pn with that of the photosynthetic electron transport rate (J-I; Ye et al., 2013) enables ‘core’ parameters to be estimated, for example, αe, PARsat and Jmax (from J-I ) and αp, Pmax and Isat (from Pn-I ) as well as novel characterization of biochemical/physical processes (Ic, Rdark and θ). Theoretically, Isat should equal PARsat where gas exchange and chlorophyll fluorescence are measured simultaneously, as βe βp and γe γp; however, PARsat ≠ Isat because ‘electron-consuming processes’, notably here photorespiration (Rp) (Tolbert & Essner, 1981) and Rlight (Atkin et al., 2000) which both vary with light intensity, will influence Isat. Even so, Rdark was found to act as a good proxy for Rlight, but we recognize that changes in the abiotic environment (temperature and humidity) could preferentially affect Rlight (Crous et al., 2012). Consequently, Pnmax and Jmax (as well as PARsat and Isat) should converge under nonphotorespiratory conditions. The close agreement between PARsat and Isat for the majority of species (contrast Tables 2 and 3) would suggest Rlight to be approximately similar for the species examined here. However, this concept requires verification, in particular under non-steady-state (stress) environmental conditions. As with Rlight, RP will decouple P from J (and hence Rp can be estimated from the difference between Pn and the PSII operating efficiency; Long & Bernacchi, 2003) but can act as a defense mechanism to protect the photosynthetic apparatus against permanent damage via enhanced reduction of Pn under high light (Kozaki & Takeba, 1996). However, this double role of photorespiration in the overall carbon balance as a key mechanism lowering Pn and thus protecting the photosynthetic apparatus has not been fully elucidated.

Values of θ determined from the J-I and Pn-I curves (Eqns 4, 15) enabled novel assessment of the total photosynthetic electron use efficiency via PSII. For example, here, the value of θ was highest for C. annuum, c. 0.252 μmol CO2 (μmol electron)−1, that is, 1 mol CO2 fixed per 4 mol electrons, and lowest for K. paniculata, c. 0.169 μmol CO2 (μmol electron)−1 (Table 3), that is, 1 mol CO2 fixed per 6 mol electrons. This reveals that net CO2 assimilation efficiency is not constant among species and potentially highlights species-specific variability in how energetic/reductant is used for CO2 uptake versus other assimilatory processes.

Photoprotection

Plants have evolved a number of photoprotective mechanisms to minimize inhibition and in turn damage from excess light energy, such as heat dissipation, fluorescence emission and state transition (Steyn et al., 2002; Ivanov et al., 2008; Goh et al., 2012). Operation of these processes manifests as nonphotochemical quenching (NPQ) of excitation energy in the PSII antenna pigment bed and is thus considered the major PSII photoprotective mechanism (Gilmore & Ball, 2000; Demmig-Adams & Adams, 2006; Ivanov et al., 2008; Goh et al., 2012). Importantly, our results indicated that σik consistently decreased with I but was not a constant between species. Such a response is consistent with that of single-celled algae, where the PSII effective absorption cross-section also typically decreases with increasing I (Suggett et al., 2007, 2008), which enables an increase in the overall photosynthetic conversion efficiency (as in the chlorophyll-deficient mutant of Chlamydomonas reinhardtii; Kirst et al., 2012) In microalgae, such a rapid reduction of σik is often associated with induction of rapidly reversible xanthophyll cycling to favor synthesis of ‘photoprotective’ versus ‘nonphotoprotective’ carotenoids (Ragni et al., 2010), a process that is also well established for higher plants and for the time-scale on which our light curves were run (minutes per light intensity).

In our study, the total quanta absorbed by the photosynthetic pigment molecules was lower for K. paniculata than for C. annuum, as σik decreased more rapidly with increasing I. Consequently, the CO2 assimilation occurred at a lower saturating light intensity for K. paniculata than for C. annuum (a similar trend was observed for S. bicolor and Z. mays, but the difference between these two species was smaller). Such a mechanism therefore provides a novel explanation of plant photoprotection processes (Ivanov et al., 2008; Galle et al., 2011; Goh et al., 2012), as the decrease in σik inevitably results in reduced absorption of light energy as I increases (see Suggett et al., 2007).

In addition to the changes in inline image, (Eqn 2) indicates that the number of photosynthetic pigment molecules in an excited state (Nk) increased with I. Even for < PARsat, some photosynthetic pigment molecules remained in the excited state, which is consistent with previous observations (Nedbal et al., 1996; Tyystjärvi & Aro, 1996; Rubio et al., 2003). For example, Nedbal et al. (1996) showed that for three algal species photoinhibition was substantially stronger under continuous light than for intermittent illumination (but the same overall light dose); their results demonstrated that the many photosynthetic pigment molecules in the excited state decayed through heat dissipation, chlorophyll fluorescence emission and/or state transitions under intermittent illumination. Such observations may help to identify the underlying nature of photoprotection under high light in plants (Murchie & Niyogi, 2011), as photosynthetic pigment molecules in an excited state will prevent further absorption of light energy and thus provide a means for additional photoprotective pathway(s) beyond existing heat dissipation (e.g. xanthophyll cycling, which acts to lower the transfer efficiency of absorbed quanta from the antenna bed to the core reaction center complex), notably chlorophyll fluorescence emission and state transitions.

Reversible photoinhibition

Reversible photoinhibition is indicative of regulatory processes that prevent the reduction of the electron transport chain to an extent where light is absorbed in excess of the capacity for photosynthetic carbon uptake/oxygen evolution (or safe dissipation as heat) (Baker, 2008), resulting in photooxidative damage (e.g. Öquist et al., 1993; Lovelock & Winter, 1996). Transitory reversible photoinhibition of PSII by direct exposure of leaves to natural sunlight has been observed in both canopy sun leaves and leaves of plants growing in tree-fall gaps of the tropical forest (Krause et al., 2001). For example, reversible photoinhibition, defined as the seasonal decrease in the maximum quantum yield of PSII photochemistry (Fv/Fm < 0.8), was found in Taxus baccata L. seedlings acclimated to different light regimes during winter (Robakowski & Wyka, 2009). The greatest decrease in Fv/Fm was observed in T. baccata seedlings acclimated to full sunlight and low temperatures, and accompanied needle discoloration. This seasonal decrease in Fv/Fm, which recovered in spring, protected the photosynthetic apparatus against permanent damage induced by high light and low temperatures (Robakowski & Wyka, 2009). Such studies demonstrate that dynamic photoinhibition acts to photoprotect (reviewed by Wiencke et al., 2007). Even so, these studies cannot reveal the detailed mechanisms responsible for the reversible inhibition (in this case light-induced reductions in the quantum efficiency of PSII).

Our model has demonstrated that reversible photoinhibition can be explained by taking into account Nk and inline image combined with τ (Eqns 1, 2 and Fig. 4), as the high numbers of photosynthetic pigment molecules in an excited state, the low values for inline image, and the longer retention time of an exciton in an excited state under high light together prevent the pigment bed from absorbing and transferring excess quanta to the reaction centers to induce transient inhibition; these excitons will decay mainly through chlorophyll fluorescence emission and heat dissipation to the ground state. Hence plants under reversible photoinhibition (Lovelock & Winter, 1996; Galle et al., 2011; Reynolds et al., 2012) or photosynthetic down-regulation induced by high light intensity (White & Critchley, 1999; Ralph & Gademann, 2005; Barron-Gafford et al., 2012) will be able to assimilate CO2 once they have recovered in the dark; this recovery time (approximately minutes) depends only on τ and Nk. Thus, reversible photoinhibition may result from the combination of inline image, τ and Nk to protect plants from high light stress.

Parameter estimations

Investigation of the underlying nature of the photosynthetic pigment molecules (inline image, inline image, gi/gk, Nk and τmin) requires parameterization of the fraction of light absorbed by PSII (α′) and leaf absorptance (β′) (Eqns 3, 13). However, β′ must be measured using an integrating sphere, which can be technically challenging for routine study, in particular for some leaf architectures such as conifer needles or thick leaves. At present, β′ is frequently assumed to be 0.84 (Rascher et al., 2000; Lüttge et al., 2003), an assumption that may be reasonable for many mature green leaves, but is not ubiquitously so, with large deviations among other species/conditions (Evans, 2009). Similarly, α′ is frequently assumed to have a value of 0.5 (Ehleringer & Pearcy, 1983; Major & Dunton, 2002), which is unlikely to be the case for many situations (Baker, 2008). Commercial modulated fluorometers automatically calculate values of J by assuming values of α' and β′ of 0.5 and 0.84, respectively, often leading to substantial errors in calculations of J (Baker, 2008; Evans, 2009) and in turn αe and Jmax. As discussed above, care should be taken when determining and interpreting properties of photosynthetic pigment molecules (inline image, inline image, gi/gk, Nk and τmin) using J-I curves. To investigate properties of photosynthetic pigment molecules we suggest using Pn-I curves as gas exchange measurements are directly determined (e.g. by infrared gas analysis) and thus provide more definitive information on photosynthesis.

To enable more widespread use of our Pn-I model, parameterization of the characteristics generated by the model, such as σik, of course next requires that key parameters, notably τ, R1, R2, ξ1, ξ2 and ξ3, should be validated. The mechanistic model for Pn-I may be improved as we presently do not know how environmental factors (e.g. CO2 concentration and temperature) will influence harvesting properties of photosynthetic pigment molecules, photosynthetic electron transport rate and net CO2 assimilation. Some of the current assumptions required for application of the model to higher plants are more readily measurable on single-celled algae (e.g. Suggett et al., 2007), and testing of these assumptions may therefore be a first step towards such validation, in particular the links between changes in effective absorption and excitation of the light-harvesting pigment array. An important part of this validation will be to evaluate the model application during ‘non-steady-state’ (stress) conditions that may decouple J and Pn; for example, in the case of higher plants, transient increases in temperature that influence not only chlorophyll fluorescence but also CO2 diffusion (via stomatal closure or metabolic impairment).

In conclusion, our newly developed model allows robust reproduction of Pn-I trends and parameterization of ‘core’ characteristics of the light response (e.g. αp, Pnmax, Isat, Ic and Rdark) but also enables parameterization of difficult to measure physical parameters of photosynthetic pigment molecules (e.g.inline image, inline image, gi/gk, Nk and τmin). Thus, the model effectively provides a novel tool for identifying mechanistic properties responsible for modifying plant and algal light-harvesting antennae that may have a key role in photoprotection, in particular reversible photoinhibition or photosynthetic down-regulation under high light intensity, as well as photoacclimation. An important next step will be towards validation by further combining this current mechanistic model of J-I and Pn-I with slow chlorophyll fluorescence induction kinetics to determine inline image and τmin.

Acknowledgements

This research was supported by the Natural Science Foundation of China (Grant no. 30960031), the Natural Science Foundation of Jiangxi Province (Grant no. 2009GZN0076) and the Key Discipline of Atomic and Molecular Physics in Jiangxi Province (2011–1015). Comments made by anonymous reviewers and by Prof. Owen K. Atkin are acknowledged with gratitude.

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