The Kok effect revisited.

The Kok effect refers to the abrupt decrease around the light compensation point in the slope of net photosynthetic rate vs irradiance. Arguably, this switch arises from light inhibition of respiration, allowing the Kok method to estimate day respiration (Rd ). Recent analysis suggests that increasing proportions of photorespiration (quantified as Γ*/Cc , the ratio of CO2 compensation point Γ* to chloroplast CO2 concentration, Cc ) with irradiance explain much of the Kok effect. Also, the Kok method has been modified to account for the decrease in PSII photochemical efficiency (Φ2 ) with irradiance. Using a model that illustrates how varying Rd , Γ*/Cc , Φ2 and proportions of alternative electron transport could engender the Kok effect, we quantified the contribution of these parameters to the Kok effect measured in sunflower across various O2 and CO2 concentrations and various temperatures. Overall, the decreasing Φ2 with irradiance explained c. 12%, and the varying Γ*/Cc explained c. 25%, of the Kok effect. Maximum real light inhibition of Rd was much lower than the inhibition derived from the Kok method, but still increased with photorespiration. Photorespiration had a dual contribution to the Kok effect, one via the varying Γ*/Cc and the other via its participation in light inhibition of Rd .

Introduction

The Kok effect refers to the abrupt change in the slope of the linear relationship between net photosynthetic rate and irradiance that occurs at very low irradiances, as observed initially in unicellular algae (Kok, 1948, 1949; Healey & Myers, 1971). The switch is reported later in leaves of many higher plant species (e.g. Ishii & Schmid, 1981; Sharp et al., 1984; Villar et al., 1994; Buckley et al., 2017). The slope decreases from the initial higher value to a lower value, mostly at an irradiance value around the light compensation point. This switch has been interpreted as a consequence of light inhibition of respiration, allowing the so‐called Kok method to estimate respiration in the light, or day respiration (R d), and quantum yield of CO2 assimilation (ΦCO2) (see Supporting Information Table S1 for all symbol definitions), using the part of the relationship with the lower slope. The absolute value of the estimated R d is lower than the respiration in the dark (R dk) (Fig. 1). The cost of total respiratory activities accounts for c. 40% of gross photosynthetic productivity of whole plants (Gifford, 1995; Amthor, 2010). Light inhibition of respiratory activities also occurs at a stand scale (Gong et al., 2017), suggesting that it is a general phenomenon, and thus would have a significant impact on projecting the net ecosystem carbon fluxes in biomes across the globe (Heskel et al., 2013). For this reason, understanding the Kok effect and its related light inhibition of respiration has continuously received attention (Tcherkez et al., 2017a,b).

Fig. 1

Illustration of a two‐phase photosynthetic response to low irradiances – the Kok effect. The early interpretation of this effect, as suppressing respiration by light, gave rise to the Kok method to estimate respiration in the light (or ‘day respiration’, R d, the intercept of phase 2; open symbols with the dashed line), which is lower than respiration in the dark (R dk), the intercept of phase 1 (closed symbols with the solid line).

The lower estimates of R d by the Kok method, relative to R dk, have been confirmed by other gas exchange‐based methods such as the popular Laisk method (Laisk, 1977). By applying the Laisk method to different light intensities, it has been shown that R d was progressively inhibited by increasing irradiance (Brooks & Farquhar, 1985; Villar et al., 1995). However, this light inhibition has been challenged by the direct measurement of R d, which exploits the differences in the time course of labelling by carbon isotopes of photosynthetic, photorespiratory and respiratory pathways. For example, using such techniques, Pinelli & Loreto (2003) suggested a significant refixation of respired and photorespired CO2 and Loreto et al. (2001) calculated that there would be no significant difference between R d and R dk if the refixation of CO2 released from respiration during illumination were taken into account. Similarly, a recent report using a direct method based on isotopic disequilibrium (Gong et al., 2018) showed that R d was underestimated by the Laisk method. Owing to inconsistent reports of this kind, whether the Kok effect was a result of light inhibition of leaf respiration has been under debate over years.

In fact, according to an extended form of the widely used model of Farquhar et al. (1980) for describing the electron transport‐limited photosynthesis, several other mechanisms could also explain the Kok effect. The extended model expresses the net pan class="Chemical">CO2 assimilation rate (A) as a function of the photosynthetically absorbed irradiance (I abs) as (Yin et al., 2004, 2006):

where C c is the CO2 concentration at the carboxylating sites of Rubisco, Γ* is the CO2 compensation point in the absence of R d, Φ2 is the photochemical efficiency of photosystem II (PSII) electron transport, ρ 2 is the fraction of the absorbed photons partitioned to PSII, and f aet is the factor accounting for fractions of alternative electron transport. So, the term (Φ2  ρ 2 I abs) is the flux of PSII electron transport. Parameters f aet and ρ 2 can be quantified by the extended model as (Yin et al., 2006): where Φ1 is the photochemical efficiency of PSI electron transport, f cyc is the fraction of the PSI electron flux that follows the cyclic electron transport around PSI, and f pseudo is the fraction of the PSI electron flux that follows the pseudocyclic electron transport (defined as all noncyclic electron‐consuming pathways other than the Calvin cycle or the photorespiratory cycle).

Eqn (1) suggests that changes not only in R d (Fig. 2a), but also in Γ*/C c, Φ2, f aet and ρ 2, with increasing I abs, result in changes in the slope of A vs I abs. Notably, Farquhar & Busch (2017) recently demonstrated that as a result of regulation of stomatal conductance (g s) and pan class="Chemical">mesophyll conductance (g m), C c decreased (thus Γ*/C c increased) sharply with increasing I abs within the range of low irradiances, and that this phenomenon accounted for much of the observed Kok effect (Fig. 2b). A similar argument might be applied to Φ2 (Fig. 2c), as Φ2 is not constant but decreases with increasing I abs (Genty & Harbinson, 1996), even within the range of low irradiances within which the Kok method is used to estimate R d and Φpan class="Chemical">CO2 (Yin et al., 2011a, 2014). Accounting for the decrease of Φ2 with increasing irradiance has resulted in a modified method to estimate R d (Yin et al., 2009, 2011a). The analysis using the modified method, now known as the Yin method (Tcherkez et al., 2017b), indicates that the inhibition of R d by light is less than the original Kok method suggests (Yin et al., 2011a).

Fig. 2

Illustration of the impact of varying values of four parameters (day respiration, R d; ratio of CO2 compensation point to chloroplast CO2 concentration, Γ*/C c; photosystem II photochemical efficiency, Φ2; and fraction for cyclic electron transport, f cyc) with absorbed irradiance I abs (upper panels of a–d, respectively) on the shape of the light response curve of net photosynthesis (A, lower panels), where there seems to be a transition from a higher‐slope phase (closed symbols) to a lower‐slope phase (open symbols). Curves in lower panels are generated from Eqns (Eqn 1), (Eqn 2), (Eqn 3), in which, when showing the impact of one parameter, other parameters were kept constant. Units are as follows: I abs, µmol m−2 s−1; R d and A, µmol m−2 s−1; Φ2, mol mol−1; Γ*/C c, unitless; and f cyc and excitation partitioning to PSII ρ 2, fractions.

Less information is available on the change in f aet or in ρ 2 with I abs that could partly explain the Kok effect. Peltier & Sarrey (1988) indicated that the inhibition of chlororespiration (a process in chloroplasts that involves a respiratory electron transport chain within the thylakoid membrane) might be responsible for the Kok effect. Data of Zhang et al. (2018) and Ver Sagun et al. (2019) suggested that cyclic electron transport around PSI increased with increasing I abs. If this also applies to the limiting light conditions, an increase in f cyc with increasing I abs would predict a part of the Kok effect (Fig. 2d). According to Eqns 2 and 3, f cyc has a dual effect on the expression of the Kok effect, that is, via both terms f aet and ρ 2. Eqn 3 suggests that parameter ρ 2, related to state transition, could be affected not only by f cyc (Fig. 2d) but also by the Φ2/Φ1 ratio. Tcherkez et al. (2017a) speculated the possible role of state transition in the Kok effect. The model of Eqns (Eqn 1), (Eqn 2), (Eqn 3) predicts that an increase in f cyc or in Φ2/Φ1 with increasing I abs leads to the state transition in favour of PSI with increasing irradiance, and this could engender part of the Kok effect (Fig. 2d).

The Kok effect is not ubiquitous. Early reports found little Kok effect at low O2 conditions and in C4 plants (Cornic & Jarvis, 1978; Ishii & Murata, 1978). These observations have led to suggestions that photorespiration might be involved in the Kok effect, as confirmed by other studies where photorespiration was manipulated by changing measurement temperatures (Ishii & Schmid, 1981; Way et al., 2019) or by lowering leaf water potential (Sharp et al., 1984). Again, the model analyses of Farquhar & Busch (2017) demonstrated that the change in Γ*/C c, therefore, in relative amounts of photorespiration, with increasing I abs can explain much of the diminution of the Kok effect in C4 plants and at low O2 or high CO2 concentrations or low temperatures. They also showed that the change in Γ*/C c can generate the apparent inhibition of R d as inferred by the Laisk method, which is based on A–C i curves at two or more irradiances (where C i is the intercellular CO2 concentration). The decrease in C i with increasing I abs is the result of stomatal regulation, and its influence on estimates of R d by the Kok method was noted by Kirschbaum & Farquhar (1987), who proposed a method to correct for this decrease in C i. The further drawdown in C c, relative to C i, is regulated by g m (Evans & von Caemmerer, 1996). The Kok method would underestimate R d if light‐dependent changes in C i (Villar et al., 1994) or in C c (Ayub et al., 2011) are not corrected for. Simple g s and g m models when coupled with photosynthesis models like Eqns (Eqn 1), (Eqn 2), (Eqn 3) can account for the refixation of CO2 released from respiration and photorespiration (von Caemmerer, 2013), and in fact, the refixation fractions of (photo)respired CO2 can be calculated analytically from stomatal, mesophyll and carboxylation resistances (Yin & Struik, 2017). As such, the light inhibition of R d predicted for photorespiratory conditions by Farquhar & Busch (2017) and the need to correct for light‐dependent changes in C i and C c are basically analogous to the statement of Loreto et al. (2001) that the lower R d than R dk resulted from the failure of the original Kok or Laisk methods in accounting for the refixation of respired CO2 in the light.

However, there are cases where the Kok effect is not always associated with photorespiration. The change in the slope was occasionally observed to be present under high‐CO2 conditions (Sharp et al., 1984), and in C4 leaves and under low‐O2 conditions albeit to a smaller extent (Yin et al., 2011a). Gong et al. (2015) reported an even lower R d : R dk ratio in C4 than in C3 leaves. Buckley et al. (2017) observed a similar extent of change in the slope under both 21% and 2% O2 conditions for broadbean (Vicia faba) mature leaves. Nevertheless, the Kok effects reported in the early years (Kok, 1949; Ishii & Schmid, 1981; Sharp et al., 1984) are mostly associated with the abrupt transition in the slope (Fig. 1), whereas the g s–g m photosynthesis model predicts only a smooth transition (Farquhar & Busch, 2017).

Of the possible mechanisms (R d, Γ*/C c, Φ2, f aet and/or ρ 2) highlighted by Eqns (Eqn 1), (Eqn 2), (Eqn 3) that potentially explain the magnitude of the Kok effect (Fig. 2), f aet and ρ 2 are hard to measure accurately by existing equipment, especially at low irradiances along the Kok curve. Also, the pattern of changing R d in response to I abs is hard to quantify with existing methods. In this study, we will illustrate, using Eqns (Eqn 1), (Eqn 2), (Eqn 3), that how R d responds to I abs would have relevance to the Kok effect and in estimating ΦCO2. We surmise that if the varying Γ*/C c ratio is a major factor accounting for the Kok effect, as stated by Farquhar & Busch (2017), then the magnitude of the Kok effect should be associated with the Γ*/C c ratio, regardless of how the variation of this ratio is created. To this end, we designed an expn>eriment in which we used various O2 and CO2 concentrations or temperatures to generate varying relative amounts of photorespiration, that is, various Γ*/C c ratios. Based on a modelling analysis of the experimental data we quantitatively assess: whether the change of Γ*/C c and the decrease of Φ2 with increasing I abs could explain, in part, the Kok effect; if so, what the relative contribution of the two components is in determining the Kok effect; and what the maximum real inhibition of R d by light is. We demonstrate that our results help to identify common threads explaining seemingly contradictory findings among previous studies on R d.

Materials and Methods

Plant materials and measurements

Plants of sunflower (Helianthus annuus, cv ‘Sunspot’) were grown in pots in a growth chamber (day : night temperature, 25 : 20°C; relative humidity, 70%; photon flux density, c. 500 μmol m−2 s−1 at the soil level; photoperiod, 16 h, 06:00–22:00 h) in Wageningen. Five seeds were sown and seedlings were thinned to one plant per 7 l pot. Initial amounts of soil nitrogen (N), phosphorus (P) and potassium (K) were 0.62, 0.83, and 1.04 g per pot, respectively. Nutrient solution was added two or three times per week based on the expected plant growth. Seeds were sown weekly for 4 wk, creating four replications. Measurements were conducted on the 11th or 12th fully expanded leaf counting from the bottom, using one plant per replication.

An open gas exchange system (Li‐Cor 6800; Li‐Cor Inc., Lincoln, NE, USA) and an integrated fluorescence chamber head of 6 cm2 were used for three sets of measurements, in which various O2 or CO2 concentrations or various temperatures were used to create different amounts of photorespiration (Table 1). The first set used five O2 concentrations. Four cylinders containing different mixtures of O2 and N2 were used. Gas from the cylinder was supplied to the Li‐Cor 6800 where CO2 was blended with O2. For the second set, five different ambient CO2 (C a) concentrations in the leaf chamber were used (Table 1). For the third set, four leaf temperatures were used (Table 1). A flow rate of 200 μmol s−1 was used, and leaf‐to‐air vapour pressure difference was maintained within 0.8–1.6 kPa, for all measurements.

Table 1

Levels of O2, ambient CO2 and leaf temperature in three sets of measurements on sunflower leaves.

Set	O2 (%)	CO2 (µmol mol−1)	Temperature (°C)
1	2, 10, 21, 35, 50	400	25
2	21	100, 250, 400, 550, 700	25
3	21	400	15, 25, 30, 35

For a given O2, CO2 or temperature, a photosynthetic response curve to incident irradiance (A−I inc) was measured. Leaves were first acclimated under 80 μmol m−2 s−1 until A reached a steady state, which took c. 45 min. Measurements were then undertaken using a sequence of 80, 70, 60, 50, 40, 30, 25, 20, 15, 10, and 5 μmol m−2 s−1, with 6 min for each step. For measurements in each of the first two sets, O2 or CO2 concentrations were chosen randomly. Measurements of the temperature set were conducted after the O2 and CO2 sets to avoid possible after‐effects of high temperature on leaves. For the same reason, the four temperatures were set up from low to high rather than randomly.

After the measurements for A−I inc curves, A−C i curves were determined to provide extra data to estimate g m. Leaves were adapted to an I inc of 100 μmol m−2 s−1 at 25°C and 21% pan class="Chemical">O2 until A became stable, and curves were measured using a C a sequence of 400, 200, 100, 75, 50, 400, 400, 550, 800 and 1500 μmol mol−1, with 3 min per step. Apparent A–C i curves were also assessed with heat‐killed leaves, which showed that pan class="Chemical">CO2 leakage was negligible during our measurement using the Li‐Cor 6800.

For each step of either the A−I inc or A−C i curve, pan class="Chemical">PSII photochemical operating efficiency (Φ2) was determined by Chl fluorescence as (1−F s/F m′), where F s is the steady‐state fluorescence and F m′ is the maximum fluorescence as revealed using the single flash of c. 8500 µmol m−2 s−1 for a duration of 1.0 s. We did not use the multiphase method to determine F m′ because all measurements were undertaken at low irradiances.

Leaf spots used for measurements were punched out, and leaf discs were measured for light absorption (STS‐VIS miniature spectrometer; Ocean Optics, Dunedin, FL, USA), twice per disc, to represent average absorption at this spot. After measuring their areas, leaf discs were dried in a 70°C oven for 24 h to determine pan class="Disease">dry matter. Each dry leaf disc was then ground into powder, and samples of 1–3 mg were analysed for N concentrations with an EA1108 CHN‐O Element Analyzer (Fisons Instruments, Waltham, MA, USA) using the Dumas combustion method.

Data and modelling analyses

All the leaf spots had a similar N content. The average leaf N was 1.6 g m−2 and average leaf absorptance was 85%. Variation among replications was small, and replicate average values were used for analysis.

Data of A vs I abs were inspected to identify the irradiance at the Kok transition point (I abs,t), based on the highest average r 2 of linear regression on points both below and above the candidate I abs,t of each curve. The regression slopes below and above I abs,t were denoted as b 1 and b 2, respectively, and the b 1 : b 2 ratio was calculated. The intercept of the regression after I abs,t is the day respiration estimated by the Kok method. Here, the intercepts of regression lines before and after I abs,t are denoted as r d1 and r d2, respectively. According to the original interpretation of the Kok effect (Fig. 1), r d1 is equivalent to the respiration rate in the darkness, R dk.

To examine if the decrease of Φ2 with increasing I abs could partly explain the Kok effect, plots of A vs I abs Φ2 were made. To be compared with the A−I abs plots, data points were allocated according to I abs,t identified earlier, and linear regression slopes both below and above I abs,t were denoted as B 1 and B 2, respectively. Any decrease in the B 1 : B 2 ratio, relative to the b 1 : b 2 ratio, would suggest that the decrease of Φ2 with increasing I abs could partly explain the Kok effect. The intercept of the linear plot of A vs I abs Φ2/4 after the Kok break point is the day respiration estimated by the Yin method (Yin et al., 2009, 2011a). As the intercept remains unchanged if the linear plot is made here for A vs I abs Φ2, the intercepts of A−I abs Φ2 lines before and after I abs,t are denoted as R D1 and R D2, respectively.

To assess the impact of Γ*/C c on the Kok effect, C c has to be known. To that end, we estimated g m using all data from combined gas exchange and Chl fluorescence measurements. g m is known to vary with temperature (Bernacchi et al., 2002), but whether g m varies with C i or with I inc or O2 is uncertain. Furthermore, recent literature suggests the necessity to dissect mesophyll resistance into its components (Tholen et al., 2012) and to consider the intracellular arrangements of organelles (Yin & Struik, 2017; Ubierna et al., 2019; Yin et al., 2020). Here we consider three g m modes: mode i assumes that g m varies only with temperature, but not with either C i or I inc or O2; mode ii assumes that g m varies with all these factors; and mode iii is similar to mode ii but uses an additional factor m that lumps subresistance proportions and several intracellular properties of mesophyll organelles (Yin et al., 2020). For mode i, we estimated g m by fitting, the NRH‐A method based on the non‐rectangular hyperbolic equation for CO2‐assimilation, described by Yin & Struik (2009) to all data (including A−C i curves). Like photosynthetic rate, g m has generally an optimum response to temperature (e.g. Bernacchi et al., 2002; Warren & Dreyer, 2006; but with caution, see von Caemmerer & Evans, 2015), and we assumed that this response followed a normal distribution function, with an optimum temperature of 30°C: g m = g m30 exp{−[(T−30)/Ω]2}, which has a minimum number of parameters to estimate. We incorporated these relationships into the NRH‐A method to fit parameter Ω. For modes ii and iii, we used an equation described by Yin et al. (2009), g m = δ(A + R d)/(C c − Γ*), which can semi‐empirically accommodate the response (if observed) of g m to I inc, C i, O2 and temperature. Here, it is the unitless coefficient δ that is an explicit parameter to be estimated, and δ represents the carboxylation resistance : mesophyll resistance ratio (Yin et al., 2020). For each mode, the simultaneously estimated parameters together with g m or δ were: the calibration factor(s) that converts Chl fluorescence‐based PSII photochemical efficiency (Φ2) into linear electron transport rate (J), with J = sI inc Φ2 (Yin et al., 2009); and Rubisco specificity at 25°C (S c/o25). The values of S c/o for other temperatures were calculated from the relation Γ* = 0.5O/S c/o (where O is the concentration of oxygen; Farquhar et al., 1980; von Caemmerer, 2013) and the Arrhenius equation using 24 460 J mol−1 of Bernacchi et al. (2002) as the activation energy for Γ* (using other activation‐energy estimates (e.g. Walker et al., 2013; Yin et al., 2014) had little impact on our calculated Γ*/C c ratios). In view of the reasoning of Farquhar & Busch (2017), we used R D1 of each curve as input for the R d term of the model in fitting. The fitting procedures for three modes were implemented using the GAUSS method in proc nlin of SAS (SAS Institute Inc, Cary, NC, USA), and the SAS codes can be obtained upon request. The SAS output gave the fitted A for each measurement point, with which C c was then solved from the model of Farquhar et al. (1980) as: C c = Γ* [J/4 + 2(A + R d)]/[J/4 – (A + R d)].

Results

Forms of light inhibition of R d in relation to the Kok effect

We consider all possible scenarios in interpreting the often‐said ‘progressive’ inhibition of respiration by light, and examine, based on Eqn 1, the consequence of these scenarios on the shape of A−I abs curves within a range of the low irradiances (Fig. 3).

Fig. 3

Illustration of six scenarios (a–f) for the so‐called ‘progressive’ decrease of day respiration, R d, with absorbed irradiance, I abs (open circles), and their impact on the shape of the light response curve of net photosynthesis, A (closed circles). Units: I abs, µmol m−2 s−1; R d and A, µmol m−2 s−1.

The scenario ‘continuously linear decrease’ of R d with light (Fig. 3a) did not at all result in a break in the linear relationship. Only two ‘bilinear’ scenarios can generate the Kok effect with an abrupt transition point (Fig. 3b,c). The ‘continuously decelerating decrease’ scenario also generated the Kok effect but without the abrupt break point (Fig. 3d). For an ‘accelerating decrease’ scenario, R d was also progressively suppressed by light, but this scenario generated an A−I abs curve where the slope did not decrease but increased (Fig. 3e), thereby being unable to reproduce the Kok curve. Finally, an ‘abrupt suppression’ scenario cannot be ruled out, but this scenario generated two linear discontinued segments with the same slope (Fig. 3f), thereby being unable to reproduce the Kok effect either.

As illustrated in Fig. 3, the difference in scenarios also has implications for the estimation of ΦCO2. Only in the second ‘bilinear’ scenario (Fig. 3c) and the abrupt‐suppression scenario (Fig. 3f) can ΦCO2 be reliably estimated by the Kok method as the slope of the A−I abs curve above the break point. For other scenarios, the slope represents the combined yield of photosynthesis and of the component of light suppression of R d. In fact, it is the scenario of Fig. 3(c) that the Kok method relies on to estimate R d and ΦCO2.

The observed Kok effect across various O2 and CO2 concentrations and various temperatures

Linear plots of A vs I abs using our experimental data identified the Kok break point in each curve (Fig. 4). The maximum values of the slope below (phase 1, b 1) and above the break point (phase 2, b 2) were achieved at 2% O2, and were 0.095 and 0.090 mol mol−1, respectively (Table 2), similar to expn>erimentally measured (Long et al., 1993) or theoretically inferred ΦCO2 (Yin et al., 2006) for C3 species under nonphotorespiratory conditions. A change in the slope from phase 1 to phase 2 became more significant with increasing O2 concentrations, with decreasing CO2 concentrations, and with increasing temperature (Fig. 4). The b 1 : b 2 ratio increased from 1.06 at 2% O2 to 1.69 at 50% O2, from 1.07 at 700 µmol mol−1 CO2 to 1.83 at 100 µmol mol−1 CO2, and from 1.10 at 15°C to > 1.30 at 30–35°C (Table 2).

Fig. 4

Net photosynthesis rates (A) vs absorbed irradiance (I abs), based on measured data from five O2 concentrations (a), five CO2 concentrations (b), and four temperatures (c) for sunflower leaves. Points represent the means of measurements on four replicated leaves. Continuous lines are for phase 1, and dotted lines are for phase 2, of the Kok plot, drawn from parameter estimates as given in Tables 2 and 3.

Table 2

Estimates of the slope values of phase 1 (b 1) and phase 2 (b 2) in the A vs I abs plot or of the slope values of phase 1 (B 1) and phase 2 (B 2) in the A vs I absΦ2 plot for sunflower leaves.

		A vs I abs plot			A vs I absΦ2 plot
		b 1	b 2	b 1 : b 2	B 1	B 2	B 1 : B 2
O2 (%)	2	0.095 (0.004)	0.090 (0.001)	1.06	0.118 (0.004)	0.115 (0.001)	1.03
	10	0.083 (0.003)	0.082 (0.001)	1.02	0.109 (0.003)	0.106 (0.001)	1.02
	21	0.081 (0.003)	0.068 (0.001)	1.19	0.103 (0.003)	0.090 (0.001)	1.15
	35	0.071 (0.005)	0.057 (0.001)	1.24	0.092 (0.006)	0.076 (0.001)	1.21
	50	0.078 (0.011)	0.046 (0.001)	1.69	0.105 (0.014)	0.063 (0.001)	1.67
CO2 (µmol mol−1)	100	0.057 (0.008)	0.031 (0.001)	1.83	0.073 (0.005)	0.042 (0.001)	1.74
	250	0.070 (0.003)	0.058 (0.001)	1.21	0.088 (0.002)	0.075 (0.001)	1.17
	400	0.080 (0.001)	0.068 (0.000)	1.18	0.099 (0.001)	0.086 (0.000)	1.15
	550	0.086 (0.003)	0.078 (0.001)	1.11	0.108 (0.003)	0.101 (0.001)	1.07
	700	0.085 (0.003)	0.080 (0.001)	1.07	0.102 (0.003)	0.103 (0.001)	0.99
Temperature (°C)	15	0.085 (0.002)	0.077 (0.000)	1.10	0.105 (0.002)	0.098 (0.000)	1.06
	25	0.079 (0.001)	0.068 (0.001)	1.16	0.099 (0.001)	0.088 (0.001)	1.13
	30	0.086 (0.004)	0.063 (0.001)	1.37	0.112 (0.004)	0.085 (0.001)	1.32
	35	0.078 (0.006)	0.059 (0.001)	1.33	0.105 (0.006)	0.081 (0.001)	1.29

The slope values have a unit of mol mol−1 and standard errors of the estimates are given in brackets; data used for estimation were from the three sets of measurements as described in Table 1.

A, net rate of leaf photosynthesis (μmol m−2 s−1); I abs, irradiance absorbed by leaf photosynthetic pigments (μmol m−2 s−1); Φ2, photochemical efficiency of photosystem II electron transport (mol mol−1).

Table 3

Estimates of the intercept values of phase 1 (r d1) and phase 2 (r d2) in the A vs I abs plot or of the intercept values of phase 1 (R D1) and phase 2 (R D2) in the A vs I abs Φ2 plot for sunflower leaves.

		A vs I abs plot			A vs I absΦ2 plot			I abs,t
		r d1	r d2	r d1 : r d2	R D1	R D2	R D1   : R D2
O2 (%)	2	1.33 (0.04)	1.28 (0.04)	1.04	1.34 (0.03)	1.34 (0.03)	1.00	9.1
	10	1.42 (0.03)	1.41 (0.03)	1.01	1.46 (0.03)	1.46 (0.03)	1.00	6.8
	21	1.41 (0.03)	1.14 (0.03)	1.24	1.41 (0.03)	1.21 (0.02)	1.17	21.0
	35	1.55 (0.05)	1.33 (0.05)	1.17	1.56 (0.06)	1.38 (0.05)	1.13	16.0
	50	1.43 (0.07)	1.13 (0.02)	1.26	1.44 (0.07)	1.15 (0.02)	1.25	9.3
CO2 (µmol mol−1)	100	1.55 (0.07)	1.14 (0.04)	1.35	1.55 (0.05)	1.17 (0.03)	1.32	15.6
	250	1.64 (0.03)	1.39 (0.03)	1.18	1.64 (0.02)	1.43 (0.02)	1.15	20.9
	400	1.44 (0.01)	1.16 (0.02)	1.24	1.44 (0.01)	1.21 (0.01)	1.19	21.9
	550	1.83 (0.03)	1.68 (0.03)	1.09	1.83 (0.03)	1.73 (0.03)	1.06	17.4
	700	1.57 (0.04)	1.53 (0.04)	1.03	1.54 (0.04)	1.56 (0.04)	0.99	8.5
Temperature (°C)	15	0.66 (0.02)	0.50 (0.02)	1.32	0.67 (0.01)	0.56 (0.01)	1.18	20.4
	25	1.36 (0.02)	1.06 (0.03)	1.28	1.36 (0.01)	1.12 (0.02)	1.22	26.7
	30	2.10 (0.04)	1.78 (0.02)	1.18	2.10 (0.03)	1.82 (0.02)	1.15	14.0
	35	2.98 (0.06)	2.71 (0.03)	1.10	2.98 (0.06)	2.75 (0.03)	1.08	13.6

The intercept values have a unit of μmol m−2 s−1 and standard errors of the estimates are given in brackets; data used for estimation were from the three sets of measurements as described in Table 1.

A, net rate of leaf photosynthesis (μmol m−2 s−1); I abs, irradiance absorbed by leaf photosynthetic pigments (μmol m−2 s−1); Φ2, photochemical efficiency of photosystem II electron transport (mol mol−1); I abs,t, the calculated value of I abs (μmol m−2 s−1) for the transition from phase 1 to phase 2 from the A vs I abs plot.

Estimates of the slope values of phase 1 (b 1) and phase 2 (b 2) in the A vs I abs plot or of the slope values of phase 1 (B 1) and phase 2 (B 2) in the A vs I absΦ2 plot for pan class="Species">sunflower leaves.

Similarly, the difference in the estimated respiration for phase 1 and phase 2, denoted as r d1 and r d2, respectively, became more significant with increasing pan class="Chemical">O2 concentrations, decreasing pan class="Chemical">CO2 concentrations, and increasing temperature (Table 3). With the estimated b 1, b 2, r d1 and r d2, the irradiance for the Kok break point, I abs,t, can be calculated, and it varied from 7 to 27 µmol m−2 s−1 (Table 3).

Estimates of the intercept values of phase 1 (r d1) and phase 2 (r d2) in the A vs I abs plot or of the intercept values of phase 1 (R D1) and phase 2 (R D2) in the A vs I abs Φ2 plot for pan class="Species">sunflower leaves.

The variable Φ2 as a possible cause for the Kok effect

As with previous reports (Yin et al., 2011a, 2014), Φ2 decreased with increasing irradiances in all three sets of measurements (Fig. S1). Compared with the A vs I abs plots, the A vs I abs Φ2 plots had a similar shape (thus, they are not shown), but the obtained B 1 : B 2 ratios were slightly lower than the b 1 : b 2 ratios (Table 2). As expected, the regression of A against I abs Φ2 yielded consistently lower intercepts, and therefore higher estimates, R D1 and R D2, compared with r d1 and r d2, respectively, confirming the results of earlier studies (Yin et al., 2011a). For the same reason, the R D1 : R D2 ratios were smaller than the r d1 : r d2 ratios (Table 3). There were no consistent trends for absolute values of r d1, r d2, R D1 and R D2 with changing pan class="Chemical">O2 or pan class="Chemical">CO2 concentrations; but unsurprisingly they increased consistently with increasing temperature (Table 3).

Association of the Kok effect with the variable Γ*/Cc

We estimated parameter values of the aforementioned three g m modes. The estimate of the m factor for mode iii was 0, which means that modes ii and iii had identical results. To test whether a nonzero m factor influenced the calculated C c, we fixed m to 0.3, our recent estimate of this parameter (Yin et al., 2020). The three g m modes yielded the same pan class="Disease">goodness of fit with R 2 of 0.966 (Table S2). The modelled A by the three modes did not differ essentially (Fig. S2a). Using the modelled A, we calculated the Γ*/C c ratio across irradiance of all the three sets of measurements. The Γ*/C c ratios calculated by mode ii or iii at first very low irradiances were more variable than those given by mode i (results not shown), but the average Γ*/C c ratio along a given A−I inc curve did not differ much between the three modes (Fig. S2b). We also used the variable J method of Harley et al (1992) to inspect any variation of g m and found no evidence that g m varied with either C i or with I inc or with pan class="Chemical">O2. In the following analysis, we show the results based on the estimate using mode i, as they did not differ much from those using mode ii or iii.

The obtained average Γ*/C c ratio varied from 0.008 to 0.195 when O2 varied from 2% to 50%, from 0.322 to 0.049 when CO2 varied from 100 to 700 µmol mol−1, and from 0.066 to 0.110 when temperature varied from 15 to 35°C. Plotting the b 1 : b 2 ratio or the B 1 : B 2 ratio against the Γ*/C c ratio showed linear relationships, and because these linear relations did not differ significantly among the three sets of measurements, the common regression line was obtained, and the intercept of the line at the zero Γ*/C c ratio was close to 1 (Fig. 5a).

Fig. 5

The slope ratios of phase 1 to phase 2 in the net photosynthesis rate (A) vs absorbed irradiance (I abs) plot (i.e. b 1 : b 2 ratios; open symbols) or in the A vs I absΦ2 plot (i.e. B 1 : B 2 ratios; closed symbols) based on measured values of A (a), or the b 1 : b 2 ratios based on modelled values of A (b), plotted against ratios of CO2 compensation point to chloroplast CO2 concentration (Γ*/C c) across various O2 concentrations (circles), CO2 concentrations (squares) and temperatures (triangles) for sunflower leaves. Equations represent the regression lines that pass the (0, 1) point. Φ2, photosystem II photochemical efficiency.

The extents to which the Kok effect was explained by variable Φ2 and Γ*/Cc

The strong correlation of the b 1 : b 2 or B 1 : B 2 ratio with the Γ*/C c ratio (with R 2 > 0.80; Fig. 5a) does not mean that the varying Γ*/C c ratio can explain more than 80% of the Kok effect because other factors (such as R d and f aet) may vary with Γ*/C c as well. However, the relative difference in the slope value between the b 1 : b 2 vs the Γ*/C c plot (2.559, Fig. 5a) and the B 1 : B 2 vs the Γ*/C c plot (2.262; Fig. 5a) should quantify the contribution of the decreasing Φ2 in explaining the Kok effect. This relative difference was (2.559–2.226)/2.559 × 100% = 11.6%, suggesting that, overall, the varying Φ2 explained c. 12% of the Kok effect across varying pan class="Chemical">O2 and pan class="Chemical">CO2 concentrations and varying temperatures.

We plotted the modelled A against I abs to generate slope values of b 1 and b 2, and thereby the modelled b 1 : b 2 ratios. The modelled b 1 : b 2 ratios did increase with the Γ*/C c ratio (Fig. 5b), in line with the statement of Farquhar & Busch (2017) that the changing Γ*/C c ratio explains much of the observed Kok effect. Farquhar & Busch (2017) did not estimate quantitatively the extent of the explanation.

The modelled b 1 : b 2 ratios were lower than the observed b 1 : b 2 ratios shown in Table 2. Our prediction used measured C i and Φ2 as input and took the effect of g m and Γ* into account, and therefore the effects of varying Φ2 and Γ*/C c were already considered in the modelling. This suggests that the plot of the modelled b 1 : b 2 ratios vs the Γ*/C c ratios should reflect the combined effect of both varying Φ2 and varying Γ*/C c. The intercept of the plot for the modelled b 1 : b 2 ratios vs the Γ*/C c ratios was again close to 1; but its slope was 0.944 (Fig. 5b), much lower than 2.559 – the slope of the observed b 1 : b 2 ratios vs the Γ*/C c ratios (Fig. 5a). As the intercept remained unaltered, this indicates that the combined contribution of varying Φ2 and Γ*/C c to the observed Kok effect can be estimated from slope values, that is, c. 36.9% (= 0.944/2.559 × 100%). Therefore, the effect of varying Γ*/C c alone explained c. 25.3% (36.9–11.6%) of the observed Kok effect across various pan class="Chemical">O2 and pan class="Chemical">CO2 concentrations and various temperatures.

Quantifying the maximum extent of inhibition of day respiration by light

Our modelling procedure aimed to quantify the contribution of Φ2 and varying Γ*/C c, and therefore, as is the usual case, assumed that R d and f aet did not vary with irradiance or with measurement O2 and CO2 conditions. The remaining unexplained contributions (c. 63%) must be a result of light inhibition of R d and possibly variable f aet and/or ρ 2. We are not able to separate the contribution of light inhibition of R d from the effect of variable f aet and/or ρ 2 if the variation of f aet and/or ρ 2 with irradiance cannot be ruled out. If we assume that the variation of either f aet and/or ρ 2 with irradiance is negligible with the limiting light range, as is often assumed in measuring ΦCO2, we can quantify the real inhibition of R d by light by removing the effect of changing Φ2 and Γ*/C c, as described in the following. As such, this estimate should be considered as the maximum real inhibition of R d by light.

The apparent relative inhibition in case of the Yin method is:

The similar apparent relative inhibition can be proposed for the Kok method. The apparent inhibition was higher according to the Kok method than according to the Yin method (Fig. 6a), owing to the fact that the Kok method ignores the decrease of Φ2 with irradiance. Overall, the Kok method overestimated the apparent inhibition of R d by c. 18%, as compared with the Yin method.

Fig. 6

Relative apparent light inhibition of day respiration, R d, identified by the Kok method vs that identified by the Yin method (a), and relative real light inhibition vs the relative apparent light inhibition of R d both identified by the Yin method (b), across various O2 concentrations (circles), CO2 concentrations (squares) and temperatures (triangles) for sunflower leaves. The dashed diagonal represents the 1 : 1 line, at which y = x.

pan class="Chemical">Plotting the modelled A against I abs resulted in lower estimates of r d2 than r d1 and plotting the modelled A against I abs Φ2 also resulted in lower estimates of R D2 than R D1 than their respective estimates using the observed A (results not shown), although a single value of R d was used for each curve in modelling. This confirmed the analysis of Farquhar & Busch (2017) that the apparent inhibition of R d by light was partly a result of the artefact of changing Γ*/C c with irradiance. The real relative inhibition of R d by light can be calculated as:

Compared with the relative apparent inhibition from the Yin method, the relative real inhibition was much lower (Fig. 6b). The results also suggested that after correcting for varying Γ*/C c, light inhibition of R d only became lower but did not disappear: the real inhibition increased generally with relative amounts of photorespiration (Fig. 7).

Fig. 7

The relative real light inhibition of respiration identified by the Yin method plotted against ratios of CO2 compensation point to chloroplast CO2 concentration (Γ*/C c) across various O2 concentrations (circles), CO2 concentrations (squares), and temperatures (triangles) for sunflower leaves.

Discussion

The ‘linear decrease’ of R d with light cannot generate the Kok effect

The Kok effect was initially, and is still often, hypothesized to arise from the suppression of respiration by light (Fig. 1; Sharp et al., 1984; Heskel et al., 2013; Tcherkez et al., 2017a; Way et al., 2019). This hypothesis has received support from studies that have identified several mechanisms for the metabolic downregulation of respiratory reactions by light, as reviewed by Tcherkez et al. (2012, 2017b). Gas exchange measurements have shown that R d, relative to R dk, progressively decreased with increasing I abs, either in a continuously linear manner (Villar et al., 1994) or in a decelerating manner (Brooks & Farquhar, 1985; Villar et al., 1995; Atkin et al., 2000). Using Eqns (Eqn 1), (Eqn 2), (Eqn 3), we assessed the effect of all possible scenarios for the often‐said ‘progressive’ inhibition of respiration by light on the shape of A−I abs curves (Fig. 3). Of the six scenarios considered, only the three scenarios for ‘decelerating decrease’ of R d with irradiance (Fig. 3b–d) can generate the Kok effect, thereby excluding the other three scenarios that are often considered relevant to the Kok effect. In particular, the scenario of a ‘continuously linear decrease’ of R d with light (Fig. 3a) did not result in a break in the linear A−I abs relationship. This is in contrast to the statement of Tcherkez et al. (2017a) in their report for the 18th New Phytologist Workshop that ‘the widely‐accepted (historical) origin of the Kok effect is the inhibition of respiratory metabolism by light (linear decrease of R d with light)’. Given the consequences of the various scenarios on the Kok effect, and thus also on the estimation of ΦCO2, future studies should aim to reveal which of the three scenarios in Fig. 3(b)–(d) is most likely for the light inhibition of R d.

Several mechanisms co‐contribute to the Kok effect

Our analyses suggest that not a single mechanism determines the Kok effect, but at least three mechanisms (i.e. decreasing Φ2 with irradiance, varying Γ*/C c, and light inhibition of R d) co‐contribute to it. Using a model, we quantitatively estimated the relative contribution of the CO2‐specific processes like refixation (reflected via Γ*/C c) vs the light‐dependent decrease in photochemical efficiency (Φ2) in expn>laining the Kok effect. Our result suggested that varying Γ*/C c expn>lained c. 25% of the Kok effect, while variable Φ2 cannot be ignored and expn>lained c. 12% of the Kok effect, across various CO2, O2 and temperature conditions. The appreciable contribution of variable Φ2 is supported by decreases in the slope of phase 2, compared with Phase 1, of the A−I abs plots under conditions where photorespiration is greatly suppressed, for example, for C3 species under low‐O2 conditions or for C4 species (Yin et al., 2011a).

However, there are still small decreases in the slope of phase 2 for C3 species under low‐O2 conditions or for C4 species when A was plotted against I absΦ2 (Yin et al., 2011a). This effect in C4 species may reflect the low efficacy of the CO2‐concentrating mechanism (CCM) caused by a high leakiness at low irradiances (Kromdijk et al., 2010; Yin et al., 2011b). However, for a C3 species, Buckley et al. (2017) observed even more significant changes for developing leaves under 2% than under 21% O2 conditions, suggesting an involvement of other mechanisms. A fourth mechanism was shown here to potentially contribute to the Kok effect (Fig. 2d), but we were not able to verify it, as any variable f aet and/or ρ 2 are hard to identify at the light intensities showing the Kok effect. Our results, that B 1 : B 2 ratios (Table 2) and R D1 : R D2 ratios (Table 3) were very close to 1 at 2% O2 or 700 µmol mol−1 CO2 suggest that significant involvement of a fourth mechanism was highly unlikely. Thus, our remaining unexplained part (c. 63%) of the Kok effect is most likely a result of the light suppression of R d, in agreement with the statement of Buckley et al. (2017) on the dominant role of this third mechanism.

A dual effect of photorespiration in contributing to the Kok effect

Our strong linear relationships between the B 1 : B 2 ratio and the Γ*/C c ratio (Fig. 5a) confirmed previous results in the literature (Cornic & Jarvis, 1978; Ishii & Murata, 1972; Ishii & Schmid, 1981; Sharp et al., 1984; Farquhar & Busch, 2017; Way et al., 2019) showing that the Kok effect was strongly associated with the occurrence of photorespiration. Perhaps it is because of the significant contribution of varying Γ*/C c that the Kok effect reported in the earlier days (Kok, 1949; Ishii & Schmid, 1981; Sharp et al., 1984) generally had sharper transition than the recent data (Farquhar & Busch, 2017; Tcherkez et al., 2017a; Way et al., 2019) because C a has been increasing over years. However, the contribution of other factors as discussed earlier means that the Kok effect will never disappear in the future high‐CO2 atmosphere; instead, it will continue, but to a lesser extent.

Our modelling analysis suggests that strong associations between the B 1 : B 2 ratio and the Γ*/C c ratio shown in Fig. 5(a) are the combined result of a dual effect of photorespiration in contributing to the Kok effect. The first‐type effect is what Farquhar & Busch (2017) discussed on the role of increasing Γ*/C c with irradiance in explaining the Kok effect, as a result of regulation of g s and g m. The second‐type effect is what we found here – the light inhibition of R d identified after removing the first‐type effect was still positively correlated with Γ*/C c (Fig. 7). Our results suggest that the second‐type effect, representing real biological inhibitions, probably contributed more to the Kok effect than the first‐type effect.

Farquhar & Busch (2017) demonstrated that the first‐type effect of photorespiration on the Kok effect can generate the apparent light inhibition of R d for photorespiratory conditions. As stated in the introduction, this inhibition via regulation of g s and g m is the same as the importance that Loreto et al. (2001) emphasized for accounting for the refixation of respired CO2 when estimating R d. Loreto et al. (2001) stated that there would be no significant difference between R d and R dk if the refixation of respiratory CO2 during illumination is taken into account. Our results showing that, after correcting for varying Γ*/C c, light inhibition of R d only became lower but did not disappear (Fig. 6b), do not agree with the conclusion of Loreto et al. (2001). The refixation is an important means to reduce the (photo)respiratory loss under photorespiratory conditions, but its net contribution to total photosynthesis should be negligible under nonphotorespiratory conditions (Yin et al., 2020). Berghuijs et al. (2019) showed that R d estimated by the Kok method was closer to the estimate made by their model (that accounted for the refixation) under nonphotorespiratory than under photorespiratory conditions. The experiment of Loreto et al. (2001) was conducted with maize, a C4 species where Rubisco is expected to be surrounded by a high CO2 partial pressure as a result of the C4 CCM, and thus the refixation of CO2 released from respiration and photorespiration should have little contribution to the total assimilation. Using 14C‐labelling, Pärnik & Keerberg (1995, 2007a,b) showed that light inhibition of R d occurs even when accounting for CO2 refixation. Gong et al. (2015) reported a high suppression of R d by light in a C4 species. If refixation does occur appreciably in C4 species as Loreto et al. stated, it may reflect the refixation more by phosphoenolpyruvate carboxylase than by Rubisco, which might contribute to leakiness.

Apparent vs real light inhibition of R d

The suppression of R d by light has been identified using the Kok method, in many experimental studies, including recent reports based on CO2‐exchange measurements (e.g. Buckley et al., 2017) or both CO2‐ and O2‐exchange measurements (e.g. Gauthier et al., 2018). Light is known to suppress the activity of enzymes that involve CO2‐releasing pathways contributing to R d (Buckley & Adams, 2011; Tcherkez et al., 2012, 2017a,b). Using the model analysis, Farquhar & Busch (2017) demonstrated that at least part of the light inhibition of R d can be generated without assuming this inhibition beforehand. Here we used the modelling approach to analyse combined CO2‐exchange and Chl fluorescence data. With such combined experimental and modelling analyses, we demonstrated quantitatively that the original Kok method that attributes the Kok effect entirely to the light inhibition of R d overestimated the real inhibition (Fig. 6), as a result of ignoring the contribution of varying Φ2 and Γ*/C c to the Kok effect. The effect of varying Φ2 on the Kok method in overestimating the inhibition has been corrected simply by the Yin method, while the correction for varying Γ*/C c is more complicated. We previously stressed that both Kok and Yin methods to estimate R d actually apply to nonphotorespiratory conditions (Yin et al., 2011a). Our analysis with Eqn 5 suggests an approach to estimate the real light suppression of R d for photorespiratory conditions, although we are unable to clarify which one of the three scenarios of suppression in Fig. 3(b–d)) is most likely. Most importantly, our analysis using Eqn 5 revealed that the real suppression still increased with relative amounts of photorespiration (Fig. 7). While this new empirical trend receives the support from a theoretical analysis of Buckley & Adams (2011) that photorespiratory NADH may be involved in the suppression, there are probably other underlying biochemical mechanisms that merit further investigation.

Author contributions

XY conceived the study, XY and PELvdP designed the experiment, YN and PELvdP implemented the experiment and conducted the measurements, XY and YN analysed the data, and XY wrote the draft and finalised it with significant input from PCS.

Fig. S1 Photosystem II photochemical efficiency (Φ2) as a function of absorbed irradiance (I abs) across various O2 and CO2 concentrations and various temperatures.

Fig. S2 Comparison of net photosynthesis rate A and the average Γ*/C c ratio modelled using three pan class="Chemical">mesophyll conductance g m modes as described in the text.

Table S1 List of all model symbols.

Table S2 Model parameter values estimated using three pan class="Chemical">mesophyll conductance g m modes.

pan class="Chemical">Please note: Wiley Blackwell are not responsible for the content or functionality of any Supporting Information supplied by the authors. Any queries (other than missing material) should be directed to the New pan class="Chemical">Phytologist Central Office.

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