Modeling Light Response of Electron Transport Rate and Its Allocation for Ribulose Biphosphate Carboxylation and Oxygenation

Accurately describing the light response curve of electron transport rate (J–I curve) and allocation of electron flow for ribulose biphosphate (RuBP) carboxylation (J C–I curve) and that for oxygenation (J O–I curve) is fundamental for modeling of light relations of electron flow at the whole-plant and ecosystem scales. The non-rectangular hyperbolic model (hereafter, NH model) has been widely used to characterize light response of net photosynthesis rate (A n; A n–I curve) and J–I curve. However, NH model has been reported to overestimate the maximum A n (A nmax) and the maximum J (J max), largely due to its asymptotic function. Meanwhile, few efforts have been delivered for describing J C–I and J O–I curves. The long-standing challenge on describing A n–I and J–I curves have been resolved by a recently developed A n–I and J–I models (hereafter, Ye model), which adopt a nonasymptotic function. To test whether Ye model can resolve the challenge of NH model in reproducing J–I, J C–I and J O–I curves over light-limited, light-saturated, and photoinhibitory I levels, we compared the performances of Ye model and NH model against measurements on two C3 crops (Triticum aestivum L. and Glycine max L.) grown in field. The results showed that NH model significantly overestimated the A nmax and J max for both species, which can be accurately obtained by Ye model. Furthermore, NH model significantly overestimated the maximum electron flow for carboxylation (J C-max) but not the maximum electron flow for oxygenation (J O-max) for both species, disclosing the reason underlying the long-standing problem of NH model—overestimation of J max and A nmax.


INTRODUCTION
Light intensity (I) is one of the most important environmental drivers affecting electron flow and its allocation for carboxylation versus oxygenation of ribulose biphosphate (RuBP). At I levels before reaching saturation intensity, the non-rectangular hyperbolic model (hereafter, NH model) is a sub-model which is widely used to characterize the light-response curve of electron transport rate (J-I curve) and to estimate the maximum J (J max ) in C 3 photosynthesis model (e.g., Farquhar et al., 1980;Farquhar and Wong, 1984;von Caemmerer, 2000;Farquhar et al., 2001;Long and Bernacchi, 2003;von Caemmerer et al., 2009;Bernacchi et al., measured leaf gas exchange and chlorophyll fluorescence over a wide range of I levels for two C 3 species [winter wheat (Triticum aestivum L.) and soybean (Glycine max L.)]. We then incorporated Ye model to reproduce A n -I, J-I, J C -I, and J O -I curves and return key quantities defining the curves, and evaluated its performance against NH model and observations.

Plant Material and Measurements of Leaf Gas Exchange and Chlorophyll Fluorescence
The experiment was conducted in the Yucheng Comprehensive Experiment Station of the Chinese Academy of Science. The detailed descriptions about soil and meteorological conditions in this experiment station were referred to Ye et al. (2019;. Winter wheat was planted on October 4 th , 2011 and the measurements were conducted on April 23 th , 2012. Soybean was sown in on May 6 th , 2013, and the measurements were performed on 27 th July, 2013. Using the Li-6400-40 portable photosynthesis system (Li-Cor, Lincoln, NE, USA), measurements on leaf gas exchange and chlorophyll fluorescence were simultaneously performed on mature fully-expanded sunexposed leaves in sunny days. J was calculated as J = F PSII × I × 0.5 × 0.84, where F PSII is the effective quantum yield of PSII (Genty et al., 1989;Krall and Edward, 1992).
For soybean, A n -I curves and J-I curves were generated from applying different light intensities in a descending order of 2000,1800,1600,1400,1200,1000,800,600,400,200,150,100,80,50, and 0 mmol m -2 s -1 . For winter wheat, the light intensity gradient started from 1800 mmol m -2 s -1 as the maximum, in alignment with environmental light availability from October to April. At each I step, CO 2 assimilation was monitored until a steady state was reached before logging a reading. Ambient CO 2 concentration in the cuvette (C a ) was kept constant at 380 mmol mol -1 . Leaf temperature in the cuvette was kept at about 30°C for winter wheat and 36°C for soybean, respectively. The observationmodeling intercomparison was conducted within each species.
A n -I and J-I Analytical Models NH model describes J-I curve as follows (Farquhar and Wong, 1984;von Caemmerer, 2000;von Caemmerer, 2013): (1) where a e is the initial slope of J-I curve, q is the curve convexity, I is the light intensity, and J max is the maximum electron transport rate. NH model describes A n -I curve as follows (Ögren and Evans, 1993;Thornley, 1998;von Caemmerer, 2000): where a is the initial slope of A n -I curve, A nmax is the maximum net photosynthetic rate, and R d is the dark respiration rate when I = 0 mmol m -2 s -1 . NH model cannot return the corresponding saturation light intensities for J max or A nmax due to its asymptotic function. The model developed by Ye et al. (2013Ye et al. ( , 2019; hereafter, Ye model) describes J-I curve as follows: where a e is the initial slope of J-I curve, and b e and g e are the photoinhibition coefficient and light-saturation coefficient of J-I curve, respectively. The saturation irradiance corresponding to the J max (I e-sat ) can be calculated as follows: Using Ye model, J max can be calculated as follows: Ye model describes A n -I curve as follows (Ye, 2007;Ye et al., 2013): where a is the initial slope of A n -I curve, b and g are the photoinhibition coefficient and light-saturation coefficient of A n -I curve, respectively. The saturation irradiance corresponding to A nmax (I sat ) can be calculated as follows: Using Ye model, A nmax can be calculated as follows: J C and J O Estimation and J C -I and J O -I Analytical Models Combining measurements of gas exchange and chlorophyll fluorescence was a reliable and easy-to-use technique widely used to determine J O and J C (e.g., Peterson, 1990;Comic and Briantais, 1991). In C 3 plants, carbon assimilation and photorespiration are two closely linked processes catalyzed by the key photosynthetic enzyme-RuBP carboxylase/oxygenase. Photorespiration is considered as an alternative sink for lightinduced photosynthetic electron, and as a process helping consume extra photosynthetic electrons under high irradiance or other stressors limiting CO 2 availability at Rubisco (Stuhlfauth et al., 1990;Valentini et al., 1995;Long and Bernacchi, 2003). When the other alternative electron sinks are ignored or kept constant, the electron flow is mainly allocated for RuBP carboxylation and RuBP oxygenation (e.g. Farquhar et al., 1980;von Caemmerer, 2000;Farquhar et al., 2001;Long and Bernacchi, 2003;von Caemmerer et al., 2009;Bernacchi et al., 2013;von Caemmerer, 2013), and J C and J O can be respectively calculated as follows (Valentini et al., 1995): where R day is the day respiration rate, and following Fila et al. (2006), R day = 0.5 R d . In this study, J C and J O values calculated from Eqs. 9 and 10 were viewed as experimental observationsto be compared with modelled values derived from NH model and Ye model, respectively. Using the same J-I modeling framework by Ye model, the light response of J C (J C -I) can be described as follows: where a C is the initial slope of J C -I curve, and b C and g C are two coefficient of J C -I curve. The maximum J C (J C-max ) and the saturation irradiance corresponding to the J C-max (I C-sat ) can be calculated as follows: Using the same J-I modeling framework by Ye model, the light response of J O (J O -I) can be described as follows: where a O is the initial slope of J O -I curve, and b O and g O are two coefficient of J O -I curve. The maximum J O (J O-max ) and the saturation irradiance corresponding to the J O-max (I O-sat ) can be calculated as follows: Meanwhile, NH model can describe the J C -I and J O -I curves as follows: where a C is the initial slope of J C -I curve, q is the curve convexity, and J C-max is the maximum J C , and where a O is the initial slope of J O -I curve, q is the curve convexity, and J O-max is the maximum J O . NH model-Eqs. 17 and 18-cannot return the corresponding saturation light intensities for J C-max or J O-max due to its asymptotic function.

Statistical Analysis
Statistical tests were performed using the statistical package SPSS 18.5 statistical software (SPSS, Chicago, IL). One-Way ANOVA was used to examine differences between parameter values estimated by NH model, Ye model and observed values of each parameter (A nmax , I sat , J max , I e-sat , J C-max , I C-sat , J O-max , I O-sat , etc.). Goodness of fit of the mathematical model to experimental observations was assessed using the coefficient of determination (R 2 = 1 -SSE/SST, where SSE is the error sum of squares, and SST is the total sum of squares).

RESULTS
Light Response of A n and J Soybean and winter wheat exhibited an immediate and rapid initial increase of A n (a) and J (a e ) with the increasing I (Figure 1  and Table 1). The increase of A n and J continued until I reached the cultivar-specific maximum values (A nmax and J max ) at their corresponding saturation light intensities (I sat and I e-sat ) ( Figure 1 and Table 1). Both NH model (Eqs. 1 and 2) and Ye model (Eqs. 3 and 6) showed high level of goodness of fit (R 2 ) to experimental observations of two species (Figure 1 and Table 1). However, compared with observations, NH model significantly overestimated A nmax and J max (P < 0.05) for both soybean and winter wheat ( Table 1). In contrast, A nmax and J max values returned by Ye model were in very close agreement with the observations for both species (Table 1).

Light Response of J C and J O
Both species exhibited an immediate and rapid initial increase of J C (a C ) with the increasing I ( Figure 1 and Table 1). The increase of J C continued until I reached the cultivar-specific maximum values (J C-max ) at the corresponding saturation light intensity (I C-sat ) ( Figure 1 and Table 1). Both Ye model (Eq. 11) and NH model (Eq. 17) showed high level of goodness of fit (R 2 ) to experimental observations of both species (Figure 1 and Table 1). However, compared with observations, NH model significantly overestimated J C-max (P < 0.05) for both soybean and winter wheat ( Table 1). In contrast, J C-max values returned by Ye model were in very close agreement with the observations for both species (Table 1).
Compared to the light-response rapidness of J C , J O exhibited a much slower initial increase (a O ) with the increasing I ( Figure 1 and Table 1). No species showed significant difference between the observed value of J O-max and that estimated by Ye model (Eq. 14) or NH model (Eq. 18) ( Table 1). Both models showed high level of goodness of fit (R 2 ) to experimental observations of both species (Figure 1 and Table 1).
0.266 ± 0.012 a 0.248 ± 0.014 a -0.221 ± 0.003 a 0.207 ± 0.002 b b C (m 2 s mmol -1 ) (2.07 ± 0.10) × 10 -4 --(2.54 ± 0.03) × 10 -4 -g C (m 2 s mmol -1 ) (3.75 ± 0.75) × 10 -4 --(1.67 ± 1.37) × 10 -5 -- 180 For A n -I curve, the parameters are: the initial slope of the A n -I curve (a p ), the maximum A n (A nmax ) and the corresponding saturation irradiance (I sat ), light compensation point (I c ) and dark respiration rate (R d ). For J-I curve, the parameters are: the initial slope of J-I curve (a e ), the maximum J (J max ) and the corresponding saturation irradiance corresponding to J max (I e-sat ). For J C -I curve, the parameters are: the initial slope of J C -I curve (a C ), the maximum J C (J C-max ) and the corresponding saturation irradiance corresponding to J C-max (I

DISCUSSION
Assessed with an observation-modeling intercomparison approach, the results in this study highlight the robustness of Ye model in accurately reproducing A n -I, J-I, J C -I, and J O -I curves and returning key quantities defining the curves, in particular: A nmax , J max , J C-max , and J O-max . On the contrary, the NH model significantly overestimates A nmax , J max , and J C-max (Table 1). For the first time, our study discloses the previously widely reported overestimation of J max (and A nmax ) by the NH model is linked to its overestimation of J C-max but not J O-max . The overestimation of A nmax by NH model found in this study is consistent with the previous reports (e.g., Calama et al., 2013;dos Santos et al., 2013;Lobo et al., 2014;Jezǐlováet al., 2015;Mayoral et al., 2015;Ogawa, 2015;Park et al., 2016;Quiroz et al., 2017;Poirier-Pocovi et al., 2018;Ye et al., 2020). The accurate returning of A nmax by Ye model found in this study is consistent with previous studies using Ye model for various species under different environmental conditions (e.g., Wargent et al., 2011;Zu et al., 2011;Xu et al., 2012a;Xu et al., 2012b;Lobo et al., 2014;Xu et al., 2014;Song et al., 2015;Chen et al., 2016;Ye et al., 2019;Yang et al., 2020;Ye et al., 2020). The robustness of Ye model has also been validated for microalgae observations, including four freshwater and three marine microalgae species (Yang et al., 2020). The Ye model reproduced the A n -I response well for all microalgae species, and produced I sat closer to the measured values than those by three widely used models for microalgae (Yang et al., 2020). Meanwhile, the overestimation of J max by NH model found in this study supports Buckley and Diaz-Espejo (2015) in highlighting the demerit of the asymptotic function (i.e. NH model).
One key novelty of the present study is its evaluation of both asymptotic and nonasymptotic functions in describing the light response of electron flow allocation for carboxylation and oxygenation respectively (i.e. J C -I and J O -I curves). To the best of our knowledge, this is the first study which has experimentally evidenced the robustness of a nonasymptotic function (Eqs. 3,11,14) in accurately (1) reproducing J-I, J C -I, and J O -I curves and (2) returning J max , J C-max , and J O-max values, as well as their corresponding the saturation light intensities. These novel findings are of significance for our understanding of light responses of plant carbon assimilation and photorespirationboth are catalyzed by RuBP carboxylase/oxygenase.
The findings, and the approach of bridging experiment and modeling, in the present study remain to be tested for (1) species of different plant function types and/or climatic origin, which could exhibit different response patterns  and (2) plant response to interaction of multiple environmental factors (e.g., temperature, rainfall pattern, soil type) involving fluctuating light. The explicit and consistent modeling framework and parameter definitions on light responses (i.e. A n -I, J-I, J C -I, and J O -I)-combined with the simplicity and robustness-allows for future transparent scaling-up of leaf-level findings to whole-plant and ecosystem scales.

CONCLUSIONS
Ye model can accurately estimate A nmax , J max , and J C-max which the NH model would overestimate. Adopting an explicit and transparent analytical framework and consistent definitions on A n -I, J-I, J C -I, and J O -I curves, this study highlights the advantage of Ye model over NH model in terms of (1) its extremely well reproduction of J-I, J C -I, and J O -I trends over a wide I range from light-limited to light-inhibitory light intensities, (2) accurately returning the wealth of key quantities defining J-I, J C -I, and J O -I curves, particularly J max , J C-max , J O-max , and their corresponding the saturation light intensities (besides A nmax and I sat of A n -I curve), and (3) being transparent in disclosing that the previously widely reported but poorly explained problem of NH modeloverestimation of J max (and the maximum plant carboxylation capacity)-is linked to its overestimation of J C-max but not J O-max . Besides, NH model cannot obtain their saturation light intensities corresponding to J max , A nmax , J C-max , and J O-max due to its asymptotic function. This study is of significance for both experimentalists and modelers working on better representation of photosynthetic processes under dynamic irradiance conditions.

DATA AVAILABILITY STATEMENT
The raw data supporting the conclusions of this article will be made available by the authors, without undue reservation.