Accuracy of photorespiration and mitochondrial respiration in the light fitted by CO2 response model for photosynthesis

Introduction: Atmospheric CO₂ elevation significantly impacts plant carbon metabolism, yet accurate quantification of respiratory parameters—photorespiration rate (R_p) and mitochondrial respiration rate in the light (R_d)—under varying CO₂ remains challenging. Current CO₂-response models exhibit limitations in estimating these parameters, hindering predictions of crop responses under future climate scenarios.

Methods: Low-oxygen treatments and gas exchange measurements, calculating CO₂ recovery/inhibition ratio in of wheat (Triticum aestivum L.) and bean (Glycine max L.) were employed to elucidate the biological significance and interrelationships of R_p and R_d. Model-derived estimates of R_p and R_d were compared with measured values to assess the accuracy of three CO₂-response models (biochemical, rectangular hyperbola, modified rectangular hyperbola). Furthermore, the effects of ambient CO₂ concentration (0~1200 μmol·mol^-1) on the measured R_p and R_d were quantified through polynomial regression.

Results: The A/C_a model achieved superior fitting performance over the A/Ci model. However, significant disparities persisted between A/Ca-derived R_p/R_d estimates and measurements (p < 0.05). CO₂ concentration exhibited dose-dependent regulation of respiratory fluxes: R_p-measured ranged from 4.923 ± 0.171 to 12.307 ± 1.033 μmol (CO₂) m^-2 s^-1 (wheat) and 4.686 ± 0.274 to 11.673 ± 2.054 μmol (CO₂) m^-2 s^{⁻ ¹} (bean), while R_d-measured varied from 0.618 ± 0.131 to 3.021 ± 0.063 μmol (CO₂) m^-2 s^-1 (wheat) and 0.492 ± 0.069 to 2.323 ± 0.312 μmol (CO₂) m^-2 s^-1 (bean). Polynomial regression revealed strong non-linear correlations between CO₂ concentrations and respiratory parameters (R^² > 0.891, p < 0.05; except bean R_p-C_a: R^² = 0.797). Species-specific CO₂ thresholds governed peak R_p (600 μmol·mol^-1 for wheat vs. 1,000 μmol·mol^-1 for bean) and R_d (400 μmol·mol^-1 for wheat vs. 200 μmol·mol^-1 for bean).

Discussion: These findings expose critical limitations in current respiratory parameter quantification methods and challenge linear assumptions of CO₂-respiration relationships. They establish a critical framework for refining photosynthetic models by incorporating CO₂-responsive respiratory mechanisms. The identified non-linear regulatory patterns and model limitations provide actionable insights for advancing carbon metabolism theory and optimizing crop carbon assimilation strategies under rising atmospheric CO₂, with implications for climate-resilient agricultural practices.

1 Introduction

Atmospheric CO₂ concentration has increased by 48% since the pre-industrial era, reaching 415 ppm in 2021 (IPCC, 2021). This elevation drives dual climate-ecosystem impacts: as a primary greenhouse gas contributing to global warming through radiative forcing, and as a photosynthetic substrate enhancing plant productivity via the “CO₂ fertilization” effect (Easterling et al., 2000; Vaughan et al., 2003). However, the physiological mechanisms underlying plant adaptation to elevated CO₂—particularly regarding respiratory metabolism—remain insufficiently quantified (Xanthopoulos et al., 2017; Jalali et al., 2020).

Photosynthesis, transpiration, and respiration are three vital processes in plant life, essential for growth and metabolism (Nilsen, 1995). Transpiration facilitates water transport across the soil-plant-atmosphere continuum (SPAC), supporting plant growth and influencing ecosystem water-heat balances (Liu and Yu, 1997). Photosynthesis allows plants to convert light energy, CO₂, and water into organic matter and oxygen, directly impacting the productivity of terrestrial ecosystems and the global carbon cycle (Schimel et al., 2001). Photorespiration, however, occurs when the photosynthetic enzyme Rubisco reacts with oxygen instead of CO₂—a common scenario under high temperature, drought, or intense light that limits CO₂ availability. This process, universal in oxygen-producing plants and algae (Carvalho et al., 2011), shares chloroplasts as the primary site with photosynthesis and relies on light-driven reactions. Crucially, photorespiration recycles harmful byproducts generated during photosynthesis, balancing energy use and protecting plants from stress, thereby acting as a “safety valve” for photosynthetic efficiency. Mitochondrial respiration involves oxidative phosphorylation in the cells’ mitochondria to produce energy for vital activities (Vercellino and Sazanov, 2022; Huang et al., 2023). These biological processes adapt to elevated CO₂ concentrations and climate warming (Luo et al., 2001), affecting carbon cycling processes in terrestrial ecosystems (Lin, 1998; Zhang et al., 2000; Wang et al., 2008). Thus, understanding how crop photorespiration and mitochondrial respiration respond to changes in atmospheric CO₂ is crucial for predicting future crop productivity and growth patterns under elevated CO₂ conditions.

Wheat and bean are globally significant crops, crucial to human food supply and agricultural production (Gan et al., 2015; Borrell et al., 2017). As typical C₃ plants, CO₂ is the main limiting factor affecting their photosynthesis (Atkin et al., 2005). Traditional theories suggest that the carbon source for photosynthesis in terrestrial plants is primarily atmospheric CO₂, often neglecting CO₂ released by photorespiration and dark respiration of the leaves (Stirbet et al., 2020). And related respiration parameters (photorespiration rate (R_P), mitochondrial respiration rate in the light (R_d), and respiration in the light (R_L)) are inconsistently applied (von Caemmerer, 2000). The chloroplast interior constitutes the primary site for photorespiratory CO₂ release, where a substantial proportion of respired CO₂ undergoes re-assimilation through the Calvin cycle. This CO₂ recycling mechanism plays a crucial physiological role by enhancing subcellular CO₂ concentration independent of diffusion limitations imposed by boundary layer resistance stomatal conductance, and mesophyll resistance (Loreto et al., 1999, 2001; Pinelli and Loreto, 2003). Quantitatively studying photorespiratory CO₂ recycling in C₃ plants is challenging due to the simultaneous occurrence of photorespiration, dark respiration, and photosynthetic carbon assimilation within mesophyll cells (Haupt-Herting et al., 2001). The carbon isotope method can distinguish between CO₂ fixed by photosynthesis and released by photorespiration, offering a potential approach to studying CO₂ recycling and reuse by plants (Ostle et al., 2000). However, this method is costly, complex, and not precise in exploring photorespiratory CO₂ recycling, because this method ignores two important factors: firstly, Rubisco’s affinity for ¹⁴CO₂ and ¹³CO₂ is much lower than that of ¹²CO₂; secondly, the measurement process inevitably involves the inhibition of photorespiration by extremely high concentrations of ¹²CO₂ (30000 μmol mol^-1) (Pärnik and Keerberg, 2007; Busch and Sage, 2017). Kang et al. (2014) used gas exchange methods to confirm that CO₂ released by light and dark respiration can be reutilized by photosynthesis, though this concept is often overlooked. Therefore, accurate estimation of photorespiratory CO₂ reutilization is essential for improving the accuracy of photosynthetic parameters and carbon metabolism processes.

The CO₂ response curve for photosynthesis is a valuable tool for studying plant physiology and ecology, providing insights into how photosynthetic properties respond to environmental factors. This understanding can optimize CO₂ concentration management in agricultural production, contributing to enhance photosynthetic efficiency and promote growth and productivity. Two types of CO₂ response models exist: biochemical and empirical. The most widely used biochemical model is the Farquhar model and its modifications (von Caemmerer and Farquhar, 1981; Bernacchi et al., 2001; Long and Bernacchi, 2003; Ethier and Livingston, 2004). Empirical models include the rectangular hyperbola model (Ye, 2010), modified version (Ye and Yu, 2009), and the Michaelis-Menten model (Harley et al., 1992). However, current biochemical models do not consider the effect of mitochondrial respiration rate in the light (R_d), and empirical models overlook the effect of CO₂ concentration on photorespiration rate. Quantitative studies on the effect of atmospheric CO₂ concentration (C_a) on R_p and R_d are limited, making the accuracy of R_p and R_d values from current CO₂ response models uncertain.

Addressing these research gaps, this study used low oxygen and gas exchange methods, with calculating CO₂ recovery and inhibition ratio, aiming to: (1) elucidate the biological significance and interrelationships of photosynthetic parameters related to light and dark respiration, and accurately measure or calculate them; (2) compare R_p and R_d values between fitted and measured data to evaluate the CO₂ photosynthetic response model’s accuracy, identifying a more precise estimation model (A/C_a or A/C_i); and (3) provide quantitative descriptions of C_a or C_i (depends on the accuracy of the model) effects on R_p-measured and R_d-measured, offering theoretical research insights for the practical application of photosynthetic carbon metabolism processes and the promotion of carbon metabolism.

2 Materials and methods

2.1 CO₂ response models

The biochemical model can be expressed as

$\begin{array}{ll}{P}_n=min\left\{w_c , w_j , w_p\right\}\left(1-\frac{{\tau }^{*}}{C_i}\right)-R_d& (1)\end{array}$

where P_n is the net photosynthetic rate; and w_c, w_j and w_p are the potential rates of CO₂ assimilation that can be supported by the enzymes of ribulose 1,5-bisphosphate (RuBP) carboxylase/oxygenase (Rubisco), RuBP- regeneration and triose-phosphate utilization, respectively. The photosynthetic compensation point (${\tau }^{*}$) is the CO₂ concentration at which the photorespiratory efflux of CO₂ equals the rate of photosynthetic CO₂ uptake. C_i is the intercellular CO₂ concentration and R_d is the mitochondrial respiration rate in the light.

Empirical models include the rectangular hyperbola model, modified version, and the Michaelis-Menten model, as following:

The rectangular hyperbola model can be represented as

$\begin{array}{ll}{P}_n=\frac{a{P}_{nmax}{C}_i}{a{C}_i+P_{nmax}}-R_p& (2)\end{array}$

where P_nmax is the maximum photosynthetic rate; R_p is the photorespiration rate (in fact this parameter represents the respiration rate in the light (R_L), which includes R_p and R_d. A detailed description is given in the text.); and α is the initial slope of the CO₂ response curve; C_i is the same as above.

The Michaelis−Menten model can be displayed as

$\begin{array}{ll}{P}_n=\frac{P_{nmax}{C}_i}{C_i+K}-R_p& (3)\end{array}$

where P_nmax, R_p, P_n and C_i are the same as above, and K is the Michaelis-Menten constant.

The modified rectangular hyperbola model can be written as

$\begin{array}{ll}{P}_n=a\frac{1-b{C}_i}{1+c{C}_i}{C}_i-R_p& (4)\end{array}$

where α, R_p, P_n and C_i are the same as above, and b and c are coefficients (mol μmol^–1) (Ye, 2010) (Equations 1–4).

According to this equation, the Michaelis-Menten and the rectangular hyperbola model are essentially the same. Therefore, the fitted results for the Michaelis-Menten model were not shown in this paper.

2.2 Theoretical considerations

2.2.1 Calculation of photorespiration rates

R_p were determined through differential gas exchange measurements under contrasting O₂ concentrations. Measurements were conducted using a LI-6400XT portable photosynthesis system (LI-COR Biosciences, Lincoln, NE, USA) with the following standardized conditions:

1. Ambient O₂ treatment (21% O₂): At ambient CO₂ (0 μmol·mol⁻¹) and saturating Photosynthetically Active Radiation (PAR) (2000 μmol·m⁻²·s⁻¹), the net photosynthetic rate (P_n21%) represents combined respiratory fluxes (R_L = R_p + R_d), as photorespiration proceeds normally while CO₂ in photosynthesis comes from respiration.

2. Low O₂ treatment (2% O₂): Under identical CO₂ and light conditions, complete inhibition of photorespiration in wheat and bean leaves was achieved based on our previous validation (Kang et al., 2014). The measured P_n2% thus corresponds specifically to R_d.

R_p was calculated using the respiratory partitioning equation (Erdei et al., 2001; Laisk et al., 2002; Parys et al., 2004):

$\begin{array}{ll}\begin{array}{c}{R}_p=P_{n2\%}-P_{n21\%}\end{array}& (5)\end{array}$

where P_n2% and P_n21% are the photosynthetic rates at 2% O₂ and 21% O₂, respectively.

2.2.2 Calculation of CO₂ recovery and inhibition ratios of photorespiration

Our prior mechanistic studies revealed concentration-dependent regulation of photorespiratory CO₂ recovery. The photorespiratory CO₂ recovery ratio (R_pe-i), defined as the proportion of respired CO₂ re-assimilated by chloroplasts, decreased progressively with increasing ambient CO₂ concentration. Beyond threshold CO₂ concentrations, competitive inhibition between photorespiration and carboxylation pathways significantly suppressed photorespiratory flux (Kang et al., 2013). R_pe-i and photorespiratory inhibition index (I_i) can be quantified through Equation 6.

$\begin{array}{ll}\begin{array}{c}{R}_{pe-i} or I_i=\frac{R_{pmax}-R_{p-i}}{R_{pmax}}\end{array}& (6)\end{array}$

where $R_{pe-i}$ and $I_i$ are the CO₂ recovery ratio and inhibition ratio of photorespiration, R_pmax is the maximum photorespiration rate and R_p−i is the photorespiration rate at i CO₂ concentrations, i represents different CO₂ concentrations.

2.2.3 Calculation of the mitochondrial respiration rates in the light

Both mitochondrial respiration-derived CO₂ and photorespiration-derived CO₂ originate from the same cellular compartment, i.e., mitochondria. Given this shared origin, it follows that CO₂ released through mitochondrial respiration undergoes similar refixation dynamics as photorespiratory CO₂ under low atmospheric CO₂ concentrations (C_a) and is comparably inhibited at elevated C_a. The recovery efficiency and inhibition ratio of mitochondrial respiration-derived CO₂ were consequently equivalent to those observed in photorespiration. To quantify R_d, we therefore integrated the maximum mitochondrial respiration rate (R_n) with the photorespiration-associated parameters R_pe-_i and I_i, using the following calculation scheme:

$\begin{array}{ll}\begin{array}{c}{R}_{d-i}=R_{n-i}\times (1-R_{pe-i}) or R_{d-i}=R_{n-i}\times (1-I_i)\end{array}& (7)\end{array}$

where $R_{d-i}$ and $R_{n-i}$ represent mitochondrial respiration rates under light and dark conditions, respectively, at a given atmospheric CO₂ concentration.

2.2 Study site and plants

The experiment was conducted at the Yucheng Comprehensive Experiment Station (36°50′N, 116°34′E; 20.3 m elevation) of the Chinese Academy of Sciences, located in the lower Yellow River basin. This semi-arid region exhibits a mean annual temperature of 13.4°C and receives 567 mm of precipitation annually, with 70% occurring between June and September (1985–2009 climate normals). The soil is classified as calcaric fluvisol (FAO-UNESCO system) with silt loam texture (12% sand, 66% silt, 22% clay; USDA classification) and pH 8.6 (Hou et al., 2012).

Wheat and bean were sown on 4 October 2013 and 3 May 2014, respectively. Field-grown plants experienced maximum photosynthetic photon flux density (PPFD) of 2000 μmol m⁻² s⁻¹ during sunny days. Measurements were conducted during key phenological stages: wheat from 12 ~ 25 May (characterized by 7 sunny days, predominantly cloudy skies, no effective precipitation, and a mean temperature of 29°C) and bean from 16 ~ 25 June (marked by predominantly cloudy conditions, 95 mm rainfall, and an average temperature of 30°C) 2014. We randomly sampled vigorous plants with homogeneous growth and measured the apical leaf of the fifth compound leaf (numbered from the base upward) on each seedling.

2.3 CO₂ gas exchange measurement

Leaf-level CO₂ exchange was quantified using a LI-6400XT portable photosynthesis system (LI-COR Biosciences, Lincoln, NE, USA) during two daily intervals (09:00 ~ 11:30 and 14:30 ~ 17:00). For each species, the leaves were acclimated in the cuvette for 15 min to stabilize gas exchange prior to measurements. Environmental conditions were maintained at leaf temperature 30 ± 0.3°C (wheat) or 33 ± 1.7°C (bean) with 60% relative humidity. Two sets of CO₂ response curves were generated by systematically exposing leaves to a sequence of 12 atmospheric CO₂ concentrations (C_a: 0, 50, 80, 100, 150, 200, 380, 400, 600, 800, 1,000, and 1,200 μmol mol⁻¹). These experiments were conducted under two distinct oxygen conditions: ambient (21% O₂) and low-oxygen (2% O₂). For measurements of R_p, R_d, and other related parameters, a PAR of 2000 μmol m⁻² s⁻¹ was used. Conversely, a PAR of 0 μmol m⁻² s⁻¹ was employed to determine the mitochondrial respiration rates in the dark (Kang et al., 2014). The hypoxic gas mixture (2% O₂) was supplied by Xinjian Air Plant (Yucheng, Shandong) and humidified via a 1.2 m³ buffer bag containing distilled water prior to entering the gas analyzer.

2.4 Statistics

Photosynthetic parameters were derived using Photosynthesis Assistant software (LI-COR Biosciences). Non-linear regression analyses implemented in SPSS 11.5 (IBM Corp., Armonk, NY, USA), based on Levenberg-Marquardt algorithm, including rectangular hyperbola model and Standard rectangular hyperbola model.

Treatment effects were assessed by two-way ANOVA with Tukey’s post-hoc test, while pairwise comparisons employed two-tailed Student’s t-tests (p< 0.05). All statistical visualizations were generated using GraphPad Prism 4.0c (GraphPad Software, San Diego, CA).

3 Results

3.1 Respiratory flux partitioning

At saturating irradiance (2000 μmol photons m⁻² s⁻¹), mitochondrial respiration (R_L-measured) reached 6.548 ± 0.136 and 6.334 ± 0.342 μmol (CO₂) m⁻² s⁻¹ in wheat and bean, respectively. R_d-measured exhibited the values of 2.036 ± 0.276 (wheat) and 1.893 ± 0.075 μmol (CO₂) m⁻² s⁻¹ (bean). R_p-measured calculated via Equation 5 at zero CO₂ (R_p-0-measured) showed interspecific divergence, with wheat (4.511 ± 0.412 μmol (CO₂) m⁻² s⁻¹) and bean (4.686 ± 0.274 μmol (CO₂) m⁻² s⁻¹), we can find that there were significantly different between R_L-measured and R_p-measured (Table 1).

Table 1

Table 1. Compared between measured and fitted values of R_L, R_d, and R_p-0 for wheat and bean.

3.2 Model performance evaluation

The three CO₂ response models (biochemical, rectangular hyperbola, modified rectangular hyperbola) were evaluated by comparing R_L-fitted (21% O₂) and R_d-fitted (2% O₂) values with experimental measurements (Table 1).

Under the A/C_i framework, the modified rectangular hyperbola model showed the smallest deviations for both R_L-fitted and R_d-fitted compared to biochemical and rectangular hyperbola models. For example, R_L-fitted in wheat were 14.172 ± 0.156 μmol m⁻² s⁻¹ (modified model) versus 21.067 ± 0.115 (biochemical) and 17.108 ± 0.978 (rectangular), contrasting with measured values of 6.548 ± 0.136 (P< 0.05 for biochemical and rectangular models). Similar trends were observed for R_d-fitted (Table 1). Under the A/C_a framework, the modified model exhibited further accuracy improvements, particularly for R_d-fitted. For wheat, A/C_a-based R_d-fitted estimates (2.716 ± 0.493 μmol m⁻² s⁻¹) reduced deviations from measured values by 80.915% compared to A/C_i predictions (5.599 ± 0.521; Δ = 3.563 vs. 0.680 μmol m⁻² s⁻¹). In bean, A/C_a R_d-fitted errors decreased by 67.414% (Δ = 2.719 vs. 0.886 μmol m⁻² s⁻¹). R_L-fitted estimations under A/C_a also approached measured values more closely than under A/C_i.

The modified rectangular hyperbola model under A/C_a framework demonstrated optimal consistency with experimental data, justifying its selection for subsequent analyses of respiratory responses to ambient CO₂ (C_a).

3.3 Photorespiration rate (R_p-measured) responses to C_a

R_p-measured exhibited a unimodal relationship with ambient CO₂ concentration in both wheat and bean, characterized by an initial increase followed by a decline at elevated C_a levels. The R_p-measured values ranged from 4.923 ± 0.171 to 12.307 ± 1.033 μmol (CO₂) m⁻² s⁻¹ for wheat (Figure 1A) and 4.686 ± 0.274 to 11.673 ± 2.054 μmol (CO₂) m⁻² s⁻¹ for bean (Figure 1B), with polynomial regression models demonstrating strong correlations (R² = 0.923 for wheat, R² = 0.797 for bean).

Figure 1

Figure 1. (A) Photorespiration rates (Rp-measured) of wheat responses to C_a. (B) Photorespiration rates (Rp-measured) of bean responses to C_a.

Crop-specific differences were evident in the C_a thresholds corresponding to peak R_p-measured. Wheat achieved maximum R_p-measured (12.307 ± 1.033 μmol (CO₂) m⁻² s⁻¹) at 600 μmol mol⁻¹ C_a, whereas bean exhibited peak R_p-measured (11.673 ± 2.054 μmol (CO₂) m⁻² s⁻¹) at 1000 μmol mol⁻¹ C_a (Figures 1A, B).

3.4 Mitochondrial respiration rate in the light (R_d-measured) responses to C_a

R_d-measured, derived from Equation 7, exhibited a unimodal relationship with C_a for both species. The R_d-measured values ranged from 0.618 ± 0.131 to 3.021 ± 0.063 μmol (CO₂) m⁻² s⁻¹ for wheat (Figure 2A) and 0.492 ± 0.069 to 2.323 ± 0.312 μmol (CO₂) m⁻² s⁻¹ for bean (Figure 2B), with polynomial regression models demonstrating strong correlations (R² = 891 for wheat, R² = 0.892 for bean). R_d-measured initially increased to peak values of 3.021 ± 0.063 μmol (CO₂) m⁻² s⁻¹ (wheat) and 2.323 ± 0.312 μmol (CO₂) m⁻² s⁻¹ (bean), followed by declines at elevated C_a. Polynomial regression confirmed robust correlations, reflecting C_a-dependent modulation of R_d-measured dynamics.

Figure 2

Figure 2. (A) Mitochondrial respiration rate in the light (R_n-measured) of wheat responses to C_a. (B) Mitochondrial respiration rate in the light (R_d-measured) of bean responses to C_a.

3.5 Mitochondrial respiration in the dark (R_n-measured) responses to C_a and O₂ concentration

R_n-measured declined progressively with increasing C_a for both wheat and bean, independent of O₂ levels (21% vs. 2%). At 21% O₂, R_n spanned 1.453 ± 0.603 to 3.862 ± 0.557 μmol (CO₂) m⁻² s⁻¹ (wheat, Figure 3A) and 1.210 ± 0.340 to 4.040 ± 0.167 μmol (CO₂) m⁻² s⁻¹ (bean, Figure 3B). Under 2% O₂, the ranges shifted to 1.512± 0.674 to 4.101 ± 0.297 (wheat) and 0.817 ± 0.607 to 3.718 ± 0.519 μmol (CO₂) m⁻² s⁻¹ (bean). Strong negative correlations between R_n and C_a were observed (R² = 0.969 for wheat, R² = 0.977 for bean), with no significant O₂ concentration effect (P > 0.05).

Figure 3

Figure 3. (A) Mitochondrial respiration rate in the dark (R_n-measured) of wheat responses to C_a and O₂ concentration. (B) Mitochondrial respiration rate in the dark (R_n-measured) of bean responses to C_a and O₂ concentration.

3.6 Recovery (R_pe−i) and inhibition (I_i) ratios response to C_a

As mentioned before, 12.307 ± 1.033 and 11.673 ± 2.054 μmol (CO₂) m⁻² s⁻¹ were the maximum photorespiration rate values for wheat and bean, respectively. On this basis, the CO₂ recovery and inhibition ratios for photorespiration at different CO₂ concentrations were estimated according to Equation 6. As C_a increased, the recovery ratios decreased from 59.995% (wheat) and 66.869% (bean) to zero, respectively (Figure 4). After that, the inhibition ratios increased sharply, reaching 57.456% (wheat) and 39.845% (bean), respectively.

Figure 4

Figure 4. (A) Recovery and inhibition rates (R_pe-i and I_i) of wheat responses to C_a. (B) Recovery and inhibition rates (R_pe-i and I_i) of bean responses to C_a.

4 Discussion

4.1 Respiratory flux partitioning

In the framework of traditional models, the overall respiration rate under light conditions (R_L), which aggregates the rates of photorespiration (R_p) and mitochondrial respiration in the light (R_d), has frequently been either conflated with photorespiration alone (Zelitch, 1980; Ye and Yu, 2009; von Caemmerer, 2000) or has overlooked the significance of the reutilization of CO₂ released during photorespiration (Kang et al., 2014). This conflation or oversight tends to result in a marked discrepancy between the observed photorespiration rates (R_p-fitted) and their actual values. Our empirical findings, obtained under conditions of 21% O₂ and atmospheric CO₂ concentration of 0 μmol mol⁻¹, indicated that the R_L-measured values for wheat and bean (6.548 ± 0.136 and 6.334 ± 0.342 μmol m⁻² s⁻¹, respectively) significantly surpassed the accurately determined photorespiration rates (R_p-0-measured = 4.511 ± 0.412 and 4.686 ± 0.274 μmol m⁻² s⁻¹ for wheat and bean, respectively), as derived through the differential method (R_L-measured − R_d-measured). This discrepancy underscores the systematic bias inherent in the traditional approach, which solely attributes R_L to photorespiration, thereby neglecting the distinct and crucial contribution of mitochondrial respiration under light conditions (R_d).

Our analysis sheds light on the intricate dynamics between photorespiration and mitochondrial respiration within the context of photosynthesis, challenging the conventional understanding that has, until now, inadequately accounted for the nuanced contributions of these two processes. By distinguishing between R_L and its constituent components, R_p and R_d, our study provides a more nuanced understanding of plant respiratory processes in the light, highlighting the significant role of R_d. This clarification is pivotal for refining existing photosynthetic models, ensuring a more accurate representation of plant respiratory mechanisms and their implications for carbon metabolism.

4.2 Model performance evaluation

In the realm of plant physiology, accurately modeling the intricate processes of photorespiration and mitochondrial respiration under photosynthetic conditions is pivotal. Our study, by comparing measured values with the fitted values (Table 1), underscores the remarkable precision of the Modified rectangular hyperbola models, especially when employing A/C_a curves for estimating R_L-fitted and R_d-fitted values. This finding aligns with the observations made by Ye and Yu (2009), who posited that the discrepancies observed in earlier models could be attributed to the misrepresentation of intercellular CO₂ concentrations by the C_i values used in those models.

However, a notable divergence persists between the fitted values generated by the A/C_a model and the actual measurements. This discrepancy led to the conclusion that previous models might have overlooked the significant impact of CO₂ concentration on R_d and R_p. Our analysis suggests an imperative need for further research aimed at refining these models to enhance their accuracy.

4.3 Photorespiration rate and Mitochondrial respiration rate in the light responses to C_a

This study revealed a nonlinear regulatory mechanism of CO₂ concentration on photorespiration rate (R_p-measured) and mitochondrial respiration rate in the light (R_d-measured) in C₃ plants: R_p-measured increased with rising CO₂ concentrations when external CO₂ levels were below species-specific thresholds (600 μmol mol⁻¹ for wheat and 1000 μmol mol⁻¹ for bean), whereas exceeding these thresholds triggered a significant suppression of R_p-measured. As for R_d-measured, the thresholds were 400 μmol mol⁻¹ for wheat and 200 μmol mol⁻¹ for bean. This phenomenon can be explained by the dynamic interplay between RuBisCO enzyme activity and chloroplast microenvironmental conditions. At low CO₂ concentrations, although the carboxylation activity of RuBisCO is globally constrained by substrate limitation (Caemmerer and Edmondson, 1986) and RuBP regeneration becomes impaired (Badger et al., 1984), the CO₂ released during photorespiration is efficiently re-assimilated by photosynthesis due to its proximity to the chloroplast inner membrane (Yadav et al., 2020). This tight coupling between photorespiratory CO₂ release and photosynthetic refixation (Häusler et al., 2002; Loreto et al., 1999; Busch et al., 2013; Kang et al., 2013) partially mitigates the inhibitory effects of low CO₂ on the Calvin cycle. Concurrently, enhanced photosynthesis elevates chloroplast O₂ levels (Sharkey, 1988), temporarily promoting RuBisCO oxygenation activity and driving the “paradoxical” increase in R_p and R_d. However, when CO₂ concentrations surpass species-specific thresholds, the chloroplast CO₂/O₂ ratio undergoes a fundamental reversal (Brooks and Farquhar, 1985), favoring RuBisCO carboxylation through competitive substrate inhibition of oxygenation, leading to a decrease in R_p-measured and R_d-measured. The observed threshold divergence between wheat and bean likely arises from two interconnected mechanisms: First, interspecific variations in RuBisCO kinetics (e.g., CO₂ affinity) and leaf anatomical adaptations regulating CO₂ diffusion resistance, consistent with the multiscale regulatory complexity of photorespiratory metabolism (Wang et al., 2020; Celebi-Ergin, 2022). Second, differential cellular metabolic demands—for example, the approximately twofold higher CO₂ threshold for peak photorespiration in bean (1,000 vs. 600 μmol·mol⁻¹ in wheat) aligns with the hypothesis proposed by Krmer et al. (2022) that elevated photorespiratory flux in legumes supports nitrogen assimilation-coupled amino acid synthesis. These findings not only provided theoretical support for crop-specific CO₂ fertilization strategies in controlled-environment agriculture but also advance our understanding of carbon-oxygen metabolic homeostasis in C₃ plants.

4.4 Mitochondrial respiration rate in dark (R_n-measured) responses to C_a and O₂ concentration

Accurately estimating the dark respiration rate of a plant facilitates the calculation of its maximum carboxylation rate, respiration rate in the light, electron flow partitioning, and other important photosynthetic parameters (Wang et al., 2001; Yin et al., 2011). Oxygen is essential for the respiration process in plant cells (Moseley et al., 2018). However, the results of our experiments showed that there was no significant difference in dark mitochondrial respiration rates between wheat and bean at 2% and 21% O₂ (Table 1). It’s meant to be sufficient oxygen for mitochondrial respiration at 2% O₂. In addition, we can notice that there is linear regulatory mechanism of CO₂ concentration on R_n-measured, i.e., the R_n decreased as C_a increased (Figures 3A, B), which was different from the relationship between R_d-measured, R_p-measured, and carbon dioxide. We speculate that this may be due to the increase in CO₂ concentration inhibiting the activity of certain enzymes related to dark respiration, and this effect is stronger than that of R_d-measured and R_p-measured. Reuveni and Gale (1985) also obtained the similar results that CO₂ concentration has a strong effect on dark respiration rates in plants.

5 Conclusion

This study advanced our understanding of respiratory parameter estimation in C₃ plants by systematically evaluating the accuracy of photorespiration (R_p) and mitochondrial respiration in the light (R_d) derived from CO₂-response models. Key findings revealed that the modified rectangular hyperbola model under the A/C_a framework outperformed traditional A/C_i models in estimating R_p and R_d, yet significant discrepancies persisted between modeled and empirical values (p< 0.01), highlighting inherent limitations in current methodologies. Notably, CO₂ concentration exhibited dose-dependent, non-linear regulation of respiratory parameters. R_p-measured in wheat and bean demonstrated unimodal responses to C_a, peaking at 600 and 1,000 μmol·mol⁻¹, respectively, before declining due to competitive inhibition of RuBisCO oxygenation. Similarly, R_d-measured displayed different thresholds between bean and wheat (400 μmol mol⁻¹ for wheat and 200 μmol mol⁻¹ for bean.). The identification of strong polynomial correlations (R² > 0.89) between C_a and respiratory fluxes challenges conventional assumptions of linear responses, emphasizing the need to integrate CO₂-responsive regulatory dynamics into photosynthetic models. Furthermore, dark respiration (R_n-measured) exhibited a linear decline with rising C_a, independent of O₂ concentration, suggesting distinct mechanistic controls compared to light-dependent respiration.

These findings provide critical insights for refining photosynthetic models by incorporating CO₂-mediated respiratory adjustments. The empirical relationships established here offer a framework for optimizing carbon assimilation strategies in crops under rising atmospheric CO₂, particularly in controlled-environment agriculture.

Data availability statement

The datasets presented in this article are not readily available because data privacy. Requests to access the datasets should be directed to a2FuZ2h1YWppbmdAMTI2LmNvbQ==.

Author contributions

HK: Conceptualization, Funding acquisition, Methodology, Supervision, Writing – review & editing. ZN: Investigation, Writing – original draft, Writing – review & editing. ZY: Data curation, Formal Analysis, Writing – review & editing. QH: Formal Analysis, Investigation, Writing – review & editing. CP: Investigation, Writing – review & editing.

Funding

The author(s) declare financial support was received for the research and/or publication of this article. This work was supported by the 863 Project under contract No. 2013AA102903, the National Key Technologies R & D Program of China No.2013BAD05B03, the Natural Science Foundation of China No. 31560069 and the Key Science and Technology Innovation Team Project of Wenzhou City No. C20150008.These funds provide expenses for data collection, measurement, and paper layout fees for this study.

Conflict of interest

The authors declare that the research was conducted in the absence of any commercial or financial relationships that could be constructed as a potential conflict of interest.

Publisher’s note

All claims expressed in this article are solely those of the authors and do not necessarily represent those of their affiliated organizations, or those of the publisher, the editors and the reviewers. Any product that may be evaluated in this article, or claim that may be made by its manufacturer, is not guaranteed or endorsed by the publisher.

References

Atkin, O. K., Bruhn, D., Hurry, V. M., and Tjoelker, M. G. (2005). Evans Review No. 2 - The hot and the cold: Unravelling the variable response of plant respiration to temperature. Funct. Plant Biol. 32, 87–105. doi: 10.1071/FP03176

PubMed Abstract | Crossref Full Text | Google Scholar

Badger, M. R., Sharkey, T. D., and von Caemmerer, S. (1984). The relationship between steady-state gas exchange of bean leaves and the levels of carbon-reduction-cycle intermediates. Planta 160, 305–313. doi: 10.1007/BF00393411

PubMed Abstract | Crossref Full Text | Google Scholar

Bernacchi, C. J., Singsaas, E. L., Pimentel, C., Portis, A. R., and Long, S. P. (2001). Improved temperature response functions for models of Rubisco-limited photosynthesis. Plant Cell Environ. 24, 253–259. doi: 10.1111/J.1365-3040.2001.00668.X

Crossref Full Text | Google Scholar

Borrell, A. N., Shi, Y., Gan, Y., Bainard, L. D., Germida, J. J., and Hamel, C. (2017). Fungal diversity associated with pulses and its influence on the subsequent wheat crop in the Canadian prairies. Plant Soil 414, 13–31. doi: 10.1007/s11104-016-3075-y

Crossref Full Text | Google Scholar

Brooks, A. and Farquhar, G. D. (1985). Effect of temperature on the CO₂/O₂ specificity of ribulose-1,5-bisphosphate carboxylase/oxygenase and the rate of respiration in the light. Planta 165, 397–406. doi: 10.1007/BF00392238

PubMed Abstract | Crossref Full Text | Google Scholar

Busch, F. A. and Sage, R. F. (2017). The sensitivity of photosynthesis to O₂ and CO₂ concentration identifies strong Rubisco control above the thermal optimum. New Phytol. 213, 1036–1051. doi: 10.1111/nph.14258

PubMed Abstract | Crossref Full Text | Google Scholar

Busch, F. A., Sage, T. L., Cousins, A. B., and Sage, R. F. (2013). C₃ plants enhance rates of photosynthesis by reassimilating photorespired and respired CO₂. Plant Cell Environ. 36, 200–212. doi: 10.1111/j.1365-3040.2012.02567.x

PubMed Abstract | Crossref Full Text | Google Scholar

Caemmerer, S. and Edmondson, D. (1986). Relationship Between Steady-State Gas Exchange, in vivo Ribulose Bisphosphate Carboxylase Activity and Some Carbon Reduction Cycle Intermediates in Raphanus sativus. Funct. Plant Biol. 13, 669–688. doi: 10.1071/pp9860669

Crossref Full Text | Google Scholar

Carvalho, J. de F.C., Madgwic, P. J., and Powers, S. J. (2011). An engineered pathway for glyoxylate metabolism in tobacco plants aimed to avoid the release of ammonia in photorespiration. BMC Biotech. 11, 111~127. doi: 10.1186/1472-6750-11-111

PubMed Abstract | Crossref Full Text | Google Scholar

Celebi-Ergin, B. (2022). Photorespiration in eelgrass (Zostera marina L.): A photoprotection mechanism for survival in a CO₂-limited world. Front. Plant Sci. 13. doi: 10.3389/fpls.2022.1025416

PubMed Abstract | Crossref Full Text | Google Scholar

Easterling, D. R., Evans, J. L., Groisman, P. Y., Karl, T. R., Kunkel, K. E., and Ambenje, P. (2000). Observed variability and trends in extreme climate events: A brief review. Bull. Am. Meteorol. Soc 81, 417–425. doi: 10.1175/1520-0477(2000)081<0417:OVATIE>2.3.CO;2

Crossref Full Text | Google Scholar

Erdei, L., Horváth, F., Tari, I., Pécsváradi, A., Szegletes, Z., and Dulai, S. (2001). Differences in photorespiration, glutamine synthetase and polyamines between fragmented and closed stands of Phragmites australis. Aquat. Bot. 69, 165–176. doi: 10.1016/S0304-3770(01)00136-X

Crossref Full Text | Google Scholar

Ethier, G. J. and Livingston, N. J. (2004). On the need to incorporate sensitivity to CO₂ transfer conductance into the Farquhar-von Caemmerer-Berry leaf photosynthesis model. Plant Cell Environ. 27, 137–153. doi: 10.1111/j.1365-3040.2004.01140.x

Crossref Full Text | Google Scholar

Gan, Y., Hamel, C., O’Donovan, J. T., Cutforth, H., Zentner, R. P., Campbell, C. A., et al. (2015). Diversifying crop rotations with pulses enhances system productivity. Sci. Rep. 5, 14625. doi: 10.1038/srep14625

PubMed Abstract | Crossref Full Text | Google Scholar

Harley, P. C., Thomas, R. B., Reynolds, J. F., and Strain, B. R. (1992). Modelling photosynthesis of cotton grown in elevated CO₂. Plant Cell Environ. 15, 271–282. doi: 10.1111/j.1365-3040.1992.tb00974.x

Crossref Full Text | Google Scholar

Haupt-Herting, S., Klug, K., and Fock, H. P. A. (2001). New approach to measure gross CO₂ fluxes in leaves. Gross CO₂ assimilation, photorespiration, and mitochondrial respiration in the light in tomato under drought stress. Plant Physiol. 126, 388–396. doi: 10.1104/pp.126.1.388

PubMed Abstract | Crossref Full Text | Google Scholar

Häusler, R. E., Hirsch, H. J., Kreuzaler, F., and Peterhänsel, C. (2002). Overexpression of C₄-cycle enzymes in transgenic C₃ plants: A biotechnological approach to improve C₃-photosynthesis. J. Exp. Bot. 53, 591–607. doi: 10.1093/jexbot/53.369.591

PubMed Abstract | Crossref Full Text | Google Scholar

Hou, R., Ouyang, Z., Li, Y., Tyler, D. D., Li, F., and Wilson, G. V. (2012). Effects of tillage and residue management on soil organic carbon and total nitrogen in the North China plain. Soil Sci. Soc Am. J. 76, 230–240. doi: 10.2136/sssaj2011.0107

Crossref Full Text | Google Scholar

Huang, D., Jing, G., and Zhu, S. (2023). Regulation of mitochondrial respiration by hydrogen sulfide. Antioxidants 12, 1644. doi: 10.3390/antiox12081644

PubMed Abstract | Crossref Full Text | Google Scholar

IPCC (2021). “Climate change 2021: the physical science basis,” in Contribution of Working Group I to the Sixth Assessment Report of the Intergovernmental Panel on Climate Change (Cambridge University Press, Oxford, UK), 7–125.

Google Scholar

Jalali, A., Linke, M., Geyer, M., and Mahajan, P. V. (2020). Shelf life prediction model for strawberry based on respiration and transpiration processes. Food Packag. Shelf Life 25, 2020. doi: 10.1016/j.fpsl.2020.100525

Crossref Full Text | Google Scholar

Kang, H., Li, H., Tao, Y., and Ouyang, Z. (2014). Photosynthetic refixing of CO₂ is responsible for the apparent disparity between mitochondrial respiration in the light and in the dark (in chinese). Acta Physiol. Plant 36, 3157–3162. doi: 10.3724/SP.J.1258.2014.00130

Crossref Full Text | Google Scholar

Kang, H., Tao, Y., Quan, W., Wang, W., Yang, X., and Ouyang, Z. (2013). The response of photorespiration of C₃ plant to different light intensities and CO₂ concentrations (in chinese). J. Triticeae Crops 33, 1252–1257. doi: 10.7606/j.issn.1009-1041.2013.06.023

Crossref Full Text | Google Scholar

Krmer, K., Brock, J., and Heyer, A. (2022). Interaction of nitrate assimilation and photorespiration at elevated CO₂. Front. Plant Sci. 13. doi: 10.3389/fpls.2022.897924

PubMed Abstract | Crossref Full Text | Google Scholar

Laisk, A., Oja, V., Rasulov, B., Rämma, H., Eichelmann, H., Kasparova, I., et al. (2002). A computer-operated routine of gas exchange and optical measurements to diagnose photosynthetic apparatus in leaves. Plant Cell Environ. 25, 923–943. doi: 10.1046/j.1365-3040.2002.00873.x

Crossref Full Text | Google Scholar

Lin, W. H. (1998). Response of photosynthesis to elevated atmospheric CO₂ (in chinese). Acta Ecol. Sinica 18, 529–538. doi: 10.3321/j.issn:1000-0933.1998.05.013

Crossref Full Text | Google Scholar

Liu, C. M. and Yu, H. N. (1997). The Soil-Plant-Atmosphere System Experimental Study on Moisture Movement (Beijing: Meteorological Press).

Google Scholar

Long, S. P. and Bernacchi, C. J. (2003). Gas exchange measurements, what can they tell us about the underlying limitations to photosynthesis? Procedures and sources of error. J. Exp. Bot. 54, 2393–2401. doi: 10.1093/jxb/erg262

PubMed Abstract | Crossref Full Text | Google Scholar

Loreto, F., Delfine, S., and Di Marco, G. (1999). Estimation of photorespiratory carbon dioxide recycling during photosynthesis. Aust. J. Plant Physiol. 26, 733–736. doi: 10.1071/pp99096

Crossref Full Text | Google Scholar

Loreto, F., Velikova, V., and Di Marco, G. (2001). Respiration in the light measured by ¹²CO₂ emission in ¹³CO₂ atmosphere in maize leaves. Aust. J. Plant Physiol. 28, 1103–1108. doi: 10.1071/pp01091

Crossref Full Text | Google Scholar

Luo, Y., Wan, S., Hui, D., and Wallace, L. L. (2001). Acclimatization of soil respiration to warming in a tall grass prairie. Nature 413, 622–625. doi: 10.1038/35098065

PubMed Abstract | Crossref Full Text | Google Scholar

Moseley, R. C., Mewalal, R., Motta, F., Tuskan, G. A., Haase, S., and Yang, X. (2018). Conservation and diversification of circadian rhythmicity between a model crassulacean acid metabolism plant kalanchoë fedtschenkoi and a model C₃ photosynthesis plant arabidopsis thaliana. Front. Plant Sci. 871. doi: 10.3389/fpls.2018.01757

PubMed Abstract | Crossref Full Text | Google Scholar

Nilsen, E. T. (1995). Stem photosynthesis: extent, patterns, and role in plant carbon economy. Plant Stems, 223–240. doi: 10.1016/B978-012276460-8/50012-6

Crossref Full Text | Google Scholar

Ostle, N., Ineson, P., Benham, D., and Sleep, D. (2000). Carbon assimilation and turnover in grassland vegetation using an in situ¹³CO₂ pulse labelling system. Rapid Commun. Mass Spectrom. 14, 1345–1350. doi: 10.1002/1097-0231(20000815)14:15<1345::AID-RCM22>3.0.CO;2-B

PubMed Abstract | Crossref Full Text | Google Scholar

Pärnik, T. and Keerberg, O. (2007). Advanced radiogasometric method for the determination of the rates of photorespiratory and respiratory decarboxylations of primary and stored photosynthates under steady-state photosynthesis. Physiol. Plant. 129, 34–44. doi: 10.1111/j.1399-3054.2006.00824.x

Crossref Full Text | Google Scholar

Parys, E., Romanowska, E., and Siedlecka, M. (2004). Light-enhanced dark respiration in leaves and mesophyll protoplasts of pea in relation to photorespiration, respiration and some metabolites content. Acta Physiol. Plant 26, 37–46. doi: 10.1007/s11738-004-0042-7

Crossref Full Text | Google Scholar

Pinelli, P. and Loreto, F. (2003). ¹²CO₂ emission from different metabolic pathways measured in illuminated and darkened C₃ and C₄ leaves at low, atmospheric and elevated CO₂ concentration. J. Exp. Bot. 54, 1761–1769. doi: 10.1093/jxb/erg187

PubMed Abstract | Crossref Full Text | Google Scholar

Reuveni, J. and Gale, J. (1985). The effect of high levels of carbon dioxide on dark respiration and growth of plants. Plant Cell Environ. 8, 623–638. doi: 10.1111/j.1365-3040.1985.tb01701.x

Crossref Full Text | Google Scholar

Schimel, D. S., House, J. I., Hibbard, K. A., Bousquet, P., Ciais, P., Peylin, P., et al. (2001). Recent patterns and mechanisms of carbon exchange by terrestrial ecosystems. Nature 414, 169–172. doi: 10.1038/35102500

PubMed Abstract | Crossref Full Text | Google Scholar

Sharkey, T. D. (1988). Estimating the rate of photorespiration in leaves. Physiol. Plant 73, 147–152. doi: 10.1111/j.1399-3054.1988.tb09205.x

Crossref Full Text | Google Scholar

Stirbet, A., Lazár, D., Guo, Y., and Govindjee, G. (2020). Photosynthesis: Basics, history and modelling. Ann. Bot. 126, 511–537. doi: 10.1093/aob/mcz171

PubMed Abstract | Crossref Full Text | Google Scholar

Vaughan, D. G., Marshall, G. J., Connolley, W. M., Parkinson, C., Mulvaney, R., Hodgson, D. A., et al. (2003). Recent rapid regional climate warming on the Antarctic Peninsula. Clim. Change 60, 243–274. doi: 10.1023/A:1026021217991

Crossref Full Text | Google Scholar

Vercellino, I. and Sazanov, L. A. (2022). The assembly, regulation and function of the mitochondrial respiratory chain. Nat. Rev. Mol. Cell Biol. 23, 141–161. doi: 10.1038/s41580-021-00415-0

PubMed Abstract | Crossref Full Text | Google Scholar

von Caemmerer, S. (2000). Biochemical models of leaf photosynthesis. (CSIRO Publishing, Collingwoo). 38. doi: 10.5860/choice.38-0936

Crossref Full Text | Google Scholar

von Caemmerer, S. and Farquhar, G. D. (1981). Some relationships between the biochemistry of photosynthesis and the gas exchange of leaves. Planta 153, 376–387. doi: 10.1007/BF00384257

PubMed Abstract | Crossref Full Text | Google Scholar

Wang, F., Gao, J., Yong, J. W. H., Wang, Q., Ma, J., and He, X. (2020). Higher atmospheric CO₂ levels favor C₃ plants over C₄ plants in utilizing ammonium as a nitrogen source. Front. Plant Sci. 11. doi: 10.3389/fpls.2020.537443

PubMed Abstract | Crossref Full Text | Google Scholar

Wang, X., Lewis, J. D., Tissue, D. T., Seemann, J. R., and Griffin, K. L. (2001). Effects of elevated atmospheric CO₂ concentration on leaf dark respiration of Xanthium strumarium in light and in darkness. Proc. Natl. Acad. Sci. U. S. A. 98, 2479–2484. doi: 10.1073/pnas.051622998

PubMed Abstract | Crossref Full Text | Google Scholar

Wang, J., Yu, G., Fang, Q., Jiang, D., Qi, H., and Wang, Q. (2008). Responses of water use efficiency of nine plant species to light and CO₂ and its modeling (in chinese). Acta Ecol. Sinica 28, 525–533. doi: 10.3321/j.issn:1000-0933.2008.02.010

Crossref Full Text | Google Scholar

Xanthopoulos, G. T., Templalexis, C. G., Aleiferis, N. P., and Lentzou, D. I. (2017). The contribution of transpiration and respiration in water loss of perishable agricultural products: The case of pears. Biosyst. Eng. 158, 76–85. doi: 10.1016/j.biosystemseng.2017.03.011

Crossref Full Text | Google Scholar

Yadav, S., Rathore, M. S., and Mishra, A. (2020). The pyruvate-phosphate dikinase (C₄-SmPPDK) gene from Suaeda monoica enhances photosynthesis, carbon assimilation, and abiotic stress tolerance in a C₃ plant under elevated CO₂ conditions. Front. Plant Sci. 11. doi: 10.3389/fpls.2020.00345

PubMed Abstract | Crossref Full Text | Google Scholar

Ye, Z. (2010). A review on modeling of responses of photosynthesis to light and CO₂ (in chinese). Chin. J. Plant Ecol. 34, 727–740. doi: 10.3773/j.issn.1005-264x.2010.06.012

Crossref Full Text | Google Scholar

Ye, Z. and Yu, Q. (2009). A comparison of response curves of winter wheat photosynthesis to flag leaf intercellular and air CO₂ concentrations (in chinese). Chin. J. Ecol. 28, 2233–2238.

Google Scholar

Yin, X., Sun, Z., Struik, P. C., and Gu, J. (2011). Evaluating a new method to estimate the rate of leaf respiration in the light by analysis of combined gas exchange and chlorophyll fluorescence measurements. J. Exp. Bot. 62, 3489–3499. doi: 10.1093/jxb/err038

PubMed Abstract | Crossref Full Text | Google Scholar

Zelitch, I. (1980). Measurement of photorespiratory activity and the effect of inhibitors. Methods Enzymol. 69, 453–464. doi: 10.1016/S0076-6879(80)69044-2

Crossref Full Text | Google Scholar

Zhang, X., Xu, D., Zhao, M., and Chen, Z. (2000). The responses of 17-years-old Chinese fir shoots to elevated CO₂ (in chinese). Acta Ecol. Sinica 20, 390–396.

Google Scholar