Simulating short-term light responses of photosynthesis and water use efficiency in sweet sorghum under varying temperature and CO2 conditions

Climate change, characterized by rising atmospheric CO2 levels and temperatures, poses significant challenges to global crop production. Sweet sorghum, a prominent C4 cereal extensively grown in arid areas, emerges as a promising candidate for sustainable bioenergy production. This study investigated the responses of photosynthesis and leaf-scale water use efficiency (WUE) to varying light intensity (I) in sweet sorghum under different temperature and CO2 conditions. Comparative analyses were conducted between the A n-I, g s-I, T r-I, WUEi-I, and WUEinst-I models proposed by Ye et al. and the widely utilized the non-rectangular hyperbolic (NRH) model for fitting light response curves. The Ye's models effectively replicated the light response curves of sweet sorghum, accurately capturing the diminishing intrinsic WUE (WUEi) and instantaneous WUE (WUEinst) trends with increasing I. The fitted maximum values of A n, g s, T r, WUEi, and WUEinst and their saturation light intensities closely matched observations, unlike the NRH model. Despite the NRH model demonstrating high R 2 values for A n-I, g s-I, and T r-I modelling, it returned the maximum values significantly deviating from observed values and failed to generate saturation light intensities. It also inadequately represented WUE responses to I, overestimating WUE. Across different leaf temperatures, A n, g s, and T r of sweet sorghum displayed comparable light response patterns. Elevated temperatures increased maximum A n, g s, and T r but consistently declined maximum WUEi and WUEinst. However, WUEinst declined more sharply due to the disproportionate transpiration increase over carbon assimilation. Critically, sweet sorghum A n saturated at current atmospheric CO2 levels, with no significant gains under 550 μmol mol−1. Instead, stomatal closure enhanced WUE under elevated CO2 by coordinated g s and T r reductions rather than improved carbon assimilation. Nonetheless, this response diminished under simultaneously high temperature, suggesting intricate interplay between CO2 and temperature in modulating plant responses. These findings provide valuable insights into photosynthetic dynamics of sweet sorghum, aiding predictions of yield and optimization of cultivation practices. Moreover, our methodology serves as a valuable reference for evaluating leaf photosynthesis and WUE dynamics in diverse plant species.


Introduction
Water plays a crucial role in maintaining the structural integrity and functionality of plants, facilitating nutrient transport, and regulating temperature (Fracasso et al., 2017;Bykova et al., 2019).Specially, it is essential for photosynthesis, providing the electrons necessary to fuel the light-dependent reactions of the process.Due to the growing population, uncontrolled urbanization, and industrialization, atmospheric CO 2 concentration has markedly risen from a pre-industrial value of 280 to 414 mmol mol −1 in 2020, and it is projected to exceed 700 mmol mol −1 by the end of 21st century (Asadi and Eshghizadeh, 2021).If the increase in CO 2 continues, global mean temperatures are expected to rise by 2.6~4.8°C(Hatfield and Dold, 2019).Consequently, alterations in precipitation patterns have been observed in numerous regions in recent years, leading to the frequent occurrence of extreme events such as recurrent droughts and durative high temperatures.This phenomenon is particularly pronounced in arid and semi-arid areas where water resources are significantly stressed (Grillakis, 2019;Feng et al., 2022).As a consequence, crop production in these regions has been significantly limited by availability of water (Kubien et al., 2003;Prasad et al., 2009;Scafaro et al., 2011;Soltani et al., 2023).
Sweet sorghum [Sorghum bicolor (L.) Moench], a C 4 species with high photosynthetic efficiency, ranks as the fifth most cereal crop globally, with the total yield lower than that of wheat, rice, maize, and barley (Loreto et al., 1995;Prasad et al., 2009;Asadi and Eshghizadeh, 2021).Due to its excellent drought tolerance, sweet sorghum is extensively cultivated in arid and semi-arid regions with annual precipitation of only 350~700 mm (Appiah-Nkansah et al., 2019;Asadi and Eshghizadeh, 2021).In 2019, global sorghum production reached 56.7 million tons, with Asia contributing 13%, and cultivation concentrated primarily in India and China (Mundia et al., 2019).Sweet sorghum can be utilized for various purposes, including starchy grains for human food, soluble sugar juice as a feedstock for producing spirits, syrup, and vinegar, and lignocellulosic biomass for manufacturing animal feed, fuel ethanol, and fiber.The crop is generating significant interest in industrial circles as a leading candidate for bioenergy production, given the remarkable accumulation of high sugar content in its stems (9~15% of dry biomass) (Appiah-Nkansah et al., 2019;Asadi and Eshghizadeh, 2021).
Photosynthesis stands as one of the pivotal life processes for plants, serving as the foundation for their growth and development.Crop yield is closely related to leaf photosynthesis (von Caemmerer and Farquhar, 1981;Allen et al., 2011;McAusland et al., 2016).During photosynthesis, leaves inevitably lose water to fix carbon gained when they open their stomata (Farooq et al., 2019).The dynamic changes between carbon flux driven by photosynthesis and water flux dominated by transpiration can be characterized by wateruse efficiency (WUE; see Table 1 for the list of abbreviations), also known as intrinsic water use efficiency (WUE i ) or instantaneous water use efficiency (WUE inst ) at the leaf level (von Caemmerer and Farquhar, 1981;Fracasso et al., 2017).WUE i is closely correlated with leaf photosynthetic capacity and stomatal behavior (von Caemmerer and Farquhar, 1981).It is commonly used to explain photosynthetic characteristics that are independent of evaporative demand (Ye et al., 2020).WUE inst represents plant dry yield per unit of water loss, which can be considered as the WUE of the whole plant.WUE changes immediately within minutes of becoming water deprived.WUE is regarded as a key physiological indicator for assessing crop growth in arid regions, illuminating the link between crop production and water consumption (McAusland et al., 2016;Fracasso et al., 2017;Bykova et al., 2019;Hatfield and Dold, 2019).Currently, research has been undertaken to explore how crops respond to environmental stress based on the functional characterization of WUE (Gago et al., 2014;Xue et al., 2016;Silva et al., 2020), revealing that an elevated CO 2 concentration can enhance WUE inst (Wall et al., 2001;Hatfield and Dold, 2019).
However, the process of photosynthesis in plants is inherently dynamic in natural conditions, with the photosynthetic rate exhibiting rapid responses to diverse environmental factors.The intensity of light incident on a leaf experiences fluctuations due to the movement of the sun, clouds, canopies, or the leaf itself, thereby influencing the photosynthetic rate (Gyimah and Nakao, 2007;McAusland et al., 2016).Plants demonstrate varied capabilities in harnessing light of different strengths, ranging from weak to strong, each with specific light requirements (Yan et al., 2019).Characterizing light response of plant photosynthesis is thus essential for elucidating photosynthetic dynamics, cultivation management, and growth potential in changing environments (von Caemmerer and Farquhar, 1981;Gyimah and Nakao, 2007;Yan et al., 2019;Ye et al., 2020).While studies have explored changes in crop WUE (mainly WUE inst ) under water deficit stress and climate change (Wall et al., 2001;Allen et al., 2011;Fracasso et al., 2017;Hatfield and Dold, 2019;Asadi and Eshghizadeh, 2021), limited information exists on how WUE i and WUE inst respond to variations in light intensity and their evolution under concurrent rising CO 2 concentration and warming (Hatfield and Dold, 2019).
Accurate characterization of the response curves of net photosynthetic rate (A n ) and WUE to light intensity (I) is paramount, serving as a prerequisite for determining key photosynthetic parameters including the maximum net photosynthetic rate (A nmax ), the maximum intrinsic water use efficiency (WUE i-max ), the maximum instantaneous water use efficiency (WUE inst-max ), and their corresponding saturation light intensity (i.e., I sat , I i-sat , I inst-sat ) (von Caemmerer, 2013;Ye et al., 2020;Yin et al., 2021).This process is essential for evaluating the impact of temperature and CO 2 concentration on plant WUE and elucidating the relationship between carbon assimilation and water use.Various models have been established to characterize the light response curve of photosynthesis (A n -I curve) in plants, such as the rectangular hyperbola (Thornley, 1998), non-rectangular hyperbolic model (hereafter called NRH model) (Thornley, 1976;Farquhar and Wong, 1984), exponential-based functions (Leakey et al., 2006), and the mechanistic model by Ye et al. (2013) (hereafter called Ye's models).While utilized to predict photosynthesis, most lack assessment of the light response of WUE i and WUE inst .Consequently, the NRH model has also been employed to describe WUE i -I and WUE inst -I curves.However, studies fitting the A n -I curve have shown the NRH model significantly over/underestimates A nmax and cannot estimates I sat .Recently, we have developed WUE i -I and WUE inst -I models based on a mechanistic photosynthesis model, demonstrating accurate fitting of WUE i -I and WUE i -I curves for Glycine max and Amaranthus hypochondriacus at ambient temperature (Ye et al., 2020).However, their applicability across species and environments remains unknown.
In this study, we examined sweet sorghum leaf gas exchange across light levels under varying temperatures and CO 2 concentrations using a portable LI-6800 photosynthesis system.Light response curves of A n , stomatal conductance (g s ),

Plant material and growth conditions
Sweet sorghum cultivar KF-JT-4 were obtained by the Institute of Modern Physics, Chinese Academic of Sciences.This early maturing cultivar was developed via heavy ion irradiation of the parental line KFJT-CK.Thirty seeds were surface sterilized by soaking in 0.025% carbendazim and germinated in Petri dishes on filter paper at 25°C in darkness until radicle emergence.Each seedling was then transplanted into a 1.86 L volume inverted truncated cone-shaped pots (top diameter 15 cm, bottom diameter 10 cm, height 15 cm) filled with field soil.Plants were grown in a controlled environment growth chamber (120 cm long, 75 cm wide, 200 cm high) (RDN-1000E-4, Ningbo Dongnan Instrument Co. Ltd., China) under conditions of 25°C , approximately 260 mmol photons m −2 s −1 radiation with a 12 h photoperiod, and 70% relative humidity.Plants were routinely watered and fertilized to prevent growth limitation.
After 40 days of cultivation (pre-jointing period), the plants were moved from the growth chamber to a natural laboratory environment to conduct measurements of leaf CO 2 gas exchange.Subsequent to the completion of each measurement, the plants were promptly returned to the growth chamber.The experiment involved the selection of five healthy and uniform seedlings for analysis.Growth performance of plants is shown in Supplementary Figure 1.Key growth traits including plant height, stem diameter, and leaf dimensions were measured with a LI-3000C leaf area meter and are provided in Supplementary Table S1.

Gas exchange measurements and experimental setup
Leaf gas exchange measurement was performed using a portable photosynthesis system (LI-6800, Li-Cor Inc., USA) equipped with an integrated fluorometer chamber head (Li-6800-01A, Li-Cor Inc., USA).From the central leaf, the downward second mature and fully expanded leaf was used for measurement.Prior to each measurement, leaf was clamped in the leaf chamber and acclimated at an irradiance intensity of 1800 mmol m −2 s −1 for 30~40 min until a steady-state CO 2 exchange was obtained.The system, featuring red and blue light sources, along with an integrated CO 2 mixer set to 500 mmol s −1 flow rate, facilitated the light-response measurements of CO 2 gas exchange.
Light-response measurements were systematically conducted in a descending order of light intensity levels : 2000, 1800, 1600, 1400, 1200, 1000, 800, 600, 400, 200, 150, 100, 50, 25, and 0 mmol m −2 s −1 at the leaf surface level.A minimum wait time of 2 minutes and a maximum of 3 minutes were set at each intensity level before recording data.The instrument automatically aligned reference and sample chamber conditions to ensure accuracy.Each measurement was replicated three times to enhance data reliability and mitigate potential variations.
The internal settings of the LI-6800 photosynthesis system enabled control of leaf temperature and CO 2 concentration during gas exchange measurements.This allowed simulation of different temperature and CO 2 treatments to assess short-term photosynthetic responses.Three leaf temperature treatments were imposed: 25, 30, and 35°C at 60-70% relative humidity.CO 2 treatments included subambient (250 mmol mol -1 ), ambient (410 mmol mol -1 ), and elevated (550 mmol mol -1 ) levels.Under each condition, total leaf exposure spanned 65-80 minutes, encompassing light acclimation (30-40 min) and light response measurements from 0 to 2000 mmol m −2 s −1 (30-45 min).Measurements occurred between 9:00-11:30 and 14:00-17:00 in April within a ~60 m 2 laboratory under natural air circulation.This experimental design examined dynamic changes in sweet sorghum photosynthesis under short-term warming and elevated CO 2 to elucidate plant responses to varying environmental conditions.

Analytical models and calculation
The dependence of A n on I in Ye's models (Ye et al., 2013) is expressed as follows: where A n is the net photosynthetic rate, a is the initial slope of the A n -I response curve, b and g are the two parameters reflecting light limitation and light saturation, respectively, and R d is the dark respiration rate.
The saturation light intensity (I sat ) corresponding to A nmax can be calculated by the following equations: and The g s -I model established by Ye and Yu (2008) was given as follows: where a s is the initial slope of the g s -I response curve, b s and g s are the two coefficients independent of I. g s0 is the residual stomatal conductance when I = 0.
The saturation light intensity (I g-sat ) corresponding to the maximum stomatal conductance (g s-max ) can be found by the following equations: and WUE i can be calculated by the ratio of A n to g s (A n /g s ) in mmol mol −1 .The WUE i -I model established by Ye et al. (2020) was given as follows: where a i denotes the initial slope of WUE i -I response curve, b i and g i are the two coefficients that are independent of I, and K i is the residual WUE i .
The saturated light intensity (I i-sat ) corresponding to the maximum WUE i (WUE i-max ) can be calculated by the following equations: and WUE inst is expressed as the ratio between A n and T r (A n /T r ) in mmol mmol −1 .The WUE inst -I model established by Ye et al. (2020) was given as follows: where a inst denotes the initial slope of WUE inst -I response curve, b inst and g inst are the two coefficients that are independent of I, and K inst is the residual WUE inst .
The saturation light intensity (I inst-sat ) corresponding to the maximum WUE inst (WUE inst-max ) can be calculated by the following equations: and The dependence of A n on I in NRH model (Thornley, 1976;Farquhar and Wong, 1984) is expressed as follows: where A n is the net photosynthetic rate at light intensity I, A nmax is the maximum net photosynthetic rate, a is the initial slope of A n -I response curve, q is the convexity of curve, and R d is the dark respiration rate.The NRH model has also been used to characterize the responses of g s , T r , WUE i , and WUE inst to I (Ye et al., 2020).

Statistical analysis
The data of A n -I, g s -I, T r -I, WUE i -I, and WUE int -I were fitted by non-linear regression using the Levenberg-Marquardt algorithm in SPSS version 24.0 and the Photosynthesis Model Simulation Software (PMSS, http://photosynthetic.sinaapp.com).Goodness of fit was evaluated by the coefficient of determination (R 2 ).Student's t-tests assessed differences in parameter values between the photosynthetic models and between fitted and observed values.The effects of temperature and CO 2 on photosynthetic parameters were analyzed by one-way ANOVA with Duncan's post-hoc test.Data were expressed as group mean ± standard errors (n = 3).Statistical significance was accepted at p<0.05.

Performance of models in reproducing light response curves and quantifying photosynthetic traits
Both the Ye's models (Equations 1, 4) and the NRH model (Equation 13) successfully reproduced the A n -I, g s -I, and T r -I curves of sweet sorghum under varying temperatures (Figures 1A-I).The NRH model showed slightly higher R 2 values in comparison to the Ye's models.However, NRH model predictions for A nmax values significantly exceeded observed values (Supplementary Table 2) (p<0.05).Additionally, g s-max and T r-max values exhibited disparities with the measured values, either overestimated or underestimated.Focusing on the curves depicting the relationship between WUE i or WUE inst and I, the Ye's WUE models (Equations 7, 10) outperformed the NRH model across all temperature treatments by accurately captured the decline in WUE i and WUE inst as I increased under high light intensity, a trend not reflected by the NRH model (Figures 1J-O).WUE i-max and WUE inst-max values from the Ye's WUE models closely matched observed values, with no statistically significant differences (p>0.05)(Supplementary Table 2).In addition, saturation light intensities (I sat , I g-sat , I T-sat , I i-sat and I inst-sat ) corresponding to A nmax , g s-max , T r-max , WUE i-max and WUE inst-max were directly obtained from the Ye's models fitting but not from the NRH model fitting (Table 2).WUE i-max and WUE inst-max values from the NRH model were significantly overestimated compared to observed values across all temperature conditions (p<0.05) (Supplementary Table 2).
Similar to its performance under varying temperatures, the NRH model was employed to fit the A n -I curves under different CO 2 concentrations, yielding A nmax values that exceeded their observed counterparts (Supplementary Table 3).While successfully reproducing the g s -I and T r -I curves (Figures 2D-I), the NRH model struggled to accurately predict g s-max and T r-max , consequently failing to determine corresponding saturation light intensities (Table 3).In contrast, the Ye's models performed exceptionally well in fitting these curves.When used to fit the WUE i -I and WUE inst -I curves under different CO 2 concentrations, Ye's WUE models consistently demonstrated outstanding performance, with R 2 exceeding 0.995 (Figures 2J-O).The fitted WUE i-max and WUE inst-max values showed no significant differences from their respective measured values (p>0.05)(Supplementary Table 3).Nevertheless, the NRH model inadequately captured changes in the responses of WUE i and WUE inst to I, particularly evident in a low fitting coefficient for WUE inst -I (Figures 2J-O).Consequently, the fitted WUE i-max and WUE inst-max values exceeded their measured counterparts by more than 20% (Supplementary Table 3).
Light response curves of A n , g s , T r , WUE i and WUE inst in sweet sorghum under varied leaf temperatures In Figures 1A-I, the responses of A n , g s , and T r to varying I under different leaf temperatures exhibited comparable patterns.Below 800 mmol m −2 s −1 , A n , g s , and T r increased rapidly with increasing I until reaching their respective peaks (A nmax , g s-max , and T r-max ) at the specific saturation light intensities (I sat , I g-sat , and I T- sat ).Notably, at high light intensity levels (I >1400 mmol m −2 s −1 ), a decrease in A n with increasing I was not observed, indicating the absence of photoinhibition.Figures 1J-O  In other words, the plant became more efficient in utilizing water for photosynthesis relative to the amount of light it received.However, upon reaching the WUE i-max and WUE inst-max at corresponding I i- sat and I inst-sat , gradual decreases were observed (Table 2), suggesting that additional light did not proportionally increase photosynthesis but potentially led to increased water loss without a corresponding increase in carbon gain.It should be noted that T r for sweet sorghum under varying CO 2 and temperature conditions did not reach saturation within the values of I applied for the T r -I curve and hence values for I T-sat (and T r-max ) are an extrapolation.
The photosynthetic processes in sweet sorghum leaves were significantly influenced by temperature (one-way and two-way ANOVA p<0.05) (Tables 2, 4).At an ambient CO 2 level (410 mmol mol −1 ), elevating temperature led to significant increases in A nmax , g s-max , and T r-max (p<0.05).This rise in temperature also corresponded with amplified values in I sat , I c , and R d .However, both WUE i-max and WUE inst-max consistently declined with increasing temperature, with WUE inst-max displaying the most pronounced decrease and significant differences across temperature levels (p<0.05).For instance, increasing the temperature from 25°C to 30°C caused increase of 47.54%, 40.58%, and 111.91% in A nmax , g s-max , and T r-max , respectively (p<0.05).No significant changes were observed in I sat and I g-sat , while I T-sat exhibited a non-significant increase (p>0.05).WUE i-max only decreased by 6.33% without significant differences, whereas WUE inst-max significantly decreased by 31.30%(Table 2).Further increasing the temperature from 30°C to 35°C, despite the moderated enhancements in A nmax , g s-max , and T r-max (increases of 23.34%, 29.90%, and 63.76%, respectively), the reduction in WUE i-max expanded to 7.23%, and WUE inst-max declined by 25.67%.Higher temperature raised the saturation light intensities corresponding to WUE i-max and WUE inst-max (Table 2).However, at an elevated CO 2 level (550 mmol mol −1 ), rising temperature from 30°C to 35°C significantly increased WUE i-max , while expanding the decline of WUE inst-max to 29.47% due to a substantial 88.55% increase in T r-max (Supplementary Table 4).
Light response curves of A n , g s , T r , WUE i and WUE inst in sweet sorghum under varied air CO 2 concentrations In Figures 2A-D, under sub-ambient CO 2 concentration, A n and g s exhibited consistent response trends to I, rapidly increasing and reaching A n-max and g s-max at corresponding I sat and I g-sat .With increasing CO 2 concentration, the responses of g s and T r to I gradually shifted from a single-peaked pattern to an approximately linear increase (Figures 2D-I).Under elevated CO 2 , A n reached saturation within the measured light intensity range, whereas g s and T r increased nearly linearly with I, especially at 35°C (Figures 2F, I).Across varying CO 2 concentrations, the patterns in WUE i -I and WUE inst -I curves displayed distinct divisions into light-limited, light-saturated, and light-inhibited segments (Figures 2J-O).At high light intensity (I>1000 mmol m −2 s −1 ) under elevated CO 2 , both WUE i and WUE inst showed a significant reduction.
At a specific temperature (30°C), increasing CO 2 concentration from 250 to 410 mmol mol −1 resulted in increased A nmax and a for sweet sorghum, while decreasing I c and R d (Table 3).I sat corresponding to A nmax remained unchanged.However, further increasing the concentration to 550 mmol mol −1 did not cause a continual increase in A nmax ; instead, it raised both I sat and I c .Elevated CO 2 significantly weakened photosynthesis under lightlimited conditions, as evidenced by reductions in a, a g , and a T (Table 3).For g s and T r , their values decreased as CO 2 levels rose, and their response curves to light became less steep (Figures 2D-I), leading to a significant decrease in g s-max and T r-max (p<0.05).Consequently, there was a substantial increase in both WUE i-max and WUE inst-max with elevated CO 2 (p<0.05).Specifically, upon elevating CO 2 concentration from 410 to 550 mmol mol −1 , g s-max decreased by 19.59%, T r-max by 26.40%, while WUE i-max increased by 42.44% and WUE inst-max by 44.85% (Table 5).At a high temperature of 35°C, elevated CO 2 concentration positively impacted photosynthesis in sweet sorghum, resulting in a 5.8% increase in A nmax (Table 5, Supplementary Table 4).Similar decreases occurred in g s-max and T r-max , but the plants' dependence on light increased, as evidenced by I sat , I g-sat and I T-sat , all exceeding 2000 mmol photons m -2 s -1 .Notably, WUE i-max showed significant improvement, reaching 255.46 ± 5.26 mmol mol -1 , significantly higher than all other treatment groups (one-way and two-way ANOVA p<0.05) (Tables 4, 5).However, the increase in WUE inst- max was significantly lower compared to the increase observed under elevated CO 2 at 30°C, reaching only 37.45% (Supplementary Table 4).

Interactive effect of temperature and CO 2 concentration on key photosynthetic parameters
The interactive effect of temperature and CO 2 concentration on key photosynthetic parameters was assessed in sweet sorghum using a two-way analysis of variance (ANOVA) (Table 4).Temperature provoked highly significant main effects (p<0.001) on A nmax , I sat , I c , R d , g s-max , T r-max , and WUE inst-max , suggesting increasing the temperature from 30°C to 35°C profoundly impacted these traits independently of CO 2 concentration.Meanwhile, elevated CO 2 concentration induced highly significant main effect (p<0.001) on I sat , g s-max , T r-max , and WUE i-max , regardless of temperature.Statistically significant interaction effects between temperature and CO 2 were observed for the intrinsic quantum yield (a) at p<0.05, as well as for WUE i-max , and WUE inst-max .Quantum yield represents the photon requirement for assimilating one CO 2 molecule during photosynthesis.This suggests that the impact of temperature differed across CO 2 levels in determining the ability of sweet sorghum to acquire and use water.

Applicability of Ye's models to NRH model
In this study, we employed a methodological approach that involved a comparative analysis of models against observed data.This facilitated a systematic assessment and differentiation of the Ye's models and the NRH model concerning their abilities to replicate the A n -I, g s -I, T r -I, WUE i -I, and WUE inst -I curves of sweet sorghum.We also focused on quantifying the key traits defining these curves.Remarkably, the Ye's models excelled not only in capturing the diminishing trends in photosynthetic parameters (e.g.A n , WUE i , WUE inst ) with increased light intensity, but also in accurately determining critical photosynthetic traits across diverse temperatures and CO 2 conditions.These findings align with previous research applying the Ye's models to Cyanobacteria (Yang et al., 2022;Yang et al., 2023), Chlorophyta, Bacillariophyta (Yang et al., 2020), and other plants (Xu et al., 2012;Atsushi et al., 2017;Martıńez-Garcıá et al., 2017;Liu et al., 2018;Ye et al., 2020), demonstrating its broad utility.
Since its establishment by Thornley in 1976, the NRH model has been extensively utilized to study the response of plant photosynthesis to light, elucidating changes in plant growth and The bold p value indicates a significant interactive effect between temperature and CO 2 concentration on the parameter.
physiology across diverse environments (Yu et al., 2004;Ye and Yu, 2008;dos Santos Junior et al., 2012;Xu et al., 2012;Domingues et al., 2014;Wassenaar et al., 2022;Wu et al., 2023).However, upon taking the first derivative of the mathematical expression characterizing the relationship between the variables A n and I, as defined by Equation 13 in the NRH model, an analytical solution was not obtained.This implies that the NRH model follows an asymptotic function for A n rather than a closed-form solution.
Consequently, the NRH model does not produce analytical solutions for the maximum A n and the specific saturation light intensity for A nmax .A nmax may be numerically estimated from the NRH model through nonlinear least squares calculations (Ye et al., 2021).When parameters such as A n , g s , T r , WUE i , and WUE inst of plants reach saturation or decrease with increasing I under high light intensities, the maximum values obtained by fitting their light response curves using the NRH model would inevitably deviate significantly from their observed values.This discrepancy explains why the A nmax , g s-max , T r-max , WUE i-max , and WUE inst-max derived from the NRH model fitting for sweet sorghum in this study significantly differed from the measured data.These findings are consistent with previous reports of similar discrepancies (dos Santos Junior et al., 2012;Xu et al., 2012;Atsushi et al., 2017;Martıńez-Garcıá et al., 2017;Liu et al., 2018).Photoinhibition is the well-documented, light-induced decrease in photosynthetic rate in plants that occurs upon exposure to excess irradiance exceeding their utilization capacity (Anderson et al., 2021).Similarly, in the present study, both the WUE i -I and WUE inst -I curves of sweet sorghum exhibited declining trends under high light intensities, consistent with our previous findings in Glycine max and Amaranthus hypochondriacus (Ye et al., 2020).This reduction in plant WUE under high irradiance appears to be common across species.Thus, light response models that do not effectively capture decreases in photosynthetic parameters under high light conditions are likely to fail in elucidate plant responses across varying irradiance environments and determine actual physiological states (Egea et al., 2011).In contrast, by incorporating light inhibition effect (b) and a light saturation parameter (g), the Ye's model (Equations 1, 7, 10 ) provided excellent fits to the A n -I, WUE i-max -I, and WUE inst-max -I curves of plants, irrespective of temperature or CO 2 concentration (Ye et al., 2013;Ye et al., 2020).

Effect of elevated temperature on dynamic photosynthesis and water use efficiency in sweet Sorghum leaves
Plants facing environmental stress commonly exhibit reduced leaf photosynthesis (Hatfield and Dold, 2019).However, our study revealed sweet sorghum exhibited robust photosynthesis and a lack of photoinhibition at high temperatures up to 35°C, aligning with literature suggesting greater photosynthetic thermotolerance in sorghum species (Loreto et al., 1995;Prasad et al., 2021;Sales et al., 2021).Specifically, previous evidence indicates that optimal temperatures exceeding 35°C sustain the enzymatic rates of key C 4 cycle enzymes like pyruvate orthophosphate dikinase and phosphoenolpyruvate carboxylase in sorghum (Loreto et al., 1995;Sales et al., 2021), thereby preserving carbon assimilation even at high temperatures.Through concentrating CO 2 at the site of Rubisco, C 4 plants effectively suppress photorespiration while simultaneously minimizing transpiration.This twin benefit confers advantages to C 4 species over C 3 plants in hot, arid climates (Sales et al., 2021).Therefore, the thermotolerant photosynthesis exhibited by sweet sorghum likely facilitates the ecological success of C 4 cereals including sorghum across tropical and subtropical agroecosystems prone to heat stress.Further examination of genotypic variation in thermal acclimation processes governing photosynthesis may inform climate-resilient crop development.g s has been considered one of the most vital indicators of a plant's response to environmental fluctuations, yet its reaction to temperature has been relatively understudied (Urban et al., 2017).Some earlier studies have suggested divergent responses of g s to increasing temperatures, including an increase (Mott and Peak, 2010;Urban et al., 2017), no significant change, or even stomatal closure.Our present results are consistent with previous research in Tradescantia pallida (Mott and Peak, 2010), Pinus taeda, and Populus deltoides x nigra (Urban et al., 2017).As temperatures increased, g s of sweet sorghum gradually increased, enhancing the exchange of CO 2 and H 2 O and elevating the CO 2 uptake.In early research, g s and A n were commonly presumed to share a stable, linear relationship, with g s and A n exhibiting synergistic increases or decreases in response to varying environmental conditions.The patterns of g s and A n in sweet sorghum leaves showed some parallels when responding to light.However, because g s is more thermally sensitive, a slight decline in WUE i was observed when leaf temperatures increased from 30°C to 35°C.Typically, increased temperature coupled with heightened vapor pressure deficit (VPD) results in increased T r , followed by cell shrinkage and stomatal closure (Urban et al., 2017;Sales et al., 2021).Interestingly in this study, even when the VPD of sweet sorghum leaves rose to 2.2 kPa at 35°C, the intercellular CO 2 concentration (C i ) remained relatively stable, implying stomata did not close.Instead, VPD, g s , and A n increased concurrently (Supplementary Figure 2, Figures 1A-F).This aligns with observations in Oryza and Flaveria bidentis under elevated temperatures (Kubien et al., 2003;Scafaro et al., 2011), contrasting the behavior of the C 4 Model Setaria viridis (Anderson et al., 2021).The differential stomatal responses to warming may be attributable to variances in plant functional type or evolutionary origin (Bykova et al., 2019).Therefore, the findings indicate photosynthesis in sweet sorghum was not suppressed by elevated temperatures; rather, it was stimulated by widening of stomatal openings to enhance CO 2 influx, expediting assimilation rates.
The variation in WUE inst of sweet sorghum became more noticeable with increasing temperature.Notably, WUE inst substantially decreased relative to WUE i , primarily due to the disproportionate increase in transpiration compared to photosynthesis under elevated temperatures.For example, from 30°C to 35°C, T r-max increased 2.73 times compared to A nmax and 2.02 times versus g s-max .WUE i indicates a long-term water use balance between assimilation and conductance, independent of vapor pressure deficit (von Caemmerer and Farquhar, 1981;Gyimah and Nakao, 2007;Ye et al., 2020).In this study, sweet sorghum exhibited a minor decrease in WUE i with elevated temperatures, highlighting adaptation via prioritizing growth and survival over short-term heat stress.In contrast, WUE inst experienced a significant decrease.As WUE inst represents plant yield per water loss, aligning with whole-plant WUE (Wall et al., 2001).Its substantial reduction indicates a trade-off of water to ensure survival under high temperatures.This could be seen as a physiological mechanism employed by sweet sorghum for leaf cooling under short-term heat stress, as adopted in other species (Scafaro et al., 2011;Anderson et al., 2021).Collectively, these results reveal that sweet sorghum adjustments to maintain photosynthesis, transpiration and respiration could outweigh slower WUE adaptations, especially diminishing dynamic WUE inst .

Effect of elevated CO 2 concentration on dynamic photosynthesis and water use efficiency in sweet sorghum leaves
Raising CO 2 levels from 250 to 410 mmol mol -1 enhanced photosynthesis in sweet sorghum at moderate temperatures, consistent with observations in many plants (Gago et al., 2014;Kimball, 2016).The heightened substrate availability drives this initial photosynthetic response.However, further elevating CO 2 concentration to 550 mmol mol -1 did not lead to a consistent and proportional increase in photosynthesis.In concordance with previous research indicating reduced sorghum yield under elevated CO 2 concentrations (Kimball, 2016;Asadi and Eshghizadeh, 2021), this suggests that sweet sorghum's photosynthetic system cannot fully capitalize on CO 2 levels beyond a saturation threshold.Instead, alternative factors such as light availability, may become limiting beyond this point.Despite lacking statistical significance, elevated CO 2 concentration did improve photosynthesis at 35°C.Two-way ANOVA analysis from Table 4 also indicated CO 2 level impacts on sweet sorghum's light use efficiency and WUE (including both intrinsic and instantaneous aspects) vary across temperatures, highlighting complex interplay between temperature and CO 2 in photosynthetic responses.Previous research emphasized that the magnitude of A n at elevated temperatures is primarily determined by the electron transfer capacity, suggesting that sweet sorghum photosynthesis has been constrained by irradiance and temperature under current atmospheric CO 2 (Loreto et al., 1995;McAusland et al., 2016;Sales et al., 2021).
The CO 2 rise induced partial stomatal closure, reducing g s and T r , consequently improving WUE, a widely observed response (Conley et al., 2001;Allen et al., 2011).The reduction in g s under high CO 2 levels is recognized as an adaptive response across various plant species (Farooq et al., 2019).Higher atmospheric CO 2 led to elevated C i in leaves, increasing stomatal sensitivity and prompting adjustments to maintain C i below ambient levels (Urban et al., 2017;Feng et al., 2023).Contrary to previous studies attributing heightened WUE i to simultaneous increases in A n and decreases in T r under elevated CO 2 (Conley et al., 2001;Ye et al., 2020), improvements here arose primarily from reductions in g s and T r , rather than an increase in A n .Furthermore, CO 2 -induced reductions in g s and T r diminished at 35°C, suggesting that this stomatal response weakens with increasing leaf temperature.This interaction emphasizes the complex CO 2 -temperature interplay in shaping plant responses.Despite the substantial increase in WUE i to 255.46 ± 5.26 mmol mol -1 under the combined influence of elevated CO 2 and temperature implies the adaptive capacity of sweet sorghum to shifting environments, the precise mechanisms remain unclear and require further investigation.Optimizing WUE likely involves intricate signaling and physiological adjustments (Hatfield and Dold, 2019).
While providing unique insights into immediate photosynthetic responses, our short-term exposures are constrained in comparison to long-term open-top chamber (OTC) and free-air CO 2 enrichment (FACE) studies.Prolonged OTC and FACE exposures over weeks or months facilitate a thorough characterization of gradual acclimation processes, revealing cumulative impacts on physiology, metabolism, tissue structure, gene/protein expression, yield, and overall plant adaptation.Looking ahead, it is imperative to conduct systematic and long-term investigations to gain a more nuanced understanding of sweet sorghum's adaptability to climate change scenarios and its potential under predicted climatic conditions.These future studies should meticulously explore morphological, physiological, and biochemical differences within the plant, encompassing variations in responses among roots, stems, and leaves.Additionally, our use of indoor-cultivated seedlings differs from field-grown plants.While growth chambers allow precise regulation of conditions like temperature, humidity, and lighting to reduce variability and stressors, indoor cultivation may heighten sensitivity to environmental shifts.Transferring seedlings from controlled growth chamber to the lab with open gas circulation for gas exchange measurements may induce physiological changes due to altered growth conditions.Despite efforts to minimize variation, the transition between environments could result in transient responses that would not occur in plants already acclimated to field settings.

Conclusion
Our study further validates the superiority of the photosynthesis models proposed by Ye et al. for simulating the light response curves of A n , g s , T r , WUE i , and WUE inst .Particularly, when employed to fit the WUE i -I and WUE inst -I curves, the models uniquely capture the decline in both WUE i and WUE inst with increasing I under high light intensity.Across all experimental conditions, it returns the values for A nmax , g s-max , T r-max , WUE i-max , and WUE inst-max closely matching measured data.In contrast, the NRH model inadequately reproduces the WUE i -I and WUE inst -I curves and severely overestimates A nmax , WUE i-max , and WUE inst-max relative to measurements.It also fails to determine the corresponding saturation light intensities for these traits.In addition, sweet sorghum exhibits remarkable heat tolerance up to 35°C, achieving higher A n through stimulated g s .However, disproportionate increase in T r lead to a sharp decline in WUE inst .Increasing CO 2 concentration from sub-ambient to ambient levels has a significant positive effect on photosynthesis in sweet sorghum, but no consistent and proportional increase is observed at 550 mmol mol −1 .Elevated CO 2 causes partial stomatal closure in sweet sorghum leaves, markedly reducing g s and T r , thereby improving WUE i and WUE inst .Nevertheless, the effect of CO 2 -induced stomatal closure in reducing transpiration progressively diminishes at high temperature owing to stomatal opening.Elucidating the physiological mechanisms governing plant responses to combined environmental factors will enable identifying adaptive traits to accelerate resilient crop development amidst intensifying environments.
FIGURE 1 Changes in gas exchange parameters of sweet sorghum leaves across varied air temperatures (25, 30, and 35°C) under atmospheric CO 2 level (410 mmol mol −1 ), alongside comparison of light response curves fitted by the Ye's models and the NRH model.(A-C) present the net photosynthetic rate (A n ); (D-F) stomatal conductance (g s ); (G-I) Transpiration rate (T r ); (J-L) intrinsic water-use efficiency (WUE i ); and (M-O) instantaneous water-use efficiency (WUE inst ).
illustrates the variations in WUE i and WUE inst in response to I at different temperatures.Both WUE i and WUE inst showed almost linear increases within the 200 mmol m −2 s −1 range, indicating improving WUE with increasing I.
FIGURE 2Changes in gas exchange parameters of sweet sorghum leaves across varied CO 2 concentrations, as well as comparison of light response curves fitted by the Ye's models and the NRH model.Figures (A, B), (D, E), (G, H), (J, K) and (M, N) present changes in A n , g s , T r , WUE i , and WUE inst at 30°C under CO 2 concentrations of 250 and 550 mmol mol −1 , respectively.Figures(C, F, I, L) and (O) show the changes in A n , g s , T r , WUE i , and WUE inst at 35°C under a CO 2 concentrations of 550 mmol mol −1 .

TABLE 1
Definitions of the abbreviations.

TABLE 2
Comparison analysis of photosynthetic parameters in sweet sorghum under varied temperature conditions at 410 mmol mol −1 CO 2 based on fitting values from light response curves using different photosynthetic models.
aMean and standard errors of three replicates are shown.Statistically significant differences (p<0.05) between temperature treatment groups are denoted by different letters under the Ye's models and the NRH model.

TABLE 3
Comparison analysis of photosynthetic parameters in sweet sorghum under varied CO 2 levels at 30°C based on fitting values from light response curves using different photosynthetic models.
aMean and standard errors of three replicates are shown.Statistically significant differences (p<0.05) between temperature treatment groups are denoted by different letters under the Ye's models and the NRH model.

TABLE 4
Summary of two-way ANOVA analysis between the effects of temperature and CO 2 concentration on key photosynthetic parameters of sweet sorghum.

TABLE 5
Comparison of results fitted by the Ye's models and the NRH model with measured data in sweet sorghum under elevated CO 2 concentration (410 mmol mol −1 ) and high temperature (35°C) in combination.