Model forms for triose phosphate utilization-limited photosynthetic rates: implications for estimation of photorespiratory carbon export and the contribution of mesophyll conductance to photosynthesis
Year: 2024
Type: article
Abstract: Leaf photosynthesis is believed to be determined by three major limiting rates. Compared with the first two limitations set by Rubisco activity and electron transport, respectively, the third limiting process—triose phosphate utilization (TPU)—has received less attention. However, the importance of the limitation set by TPU in whole-plant physiology and crop yield determination has been demonstrated recently (Zhou et al. 2023; Ma et al. 2024). Yet, with progressive comprehension of the TPU-limited rate, the corresponding photosynthetic model equation has undergone several rounds of updating. Herein, the far-reaching consequences of adopting one widely used and three newly updated model forms in estimating relevant photosynthetic parameters are assessed. The results suggested that it is time to shift from the widely used model form to one of the newly updated model forms for the purpose of accuracy as well as simplicity in describing the TPU-limited photosynthetic rate in the context of designing crop ideotypes and modelling vegetation systems. According to the model of Farquhar et al. (1980; known as the FvCB model), the leaf photosynthetic rate (A) can be limited by Rubisco activity (Ac) or by electron transport (Aj). Subsequently, Sharkey (1985) and Harley and Sharkey (1991) extended the model by introducing the TPU-limited photosynthetic rate (Ap). With an increase in the chloroplastic [CO2] level (Cc) from a low level such as the CO2 compensation point, first Rubisco activity limits, and then electron transport starts to limit, photosynthetic rates. With a further increase in Cc, A may be limited by TPU. Within Rubisco- or electron transport-limited ranges, A increases with an increase in Cc, whereas when TPU limits photosynthetic rates, A either remains insensitive, or has a reversed sensitivity, to an increase in Cc. There are several forms of the model for describing photosynthetic rates as limited by TPU. When it is insensitive to Cc, Ap can be simply described as (Sharkey, 1985): where Tp is the rate of TPU and Rd is the leaf day respiration rate. The reversed sensitivity has long been explained by an assumption that a fraction of glycolate carbon (α), after converting to glycine, exits from the photorespiratory pathway and is used elsewhere for amino acid synthesis (Harley and Sharkey, 1991), thereby increasing A with increasing photorespiration. With this assumption, von Caemmerer (2000) formulated the model as: where Γ* is the CO2 compensation point in the absence of Rd, and Equation (2) becomes Equation (1) if α=0 (note that 0≤α≤1). Since then, Equation (2) has been widely used for modelling the TPU-limited rate (e.g. Gu et al., 2010; Busch and Sage, 2017; Kumarathunge et al., 2019). However, recent studies have suggested that photorespiratory carbon exit, if in the form of amino acids, can be either in glycine or in serine (Fig. 1A), and experimental evidence suggests that serine is the more likely form that exits (Abadie et al., 2016, 2018; Fu et al., 2023). If it is serine that exits, the model should be (Busch et al., 2018; Yin et al., 2021): Photosynthetic rate in relation to glycolate carbon exit from the photorespiratory pathway. (A) Illustration of the photorespiratory pathway [thin arrows, which start with ribulose 1,5-bisphosphate (RuBP) oxygenation], with focus on glycolate-derived carbon exits from the pathway in the form of glycine or serine or CH2-tetrahydrofolate (THF) for other uses in plant metabolism (revised from Busch, 2020, with permission from John Wiley and Sons). Also shown is the Calvin cycle (thick arrows, which start with RuBP carboxylation). Theoretically, the photosynthetic rate (A) is equal to the sum of those individual sinks for assimilated carbon indicated by black boxes [which include triose-P used as sugar precursors for processes such as starch synthesis in chloroplasts or sucrose synthesis in the cytosol (dashed arrows), and carbon for glycine, serine, and CH2-THF exit] minus CO2 released by glycine decarboxylase (GDC) in the mitochondrion (the source of ‘photorespiration’) and minus day respiration (Rd). Note that the CO2 release by GDC will be decreased if glycine exits, but will not change if serine exits. If CH2-THF exits, however, the CO2 release by GDC will need to increase in order to meet the required stoichiometric proportion of glycine and CH2-THF for forming serine. These differences have implications for the CO2 compensation point and, thus, the photosynthetic rate (A) is modelled by Equation (3) if serine exits, whereas the model has to be changed to Equation (4) if glycine exits and to Equation (5) if CH2-THF exits (3-PGA, 3-phosphoglycerate; triose-P, triose phosphate). (B) Illustration of the underestimation of A by the widely used Equation (2) that does not account for the CO2 compensation point decrease for the glycine-exit scenario, as shown by A–Cc curves within the range of TPU limitation generated by Equation (2) versus Equations (3–5) with a given set of parameter values (Tp=10 µmol m−2 s−1, Γ*=40 μbar, α=0.2, and Rd=1 µmol m−2 s−1). Also shown is the gap between the horizontal line (Equation 1) and points (Equations 2–5), which indicates an increase of photosynthetic rate due to the exit of glycolate carbon from the photorespiratory pathway: the lower Cc is, the higher RuBP oxygenation is, the more the glycolate carbon exit is, and the higher the photosynthetic rate A is; thereby, Equations (2–5) generate a reversed CO2 sensitivity. where a stoichiometric coefficient in the denominator has been changed to 4 (note that for this case, 0≤α≤0.75). If it is glycine that exits, the model should be revised to account for a decreased rate of photorespiratory CO2 release from glycine decarboxylation (Busch et al., 2018; Yin et al., 2021): Note that compared with Equation (2), Equation (4) has an additional term (1−α) in front of Γ* in the numerator, which is meant to account for the decreased rate of glycine decarboxylation if glycine exits. In addition, glycolate carbon could be diverted, in the form of CH2 (methylene)-tetrahydrofolate (Fig. 1A), from the photorespiratory pathway to supply carbon for C1 metabolism, despite little information being currently available for this route (Busch, 2020). If it occurs, the glycine decarboxylation rate does not decrease, but increases relatively, and the model becomes, with 0≤α≤0.5 (Busch, 2020; Yin et al., 2021): Compared with Equations (3), (4), and (5), the widely used model form, Equation (2), not only underpredicts Ap but also gives a different curvature of the A–Cc curve for a given set of input parameter values (Fig. 1B). In this Viewpoint, we assess the implications of choosing the widely used Equation (2) versus these updated model forms for estimating the fraction of photorespiratory carbon exit (α) in modelling the TPU-limited photosynthetic rates. Additionally, given that there is continuous interest in studying mesophyll conductance (gm) that determines the drawdown from the intercellular airspace CO2 level (Ci) to Cc (e.g. Evans, 2021), and gm has often been estimated from exploring the curvature of A–Ci curves by use of the FvCB model (von Caemmerer, 2000), we also examine how various model forms of TPU-limited photosynthesis could influence the estimation of gm. For both purposes, we used a recent dataset of Zhou et al. (2023) for A–Ci curves that covers both electron transport- and TPU-limited parts but especially includes sufficient data points where A was limited by TPU. Box 1 gives details about the dataset and model parameterization schemes. We began by re-analysing the experimental dataset of rice photosynthetic CO2 response curves (A–Ci curves) provided by Zhou et al. (2023) from gas exchange and chlorophyll fluorescence measurements at 25 °C. This dataset was collected to quantify if the TPU limitation was modulated by whole-plant source–sink ratios and nitrogen budget, and thus contained measurements across five experimental measurement factors: four genotypes, adaxial versus abaxial measurements, three growth stage measurements, two nitrogen levels, and pruning versus non-pruning of panicles. For the sake of relevance to our analysis here, we used only the data from adaxial measurement on four rice genotypes under two nitrogen levels at the early growth stage (i.e. the tillering stage) where TPU limitation was the most obvious and occurred at relatively low Ci. Details about the dataset were described by Zhou et al. (2023). The model parameters were estimated, using the procedures described by Yin et al. (2020; see also Zhou et al., 2023), with some modifications according to the context here. First, the required Rd and linear electron transport rate (J) were calculated, according to the method of Yin et al. (2009), in which data for measured A were linearly regressed against IincΦ2/4 within low-light and 2% O2 conditions (where Iinc is incident irradiance, and Φ2 is chlorophyll fluorescence-assessed quantum yield of PSII’s electron transport). The intercept of the regression gives the estimate of Rd, and the slope of the regression gives a calibration factor s for converting Φ2 into J, namely J=sIincΦ2. Second, Fick’s diffusion law (i.e. Cc=Ci–A/gm) was combined with the FvCB model: where for the Aj part, x1=J/4 and x2=2Γ*; for the Ap part that limits photosynthesis at high Ci, x1=3Tp for all Equations (2–5) but x2= –(1 + 3α)Γ* for Equation (2) and Equation (4), –(1 + 4α)Γ* for Equation (3), and –(1 + 6α)Γ* for Equation (5). Note that the symbol Γ*GT (instead of the usual Γ*) is used; this is to account for the change in the CO2 compensation point due to the glycolate carbon exit via glycine or via CH2-tetrahydrofolate from the photorespiratory pathway in the case of the TPU limitation. Γ*GT=(1−α)Γ* in the case of the glycine exit [see Equation (4)], or Γ*GT=(1 + 2α)Γ* in the case of CH2-tetrahydrofolate exit [see Equation (5)]. However, Γ*GT=Γ* in the case of serine exit [see Equation (3)]. Also for the Aj part, Γ*GT was set to be Γ* as J is defined here as in a standard FvCB model as the linear electron transport supporting the Calvin cycle and photorespiration not being associated with de novo N assimilation or C1 metabolism. In all these formulae, Γ* is the standard CO2 compensation point described as: Γ*=0.5O/Sc/o, where Sc/o is the relative CO2/O2 specificity factor for Rubisco. We take here an estimate of 3.022 mbar μbar−1 for Sc/o at 25 °C (Cousins et al., 2010). The solution to the combined Fick’s law and FvCB model is quadratic (von Caemmerer, 2000): Where The term (b2−4c) is always ≥0 for the Aj-limited part. However, care needs to be taken for Equation (B1.2) as there is no guarantee that (b2−4c) is always ≥0 for the Ap-limited part (Gu et al., 2010). The threshold value of Ci (Ci,th) that guarantees mathematically a real root for Ap yet physiologically the TPU limitation occurred at high Ci can be solved from (b2−4c)≥0 as: where x1p and x2p are x1 and x2 defined above for Ap equations. Thus, the model used to analyse our data when simultaneously fitting to both Aj and Ap was set as: The model-fitting procedure was implemented using the GAUSS method in PROC NLIN of the statistical software SAS version 9.4 (SAS Institute Inc, Cary, NC, USA). The SAS codes can be found in Supplementary Protocol S1. Given the diversity in parameterizing the Ap-limited model, three fitting schemes were designed to estimate the photosynthetic parameters. Scheme 1. All the parameters gm, Tp, and α were simultaneously estimated by fitting curves based on data from Aj- and Ap-limited parts or based on data only from the Ap-limited part. Scheme 2. Parameters gm, Tp, and α were estimated stepwise. First, gm was estimated based on data from the Aj-limited part. Second, Tp and α were estimated based on data from the Ap-limited part, with the already estimated gm as input. Scheme 3. First, in analogy with the sometimes used procedure where parameter α is pre-fixed (e.g. Busch and Sage, 2017; Kumarathunge et al., 2019), we fixed α to a physiologically relevant value of 0.2 (an average value of the estimation results from Zhou et al., 2023). Then parameters gm and Tp were simultaneously estimated by fitting curves based on data from Aj- and Ap-limited parts or based on data only from the Ap-limited part. When fitting Aj and Ap parts of the FvCB model separately, we first determined the transition point from the Aj limitation to the Ap limitation by solving the second-order polynomial regression equations that were fitted to the two parts, respectively, of A–Ci curves. Our previous analysis (Zhou et al., 2023) has shown that the transition point values estimated by this method are highly consistent with those identified by Equation (B1.4). All the model estimation results for each combination of nitrogen levels×genotypes per replicate are listed in Supplementary Dataset S1. For all model estimation schemes, parameter Tp can be fitted reliably and its estimates were hardly affected by the model forms (Figs 2–4). Comparisons in photosynthetic parameters estimated by the widely used model form (Equation 2) versus those by updated forms (Equations 3–5) within the fitting scheme 1 (see text in Box 1). Tp (µmol m─2 s─1), rate of triose phosphate utilization; α, the proportion of glycolate carbon exported from the photorespiratory pathway; gm (mol m−2 s−1 bar−1), mesophyll diffusion conductance. The solid line represents the 1:1 relationship, while dashed lines represent an overall proportional factor between the y-axis and x-axis (if applicable). Data points are drawn from those parameter values that were estimated for measurement replicates, as listed in Supplementary Dataset S1. Comparisons in photosynthetic parameters estimated by the widely used model form (Equation 2) versus those by updated forms Equations 3–5) within the fitting scheme 2 (see the text in Box 1). Tp (µmol m─2 s─1), rate of triose phosphate utilization; α, the proportion of glycolate carbon exported from the photorespiratory pathway. The solid line represents the 1:1 relationship, while dashed lines represent an overall proportional factor between the y-axis and x-axis (if applicable). Data points are drawn from those parameter values that were estimated for measurement replicates, as listed in Supplementary Dataset S1. Comparisons in photosynthetic parameters estimated by the widely used model form (Equation 2) versus those by updated forms (Equations 3–5) within the fitting scheme 3, where α, the proportion of glycolate-carbon exported from the photorespiratory pathway, was fixed at 0.2 (see text in Box 1). Tp (µmol m─2 s─1), rate of triose phosphate utilization; gm (mol m−2 s−1 bar−1), mesophyll diffusion conductance. The solid line represents the 1:1 relationship, while dashed lines represent an overall proportional factor between the y-axis and x-axis (if applicable). Data points are drawn from those parameter values that were estimated for measurement replicates, as listed in Supplementary Dataset S1. In scheme 1, when both Aj and Ap models were combined to fit the full range of data, all the parameters can be estimated (Fig. 2A–I); when the Ap model alone was used to fit the TPU-limited range of data, gm often reached infinitity (Fig. 2J, M, P; Supplementary Dataset S1), indicating the occurrence of overfitting. This result is foreseeable, as Sharkey (2019) suggested that Aj-limited data, rather than Ap-limited data, provide the most information about gm. In particular, when integrating Aj-limited data into the model analysis, the Aj model, with J derived from chlorophyll fluorescence as sIincΦ2 (see Box 1), may take over part of the TPU-limited range of data, since TPU limitation will exert a feedback effect on the electron transport rate J. For scheme 2, when we fixed gm as had been estimated from the Aj-model fitted to Aj-limited data, Equation (2) overestimated α, by a factor of 4/3 (Fig. 3B), compared with Equation (3). This factor of overestimation of α from Equation (2) can be seen as a mathematical consequence of the altered factor preceding α in the updated model form in Equation (3). As the three updated forms predict similar values for the photosynthetic rate (Fig. 1B), Equations (3–5) when fitting to data gave similar estimates of α (Fig. 3B, D, F). When we applied the sometimes used practice of fitting the TPU-limited model with a pre-fixed α (assumed to be 0.2, scheme 3), the estimated gm and Tp values were comparable between Equation (2) and each of updated equations when both Aj- and Ap-models were simultaneously fitted (Fig. 4A–F), again suggesting that the Aj-model may have taken over part of the TPU-limited range of data. However, when the Ap-model alone was fitted (to the TPU-limited range), the gm value estimated by the Equation (2)-based Ap-model was surprisingly lower than those obtained from updated model forms, by 17–30% (Fig. 4G, I, K). As stated earlier, compared with Equations (3–5), Equation (2) underpredicts A (Fig. 1B); so, one would expect that compared with Equation (3), (4), or (5), Equation (2) would result in a higher estimated gm to achieve the same fit to the data, since a higher estimated gm would allow higher Cc values. However, we realize only in hindsight that this expectation holds true for the range of Ac or Aj, where A increases with increasing Cc. Within the TPU-limited range, A is either insensitive to or decreases with increasing Cc. Therefore, contrary to common sense, Equation (2) requires a lower estimated gm to achieve the same fit to the data, compared with updated equations. The very similar estimates of α or gm given by Equations (3), (4), and (5) (Supplementary Dataset S1) are expected, because, as stated above, these updated equations yield similar values of Ap for a given set of input parameter values (Yin et al., 2021; see also Fig. 1B). In reality, photorespiratory carbon may exit from the pathway in all the forms (glycine, serine, and CH2-tetrahydrofolate; Fig. 1A), and the generalized model (Busch, 2020; Yin et al., 2021) should be used. However, it is practically impossible to accurately estimate all three carbon-exit fraction parameters from simple A–Ci data, again because the three carbon-exit forms give rise to a similar curvature of the photosynthetic CO2 response (Fig. 1B). We prefer to use Equation (3) as it receives more experimental support (Abadie et al., 2016, 2018; Fu et al., 2023). Moreover, the term (Cc−Γ*) in the numerator of Equation (3) is consistent with that for Ac or Aj equations of the FvCB model. Given that the presently widely used form Equation (2) underpredicts Ap and wrongly estimates α or gm, it is time to switch from Equation (2) to Equation (3) for describing the (reversed [CO2] sensitivity of) TPU-limited Ap of the FvCB model. One of our key findings in this analysis is the model heuristic result indicating that the gm values estimated by Equation (2) were lower than those obtained from Equation (3). This suggests that a lower gm is preferred to achieve higher photosynthesis under the TPU-limited range. Improving gm has been proposed as a viable strategy to improve crop photosynthesis (e.g. Salesse‐Smith et al., 2024) and water use efficiency (e.g. Flexas et al., 2013). Fabre et al. (2019) and Zhou et al. (2023) have shown that TPU limitation frequently occurred at quite a low CO2 level, especially in early growth stages and under conditions where the whole-plant sink strength is limited. Given that gm scales with leaf nitrogen content (e.g. Yin et al., 2009; Xiong et al., 2015), increasing gm has been modelled to have limited potential for improving rice yield in high-input environments (Yin and Struik, 2017). Our results here suggest that enhancing gm may not be an effective strategy to improve crop productivity (particularly not under the forthcoming high-CO2 environment), unless there is a significant increase in the whole-plant sink size to remove the TPU limitation or plants metabolically increase α to make up for drops in Ap caused by higher gm. with the same parameter the updated model forms give a higher photosynthetic rate than the widely used model In with the updated model forms, the widely used form overestimated α by a factor of Our results also that the widely used form not but rather the gm values by 17–30% when only fitting to the TPU-limited data. Given these we that it is time to shift from the widely used model form to one of the updated forms to Equation for accurately and modelling the TPU-limited photosynthetic rates. Additionally, our model heuristic results that there will be limited potential for enhancing photosynthesis by improving gm under high CO2 unless a significant whole-plant sink size is that the TPU limitation. The data are available at Protocol S1. SAS for fitting of Aj- and Ap-models to data. Dataset S1. parameter values of three model-fitting schemes. We and and for for that generated data used in this and and the for that to improve the data and the The that have no This was by the for by
Source: Journal of Experimental Botany
DOI: 10.1093/jxb/erae369
Authors: Zhenxiang Zhou, Xinyou Yin
Institutions: Hainan University, Wageningen University & Research
Language: English
Subfield: Molecular Biology
Domain: Life Sciences
Open Access status: bronze
Award: G8907717105
OpenAlex ID: W4402253440