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# Plants increase CO2 uptake by assimilating nitrogen via the photorespiratory pathway

## Abstract

Photorespiration is a major bioengineering target for increasing crop yields as it is often considered a wasteful process. Photorespiratory metabolism is integrated into leaf metabolism and thus may have certain benefits. Here, we show that plants can increase their rate of photosynthetic CO2 uptake when assimilating nitrogen de novo via the photorespiratory pathway by fixing carbon as amino acids in addition to carbohydrates. Plants fed NO3 had higher rates of CO2 assimilation under photorespiratory than low-photorespiratory conditions, while plants lacking NO3 nutrition exhibited lower stimulation of CO2 uptake. We modified the widely used Farquhar, von Caemmerer and Berry photosynthesis model to include the carbon and electron requirements for nitrogen assimilation via the photorespiratory pathway. Our modified model improves predictions of photosynthetic CO2 uptake and of rates of photosynthetic electron transport. The results highlight how photorespiration can improve photosynthetic performance despite reducing the efficiency of Rubisco carboxylation.

## Main

Theoretical models of carbon assimilation in plants, in particular the Farquhar, von Caemmerer and Berry (FvCB) model1, are widely used to predict the rate of photosynthetic CO2 assimilation (A) from the leaf level to the global scale. The FvCB model assumes that A is limited by one of two biochemical processes: the consumption of ribulose 1,5-bisphosphate (RuBP) by Rubisco (A c), and the regeneration of RuBP in the Calvin–Benson cycle, which can be restricted either by the availability of NADPH (A j) generated by the photosynthetic electron transport chain, or of ATP (A p) following the release of phosphate in the chloroplast due to triose phosphate utilization (TPU). The FvCB model also incorporates the substrate-specificity of Rubisco, which can carboxylate or oxygenate RuBP. Metabolites produced by the oxygenase reaction are recycled back to RuBP in a process termed photorespiration. A key step in photorespiration is the conversion of glycine to serine with the release of CO2 and ammonia. Much of the released CO2 exits the leaf and thus represents a loss of carbon2, while the recycling of ammonia is energetically costly, as it requires ATP and reduced ferredoxin. Photorespiration is also considered wasteful, because O2 competes with CO2 for Rubisco active sites during the oxygenase reaction, consuming RuBP and reducing the energy efficiency of net carbon assimilation3. Typically, the rate of photorespiratory CO2 release is about 15–20% of A at a leaf temperature of 25 °C4. These considerations have led to a widely accepted view that photorespiration is inhibitory for carbon gain, and thus an impediment to growth and yield. However, while inhibitory at one level, photorespiratory metabolism may also be beneficial; for example, photorespiration consumes reductant (four electrons per oxygenation reaction) and thus is an important form of excess energy dissipation5. Here, we argue that the integration of carbon and nitrogen metabolisms in the photorespiratory pathway can result in increased CO2 assimilation rates, offsetting some of the negative aspects of photorespiration.

The photorespiratory pathway is intrinsically linked to nitrogen assimilation in two ways: first, through the energy demand associated with reassimilating the ammonia, and second, through the reduction and assimilation of new nitrogen, which usually enters the leaf as NO3 6. De novo assimilation of nitrogen in leaves of C3 plants can occur via the photorespiratory pathway, and in photosynthetic tissue this pathway is considered the main source of serine, which acts as a precursor of several other amino acids7. Thus, nitrogen assimilation has the potential to be affected by the rate of photorespiration. Under low photorespiratory conditions, NO3 assimilation decreases overall8, and serine is increasingly synthesized via the phosphoserine pathway, compensating for the lack of photorespiratory serine biosynthesis9.

In most vascular plant species, a large proportion of the absorbed NO3 is reduced to ammonium (NH4 +) in the shoot10,11. There, electrons supplied via photosynthetic electron transport provide the reducing equivalent, and part of the resulting NH4 + is assimilated into amino acids using photorespiratory metabolites as carbon skeletons (Fig. 1). Depending on NO3 availability, up to a quarter of the photosynthetic electron transport rate supports nitrogen assimilation12, especially during the first part of the light period13. Like other ‘excess electron sinks’, this electron requirement is usually not accounted for in photosynthesis models. While the electron requirement for the recycling of ammonia released by photorespiration is integrated in the FvCB model1, the model does not account for de novo nitrogen assimilation. Here, we develop an approach to incorporate the electron requirement for nitrate reduction in the existing FvCB model in order to formally link the carbon and nitrogen assimilation pathways in C3 plants. Our results highlight important beneficial aspects of photorespiration; in particular, that the diversion of photorespiratory carbon into amino acids can increase the net CO2 assimilation rate.

## Theory

In the FvCB model, net CO2 uptake (A) is modelled as a function of the two competing reactions catalysed by Rubisco1,14, as

$$A={V}_{{\rm{c}}}-0.5{V}_{{\rm{o}}}-{R}_{{\rm{d}}}$$
(1)

where R d stands for the rate of mitochondrial respiration in the light and V c and V o denote the rates of RuBP carboxylation and oxygenation, respectively. The ratio of V o to V c, denoted Φ, relates to the relative specificity of Rubisco (S c/o) through the relationship

$$\Phi =\frac{{V}_{{\rm{o}}}}{{V}_{{\rm{c}}}}=\left(\frac{1}{{S}_{{\rm{c/o}}}}\right)\frac{O}{C}$$
(2)

Here, C and O are the chloroplastic CO2 and O2 concentrations, respectively. The original FvCB model assumes that photorespiration is a fully closed pathway and 0.5 moles of CO2 are released for every mole of oxygenation reactions. Then, the chloroplastic CO2 compensation point in the absence of mitochondrial respiration (Γ *) can be derived by combining equations (1) and (2) and is described by

$${{\Gamma }}^{* }=\frac{0.5O}{{S}_{{\rm{c/o}}}}$$
(3)

and therefore

$$\Phi =\frac{2{{\Gamma }}^{{\rm{* }}}}{C}$$
(4)

Depending on the biochemical process limiting CO2 assimilation, A can then be described by combining equations (1)–(4) with the minimum of the three rates W c, W j and W p, which are the carboxylation rates that can be supported under a Rubisco, electron transport or TPU limitation, respectively, so that

$$A={\rm{\min }}\left\{{W}_{{\rm{c}}},{W}_{{\rm{j}}},{W}_{{\rm{p}}}\right\}\left(1-\frac{{{\Gamma }}^{{\rm{* }}}}{C}\right)-{R}_{{\rm{d}}}$$
(5)

The potential net CO2 assimilation rates corresponding to W c, W j and W p are denoted as A c, A j and A p.

When RuBP supply is not limiting the rate of Rubisco carboxylation, W c is the limiting factor described by

$${W}_{{\rm{c}}}=\frac{{V}_{{\rm{c\; max}}}C}{C+{K}_{{\rm{c}}}\left(1+O{\rm{/}}{K}_{{\rm{o}}}\right)}$$
(6)

where K c and K o are the Michaelis–Menten constants of Rubisco for CO2 and O2, respectively. This RuBP-saturated carboxylation rate has been termed the Rubisco-limited assimilation rate, as it is largely dependent on the maximum rate of carboxylation by Rubisco, V cmax. Under conditions where the regeneration of RuBP limits A via the photosynthetic electron transport rate (J), W j is described by1

$${W}_{{\rm{j}}}=\frac{J}{4+4\Phi }$$
(7)

This equation takes into account the electron requirement for Rubisco carboxylation as well as oxygenation, assuming the availability of NADPH limits the regeneration of RuBP.

At high CO2 concentrations, RuBP regeneration may be controlled by the capacity for starch and sucrose synthesis from triose phosphates to regenerate inorganic phosphate for sustained ATP synthesis15,16. Under conditions where TPU capacity is limiting, W p has been modelled by

$${W}_{{\rm{p}}}=\frac{3{T}_{{\rm{p}}}}{1-0.5\left(1+3{\alpha }_{{\rm{old}}}\right)\Phi }$$
(8)

where T P is the rate of triose phosphate export from the chloroplast17,18, and where 0 ≤ α old ≤ 1 in this notation was defined in prior studies as the fraction of photorespiratory glycolate carbon that is not returned to the chloroplast18. The loss of CO2 during glycine decarboxylation should also be included in such a definition. In the following we will redefine the above equations to match the stoichiometries outlined in Fig. 1.

In C3 plants, the TPU limitation is common at saturating light intensity, cooler temperatures and elevated CO2 concentration15,16,17,19,20. When inorganic phosphate supply limits A it is frequently observed that CO2 assimilation rate declines with increasing CO2 concentration or decreasing O2 concentration19,20,21,22. This has been attributed to a fraction α old of the carbon in the photorespiratory metabolite pool leaving the photorespiratory pathway to be used for other processes, such as amino acid synthesis17,18,23. In experiments on sweet potato α old was shown to be of the order of 0.316. The export of amino acids from the photorespiratory pathway was experimentally confirmed in other C3 plants and its magnitude was dependent on the rate of photorespiration24. A large fraction of the nitrogen assimilated in the shoots may be incorporated into organic compounds via this process25, which includes in particular the amino acids derived from 3-phosphoglycerate. These amino acids include glycine and serine, two photorespiratory metabolites that are intermediary in the recycling of glycolate back to 3-phosphoglycerate and can be taken out of this cycle for other uses or accumulated temporarily.

In the model outlined by equations (1)–(8), the parameter α old addresses the carbon side of the amino acid export, but not the electron requirement for NO3 reduction. In addition, amino acid export from the photorespiratory pathway needs to be treated differently depending on whether glycine or serine is exported, both in terms of carbon and electrons as outlined below. We therefore introduce two new variables, α G and α S, where 0 ≤ α G ≤ 1 is the proportion of glycolate carbon taken out of the photorespiratory pathway as glycine, and 0 ≤ α S ≤ 0.75(1 − α G) the proportion taken out as serine. The 0.75 value in the latter relation takes into account that a quarter of the carbon is lost in the conversion of glycine to serine (see Fig. 1). We can then account in the model for the carbon and electron requirement of different rates of glycine and serine export by incorporating the flux rates of carbon and nitrogen (and thereby electrons) outlined in Fig. 1.

The reduction of NO3 to NO2 occurs in the cytosol26,27 with reducing equivalents supplied to cytosolic nitrate reductase by the chloroplast via a malate shuttle, which balances redox equivalents between chloroplasts, mitochondria, peroxisomes and the cytosol28,29. When nitrite is present in the chloroplast at high concentrations, its reduction competes for electrons with higher affinity than other major electron consuming processes, including CO2 assimilation, which highlights the importance of considering nitrogen assimilation in photosynthetic models30. Electrons from photosynthetic electron transport are also used for sulfur assimilation in the chloroplast, which is quantitatively less significant than nitrogen assimilation by one order of magnitude31,32 and is therefore not considered here.

Two electrons generated by the photosynthetic light reactions are necessary for each reduction of NADP+ to NADPH. This PSII electron flow supports the regeneration of RuBP in the Calvin–Benson cycle, facilitates the recycling of photorespiratory metabolites and provides the electrons required to supply the nitrogen that will leave the photorespiratory pathway as amino acids (2 e for NO3 reduction, 6 e for nitrite (NO2 ) reduction and 2 e in the form of reduced ferredoxin for the glutamate synthesis by glutamate synthase). The extra requirement for electrons used for NO3 reduction adds to $$\left(2{\alpha }_{{\rm{G}}}+\left(6{\alpha }_{{\rm{G}}}+4{\alpha }_{{\rm{S}}}\right)+\left({\alpha }_{{\rm{G}}}+\frac{4}{3}{\alpha }_{{\rm{S}}}\right)\right)\Phi =\left(9{\alpha }_{{\rm{G}}}+\frac{16}{3}{\alpha }_{{\rm{S}}}\right)\Phi$$, which is partially balanced by the decreased requirement of $$\left({\alpha }_{{\rm{G}}}+\frac{4}{3}{\alpha }_{{\rm{S}}}\right)\Phi$$ electrons for RuBP regeneration due to a proportion of the carbon not returned to the chloroplast (Fig. 1). Here, and in the following, Φ is the ratio V o/V c as defined by equation (2). Assuming no further alternative electron sinks, the actual photosynthetic electron transport rate J a can therefore be calculated as

$${J}_{{\rm{a}}}=\left(4+\left(4+8{\alpha }_{{\rm{G}}}+4{\alpha }_{{\rm{S}}}\right)\Phi \right){V}_{{\rm{c}}}$$
(9)

In the case of glycine being removed from the photorespiratory pathway, not only is the rate of electron transport used for nitrogen assimilation affected, but so also is the amount of CO2 released per oxygenation reaction. A complete conversion from glycine to serine in the photorespiratory pathway involves a loss of 0.5 moles of CO2 for every mole of oxygenation reactions (equation (1)). For modelling purposes, it is commonly assumed that the conversion from glycine to serine is complete. If a fraction 0 ≤ α G ≤ 1 of glycine leaves the pool of photorespiratory metabolites, however, the CO2 release per oxygenation is decreased by α G and equation (1) therefore becomes

$$A={V}_{{\rm{c}}}-0.5\left(1-{\alpha }_{{\rm{G}}}\right){V}_{{\rm{o}}}-{R}_{{\rm{d}}}$$
(10)

Thus, when both serine and glycine leave the photorespiratory pathway, equation (5) is generalized by

$$A={\rm{\min }}\left\{{W}_{{\rm{c}}},{W}_{{\rm{j}}},{W}_{{\rm{p}}}\right\}\left(1-\frac{{{\Gamma }}_{{\alpha }_{{\rm{G}}}}^{* }}{C}\right)-{R}_{{\rm{d}}}$$
(11)

with W c, W j and W p as defined below, and where we set

$${{\Gamma }}_{{\alpha }_{{\rm{G}}}}^{* }=\frac{0.5\left(1-{\alpha }_{{\rm{G}}}\right)O}{{S}_{{\rm{c}}/o}}$$
(12)

to account for a change in the amount of CO2 released per oxygenation reaction. It follows that the CO2 compensation point in the absence of mitochondrial respiration at any given temperature and O2 partial pressure is not a constant, but depends on the proportion of glycine removed from the photorespiratory pathway.

While W c remains unaffected, including nitrogen assimilation in the FvCB model has consequences for calculating W j, the rate of carboxylation that can be sustained by electron transport, since the potential electron transport rate J has to support both carbon assimilation and NO3 reduction. With the inclusion of nitrogen assimilation, we use equation (9) to redefine W j in equation (7) as

$${W}_{{\rm{j}}}{\rm{=}}\frac{J}{4+\left(4+8{\alpha }_{{\rm{G}}}+4{\alpha }_{{\rm{S}}}\right)\Phi }$$
(13)

assuming nitrogen is supplied in the form of NO3 . In the case of a TPU limitation we can write W p in a manner equivalent to equation (8) as

$${W}_{{\rm{p}}}{\rm{=}}\frac{3{T}_{{\rm{p}}}}{1-0.5\left(1+3{\alpha }_{{\rm{G}}}+4{\alpha }_{{\rm{S}}}\right)\Phi }$$
(14)

where the denominator corresponds to the flux of carbon (scaled by V c) exported as triose-phosphates (Fig. 1), with $${\rm{0}}\le {\alpha }_{{\rm{G}}}{\rm{+}}\frac{4}{3}{\alpha }_{{\rm{S}}}\le 1$$.

The flux of reduced nitrogen necessary for the production of amino acids via the photorespiratory pathway equals the sum of the fluxes of glycine and serine leaving the pathway. This flux, equal to $$\left({\alpha }_{{\rm{G}}}{\rm{+}}\frac{2}{3}{\alpha }_{{\rm{S}}}\right)\Phi {V}_{{\rm{c}}}$$, can then be estimated from gas exchange measurements. With the modifications in equations (10)–(14) this allows us to account for the de novo nitrogen assimilation related to carbon metabolism in the FvCB model (Fig. 1). In addition to affecting the electron requirement for carbon fixation, N assimilation also impacts the ATP budget. The overall ATP consumption becomes equal to $$\left(3+\left(3.5-0.5{\alpha }_{{\rm{G}}}-\frac{2}{3}{\alpha }_{{\rm{S}}}\right)\Phi \right){V}_{{\rm{c}}}$$, when glycine and serine are diverted from the photorespiratory pathway (Fig. 1).

Now that we have outlined the general model of CO2 and nitrogen assimilation, we need to parameterize it with reasonable values of α G and α S. In the absence of biochemically determined values, we can approach the nature of these parameters by setting some bounds to them. They are likely not constants, and probably vary with the rate of photorespiration and, most importantly, will be limited by the maximum rate of de novo nitrogen supply to the chloroplast (N max). N max can be limited by the nitrogen availability, the demand for nitrogen in the form of glycine and serine or by the activities of the enzymes involved in the reduction of NO3 to NH4 +. α G is likely to have an upper bound (α G max) determined by how well the export of glycine can compete with its decarboxylation via glycine decarboxylase. Analogously, we set α S max as the upper bound of how well serine export can compete with serine:glyoxylate aminotransferase, with combined bounds of α G max and α S max of $${\rm{0}}\le {\alpha }_{{\rm{G}}}^{{\rm{\max }}}{\rm{+}}\frac{4}{3}{\alpha }_{{\rm{S}}}^{{\rm{\max }}}\le 1$$. We therefore model α G and α S from N max, α G max and α S max.

Since the flux of nitrogen assimilated into glycine equals N G = α G V o and that into serine equals $${N}_{{\rm{S}}}{\rm{=}}\frac{2}{3}{\alpha }_{{\rm{S}}}{V}_{{\rm{o}}}$$ (Fig. 1), we can estimate the proportion of N being assimilated as glycine as

$$\beta =\frac{3{\alpha }_{{\rm{G}}}^{{\rm{\max }}}}{3{\alpha }_{{\rm{G}}}^{{\rm{\max }}}+2{\alpha }_{{\rm{S}}}^{{\rm{\max }}}}$$
(15)

assuming the ratio of glycine to serine export stays constant. We can then estimate α G and α S so that the following conditions are met: (1) α G and α S are always smaller than or equal to α G max and α S max, and (2) the amount of N exported as glycine and serine is not greater than N max. Under a Rubisco limitation this is the case with

$${\alpha }_{{\rm{G}}}={\rm{\min }}\left\{{\alpha }_{{\rm{G}}}^{{\rm{\max }}},\frac{{N}^{{\rm{\max }}}\beta }{{V}_{{\rm{o}}}}\right\}$$
(16)

and

$${\alpha }_{{\rm{S}}}={\rm{\min }}\left\{{\alpha }_{{\rm{S}}}^{{\rm{\max }}},\frac{3{N}^{{\rm{\max }}}\left(1-\beta \right)}{2{V}_{{\rm{o}}}}\right\}$$
(17)

(see Supplementary Information for the derivations). Under a RuBP regeneration limitation, the conditions are met with

$${\alpha }_{{\rm{G}}}=\left\{\begin{array}{l}{\rm{\min }}\left\{{\alpha }_{{\rm{G}}}^{{\rm{\max }}},\frac{4{N}^{{\rm{\max }}}\beta \left(\frac{1}{\Phi }+1\right)}{J-{N}^{{\rm{\max }}}\left(2\beta +6\right)}\right\},{\rm{if}}\,J > {N}^{{\rm{\max }}}\left(2\beta +6\right)\\ {\alpha }_{{\rm{G}}}^{{\rm{\max }}},{\rm{if}}\,J\le {N}^{{\rm{\max }}}\left(2\beta +6\right)\end{array}\right.$$
(18)

and

$${\alpha }_{{\rm{S}}}=\left\{\begin{array}{l}{\rm{\min }}\left\{{\alpha }_{{\rm{S}}}^{{\rm{\max }}},\frac{6{N}^{{\rm{\max }}}\left(1-\beta \right)\left(\frac{1}{\Phi }+1\right)}{J-{N}^{{\rm{\max }}}\left(2\beta +6\right)}\right\},{\rm{if}}\,J > {N}^{{\rm{\max }}}\left(2\beta +6\right)\\ {\alpha }_{{\rm{S}}}^{{\rm{\max }}},{\rm{if}}\,J\le {N}^{{\rm{\max }}}\left(2\beta +6\right)\end{array}\right.$$
(19)

Finally, under a TPU limitation, α G and α S are modelled as

$${\alpha }_{{\rm{G}}}={\rm{\min }}\left\{{\alpha }_{{\rm{G}}}^{{\rm{\max }}},\frac{{N}^{{\rm{\max }}}\beta \left(\frac{2}{\Phi }-1\right)}{6{T}_{{\rm{p}}}+3{N}^{{\rm{\max }}}\left(2-\beta \right)}\right\}$$
(20)

and

$${\alpha }_{{\rm{S}}}={\rm{\min }}\left\{{\alpha }_{{\rm{S}}}^{{\rm{\max }}},\frac{\frac{3}{2}{N}^{{\rm{\max }}}\left(1-\beta \right)\left(\frac{2}{\Phi }-1\right)}{6{T}_{{\rm{p}}}+3{N}^{{\rm{\max }}}\left(2-\beta \right)}\right\}$$
(21)

Equations (16)–(21) highlight that α G and α S can be described under any biochemical limitation by the addition of only three parameters (N max, α G max and α S max), replacing α old in the current use of the FvCB model. In the following results, we show how we make use of this parameterization to fit experimental data.

## Results

We estimated the carbon export from the photorespiratory pathway (α old) by measuring A in response to the intercellular CO2 concentration (C i) and fitting equation (5) over the TPU-limited range, to get an estimate of the value of α old in its previous usage17,18. The plants were then subjected to additional supply of NO3 or NH4 + and the measurements were repeated after 2 days. Both fertilization treatments resulted in increased CO2 assimilation rates at high CO2 concentrations, but did not show increased rates of A at low CO2 concentrations, which represent the Rubisco-limited range (Fig. 2a). To highlight differences in α old between the treatments, Fig. 2b displays the same curves normalized to their respective values of T P, together with the corresponding model fits for electron transport and TPU-limited CO2 assimilation rates, from which α old was calculated. In plants fertilized with NO3 , values of α old reached almost 0.6 on average, with individual values as high as 0.77 (Fig. 2b,c). In contrast, the proportion of photorespiratory carbon that is exported from the photorespiratory pathway decreased to minimal values after the addition of NH4 + (Fig. 2d). This shows that the carbon export from the photorespiratory pathway depends on the availability of NO3 , detectable as a relaxation of the TPU limitation at intercellular CO2 concentrations greater than about 500 μmol mol−1. Our results are consistent with the observation that the proportion of nitrate assimilation that occurs in the leaves rather than the roots is larger when NO3 availability is high10.

Average A/C i data from the KNO3-fertilized plants were fitted with the model developed here. Figure 3a shows the fitted curves assuming a Rubisco, RuBP-regeneration or TPU limitation and shows the fitted parameter values. The CO2 response of the fitted parameters α G, α S and the total fraction of exported photorespiratory carbon, α total, are plotted in Fig. 3b, along with the rate of nitrogen exported from the photorespiratory pathway as glycine (N G), serine (N S) and the effective total rate of N assimilation (N total). Values for α G and α S stay constant at high CO2 concentrations, where rates of photorespiration are lower than the available N-supply. At low CO2 concentrations, where rates of photorespiration are high, N max is limiting N assimilation, and α G and α S decrease with increasing photorespiratory flux (Fig. 3b). A summary of the fitting results of plants from all three treatments is given in Supplementary Figs. 1 and 2, and Supplementary Table 1. Accounting for the electrons needed for nitrate reduction generally increases calculated rates of J a (Supplementary Fig. 3).

The CO2 response of A was measured on a separate set of plants fertilized with KNO3 at ambient concentrations of O2 (21%), as well as at very low concentrations of O2 (0.2%) to minimize photorespiration and thereby minimize photorespiratory N assimilation (Fig. 3c). At CO2 concentrations above roughly ambient, A was higher under photorespiratory conditions than under non-photorespiratory conditions. At ambient concentrations of C a and below, A was only marginally higher at 0.2% than at 21% O2. The response curves at both O2 concentrations were recreated with our model using the same set of parameter values, indicated in Fig. 3c. This includes the N assimilation parameters determined in Fig. 3a.

Figure 4 demonstrates how different rates of glycine and serine export are expected to impact CO2 assimilation rates based on our modifications of the FvCB model for the light-saturated (Fig. 4a) and light-limited case (Fig. 4b). Under a Rubisco limitation, A c is increased when amino acids are exported in the form of glycine. This is due to a decrease of photorespiratory CO2 release and the associated change in Γ * by a factor of (1-α G) (see equation (12)). Under a TPU limitation, both glycine and serine export increase A p, but to different degrees. While a change in Γ * affects the shape of the curve somewhat, the majority of the increase in A p is driven by the additional assimilation of two CO2 molecules into glycine and three CO2 molecules into serine per assimilated nitrogen atom (Fig. 4a). The relative increase in A for values of α total > 0, as compared to α total = 0, is displayed in the insert for the case of α G max = 0.5, α S max = 0.4 and a mix of glycine and serine export (α G max = 0.10 and α S max = 0.35). Under these three scenarios, A is stimulated by 9, 13 and 12%, respectively, when the plant is TPU-limited. Note that the relative increase in A at CO2 concentrations below ambient can be even more substantial when glycine is exported from the photorespiratory pathway. In contrast, under light-limited conditions, A j is decreased with N assimilation, except for glycine export at very low CO2 concentrations (Fig. 4b). Since photosynthetic electron transport needs to support NO3 reduction as well as CO2 assimilation, electron transport-limited A j is decreased for any given J.

## Discussion

Traditionally, photosynthesis models consider photorespiration to be a closed pathway, in which all glycolate carbon is recycled back to RuBP. Our results demonstrate that nitrogen assimilation is integrated with photosynthetic carbon metabolism, suggesting that the metabolites glycine and serine can be diverted at significant rates from the photorespiratory pathway. In this way, photorespiration impacts nitrogen assimilation, and, conversely, nitrogen assimilation influences A. As a result, plants can increase A by assimilating carbon into amino acids in addition to carbohydrates, and by doing so photorespiratory metabolism can partially compensate for the carbon loss arising from the oxygenase reaction. The mechanistic photosynthesis model developed here takes into account the interaction between carbon and nitrogen metabolism, thereby improving the model’s predictive ability.

### Carbon export is dependent on de novo NO3− assimilation

Decreasing rates of photorespiration by increasing the CO2 concentration slows the growth of plants receiving NO3 nutrition, but not that of plants receiving NH4 + 33, indicating that photorespiratory N assimilation relies largely on NO3 instead of NH4 +. We therefore based equation (9) on the assumption that the inorganic nitrogen used in amino acid synthesis in leaves is supplied in the form of NO3 as opposed to NH4 +. This is supported by observations that the dominant source of inorganic nitrogen in the soil is often NO3 , especially in an agricultural context, and the NH4 + taken up by the plant is preferentially assimilated into organic compounds in the roots instead of being transported to the shoot26. Experiments on barley plants fertilized with either NO3 or NH4 + alone, or with a mix of both nitrogen sources, showed that NO3 is predominantly transported to and assimilated in the shoot, whereas the export of NH4 + to the shoot is marginal34. Similarly, root to shoot transport of NH4 + in maize plants is insignificant compared to NO3 35. Based on these observations one would expect α old, if linked to de novo amino acid synthesis, to be larger in plants that rely on NO3 rather than NH4 + as their nitrogen source, and the same would apply to the photosynthetic electron requirement per unit CO2 assimilated.

We tested this in sunflower plants and show that α old derived from photosynthetic gas exchange increases with the additional supply of NO3 , but not NH4 + (Fig. 2). This is consistent with the hypothesis that the α old-related decrease in CO2 assimilation observed with increasing CO2 concentrations is caused by the export of nitrogen-containing compounds from the photorespiratory pathway, and that NO3 is the nitrogen source for this export. Our assumption for equation (9) that electrons are required to reduce NO3 to NH4 + for de novo nitrogen assimilation via the photorespiratory pathway and the differential treatment of glycine and serine in equations (10)–(14) therefore appears justified.

### NO3− assimilation can increase CO2 assimilation rates

As a beneficial side effect of utilizing the photorespiratory pathway to assimilate inorganic nitrogen, plants with a large α total can increase A by about 10% above and beyond that occurring in non-photorespiratory conditions. They achieve this by supplementing the limited triose phosphate sink for carbon with an amino acid sink (Figs. 3a and 4). This increase in A is an effect that has been suggested previously17, and that we can now attribute to NO3  assimilation. The carbon benefit of photorespiratory nitrogen assimilation is substantial, with every mole of nitrogen exported as serine under a TPU limitation increasing A by 3 moles of carbon, and by 2 moles for every mole of glycine exported. Under a Rubisco limitation, serine export does not confer a carbon benefit (Fig. 4a), while glycine export involves a substantial carbon gain via lowering $${\Gamma }_{{\alpha }_{{\rm{G}}}}^{* }$$, especially at the low internal CO2 concentrations occurring when stomata are largely closed due to water stress. A decrease in the related apparent CO2 compensation point Γ was observed in barley fed with NO3 , relative to plants fed with NH4 + 36.

Under an electron transport-limited condition, nitrogen assimilation is expected to decrease A due to competition for reductant (Fig. 4b). Plants may have evolved a mechanism to circumvent this carbon-negative effect of nitrogen assimilation by controlling the flux of the malate/oxaloacetate shuttle (malate-valve)28. The malate-valve is responsible for the net transport of electrons from the chloroplast to the cytosol, where NO3 is reduced to NO2 (Fig. 1). Plants increase the flux through the malate-valve under conditions where the chloroplast stroma is highly reduced37 and therefore seem to curb photorespiratory nitrogen assimilation when photosynthesis is light limited. Further research is needed to elucidate how amino acid export changes with environmental conditions.

### Stresses leading to high photorespiratory rates are mitigated

In our experiments, the model indicates that about 2–9% of the glycolate carbon was exported from the photorespiratory pathway as glycine, depending on CO2 concentration (Fig. 3b). These numbers are similar to recent quantitative isotopic measurements in Helianthus annuus, for which the proportion of glycine exported from the photorespiratory pool was estimated to be of the order of 1–5%38. We found that the proportion of carbon exported from the photorespiratory pathway as glycine was dwarfed by the proportion of carbon exported as serine, which the model indicates was up to 38% when plants were TPU-limited (Fig. 3b). This reflects the high demand for serine due to the fundamental role it has in many aspects of plant metabolism, such as the one-carbon metabolism and as precursor for several other amino acids, such as cysteine and tryptophan, as well as phospholipids7. Our estimates also agree well with experimental evidence from metabolome kinetics, indicating that at ambient O2 concentrations in the order of 30% of the photorespiratory serine is not metabolized by serine:glyoxylate aminotransferase, but used elsewhere38.

Under drought stress, when stomata are almost closed, amino acids produced via the photorespiratory pathway can be used for the production of glycine- and serine-rich dehydrins39, which help the plant protect itself from desiccation40. Glycine is also used for the synthesis of glycine betaine, a small molecule involved in increasing stress tolerance in plants41. Further, glycine and cysteine are precursors for the production of glutathione, an important antioxidant that prevents damage from reactive oxygen species42. Glycine and serine produced under conditions of high rates of photorespiration, a consequence of stomatal closure as caused by drought or heat stress, are therefore important for the synthesis of compounds that help to alleviate this stress. In water-stressed leaves of Glycine max, almost all the photorespiratory carbon can end up in peptides and proteins in low CO2 conditions24. In contrast, when leaves are exposed to high CO2 concentrations, or notably when plants are nitrogen-starved, the photorespiratory carbon is largely returned to the Calvin–Benson cycle24.

Increasing the carbon uptake via a short-circuiting of carbon flux to amino acids should become especially important in plants growing under a TPU limitation, such as at low temperatures16. This increase in A should also be beneficial under future CO2 scenarios, under which plants are more likely to be TPU-limited. Plants supplied with excess NH4 +, where nitrogen is assimilated in the roots leaving no trace in leaf gas exchange, do not show the same stimulation of CO2 uptake (indicated by α old values close to zero; Fig. 2b). These plants seem to either decrease their NO3 uptake, or are supplied with enough amino acids from the roots that their production via the photorespiratory pathway is suppressed.

### New model improves predictions of electron transport rates

The addition of nitrogen assimilation as described here addresses an inconsistency within the FvCB model as modified by Harley and Sharkey17. That modified model attributes the decline in A under decreasing rates of photorespiration to decreased amino acid export from the photorespiratory pathway, but currently only includes the carbon associated with the amino acid export, and omits the nitrogen- and therefore electron-requirement17. The model presented here accounts for the electron requirement (Supplementary Fig. 3), and thereby also contributes to our understanding of how carbon and nitrogen metabolism interact. Here, we show that α G and α S, and hence Γ * and amino acid export, are not constants, but change with NO3 availability (Fig. 2) and Rubisco oxygenation rate (Fig. 3).

Nitrogen assimilation is a major contributor to the often-observed gap between J f measured by chlorophyll fluorescence and J a calculated from gas exchange measurements43. While it is likely that photosynthetic electrons are used to reduce NO3 destined for non-photorespiratory amino acid production, accounting for the electrons used for photorespiratory amino acid production is important when other parameters, such as mesophyll conductance, are estimated from the comparison of the two measures of J 44. Being mindful of nitrogen assimilation when estimating CO2 assimilation rates from chlorophyll fluorescence measurements is especially important when values of α G and α S are expected to be high and a significant portion of photosynthetic electron transport is used for NO3 reduction. The model proposed here should prove useful for quantifying nitrogen assimilation in the shoot in vivo by comparing gas exchange and chlorophyll fluorescence measurements.

In controlled laboratory experiments, as well as free-air CO2 enrichment experiments, it is frequently observed that nitrogen content in plants grown at elevated CO2 concentrations declines6. Combining data from several free-air CO2 enrichment experiments, it was recently shown that this reduction in plant nitrogen content was not primarily related to a dilution by increased CO2 uptake, but to reductions in plant nitrogen assimilation at elevated CO2 concentrations45. This likely affects the productivity of natural ecosystems, as they are often N-limited, and incorporating N assimilation into the FvCB model may help to improve our predictions of how plants and ecosystems will behave under future CO2 conditions. It could also improve our understanding of the behaviour of annual crops at elevated CO2 concentrations, since these cultivated ecosystems are often supplied with large amounts of nitrate and therefore are likely to exhibit large rates of photorespiratory N assimilation.

## Conclusion

Here, we show that the counterintuitive response of CO2 assimilation to changes in photorespiration at high CO2 concentrations is related to de novo N assimilation. While photorespiration is often considered a wasteful side reaction that needs to be decreased to boost crop yields, our results emphasize several of its beneficial features that may have decreased somewhat the evolutionary pressure to eliminate the oxygenation reaction of Rubisco:

1. (1)

The proportion of photorespiratory carbon that is used for de novo amino acid synthesis increases with increasing NO3 availability. This indicates that the high rates of photorespiration enable C3 plants to efficiently take up transiently available nitrogen, and assimilate it into organic compounds at high rates. This can be a valuable advantage for plants growing in a competitive environment.

2. (2)

Under a TPU limitation, when electrons are available in excess and carbon uptake is limited by the rate at which carbohydrates can be metabolized, total net CO2 uptake can be further increased via the short-circuiting of carbon flux to glycine and serine through the photorespiratory pathway. Similarly, under a Rubisco limitation the export of photorespiratory glycine can increase CO2 uptake at low CO2 concentrations via decreasing the rate of glycine decarboxylation.

3. (3)

The reduction of NO3 to NH4 + associated with photorespiratory nitrogen assimilation provides a beneficial sink for excess electrons and helps balance the ATP:NADPH budget46.

4. (4)

The high rates of photorespiration observed under a Rubisco limitation can provide a large flux of metabolites necessary to sustain high rates of N assimilation. When nitrogen becomes available, it can therefore be assimilated readily and without the need for large metabolic adjustments.

## Methods

### Plant material

Sunflower (H. annuus L.) plants were grown in glasshouse conditions in 5 l pots filled with Martins Potting Mix (Martins Fertilizers, Yass, NSW, Australia) and an initial addition of 10 g of slow-release Osmocote fertilizer (Scotts Australia, Bella Vista, NSW, Australia). Plants were watered once or twice daily, depending on water demand. Photosynthetic CO2 response curves were measured on the youngest fully expanded leaf of 8-week-old plants (control). The plants were subsequently treated with 0.5 l per day of 25 mM KNO3 or 12.5 mM (NH4)2SO4 for 2 days, after which the measurements of the photosynthetic CO2 response were repeated in the same place on the same leaves. There were no trends in gas exchange parameters of the control measurements with progression of the experiment, indicating that developmental effects during the experiment were negligible.

### Gas exchange measurements

Photosynthetic gas exchange was measured with an LI-6400XT (LICOR Biosciences) at a leaf temperature of 25 °C and a light intensity of 2000 μmol m−2 s−1. For the A/C i curves the sequence of reference CO2 concentrations was 400, 300, 200, (150), 100, (75), 50, 400, 400, 500, 600, 700, 800, 900, 1,000, 1,200, 1,400, 1,600, 1,800 and 2,000 μmol mol−1. The second measurement at 400 μmol mol−1 was excluded from the analysis due to extra time needed to reach steady-state changing from 50 to 400 μmol mol−1 CO2. The measurements were corrected for potential diffusion leaks as outlined in the LI-6400XT manual. For Fig. 2, photosynthetic parameters, including T P, R d and α old, were estimated from the measured A/C i curves with an Excel fitting tool47, where we substituted the TPU-limited model, which does not parameterize α old, with equation (8). For Fig. 3, we fitted our photosynthesis model including N assimilation (equations (10)–(21)) to the measured data using the solver tool in Excel.

### Statistical analysis

Statistical analysis was carried out using a two-sided Student’s t-test to determine the treatment effects on values of α old. A one-sample t-test was used to assess the fold-change of α old due to the treatment, relative to the normalized value of α old of the control treatment.

### Life Sciences Reporting Summary

Further information on experimental design is available in the Life Sciences Reporting Summary.

### Data availability

The data that support the findings of this study are available from the corresponding author upon reasonable request.

Publisher’s note: Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

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## Acknowledgements

We thank M. Holloway-Phillips for assistance with growing the plants. This work was supported by the ARC Centre of Excellence for Translational Photosynthesis and by the Australian Science Industry and Endowment Fund (SIEF grant RP04-122). R.F.S. was supported by Discovery grants 154273-2007 and 154273-2012 from the Natural Science and Engineering Research Council (NSERC) of Canada.

## Author information

### Affiliations

1. #### Research School of Biology and ARC Centre of Excellence for Translational Photosynthesis, Australian National University, Acton, Australian Capital Territory, Australia

• Florian A. Busch
•  & Graham D. Farquhar
2. #### Department of Ecology and Evolutionary Biology, University of Toronto, Toronto, Ontario, Canada

• Rowan F. Sage

### Contributions

F.A.B. conceived the study and undertook the experimental work, with input from R.F.S. F.A.B. and G.D.F. carried out the modelling. F.A.B. wrote the manuscript with help from all authors.

### Competing interests

The authors declare no competing financial interests.

### Corresponding author

Correspondence to Florian A. Busch.

## Supplementary information

1. ### Supplementary Information

A description of the derivation of expressions for α G and α S, Supplementary Figures 1–4. Supplementary Table 1.