A cyanobacterial photorespiratory bypass model to enhance photosynthesis by rerouting photorespiratory pathway in C3 plants

Plants employ photosynthesis to produce sugars for supporting their growth. During photosynthesis, an enzyme Ribulose 1,5 bisphosphate carboxylase/oxygenase (Rubisco) combines its substrate Ribulose 1,5 bisphosphate (RuBP) with CO2 to produce phosphoglycerate (PGA). Alongside, Rubisco also takes up O2 and produce 2-phosphoglycolate (2-PG), a toxic compound broken down into PGA through photorespiration. Photorespiration is not only a resource-demanding process but also results in CO2 loss which affects photosynthetic efficiency in C3 plants. Here, we propose to circumvent photorespiration by adopting the cyanobacterial glycolate decarboxylation pathway into C3 plants. For that, we have integrated the cyanobacterial glycolate decarboxylation pathway into a kinetic model of C3 photosynthetic pathway to evaluate its impact on photosynthesis and photorespiration. Our results show that the cyanobacterial glycolate decarboxylation bypass model exhibits a 10% increase in net photosynthetic rate (A) in comparison with C3 model. Moreover, an increased supply of intercellular CO2 (Ci) from the bypass resulted in a 54.8% increase in PGA while reducing photorespiratory intermediates including glycolate (− 49%) and serine (− 32%). The bypass model, at default conditions, also elucidated a decline in phosphate-based metabolites including RuBP (− 61.3%). The C3 model at elevated level of inorganic phosphate (Pi), exhibited a significant change in RuBP (+ 355%) and PGA (− 98%) which is attributable to the low availability of Ci. Whereas, at elevated Pi, the bypass model exhibited an increase of 73.1% and 33.9% in PGA and RuBP, respectively. Therefore, we deduce a synergistic effect of elevation in CO2 and Pi pool on photosynthesis. We also evaluated the integrative action of CO2, Pi, and Rubisco carboxylation activity (Vcmax) on A and observed that their simultaneous increase raised A by 26%, in the bypass model. Taken together, the study potentiates engineering of cyanobacterial decarboxylation pathway in C3 plants to bypass photorespiration thereby increasing the overall efficiency of photosynthesis.


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| (2020) 10:20879 | https://doi.org/10.1038/s41598-020-77894-2 www.nature.com/scientificreports/ RuBP produces one molecule each of 2-phosphoglycolate (PG, 2 carbon compound) and PGA 6,7 . PG is a toxic compound which inhibits the activities of Calvin cycle enzymes such as Rubisco and triose phosphate isomerase 8 and needs to be metabolized. Plants have evolved photorespiration as a mechanism to metabolize PG into PGA by a series of enzymatic reactions that take place in the peroxisomes, mitochondria and chloroplasts 5,9,10 . During photorespiration, hydrogen peroxide (H 2 O 2 ) and ammonia (NH 3 ) are also produced along with the loss of one molecule of fixed CO 2 from mitochondria 10,11 . The loss of fixed carbon molecules along with re-assimilation of NH 3 and detoxification of H 2 O 2 renders photorespiration a high-energy demand process 5 . Furthermore, with an increase in temperature, Rubisco's specificity for O 2 increases in comparison with that of CO 2 which enhances oxygenation reaction thus adding to the cost of photorespiration 4,12 . Though photorespiration is crucial for metabolizing PG, it increases the cost of carbon fixation in photosynthesis by up to 50% 4,13 . These losses are more prevalent in C 3 plants which lack the CO 2 concentrating mechanism (CCM) to increase the supply of CO 2 in the vicinity of Rubisco to suppress photorespiration 14 . This makes photorespiration an important target for modification in the C 3 plants, to avoid carbon loss and conserve energy towards improvement of photosynthesis.
To achieve this goal, various attempts have been made to either downregulate the genes involved in photorespiratory pathway or decrease the oxygenation reaction of Rubisco 5,11 . Initial efforts in this regard aimed to identify genes that code photorespiratory enzymes such as phosphoglycolate phosphatase in Arabidopsis thaliana 15,16 . The resultant photorespiratory mutants, however, exhibited stunted growth, chlorosis and poor performance under ambient conditions due to the accumulation of photorespiratory pathway intermediates 15,16 . Chemical inhibition of glycolate oxidase (GO) activity in soybean resulted in a significant reduction of starch levels which suggested that metabolism of photorespiratory intermediates is essential to recycle carbon into Calvin cycle 17 . Efforts were also made to reduce oxygenation reaction by modifying enzymatic properties of Rubisco as well as engineering foreign Rubisco in plants 18,19 . Cyanobacterial Rubisco with associated chaperons was engineered in tobacco plants and the transgenic lines exhibited successful assembly of cyanobacterial Rubisco within plant chloroplast 20 . Later on, successful assembly of functional cyanobacterial Rubisco without associated proteins was also reported in tobacco 21 . In both studies, transgenic plants showed autotrophic growth, albeit at elevated CO 2 , owing to the very nature of cyanobacterial Rubisco 20,21 . However, these findings necessitate the introduction of CO 2 concentrating mechanism (CCM) along with cyanobacterial Rubisco, to concentrate CO 2 around Rubisco for improving photosynthesis. The limited success in abolishment of photorespiration by mutating photorespiratory pathway enzymes or Rubisco oxygenation reaction indicated that photorespiration is inevitable in C 3 plants. This led to employment of PG metabolism rerouting strategies in order to minimize photorespiration losses 11 . The first report of photorespiratory bypass involved introduction of complete E. coli glycerate pathway into the chloroplast of Arabidopsis 22 . This bypass catabolized the glycolate (GCA, immediate product of PG) into glyoxylate (GOA), tartronic semi-aldehyde (TSA) and glycerate (GCEA) 22 . The resultant transgenic plants exhibited enhanced photosynthesis due to liberation of CO 2 by the bypass in chloroplast. Later on, Maier et al. (2012) also reported the catabolism of GCA in chloroplast by using plant glycolate oxidase (GO), malate synthase (MS) and bacterial catalase (CAT) 23 . The release of CO 2 in chloroplast enhanced the rate of carboxylation which led to improvement in photosynthetic rates 23 24 to catabolize GCA. Additionally, glycolate flux was maximized towards the bypass by blocking glycolate-glycerate transporter through RNA interference (RNAi) 24 . The transgenic plants containing algal glycolate dehydrogenase exhibited enhanced photosynthetic rates, which was further increased by modulation of glycolate-glycerate transporter with RNAi 24 . Interestingly, Cyanobacteria also possesses three photorespiratory pathways i.e. plant like, E. coli like glycerate and unique glycolate decarboxylation pathway, which employ glycolate dehydrogenase (GDH) to catabolize GCA 25,26 . The glycolate decarboxylation pathway comprises of glycolate dehydrogenase (GDH), hydroxyacid dehydrogenase (HDH), oxalate decarboxylase (ODC), and formate dehydrogenase (FDH) for complete decarboxylation of GCA 25 . GDH catabolizes GCA into glyoxylate which is then catalyzed by HDH into oxalate, ODC catabolizes oxalate into formate and releases one molecules of CO 2 . Eventually, Formate is catalyzed by FDH and releases a second molecule of CO 2 25 . Note that just like the modified Maier et al.'s bypass, cyanobacterial glycolate decarboxylation pathway also yields two molecule of CO 2 as a result of GCA catabolism 24,25 . Transformation of individual genes of cyanobacterial glycerate and glycolate decarboxylation pathways in chloroplast of potato and Arabidopsis catabolized GCA and exhibited promising results 8,27 .
Alongside these efforts, synthetic biology approaches have become invaluable in investigating dynamical behavior of metabolic networks towards improving photosynthesis 28 . Several such kinetic models have been developed to evaluate the impact of environmental conditions on photosynthesis, distribution of plant resources to improve photosynthesis, and explore different conditions which can influence photosynthetic processes to improve plant productivity [29][30][31][32][33] 22,23,33 . Mathematical modelling of cyanobacterial glycolate decarboxylation pathway can, therefore, assist in systematic evaluation of its impact on photosynthetic processes. Such a model can provide invaluable assistance in development of a comprehensive strategy for genetic engineering of cyanobacterial decarboxylation pathway in C 3 plants.
In this work, we report a novel kinetic model of cyanobacterial photorespiratory bypass by integrating cyanobacterial glycolate decarboxylation and C 3 photosynthetic pathways 25,34 and evaluate its synergistic effect on photosynthesis and photorespiration. Our results showed that the proposed cyanobacterial photorespiratory bypass successfully diverts the photorespiratory flux into the chloroplast by catabolizing GCA which resulted in production of two molecules of CO 2 . Increased availability of intercellular CO 2 (C i ) resulted in an increased www.nature.com/scientificreports/ rate of carboxylation besides reducing the level of photorespiratory pathway intermediates and phosphate based metabolites in Calvin cycle. Furthermore, an elevation of inorganic phosphate (Pi) pool augmented the level of phosphate based metabolites. Lastly, an increase in intercellular CO 2 (C i ) was observed to significantly enhance the net photosynthetic rate (A). Taken together, our findings suggest that integration of cyanobacterial photorespiratory bypass can significantly enhance the overall rate of photosynthesis in C 3 plants. We report that an optimal distribution of Pi is critical in maintenance of energy supply to Calvin cycle for regenerating RuBP and has a synergistic effect on photosynthesis. In conclusion, this study highlights the potential of engineering cyanobacterial decarboxylation pathway into C 3 plants to enhance photosynthetic rates leading to better crop yields.

Results
Integration of the cyanobacterial decarboxylation bypass into C 3 photosynthetic pathway catabolizes glycolate (GCA) and produces CO 2 in chloroplast. We integrated the cyanobacterial glycolate decarboxylation bypass 25 into a literature-based C 3 model 34 that comprised of Calvin cycle, photorespiratory and sucrose pathways, towards catabolizing GCA (Fig. 1). For that, kinetic parameters of 4 enzymes including glycolate dehydrogenase (GDH), hydroxyacid dehydrogenase (HDH), oxalate decarboxylase (ODC) and formate dehydrogenase (FDH) were obtained from the literature [35][36][37][38][39][40] . Next, these parameters were tuned until the cyanobacterial photorespiratory bypass model (termed onward as 'bypass model') attained steady state. At steady state, the enzyme maximum capacity (V max ) for GDH, HDH, ODC and FDH were 0.12 mmol l −1 s −1 , 0.06 mmol l −1 s −1 , 0.03 mmol l −1 s −1 and 0.015 mmol l −1 s −1 , respectively. The bypass model catabolized GCA in the chloroplast and released two molecules of CO 2 for onward uptake by Rubisco for carboxylation. GCA concentration was observed to decrease to 0.027 mmol l −1 in the bypass model against 0.0518 mmol l −1 of the C 3 model ( Fig. 2A) and 25.13 mmol l −1 of CO 2 were produced by the bypass model (Fig. 2B). GCA production was regulated dynamically by the availability of substrates i.e. RUBP and O 2 . Moreover, no condition was set on oxygenation reaction in the bypass model. CO 2 production from the bypass depends upon GCA availability to the bypass enzymes which produces two molecules of CO 2 per GCA. Next, to validate the integration of decarboxylation bypass in the C 3 model, we varied the concentration of intercellular CO 2 (C i = 0.009 mmol l −1 ) while maintaining level of O 2 . CO 2 production from the bypass model decreased in comparison with the original concentration of 25.13 mmol l −1 which was observed using default conditions. Specifically, CO 2 fell by 51%, 81% and 85.4% as C i levels increased to 0.05 mmol l −1 , 0.15 mmol l −1 , and 0.2 mmol l −1 , respectively (Fig. 2B). www.nature.com/scientificreports/ The decrease in the production of CO 2 by the bypass corresponds to the low availability of GCA (catabolized by GDH) coupled with low rate of photorespiration due to an increase in concentration of C i . This result is in line with the published studies which report a reduced photorespiration rate followed by the decline in the production of photorespiratory pathway intermediates due to an increased concentration of C i 24,41,42 . Next, we evaluated model sensitivity to variability in V max of GDH, ODC, and FDH enzymes while maintaining default conditions of C 3 model. At V maxGDH = 0, bypass shutdown was observed with no CO 2 production while GCA attained the steady state concentration reported in the C 3 model (Fig. 2C). Modulation of V maxODC and V maxFDH level to 10%, 50% and 100%, while maintaining V maxGDH at 0.12 mmol l −1 s −1 , resulted in a corresponding decrease of CO 2 production by 90.4%, 98.1% and 99% in the bypass (Fig. 2D). These results showed that the bypass model successfully catabolized GCA and exhibited sensitivity to the model parameters, enzyme capacities of bypass enzymes, and concentration of C i. Photorespiratory bypass enhances the rate of carboxylation by diverting the photorespiratory flux to the chloroplast. Following the integration of cyanobacterial photorespiratory bypass into C 3 model, we set out to evaluate its impact on photorespiratory and Calvin cycle intermediates along with rate of carboxylation. For that, the initial metabolite concentrations set in C 3 model, were used and the model was run over time to steady state. Next, metabolite concentrations at steady state were compared with those reported in the C 3 model. Serine (SER), a determinant of photorespiratory flux downstream of chloroplast 22 , was observed to decrease to 8.75 mmol l −1 in the bypass model in comparison with 14.33 mmol l −1 of the C 3 model (Fig. 3A). Alongside, a reduction in photorespiratory flux was observed in the bypass model as glycerate (GCEA) concentration dropped from 0.72 to 0.43 mmol l −1 (Fig. 3A). Phosphoglycerate (PGA), a product of carboxylation (C,D) Model sensitivity to variation in enzyme capacity (V max ) of GDH, ODC and FDH over time. V maxGDH was set at '0' to shut down the bypass. V maxODC and V maxFDH were decreased by 10%, 50% and 100% of their respective steady state enzyme capacities (0.03 mmol l −1 s −1 and 0.015 mmol l −1 s −1 ). (C) GCA attained the steady state concentration reported in the C 3 model and no CO 2 production was observed in the bypass model, and (D) CO 2 produced with no perturbation of steady state V maxODC and V maxFDH , 10%, 50% and 100% decrease of V maxODC and V maxFDH .

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| (2020) 10:20879 | https://doi.org/10.1038/s41598-020-77894-2 www.nature.com/scientificreports/ reaction in the Calvin cycle, was observed to increase to 9.96 mmol l −1 in the bypass model in comparison with 6.43 mmol l −1 of the C 3 model (Fig. 3B). A concomitant reduction in the concentration of substrate (RuBP) for carboxylation reaction, was observed as its concentration dropped to 0.56 mmol l −1 from 1.45 mmol l −1 (Fig. 3B). Adenosine triphosphate (ATP), which is involved in energy consuming reactions in the Calvin cycle, decreased to 0.11 mmol l −1 from 0.14 mmol l −1 while adenosine diphosphate (ADP) increased to 1.38 mmol l −1 from 1.35 mmol l −1 of the C 3 model (Fig. 3C). Inorganic phosphate (Pi), a major contributor in the reactions of the phosphate based metabolites in chloroplast, was observed to decrease to 0.057 mmol l −1 from 0.084 mmol l −1 (Fig. 3D). Reduction in the concentration of triose phosphate (TP), a precursor of starch and sucrose synthesis pathway, was also observed to drop to a level of 2.08 mmol l −1 in comparison with 3.02 mmol l −1 (Fig. 3D). Fructose 1,6 bisphosphate (FBP) involved in the starch synthesis, was observed to decrease to 0.016 mmol l −1 from 0.028 mmol l −1 while fructose 6, phosphate (F6P) concentration level was dropped to 0.076 mmol l −1 from 0.119 mmol l −1 (Fig. 3E). Sedoheptulose 1,7 bisphosphate (SBP), which is involved in the RuBP regeneration, decreased to 0.09 mmol l −1 from 0.33 mmol l −1 while sedoheptulose 7 phosphate (S7P) concentration level increased to 0.52 mmol l −1 from 0.47 mmol l −1 of the C 3 model (Fig. 3F). Hence, the integration of the photorespiratory bypass diverted the normal C 3 photorespiratory pathway flux to chloroplast and utilized the GCA to  43 . Furthermore, simultaneous elevation of CO 2 and Pi has also been reported previously in a free air CO 2 enrichment (FACE) study which demonstrated an enhancement in the total plant biomass and phosphate (P) content in chick pea and field pea plants 44 . Therefore, to evaluate the coordinated action of enhanced supply of C i by the bypass with elevated Pi, we increased the total Pi concentration (15 mmol l −1 ) by 70% 45 in both C 3 and bypass models and simulated each model to steady state. PGA, the immediate product of carboxylation reaction, increased to 17.25 mmol l −1 in the bypass model while for the C 3 model, its concentration dropped to 0.089 mmol l −1 (Fig. 4A). Alongside, RuBP concentration was observed to increase to 0.75 mmol l −1 and 6.6 mmol l −1 for the two models (Fig. 4A). Pentose phosphate (PeP), pentose sugar molecule complex involved in the regeneration of RuBP, was observed to increase to 0.89 mmol l −1 in the bypass model while in the C 3 model its concentration dropped to 0.48 mmol l −1 (Fig. 4B). Hexose phosphate (HeP) involved in the starch synthesis was observed to increase www.nature.com/scientificreports/ in both bypass and C 3 models to 0.45 mmol l −1 and 0.92 mmol l −1 , respectively (Fig. 4B). ATP concentration increased to 0.136 mmol l −1 and 0.55 mmol l −1 whereas ADP level dropped to 1.36 mmol l −1 and 0.94 mmol l −1 in the bypass and C 3 models, respectively (Fig. 4C). This increase in ATP indicated that Pi regulates energy supply by photophosphorylation of ADP during photosynthesis. TP was observed to increase to 2.8 mmol l −1 and 4.04 mmol l −1 in the bypass and C 3 models, respectively (Fig. 4D). With increasing total Pi concentration pool and its subsequent incorporation into phosphate metabolites, the Pi concentration was also observed to increase to 0.074 mmol l −1 in the bypass model and 0.2 mmol l −1 in the C 3 model (Fig. 4D). An increasing trend was observed in FBP and F6P, FBP and F6P concentration was observed to increase to 0.026 mmol l −1 and 0.13 mmol l −1 in the bypass model while 0.049 mmol l −1 and 0.27 mmol l −1 in the C 3 model, respectively (Fig. 4E). SBP concentration was observed to increase to 0.21 mmol l −1 and 2.11 mmol l −1 in the bypass and C 3 models, respectively (Fig. 4F). The overall increase in the concentration of phosphate based metabolites indicates that Pi content augments the production of these metabolites during carbon metabolism. At elevated Pi, S7P concentration increased to 1.21 mmol l −1 in the bypass model, however it decreased to 0.3 mmol l −1 from 0.47 mmol l −1 (Pi = 15 mmol l −1 ) in the C 3 model (Fig. 4F). A previous FACE study that also evaluated augmented phosphate (P) supply, reported an increase in total root, shoot biomass and phosphate contents, which is indicative of a synergistic action of CO 2 and Pi on plant metabolome 44 . Furthermore, in a non-FACE study, elevation of P along with elevated CO 2 resulted in an enhanced photosynthetic rate and plant biomass accumulation 46 . In line with these reported studies, results from our bypass model indicate that increasing the total pool of Pi together with an increased availability of C i by the cyanobacterial glycolate decarboxylation pathway improves the rate of carboxylation. Additionally, an increased rate of carboxylation utilized excessive phosphate based metabolites, thus increasing the consumption of Pi which concomitantly affects phosphate based metabolites pool.

Augmented supply of CO 2 by cyanobacterial photorespiratory bypass enhances the net photosynthetic rate (A).
Having observed that an increased supply of intercellular CO 2 (C i ) from the bypass and elevated level of Pi (25 mmol l −1 ) resulted in an enhanced rate of carboxylation in the vicinity of Rubisco, we set out to determine the resultant effect of CO 2 , Pi and carboxylation rate on the net photosynthetic rate (A). For that, we used the default conditions set in the C 3 model and measured the enhancement in A after the integration of photorespiratory bypass into the C 3 pathway. A 10% increase was observed in A for the bypass model as  Having observed an increase in A at elevated levels of Rubisco V cmax (+ 100%) and Pi (25 mmol l −1 ) in tandem, we set out to evaluate the simultaneous effect of perturbations in Pi and Rubisco V cmax on A. For that, the model was run to steady state for each C i (20-67 Pa), together with elevated levels of Pi (25 mmol l −1 ) and Rubisco V cmax (+ 100%). The bypass model exhibited an increase of 17.36 µmol m −2 s −1 at 20 Pa (Fig. 5B), while in the C 3 model, A increased from 12.80 µmol m −2 s −1 at 20 Pa to 16.84 µmol m −2 s −1 at 67 Pa (Fig. 5B). Taken together, our results indicate that higher quantities of CO 2 produced by the bypass enhanced A which was further amplified by increasing the level of Pi and Rubisco carboxylation velocity (V cmax ).

Discussion
Photorespiratory bypasses engineered into C 3 plants have resulted in enhancement of photosynthetic rates and plant productivity 11,24,47 . Cyanobacterial glycolate decarboxylation pathway, which employs single gene coded glycolate dehydrogenase (GDH) to catabolize GCA 25,26,48 has become an attractive target for bypassing photorespiration in C 3 plants. Engineering of cyanobacterial GDH in C 3 plants has also resulted in enhanced biomass production 8,27 . Therefore, a systematic evaluation of cyanobacterial decarboxylation pathway using systems biology approach can help to further elucidate its potential in improvement of photosynthesis. In this work, we have investigated the impact of engineering cyanobacterial glycolate decarboxylation pathway on photosynthesis and photorespiration in C 3 plants through mathematical model. Towards this goal, we have integrated cyanobacterial decarboxylation pathway into literature based model of C 3 photosynthetic pathway and developed a kinetic model of cyanobacterial photorespiratory bypass (Fig. 1). Our model exhibited an enhanced rate of carboxylation due to an increased level of intercellular CO 2 (C i ) and a concomitant decline in level of photorespiratory pathway intermediates ( Figs. 2A,B, 3A,B). Despite the enhanced rate of carboxylation, a decline in concentration of phosphate based metabolites within the Calvin cycle was observed (Fig. 3C-F). We further identified inorganic phosphate (Pi) pool as a key limiting factor of Calvin cycle and reported the coordinated action of elevated CO 2 and Pi pool in enhancement of carboxylation rate and phosphate based metabolites (Fig. 4). Lastly, we also demonstrated enhancement in net photosynthetic rate A at elevated levels of CO 2 , Pi and Rubisco maximum carboxylation capacity (V cmax ) (Fig. 5).
Cyanobacterial glycolate decarboxylation pathway first reported by Eisenhut et al. (2008) in a mutagenic study, completely detoxifies GCA utilizing GDH, and yields two molecules of CO 2 in chloroplast 25,48  . However, it would be interesting to evaluate the synergistic effect of blocking glycolate-glycerate transporter along with cyanobacterial glycolate decarboxylation pathway, on photosynthesis and metabolic intermediates.
Previous studies reported that integration of photorespiratory bypass enhances the rate of carboxylation due to higher concentration of C i in the vicinity of Rubisco and reduction in levels of photorespiratory intermediates [22][23][24]27,56 . Our model also exhibited an enhanced rate of carboxylation which resulted in an increase in levels of phosphoglycerate (PGA) and a concomitant decrease in Ribulose 1,5 bisphosphate (RuBP) concentration (Fig. 3B). Moreover, a decline in GCA (− 49%) was observed in chloroplast, which confirms its catabolism by decarboxylation pathway to yield CO 2 ( Fig. 2A,B). In agreement with experimental studies [22][23][24]56 , serine (SER), a key determinant of photorespiratory pathway 57,58 and glycerate (GCEA) was also observed to decrease due to diversion of normal photorespiratory flux into chloroplast (Fig. 3A). It is pertinent to note that in the C 3 model, GCA flux from chloroplast to cytosol is regulated through kinetics of glycolate-glycerate transporter 32,34 . In case of the bypass model, the kinetics of transporter was maintained to allow the GCA flux from chloroplast into cytosol like normal photorespiratory pathway, which also provided an opportunity to evaluate the catabolism of GCA by the bypass enzymes dynamically.

Scientific Reports
| (2020) 10:20879 | https://doi.org/10.1038/s41598-020-77894-2 www.nature.com/scientificreports/ The decline observed in levels of phosphate based metabolites, which stands in contradiction to experimental observations 22,23,56 suggests an enhanced demand of Pi to keep the photosynthetic apparatus functional (Fig. 3C-F) as reported in the literature 59 . It is important to note that a decline in Pi acts to impair the photophosphorylation of ADP, which affects the ATP production thereby altering the level of phosphorylated sugars in the Calvin cycle and limiting the RuBP regeneration 46,60,61 . Under natural conditions, elevated level of CO 2 and Pi deficiency coexist, which may reduce photosynthesis indicating an increased sensitivity of plants to phosphate stress 46 . Zheng et al. (2019) also reported that plants may respond adversely to elevated levels of CO 2 and observe downregulation in photosynthesis due to nutrient unavailability 62 . These reports support our results and suggest that nutrient availability and carbon feedback mechanism both play an important role in positively regulating photosynthesis 46,63,64 .
The coordinated action of elevated level of Pi and CO 2 in stimulating photosynthetic efficiency has been observed in free air CO 2 enrichment (FACE) experiment conducted on legume plants 44 . Jin et al. (2012) reported that simultaneous elevation in CO 2 and Pi resulted in improved P content and plant growth in chick pea and field pea 44 . At elevated level of Pi, our model exhibited an enhancement in phosphate based metabolites and A (Figs. 4, 5B) which conforms with the findings from the FACE experiment at elevated level of Pi 44 . In a non-FACE study, Singh et al. (2013) also reported enhancement in photosynthesis in cotton plants at elevated level of CO 2 and P 46 . Interestingly, our model also exhibited an increase in sedoheptulose 7 phosphate (S7P) at both ambient and elevated level of Pi (Figs. 3F, 4F). Dephosphorylation rate of sedoheptulose 1,7 bisphosphate (SBP) via SBPase, to yield S7P, is regulated according to demand of S7P to regenerate RuBP 65 . RuBP regeneration is critical in maintaining functioning of Calvin cycle and avoid depletion of metabolites 66 . Higher levels of S7P can be attributed to an enhanced demand of RuBP regeneration for sustaining an increased rate of carboxylation. On the other hand, in the C 3 model, an increase in RuBP content and a concomitant decline in S7P was observed at elevated Pi (Fig. 4A,F), which suggests a reduced utilization of RuBP owing to low availability of C i . Nonetheless, further investigation is required to elucidate the impact of elevated levels of Pi on S7P and other metabolites.
Our model exhibited an enhanced A after the integration of bypass which conforms to the previous studies [22][23][24]56 . However, our results show a 10% increase in A (Fig. 5A) 24 . Also in terms of plant productivity, no change was observed with Maier et al. 's bypass, both with and without RNAi 24 .
We also evaluated the response of A under different concentrations of C i which corresponds to expected levels of atmospheric CO 2 (C a ) (Fig. 5B). In our model, the integration of bypass led to augmentation of the C i pool in chloroplast which led to a rapid increase in A at 20 Pa (Fig. 5B). No change was observed with a further increase in C i (27 Pa to 67 Pa) (Fig. 5B). The rapid rise and ensuing steady state of A can be explained by the FvCB model reported by Farquhar et al. 29 . The FvCB model hypothesized that the rate of photosynthesis can be limited either by Rubisco or by RuBP regeneration 29,67 . Rubsico-limited photosynthetic state exists when CO 2 concentration is low and RuBP-regeneration limited state emerges at higher levels of CO 2 due to an enhanced rate of carboxylation 68 . Bernacchi et al. (2013) also reported that A increases with an increase in C i until it reaches a point of inflection beyond which a further increase in C i may not enhance A due to limited RuBP regeneration 69 . Busch et al. (2017) reported that RuBP regeneration limited A at CO 2 levels between 380 ppm (38 Pa) to 1000 ppm (100 Pa) 70 . This could be a possible explanation for the initial increase in A due to CO 2 enrichment in our model which steadies beyond 20 Pa. On the other hand, in the C 3 model, A gradually increased with increment in C i concentration (Fig. 5B).
Rubisco V cmax is an important kinetic parameter that regulates photosynthesis and determines the rate of carboxylation 64,71 . Our model hypothesizes that an elevation in Rubisco V cmax alone does not bring a significant change in A, however, a simultaneous increase in Rubisco V cmax and Pi resulted in a significant enhancement in A (Fig. 5B). This suggests that a higher Rubisco V cmax requires more RuBP to enhance A. In 2003, Raines et al. reported that an increased photosynthetic capacity can be attained by simultaneously increasing carboxylation and RuBP regeneration 72 . An elevation in the Pi pool results in a higher regeneration of RuBP to support Rubisco's substrate availability. Walker et al. (2014) described the correlation that exists between Rubisco V cmax and plant nutritional status such as Pi, which influences photosynthetic rate 64 .
The proposed bypass model requires further evaluation of photorespired CO 2 loss, ammonia (NH 3 ) release and energy balance sheet to accurately estimate the benefits of the bypass in C 3 plants. Investigation of model under enhanced photorespiratory conditions i.e. high temperature, drought and salt will help predict the response of plants in changing climatic conditions. Lastly, it is also pertinent to elucidate the interaction between nitrogen and elevated CO 2 to analyze the impact of the bypass on nitrogen use efficiency, nutritional requirement and value in plants.

Conclusion
The model developed in this study reveals the potential of cyanobacterial glycolate decarboxylation pathway to suppress photorespiration by catabolizing GCA in chloroplast and enhance photosynthesis. The study reports that an excess of CO 2 requires an additional supply of nutrients such as Pi to maintain the enhanced rate of carboxylation. Furthermore, the study also emphasizes that expected elevation of atmospheric CO 2 in the future will require an enhanced nutrient supply for regulating photosynthesis It would also be interesting to evaluate bypass engineered plants at varying concentrations of phosphate and the resultant impact on photosynthesis and plant biomass accumulation. Furthermore, elucidation of phosphate and nitrogen use efficiency along with

Materials and methods
Biological pathways and kinetic parameters for the model. To develop bypass model, the cyanobacterial glycolate decarboxylation pathway containing four enzymes i.e. glycolate dehydrogenase (GDH), hydroxyacid dehydrogenase (HDH), oxalate decarboxylase (ODC), and formate dehydrogenase (FDH) 25 was integrated into the photosynthetic pathway 34 (Fig. 1). The literature-based C 3 model included Calvin cycle, photorespiratory and sucrose synthesis pathway 34 . The enzyme kinetic parameters for the cyanobacterial glycolate decarboxylation pathway were adopted from enzyme database BRENDA 73 as well as from the literature. These kinetic parameters included enzyme commission (EC) no, maximum enzyme velocity (V max ) and Michaelis-Menten rate constants (K m and K eq ) for each enzyme (Table 1). Enzymatic data on GDH, ODC and FDH (Table 1) were adopted from other bacterial species due to lack of data from cyanobacteria. For HDH, we used data on its homologue, aldehyde dehydrogenase (Table 1). V max of bypass enzymes were tuned to balance the photorespiratory flux between bypass and normal C 3 photorespiratory pathway, at steady state.
Formulation of rate equations. Rate equations for enzymatic reactions of cyanobacterial glycolate decarboxylation pathway were developed using kinetic parameters and type of reactions i.e. irreversible and reversible reactions. All enzymatic reactions (Table 2) within the bypass obeyed the Michaelis-Menten (MM) enzyme kinetics 74 while CO 2 regulation reaction ( Table 2) followed the law of mass action kinetics 75,76 . Standard equations for Michaelis-Menten (MM) irreversible and reversible reactions 74,77 and mass action kinetics (k = 0.036 s −1 ) 78 were used to develop the rate equations for GDH, HDH, ODC, FDH and CO 2 regulation, respectively. CO 2 regulation reaction was incorporated in the bypass model to stabilize the model and regulate CO 2 flux within chloroplast. The change in rate of metabolite concentrations over time was determined by system of ordinary differential equations 79 , which involved the rate of reactions producing and consuming the metabolite 71 .
Development of the bypass model. BioModels database 80 was used to obtain the C 3 model (BIOMD0000000393) 34 in system biology markup language (SBML) format, for onward integration with the cyanobacterial photorespiratory pathway 25 81 , was used to develop the bypass model. Metabolite concentrations, rate equations and reactions corresponding to cyanobacterial decarboxylation pathway were specified under species, functions and reactions section, respectively. The concentration of glyoxylate (GOA), oxalate and formate was set to zero with simulation type 'reaction' to determine their level according to the rate equations defined as functions while the energy cofactor NAD/NADH was fixed at 1 mmol l −133 . For rate equations (Table 2), Henry Michaelis-Menten irreversible function 74 and Law of mass action were selected from the functions list of COPASI, while a standard kinetic equation for reversible reaction 77 was defined. Reactions (Table 2) were created for enzymes and regulation of  www.nature.com/scientificreports/ CO 2 flux. COPASI's built in functions were then used to generate the complete set of ordinary differential equations.
Net photosynthetic rate (A) computation. The FvCB model (A = V c − 0.5 * V o − R d ) 29 was used to compute A, where V c , V o and R d indicated the rate of carboxylation, oxygenation and mitochondrial respiration, respectively. The flux rate of Rubisco carboxylation and oxygenation along with ATP synthesis (representing photon flux density) 32 at model steady state was used to compute A whereas R d was set to 0.01 mmol l −1 s −129 . The model was then run to steady state and A was computed at model default value of C i (0.009 mmol, equivalent to 27 Pa) to determine the change in A after integration of bypass. Photosynthesis CO 2 response was generated by using varied levels of C i which reflected the expected levels of atmospheric CO 2 (C a ). Variations in level of C a were obtained from National Oceanic and Atmospheric Administration Earth System Research Laboratories (NOAA ESRL) 82 for years between 1780 to 2100 62,83 . The C i was then calculated (C a * 0.7) 83 against each level of C a and set to 20 Pa, 27 Pa, 29 Pa, 33 Pa, 39 Pa, 50 Pa and 67 Pa which corresponds to C a in 1780, 2004, 2019, 2025, 2050, 2075 and 2100 respectively. Henry's Law of partial pressure 84 was used for inter conversion between CO 2 gas and liquid phase while chloroplast volume 85 was used to convert the units of A from mmol l −1 s −1 to µmol m −2 s −1 .
Model validation. The bypass model was simulated to attain steady state and its stability was checked.
Default conditions of the C 3 model were maintained while validating the bypass model and simulations were run using 'Time course' and 'steady state analysis' in COPASI. In time course, deterministic algorithm, LSODA was employed for solving the ordinary differential equations 86 . The bypass model was run for 6000 s by which it had attained steady state. Next, steady state and stability of the bypass model was determined by performing steady state analysis with resolution parameter set at 1e−08. The impact of elevated level of Pi and Rubisco V cmax on the rate of carboxylation and metabolic levels was evaluated by varying Pi from 15 mmol l −1 (C 3 model) to 25 mmol l −1 (+ 70%) 45 and Rubisco V cmax from 2.91 mmol l −1 s −1 (C 3 model) to 5.82 mmol l −1 s −1 (+ 100%).