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There is possibility to engineer C4 photosynthesis into C3 plants, because all C4 key enzymes are also present in C3 plants, although the expression levels are much lower than that in C4 species []. However it is an enormous challenge. To realize the transition from C3 to C4, systems biology will play a critical role in many aspects, including identification of key regulatory elements controlling development of C4 features and viable routine towards C4 using constraint-based modeling approach []. In this study, we improved the current metabolism models AraGEM and C4GEM by setting the ratio of carboxylation and oxygenation by Rubisco, and then systematically compared the constraint-based metabolic networks of C3 and C4 plants for the first time. We found C4 plants have less dense topology, higher robustness, better modularity, and higher CO2 and radiation use efficiency, which provide important basis for engineering C4 photosynthesis into C3 plants. In addition, preliminary analysis indicated that the rate of CO2 fixation and biomass production in PCK subtype are superior to NADP-ME and NAD-ME subtypes under enough supply of water and nitrogen. All results are consistent with the actual situation, which indicate that Flux Balance Analysis is a useful method to analyze and compare large-scale metabolism systems of plants.

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The effects of single reaction deletion on C3 and C4 networks when objective function is CO2 fixation are shown in Table which is similar with Table . More than 96% reactions have no influence on the maximal flux of CO2 fixation when being deleted in C3 and C4 networks. We concluded that more reactions have no influence on the maximal flux of CO2 fixation than biomass. Since biomass synthesis includes many components which deal with more than one reaction, their deletion will affect the flux of biomass synthesis. In addition, it is obvious that C4 plants exhibit much better robustness than C3 plants, since higher percentage of enzyme knockouts result no change on the objective flux and lower percentage result in zero flux. Moreover, we found all the essential reactions in C3 network are also essential for C4, while there are some other reactions specifically essential for C4. This result proved that the basic metabolism of C4 plants was similar to C3, but C4 became more complex during long period of evolution.

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We compared C3 and C4 metabolic networks using the improved constraint-based models for Arabidopsis and maize. By graph theory, we found the C3 network exhibit more dense topology structure than C4. The simulation of enzyme knockouts demonstrated that both C3 and C4 networks are very robust, especially when optimizing CO2 fixation. Moreover, C4 plant has better robustness no matter the objective function is biomass synthesis or CO2 fixation. In addition, all the essential reactions in C3 network are also essential for C4, while there are some other reactions specifically essential for C4, which validated that the basic metabolism of C4 plant is similar to C3, but C4 is more complex. We also identified more correlated reaction sets in C4, and demonstrated C4 plants have better modularity with complex mechanism coordinates the reactions and pathways than that of C3 plants. We also found the increase of both biomass production and CO2 fixation with light intensity and CO2 concentration in C4 is faster than that in C3, which reflected more efficient use of light and CO2 in C4 plant. Finally, we explored the contribution of different C4 subtypes to biomass production by setting specific constraints.

The genome scale metabolism models of C3 plant Arabidopsis [] and C4 plant [] have been constructed, but no comparative analysis between them. In this study, we improved the two models, AraGEM and C4GEM, by setting ratio of carboxylation and oxygenation by Rubisco, and compared the differences of network structure and metabolic flux to elucidate the evolutionary significance. We explored the effects of enzyme knockouts on photosynthesis and biomass synthesis, and compared the contribution of different C4 subtypes to biomass production. In addition, we revealed the different response to environment conditions in C3 and C4 plants. The system flow of our analysis is shown in Figure . This study will shed light on the metabolism changes from C3 to C4 at systems level, which is important for feasible engineering of C3 to C4 plants.

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In addition, our motivation was to compare the differences between C3 and C4 photosynthesis mechanism and their responses under different environments, therefore we set the objective function as maximization of CO2 fixation and biomass synthesis. Since in previous AraGEM and C4GEM, the objective was to minimize the use of light energy while achieving a specified growth rate, we need to reset some flux constraints according to biochemistry knowledge. For example, the CO2 leakage was blocked from bundle sheath to mesophyll cell with zero flux in C4GEM, which was not consistent with actual situation; here we adjusted the upper bound of this reaction to permit the leakage of CO2. In addition, because starch is not synthesized in mesophyll cell of C4 plants, the biomass components of C4GEM were also reset. The lower and upper bounds of flux in TCA cycle were adjusted as -50 and 50, to restrict flux of respiration in mitochondria. The detail of modified constraints in our improved models can be got from the Additional File.

In C4 plants, Phosphoenolpyruvate carboxylase (PEPC, EC: 4.1.1.31) notably performs the initial fixation of atmospheric CO2 in photosynthesis, which catalyzes the carboxylation of phosphoenolpyruvate (PEP) in a reaction that yields oxaloacetate and inorganic phosphate []. Therefore, knockout of PEPC resulted in zero flux of biomass, which validates its crucial role in C4 photosynthesis. Pyruvate phosphate dikinase (PPDK, EC: 2.7.9.1) catalyzes the conversion of the 3-carbon compound pyruvate into phosphoenolpyruvate. Its deletion reduced the flux of CO2 fixation and biomass, which is consistent with experiment results that inhibition of PPDK significantly hinders C4 plant growth []. In comparison, these two enzymes have no effect on CO2 fixation and biomass in C3 network.

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The C4 photosynthetic cycle supercharges photosynthesis by concentrating CO2 around ribulose-1,5-bisphosphate carboxylase and significantly reduces the oxygenation reaction. Therefore engineering C4 feature into C3 plants has been suggested as a feasible way to increase photosynthesis and yield of C3 plants, such as rice, wheat, and potato. To identify the possible transition from C3 to C4 plants, the systematic comparison of C3 and C4 metabolism is necessary.

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Unlike C3 plants, C4 photosynthesis requires the coordinated functioning of mesophyll and bundle sheath cells by CO2 concentrating mechanism. The ratio r of carboxylation to oxygenation can be expressed as equation (7-15) []:

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