BACKGROUND
c <dig> plants such as maize, sorghum, and sugarcane, approximately have 50% higher photosynthesis efficiency than those of c <dig> plants such as rice, wheat, and potato  <cit> .
this is because the different mechanism of carbon fixation by the two types of photosynthesis, as illustrated in figure  <dig>  c <dig> photosynthesis only uses the calvin cycle for fixing co <dig> catalyzed by ribulose- <dig> -bisphosphate carboxylase , which takes place inside of the chloroplast in mesophyll cell.
for c <dig> plants such as maize , photosynthetic activities are partitioned between mesophyll and bundle sheath cells that are anatomically and biochemically distinct.
the initial carbon fixation is catalyzed by phosphoenolpyruvate carboxylase  forming oxaloacetate  from co <dig> and phosphoenolpyruvate .
oaa is metabolized into malate, and then diffuses into the bs cell where it is decarboxylated to provide increased concentration of co <dig> around rubisco.
finally, the initial substrate of the c <dig> cycle, pep, is regenerated in mesophyll cell by pyruvate orthophosphate dikinase   <cit> .
the co <dig> concentration mechanism suppresses the oxygenation reaction by rubisco and the subsequent energy-wasteful photorespiratory pathway, resulting in increased photosynthetic yield and more efficient use of water and nitrogen comparing to c <dig> plants  <cit> .
therefore genetic engineering of c <dig> features into c <dig> plants such as rice  has the potential to increase crop productivity  <cit> .
however, attempts to use these tools to engineer plant metabolism have met with limited success due to the complexity of plant metabolism.
genetic manipulations rarely cause the predicted effects, and new rate-limiting steps prevent the accumulation of some desired compounds  <cit> .
in a bid to improve our understanding of plant metabolism and thereby the success rate of plant metabolic engineering, a systems-based framework to study plant metabolism is needed  <cit> .
systems biology involves an iterative process of experimentation, data integration, modeling, and generation of hypotheses  <cit> .
with the recent advancement of genome sequencing, several plants have complete genomic sequence and annotation, including arabidopsis   <cit> , rice , sorghum   <cit> , and maize , which make it possible to reconstruct the genome-scale metabolic network of plants.
constraint-based model, also called flux balance analysis , is a useful method to analyze large-scale metabolic network without requiring detail kinetic parameters.
in fba, flux states are predicted which are optimal with regard to an assumed cellular objective such as maximizing biomass yield  <cit> .
for microbial organisms, fba has been successful in predicting in vivo maximal growth rate, substrate preference and the requirement for particular biochemical reactions for cellular growth  <cit> .
for plants, highly compartmentalized stoichiometric models have been developed for barley seeds  <cit>  and chlamydomonas  <cit> , especially several models have been reported for arabidopsis  <cit> .
in addition, the analysis of metabolic network for photosynthetic bacteria has also been conducted, such as synechocystis  <cit>  and purple nonsulfur bacteria  <cit> .
the genome scale metabolism models of c <dig> plant arabidopsis  <cit>  and c <dig> plant  <cit>  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 c <dig> subtypes to biomass production.
in addition, we revealed the different response to environment conditions in c <dig> and c <dig> plants.
the system flow of our analysis is shown in figure  <dig>  this study will shed light on the metabolism changes from c <dig> to c <dig> at systems level, which is important for feasible engineering of c <dig> to c <dig> plants.
RESULTS
topological characteristics of c <dig> and c <dig> metabolic networks
the metabolism model of arabidopsis aragem includes  <dig> unique reactions,  <dig> metabolites,  <dig> inter-organelle transporters, and  <dig> inter-cellular transporters  <cit> .
for the metabolism model of c <dig> plants c4gem, there are  <dig> reactions,  <dig> metabolites,  <dig> inter-organelle transporters, and  <dig> external transporters  <cit> .
the topological properties of aragem and c4gem models were analyzed using pajek  <cit> , where reactions are represented as nodes and metabolites as edges.
some important topological parameters such as average degree, betweenness centrality, average clustering coefficient and distance were compared between these two models, as shown in table  <dig> the results demonstrated that the aragem has a more dense structure than c4gem, because c <dig> plant is single-cell, while c <dig> plant consists of mesophyll cell and bundle sheath cell, the connections between two-cells are not as close as single-cell.
then we extracted the primary metabolism from c <dig> and c <dig> networks, including calvin cycle, photorespiration, tca cycle, nitrogen metabolism, sucrose and starch metabolism, and some major amino acid metabolism pathways.
using net-synthesis  <cit> , we calculated the redundancy of primary metabolic network of c <dig> and c <dig>  which is  <dig>  and  <dig>  respectively.
it means c <dig> network is more redundant so that c <dig> plant could be more robust to gene mutation or environment changes.
improved models by setting the ratio of carboxylation and oxygenation by rubisco
rubisco enzyme  catalyzed two different reactions with co <dig> and o <dig> respectively in photosynthesis and photorespiration:
rubp+co2+h2o ->2pga
rubp+o2->pga+pgca
there is constant ratio between rate of carboxylation and oxygenation under specific partial pressure of co <dig> and o <dig> in environment  <cit> .
therefore, it is hard to accurately simulate the flux change under different co <dig> concentration without constraints on rate of the two reactions by rubisco, which is just the limitation of aragem and c4gem.
here we improved the two models by combining the two reactions into one reaction:
rubp+rco2+rh2o+o2 - > pga+pgca
the ratio r between carboxylation and oxygenation under different co <dig> concentration in c <dig> and c <dig> model is shown in table  <dig>  the detail calculation of r is in the methods section.
in addition, our motivation was to compare the differences between c <dig> and c <dig> photosynthesis mechanism and their responses under different environments, therefore we set the objective function as maximization of co <dig> 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 co <dig> 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 co <dig>  in addition, because starch is not synthesized in mesophyll cell of c <dig> plants, the biomass components of c4gem were also reset.
the lower and upper bounds of flux in tca cycle were adjusted as - <dig> and  <dig>  to restrict flux of respiration in mitochondria.
the detail of modified constraints in our improved models can be got from the additional file.
the effects of knock-out enzymes on metabolic flux
based on the improved c <dig> and c <dig> metabolic networks, we compared the optimal flux of biomass synthesis and co <dig> fixation using fba.
when biomass synthesis is the objective function, the maximal flux of biomass is  <dig>  and  <dig>  mmol·gdw-1·hr- <dig> respectively in c <dig> and c <dig> networks.
similarly, when optimizing co <dig> fixation, the maximal flux is  <dig>  mmol·gdw-1·hr- <dig> in c <dig> network and  <dig>  mmol·gdw-1·hr- <dig> in c <dig> network.
it demonstrated that c <dig> network exhibited both higher fluxes of biomass and co <dig> fixation than c <dig> network, which was consistent with the actual tendency.
we concluded that the two genome-scale metabolic networks could explain actual situations and be compared for understanding the similarities and differences of c <dig> and c <dig> plants.
next, we evaluated the effects of enzyme knockouts on flux of co <dig> fixation and biomass.
when one enzyme was knockout, its corresponding reactions would be deleted, which resulted in changes of the optimal flux of biomass or co <dig> fixation.
the objective results from the simulation were classified as unchanged objective , reduced objective ) and no objective .
the effects of single reaction deletion on maximal flux of biomass in c <dig> and c <dig> network are shown in table  <dig>  more than 85% reactions have no effects on the maximal biomass of c <dig> and c <dig> network when being knocked-out, so we concluded that the two networks have amazing robustness.
almost 10% of the reactions would result in zero biomass in c <dig> and c <dig> networks, which include some important transporters.
the single deletion of important reactions or enzymes such as phosphoribulokinase  and light reactions can result in no biomass, which is consistent with the real characteristics of plants  <cit> .
the effects of single reaction deletion on c <dig> and c <dig> networks when objective function is co <dig> fixation are shown in table  <dig> which is similar with table  <dig>  more than 96% reactions have no influence on the maximal flux of co <dig> fixation when being deleted in c <dig> and c <dig> networks.
we concluded that more reactions have no influence on the maximal flux of co <dig> 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 c <dig> plants exhibit much better robustness than c <dig> 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 c <dig> network are also essential for c <dig>  while there are some other reactions specifically essential for c <dig>  this result proved that the basic metabolism of c <dig> plants was similar to c <dig>  but c <dig> became more complex during long period of evolution.
we found there are some gaps in c4gem when checking the xylose pathway in the two networks.
in aragem, there are two pathways to produce xylose, so knockout of udp-glucose 6-dehydrogenase  will not influence on the biomass synthesis.
but in c4gem, only udpgdh was responsible for xylose production, the other alternative pathway does not work because of two missing enzymes, xylose isomerase  and xylulokinase .
we searched the genebank database  <cit>  to find that genes  encoding xylose isomerase and genes  encoding xylulokinase.
so we complemented the xylose pathway in c4gem, thus the biased results can be avoided.
next we investigated the effects of particular key enzymes on photosynthesis and biomass synthesis in c <dig> and c <dig> plants.
table  <dig> illustrated these enzymes, their functions and the ratio of objective flux after deletion.
'0' means the knocked-out enzyme resulting no flux of biomass or co <dig> fixation, while '1' means there is no influence on maximal flux of biomass or co <dig> fixation.
knockouts of enzymes in calvin cycle have lethal effects on both c <dig> and c <dig> networks.
for example, the central enzyme of calvin cycle, rubisco  catalyzes the fixation of both co <dig> and o <dig>  its deletion results in zero flux of co <dig> fixation and biomass, which accords with the fact that photosynthesis and plant growth is positively correlated with rubisco activity  <cit> .
when deleting transaldolase  in pentose phosphate pathway and glycolate oxidase  in glyoxylate and dicarboxylate metabolism pathway, the co <dig> fixation and biomass will also reduce to zero flux in these two plants  <cit> .
aconitases  is an important enzyme in tca cycle, its knockout reduced the flux of co <dig> fixation, and completely no flux of biomass in both c <dig> and c <dig> networks  <cit> .
the knockout of hosphoglycolate phosphatase  has no effect on the co <dig> fixation and biomass synthesis, because it catalyzes the first reaction of the photorespiratory c <dig> cycle  <cit> .
sucrose-6-phosphate phosphohydrolase  catalyzes the final step in the pathway of sucrose biosynthesis  <cit> .
its deletion has no influence, because sucrose synthesis locates in cytosol and has no direct connection with photosynthesis.
amylase isomerase  is responsible for the synthesis of transitory starch in chloroplast, which is the critical reaction for the normal biosynthesis of storage starch, so its deletion has lethal effect on biomass flux for both c <dig> and c <dig> plants  <cit> .
in c <dig> plants, phosphoenolpyruvate carboxylase  notably performs the initial fixation of atmospheric co <dig> in photosynthesis, which catalyzes the carboxylation of phosphoenolpyruvate  in a reaction that yields oxaloacetate and inorganic phosphate  <cit> .
therefore, knockout of pepc resulted in zero flux of biomass, which validates its crucial role in c <dig> photosynthesis.
pyruvate phosphate dikinase  catalyzes the conversion of the 3-carbon compound pyruvate into phosphoenolpyruvate.
its deletion reduced the flux of co <dig> fixation and biomass, which is consistent with experiment results that inhibition of ppdk significantly hinders c <dig> plant growth  <cit> .
in comparison, these two enzymes have no effect on co <dig> fixation and biomass in c <dig> network.
correlated reaction sets identified by sampling
there are some reactions co-utilized in precise stoichiometric ratios and exhibit correlated flux in the metabolic network, which called correlated reaction sets.
we used the uniform random sampling method to determine dependencies between reactions which can be further used to define modules of reactions .
the simplified model of the c <dig> network has  <dig> reactions,  <dig> metabolites and narrow range on constraints, which can be separated into  <dig> modules and the largest module consists of  <dig> reactions.
the simplified model of the c <dig> network has  <dig> reactions,  <dig> metabolites and narrow range on constraints, which can be separated into  <dig> modules and the largest module consists of  <dig> reactions.
there are more correlated reaction sets in c <dig> than c <dig> network.
the fluxes of reactions in the same module exhibit linear correlation.
we found the reactions in calvin cycle are correlated in both c <dig> and c <dig> network, as illustrated in figure  <dig> and  <dig> respectively.
however, there are some reactions from different pathways also exhibit linear correlation in c <dig> network, but they are not correlated in c <dig> model.
for example, the reactions from sugar metabolism, stibene, counarine and lignin biosynthesis, and coumarine and phenylpropanoid biosynthesis pathways are significantly correlated in c <dig> , but no correlation among them in c <dig> .
it demonstrated that c <dig> plants have better modularity with complex mechanism coordinates the reactions and pathways than that of c <dig> plants.
comparison of response to different environment conditions
the biomass and co <dig> fixation of c <dig> and c <dig> models were simulated under different light intensity, as shown in figure  <dig> and  <dig>  the c <dig> model  and c <dig> model  presented linear relationship between biomass and light intensity when light intensity is less than  <dig>  then with the light intensity increasing, the biomass would be unchanged in c <dig> model and still increased in c <dig> model.
the c <dig> model  and c <dig> model  also presented linear relationship between co <dig> fixation and light intensity when light intensity is less than  <dig>  then the co <dig> fixation was almost keeping unchanged.
the increase of both biomass and co <dig> fixation with light intensity in c <dig> are faster than that in c <dig>  which reflect more efficient use of solar energy in c <dig> plants  <cit> .
in addition, we simulated the flux of biomass synthesis and co <dig> fixation under different co <dig> concentration, as shown in figure  <dig> and  <dig>  the more co <dig> concentration increases, the more flux of biomass and co <dig> fixation, and the increase gradually change slowly until to steady state.
the simulated curve was consistent with experiment a-ci curve  <cit> .
we found that the increase of both biomass and co <dig> fixation with co <dig> concentration in c <dig> are faster than that in c <dig>  which reflect more efficient use of co <dig> in c <dig> plants.
contribution of different c <dig> subtypes to biomass production
c <dig> plants can be classified to three subtypes according to decarboxylation modes: nadp-malic enzyme , nad-malic enzyme  and pep carboxykinase .
we explored the influence of each subtype on biomass synthesis and co <dig> fixation, by blocking the flux of other two enzymes and giving enough supply of water and nitrogen.
as shown in table  <dig>  for each specific subtype, only the corresponding enzyme has flux and the other two enzymes have zero flux.
there are little differences on biomass in the three subtypes.
in comparison, the flux of biomass and co <dig> fixation are maximal in pck subtype.
moreover, when all the three subtypes are assumed to be active in one metabolism system, the pck subtype is superior to be used for co <dig> decarboxylation.
these results are consistent with fravolini's experiments that photosynthetic performance and above-ground biomass production of b.curtipendula,  are greater than nadp-me and nad-me types  <cit> .
however, the photosynthesis and biomass of different subtypes also depend on environment conditions, including water and nitrogen supply  <cit> .
for example, some species of nadp-me type show higher rates of photosynthetic and biomass production under low nitrogen availability  <cit> .
therefore, to clearly elucidate the superiority of c <dig> subtypes, further design and analysis under multi-factorial combination of environment conditions are required.
CONCLUSIONS
there is possibility to engineer c <dig> photosynthesis into c <dig> plants, because all c <dig> key enzymes are also present in c <dig> plants, although the expression levels are much lower than that in c <dig> species  <cit> .
however it is an enormous challenge.
to realize the transition from c <dig> to c <dig>  systems biology will play a critical role in many aspects, including identification of key regulatory elements controlling development of c <dig> features and viable routine towards c <dig> using constraint-based modeling approach  <cit> .
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 c <dig> and c <dig> plants for the first time.
we found c <dig> plants have less dense topology, higher robustness, better modularity, and higher co <dig> and radiation use efficiency, which provide important basis for engineering c <dig> photosynthesis into c <dig> plants.
in addition, preliminary analysis indicated that the rate of co <dig> 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.

 c plants such as maize, sorghum, and sugarcane, approximately have 50% higher photosynthesis efficiency than those of c plants such as rice, wheat, and potato. this is because the different mechanism of carbon fixation by the two types of photosynthesis, as illustrated in figure c photosynthesis only uses the calvin cycle for fixing co catalyzed by ribulose- -bisphosphate carboxylase, which takes place inside of the chloroplast in mesophyll cell. for c plants such as maize, photosynthetic activities are partitioned between mesophyll and bundle sheath cells that are anatomically and biochemically distinct. the initial carbon fixation is catalyzed by phosphoenolpyruvate carboxylase forming oxaloacetate from co and phosphoenolpyruvate. oaa is metabolized into malate, and then diffuses into the bs cell where it is decarboxylated to provide increased concentration of co around rubisco. finally, the initial substrate of the c cycle, pep, is regenerated in mesophyll cell by pyruvate orthophosphate dikinase. the co concentration mechanism suppresses the oxygenation reaction by rubisco and the subsequent energy-wasteful photorespiratory pathway, resulting in increased photosynthetic yield and more efficient use of water and nitrogen comparing to c plants. therefore genetic engineering of c features into c plants such as rice has the potential to increase crop productivity. however, attempts to use these tools to engineer plant metabolism have met with limited success due to the complexity of plant metabolism. genetic manipulations rarely cause the predicted effects, and new rate-limiting steps prevent the accumulation of some desired compounds. in a bid to improve our understanding of plant metabolism and thereby the success rate of plant metabolic engineering, a systems-based framework to study plant metabolism is needed. systems biology involves an iterative process of experimentation, data integration, modeling, and generation of hypotheses. with the recent advancement of genome sequencing, several plants have complete genomic sequence and annotation, including arabidopsis, rice, sorghum, and maize, which make it possible to reconstruct the genome-scale metabolic network of plants. constraint-based model, also called flux balance analysis, is a useful method to analyze large-scale metabolic network without requiring detail kinetic parameters. in fba, flux states are predicted which are optimal with regard to an assumed cellular objective such as maximizing biomass yield. for microbial organisms, fba has been successful in predicting in vivo maximal growth rate, substrate preference and the requirement for particular biochemical reactions for cellular growth. for plants, highly compartmentalized stoichiometric models have been developed for barley seeds and chlamydomonas, especially several models have been reported for arabidopsis. in addition, the analysis of metabolic network for photosynthetic bacteria has also been conducted, such as synechocystis and purple nonsulfur bacteria. the genome scale metabolism models of c plant arabidopsis and c 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 c subtypes to biomass production. in addition, we revealed the different response to environment conditions in c and c plants. the system flow of our analysis is shown in figure this study will shed light on the metabolism changes from c to c at systems level, which is important for feasible engineering of c to c plants.  topological characteristics of c and c metabolic networks the metabolism model of arabidopsis aragem includes unique reactions, metabolites, inter-organelle transporters, and inter-cellular transporters. for the metabolism model of c plants c4gem, there are reactions, metabolites, inter-organelle transporters, and external transporters. the topological properties of aragem and c4gem models were analyzed using pajek, where reactions are represented as nodes and metabolites as edges. some important topological parameters such as average degree, betweenness centrality, average clustering coefficient and distance were compared between these two models, as shown in table the results demonstrated that the aragem has a more dense structure than c4gem, because c plant is single-cell, while c plant consists of mesophyll cell and bundle sheath cell, the connections between two-cells are not as close as single-cell. then we extracted the primary metabolism from c and c networks, including calvin cycle, photorespiration, tca cycle, nitrogen metabolism, sucrose and starch metabolism, and some major amino acid metabolism pathways. using net-synthesis, we calculated the redundancy of primary metabolic network of c and c which is and respectively. it means c network is more redundant so that c plant could be more robust to gene mutation or environment changes. improved models by setting the ratio of carboxylation and oxygenation by rubisco rubisco enzyme catalyzed two different reactions with co and o respectively in photosynthesis and photorespiration: rubp+co2+h2o ->2pga rubp+o2->pga+pgca there is constant ratio between rate of carboxylation and oxygenation under specific partial pressure of co and o in environment. therefore, it is hard to accurately simulate the flux change under different co concentration without constraints on rate of the two reactions by rubisco, which is just the limitation of aragem and c4gem. here we improved the two models by combining the two reactions into one reaction: rubp+rco2+rh2o+o2 - > pga+pgca the ratio r between carboxylation and oxygenation under different co concentration in c and c model is shown in table the detail calculation of r is in the methods section. in addition, our motivation was to compare the differences between c and c photosynthesis mechanism and their responses under different environments, therefore we set the objective function as maximization of co 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 co 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 co in addition, because starch is not synthesized in mesophyll cell of c plants, the biomass components of c4gem were also reset. the lower and upper bounds of flux in tca cycle were adjusted as - and to restrict flux of respiration in mitochondria. the detail of modified constraints in our improved models can be got from the additional file. the effects of knock-out enzymes on metabolic flux based on the improved c and c metabolic networks, we compared the optimal flux of biomass synthesis and co fixation using fba. when biomass synthesis is the objective function, the maximal flux of biomass is and mmol·gdw-1·hr- respectively in c and c networks. similarly, when optimizing co fixation, the maximal flux is mmol·gdw-1·hr- in c network and mmol·gdw-1·hr- in c network. it demonstrated that c network exhibited both higher fluxes of biomass and co fixation than c network, which was consistent with the actual tendency. we concluded that the two genome-scale metabolic networks could explain actual situations and be compared for understanding the similarities and differences of c and c plants. next, we evaluated the effects of enzyme knockouts on flux of co fixation and biomass. when one enzyme was knockout, its corresponding reactions would be deleted, which resulted in changes of the optimal flux of biomass or co fixation. the objective results from the simulation were classified as unchanged objective, reduced objective ) and no objective. the effects of single reaction deletion on maximal flux of biomass in c and c network are shown in table more than 85% reactions have no effects on the maximal biomass of c and c network when being knocked-out, so we concluded that the two networks have amazing robustness. almost 10% of the reactions would result in zero biomass in c and c networks, which include some important transporters. the single deletion of important reactions or enzymes such as phosphoribulokinase and light reactions can result in no biomass, which is consistent with the real characteristics of plants. the effects of single reaction deletion on c and c networks when objective function is co fixation are shown in table which is similar with table more than 96% reactions have no influence on the maximal flux of co fixation when being deleted in c and c networks. we concluded that more reactions have no influence on the maximal flux of co 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 c plants exhibit much better robustness than c 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 c network are also essential for c while there are some other reactions specifically essential for c this result proved that the basic metabolism of c plants was similar to c but c became more complex during long period of evolution. we found there are some gaps in c4gem when checking the xylose pathway in the two networks. in aragem, there are two pathways to produce xylose, so knockout of udp-glucose 6-dehydrogenase will not influence on the biomass synthesis. but in c4gem, only udpgdh was responsible for xylose production, the other alternative pathway does not work because of two missing enzymes, xylose isomerase and xylulokinase. we searched the genebank database to find that genes encoding xylose isomerase and genes encoding xylulokinase. so we complemented the xylose pathway in c4gem, thus the biased results can be avoided. next we investigated the effects of particular key enzymes on photosynthesis and biomass synthesis in c and c plants. table illustrated these enzymes, their functions and the ratio of objective flux after deletion.'0' means the knocked-out enzyme resulting no flux of biomass or co fixation, while'1' means there is no influence on maximal flux of biomass or co fixation. knockouts of enzymes in calvin cycle have lethal effects on both c and c networks. for example, the central enzyme of calvin cycle, rubisco catalyzes the fixation of both co and o its deletion results in zero flux of co fixation and biomass, which accords with the fact that photosynthesis and plant growth is positively correlated with rubisco activity. when deleting transaldolase in pentose phosphate pathway and glycolate oxidase in glyoxylate and dicarboxylate metabolism pathway, the co fixation and biomass will also reduce to zero flux in these two plants. aconitases is an important enzyme in tca cycle, its knockout reduced the flux of co fixation, and completely no flux of biomass in both c and c networks. the knockout of hosphoglycolate phosphatase has no effect on the co fixation and biomass synthesis, because it catalyzes the first reaction of the photorespiratory c cycle. sucrose-6-phosphate phosphohydrolase catalyzes the final step in the pathway of sucrose biosynthesis. its deletion has no influence, because sucrose synthesis locates in cytosol and has no direct connection with photosynthesis. amylase isomerase is responsible for the synthesis of transitory starch in chloroplast, which is the critical reaction for the normal biosynthesis of storage starch, so its deletion has lethal effect on biomass flux for both c and c plants. in c plants, phosphoenolpyruvate carboxylase notably performs the initial fixation of atmospheric co in photosynthesis, which catalyzes the carboxylation of phosphoenolpyruvate 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 c photosynthesis. pyruvate phosphate dikinase catalyzes the conversion of the 3-carbon compound pyruvate into phosphoenolpyruvate. its deletion reduced the flux of co fixation and biomass, which is consistent with experiment results that inhibition of ppdk significantly hinders c plant growth. in comparison, these two enzymes have no effect on co fixation and biomass in c network. correlated reaction sets identified by sampling there are some reactions co-utilized in precise stoichiometric ratios and exhibit correlated flux in the metabolic network, which called correlated reaction sets. we used the uniform random sampling method to determine dependencies between reactions which can be further used to define modules of reactions. the simplified model of the c network has reactions, metabolites and narrow range on constraints, which can be separated into modules and the largest module consists of reactions. the simplified model of the c network has reactions, metabolites and narrow range on constraints, which can be separated into modules and the largest module consists of reactions. there are more correlated reaction sets in c than c network. the fluxes of reactions in the same module exhibit linear correlation. we found the reactions in calvin cycle are correlated in both c and c network, as illustrated in figure and respectively. however, there are some reactions from different pathways also exhibit linear correlation in c network, but they are not correlated in c model. for example, the reactions from sugar metabolism, stibene, counarine and lignin biosynthesis, and coumarine and phenylpropanoid biosynthesis pathways are significantly correlated in c, but no correlation among them in c. it demonstrated that c plants have better modularity with complex mechanism coordinates the reactions and pathways than that of c plants. comparison of response to different environment conditions the biomass and co fixation of c and c models were simulated under different light intensity, as shown in figure and the c model and c model presented linear relationship between biomass and light intensity when light intensity is less than then with the light intensity increasing, the biomass would be unchanged in c model and still increased in c model. the c model and c model also presented linear relationship between co fixation and light intensity when light intensity is less than then the co fixation was almost keeping unchanged. the increase of both biomass and co fixation with light intensity in c are faster than that in c which reflect more efficient use of solar energy in c plants. in addition, we simulated the flux of biomass synthesis and co fixation under different co concentration, as shown in figure and the more co concentration increases, the more flux of biomass and co fixation, and the increase gradually change slowly until to steady state. the simulated curve was consistent with experiment a-ci curve. we found that the increase of both biomass and co fixation with co concentration in c are faster than that in c which reflect more efficient use of co in c plants. contribution of different c subtypes to biomass production c plants can be classified to three subtypes according to decarboxylation modes: nadp-malic enzyme, nad-malic enzyme and pep carboxykinase. we explored the influence of each subtype on biomass synthesis and co fixation, by blocking the flux of other two enzymes and giving enough supply of water and nitrogen. as shown in table for each specific subtype, only the corresponding enzyme has flux and the other two enzymes have zero flux. there are little differences on biomass in the three subtypes. in comparison, the flux of biomass and co fixation are maximal in pck subtype. moreover, when all the three subtypes are assumed to be active in one metabolism system, the pck subtype is superior to be used for co decarboxylation. these results are consistent with fravolini's experiments that photosynthetic performance and above-ground biomass production of b.curtipendula, are greater than nadp-me and nad-me types. however, the photosynthesis and biomass of different subtypes also depend on environment conditions, including water and nitrogen supply. for example, some species of nadp-me type show higher rates of photosynthetic and biomass production under low nitrogen availability. therefore, to clearly elucidate the superiority of c subtypes, further design and analysis under multi-factorial combination of environment conditions are required.  there is possibility to engineer c photosynthesis into c plants, because all c key enzymes are also present in c plants, although the expression levels are much lower than that in c species. however it is an enormous challenge. to realize the transition from c to c systems biology will play a critical role in many aspects, including identification of key regulatory elements controlling development of c features and viable routine towards c 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 c and c plants for the first time. we found c plants have less dense topology, higher robustness, better modularity, and higher co and radiation use efficiency, which provide important basis for engineering c photosynthesis into c plants. in addition, preliminary analysis indicated that the rate of co 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. 
we also found the increase of both biomass production and co fixation with light intensity and co concentration in c is faster than that in c which reflected more efficient use of light and co in c plant. we also identified more correlated reaction sets in c and demonstrated c plants have better modularity with complex mechanism coordinates the reactions and pathways than that of c plants. all results are consistent with the actual situation, which indicate that flux balance analysis is a powerful method to study plant metabolism at systems level. in addition, preliminary analysis indicated that the rate of co fixation and biomass production in pck subtype are superior to nadp-me and nad-me subtypes under enough supply of water and nitrogen. in addition, all the essential reactions in c network are also essential for c while there are some other reactions specifically essential for c which validated that the basic metabolism of c plant is similar to c but c is more complex. moreover, c plant has better robustness no matter the objective function is biomass synthesis or co fixation. by graph theory, we found the c network exhibit more dense topology structure than c the simulation of enzyme knockouts demonstrated that both c and c networks are very robust, especially when optimizing co fixation. we demonstrated that in contrast to c c plants have less dense topology, higher robustness, better modularity, and higher co and radiation use efficiency. finally, we explored the contribution of different c subtypes to biomass production by setting specific constraints. the c photosynthetic cycle supercharges photosynthesis by concentrating co around ribulose- -bisphosphate carboxylase and significantly reduces the oxygenation reaction.
 the c photosynthetic cycle supercharges photosynthesis by concentrating co around ribulose- -bisphosphate carboxylase and significantly reduces the oxygenation reaction. therefore engineering c feature into c plants has been suggested as a feasible way to increase photosynthesis and yield of c plants, such as rice, wheat, and potato. to identify the possible transition from c to c plants, the systematic comparison of c and c metabolism is necessary.  we compared c and c metabolic networks using the improved constraint-based models for arabidopsis and maize. by graph theory, we found the c network exhibit more dense topology structure than c the simulation of enzyme knockouts demonstrated that both c and c networks are very robust, especially when optimizing co fixation. moreover, c plant has better robustness no matter the objective function is biomass synthesis or co fixation. in addition, all the essential reactions in c network are also essential for c while there are some other reactions specifically essential for c which validated that the basic metabolism of c plant is similar to c but c is more complex. we also identified more correlated reaction sets in c and demonstrated c plants have better modularity with complex mechanism coordinates the reactions and pathways than that of c plants. we also found the increase of both biomass production and co fixation with light intensity and co concentration in c is faster than that in c which reflected more efficient use of light and co in c plant. finally, we explored the contribution of different c subtypes to biomass production by setting specific constraints.  all results are consistent with the actual situation, which indicate that flux balance analysis is a powerful method to study plant metabolism at systems level. we demonstrated that in contrast to c c plants have less dense topology, higher robustness, better modularity, and higher co and radiation use efficiency. in addition, preliminary analysis indicated that the rate of co fixation and biomass production in pck subtype are superior to nadp-me and nad-me subtypes under enough supply of water and nitrogen. 12- december 23rd international conference on genome informatics tainan, taiwan 