Volume 6 Supplement 2
Systematic Comparison of C3 and C4 Plants Based on Metabolic Network Analysis
© Wang et al.; licensee BioMed Central Ltd. 2012
Published: 12 December 2012
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.
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.
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 C3, C4 plants have less dense topology, higher robustness, better modularity, and higher CO2 and radiation use efficiency. 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.
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 [7, 8]. Systems biology involves an iterative process of experimentation, data integration, modeling, and generation of hypotheses [9, 10]. With the recent advancement of genome sequencing, several plants have complete genomic sequence and annotation, including Arabidopsis (Arabidopsis thaliana) , rice (Oryza sativa), sorghum (Sorghum bicolor) , and maize (Zea mays), which make it possible to reconstruct the genome-scale metabolic network of plants. Constraint-based model, also called Flux Balance Analysis (FBA), 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 [13–16]. 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 [19–22]. In addition, the analysis of metabolic network for photosynthetic bacteria has also been conducted, such as Synechocystis  and purple nonsulfur bacteria .
Results and Discussion
Topological characteristics of C3 and C4 metabolic networks
Topological properties of AraGEM and C4GEM
Average Clustering Coefficient
Redundancy of primary network
Improved models by setting the ratio of carboxylation and oxygenation by Rubisco
The ratio r between carboxylation and oxygenation under different CO2 concentration in C3 and C4 model
CO2 (μbar) in the air
r in C3
r in C4
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.
The effects of knock-out enzymes on metabolic flux
Based on the improved C3 and C4 metabolic networks, we compared the optimal flux of biomass synthesis and CO2 fixation using FBA. When biomass synthesis is the objective function, the maximal flux of biomass is 3.661 and 4.625 mmol·gDW-1·hr-1 respectively in C3 and C4 networks. Similarly, when optimizing CO2 fixation, the maximal flux is 200.95 mmol·gDW-1·hr-1 in C3 network and 387.619 mmol·gDW-1·hr-1 in C4 network. It demonstrated that C4 network exhibited both higher fluxes of biomass and CO2 fixation than C3 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 C3 and C4 plants.
The effects of knockout reactions on maximal flux of biomass
Ratio of objective flux
Ratio = 1
The effects of knockout reactions on maximal flux of CO2 fixation
Ratio of objective flux
Ratio = 1
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 (UDPGDH, EC:126.96.36.199) 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 (EC: 188.8.131.52) and xylulokinase (EC:184.108.40.206). We searched the GeneBank database  to find that genes (GeneID: 100194128, 100194385) encoding xylose isomerase and genes (GeneID:100282641, 100382670) encoding xylulokinase. So we complemented the xylose pathway in C4GEM, thus the biased results can be avoided.
The effects of key enzyme knockouts on optimal flux of biomass and CO2 fixation
Ratio of biomass
Ratio of CO2 fixation
Pentose phosphate pathway
Glyoxylate and dicarboxylate metabolism
Transitory starch biosynthesis
The knockout of hosphoglycolate phosphatase (PGLP, EC: 220.127.116.11) has no effect on the CO2 fixation and biomass synthesis, because it catalyzes the first reaction of the photorespiratory C2 cycle . Sucrose-6(F)-phosphate phosphohydrolase (SPP, EC: 18.104.22.168) 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 (EC: 22.214.171.124) 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 C3 and C4 plants .
In C4 plants, Phosphoenolpyruvate carboxylase (PEPC, EC: 126.96.36.199) 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: 188.8.131.52) 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.
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 [See Methods section]. The simplified model of the C3 network has 494 reactions, 483 metabolites and narrow range on constraints, which can be separated into 65 modules and the largest module consists of 92 reactions. The simplified model of the C4 network has 826 reactions, 806 metabolites and narrow range on constraints, which can be separated into 113 modules and the largest module consists of 169 reactions. There are more correlated reaction sets in C4 than C3 network.
Comparison of response to different environment conditions
Contribution of different C4 subtypes to biomass production
The influences of different C4 subtypes on flux of biomass synthesis and CO2 fixation
Flux of reactions (mmol·gDW -1 ·hr -1 )
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.
Determination of the ratio between carboxylation and oxygenation
Equation (5) and (6) include mechaelis constants for CO2 with K c = 460μbar and O2 with K o = 330mbar . The O2 concentration is 210 mbar and the intercellular CO2 concentration is about 70 percent of CO2 in air, which is 380μbar under standard condition.
Where C s and C m are CO2 partial pressures respectively in bundle sheath and mesophyll cells; O s and O m are O2 partial pressures in the two cells; V p is the rate of PEP carboxylation; V pmax (120μmol·m-2·s-1) is the maximum PEP carboxylation rate; K p (80μbar) is Michaelis constant of PEP carboxylase for CO2; V pr (80μmol·m-2·s-1)is the constant rate of PEP regeneration; g s (3mmol·m-2·s-1) is the physical conductance to CO2 leakage; A c is Rubisco-limited rate of CO2 assimilation; A j is electron-transport-limited rate; A is the CO2 assimilation rate; V cmax (60μmol·m-2·s-1) is the maximum Rubisco activity; γ (0.5/2590) is half the reciprocal of Rubisco specificity; R d = 0.01V cmax = 0.6μmol·m-2·s-1 is leaf mitochondrial respiration; R m = 0.5 R d = 0.3μmol·m-2·s-1 is mesophyll mitochondrial respiration; α (0<α<1, α were assumed to be zero in our results) is fraction of PSII activity in the bundle sheath; x (x = 0.4) is partitioning factor of electron transport rate. J max (400μmol electron m-2·s-1) is maximal electron transport rate; K c (650μbar) for CO2 and K o (450mbar) for O2 are mechaelis constants of Rubisco. In C4 plants, CO2 concentration in mesophyll cell is only 37 percent of CO2 in air  and the other parameters can be obtained in .
Topological parameters in metabolic network
The topological properties of metabolic network can be analyzed based on graph theory, which can reflect the structure and robustness of large-scale network. In this study, the reactions are represented as nodes, if the product of reaction A is the substrate of a reaction B, there will be an edge from A to B. We consider some important parameters including degree, clustering coefficient, betweenness centrality and distance (path length). The degree of a node is the number of edges connected with other reactions. Degree centralization of a network is the variation in the degrees of vertices divided by the maximum degree variation which is possible in a network of the same size. Clustering coefficient is used to compute different inherent tendency coefficients in undirected network. Betweenness centralization is the variation in the betweenness centrality of vertices divided by the maximum variation in betweenness centrality possible in a network of the same size. The distance between two nodes is the shortest path length from one to the other. The diameter of network is the maximal distance among all pairs of nodes. All the topology analysis was conducted using the visual software Pajek .
Flux Balance Analysis
Where c is a vector of weights indicating how much each reaction contributes to the objective function. In this study, we choose CO2 fixation and biomass synthesis as two objective functions.
The COBRA toolbox is a free MATLAB toolbox for performing the simulation. The fluxes that are identified at various perturbations can be compared with each other and with experimental data.
Uniform random sampling
Uniform random sampling of the solution space in any environmental condition is a rapid and scalable way to characterize the structure of the allowed space of metabolic fluxes. Before the sampling was performed, the effective constraints for each reaction were calculated using the method of Flux Balance Analysis in COBRA toolbox . Specifically in sampling, COBRA toolbox uses an implementation of the artificial centered hit-and-run (ACHR) sampler algorithm with slight modifications to generate such a set of flux distributions that uniformly sample the space of all feasible fluxes. Initially, a set of 5000 non-uniform pseudo-random points, called warm-up points, was generated. In a series of iterations, each point was randomly moved while keeping it within the feasible flux space. This was accomplished by choosing a random direction, computing the limits on how far a point could travel in that direction (positive or negative), and then choosing a new point randomly along that line. After numerous iterations, the set of points was mixed and approached a uniform sample of the solution space  and 2000 points was loaded for analysis. The sampling procedure can be achieved with the function 'sampleCbModel' and the correlated reaction sets can be identified by 'identifyCorrelSets' in the COBRA toolbox. Correlated reaction sets are mathematically defined as modules in biochemical reaction network which facilitate the study of biological processes by decomposing complex reaction networks into conceptually simple units. This sampling approach is used to fully determine the range of possible distributions of steady-state fluxes allowed in the network under defined physicochemical constraints and used to analyze the general properties of networks by testing their robustness to parameter variation .
We thank de Oliveira Dal'Molin for providing us the SBML file of C4GEM model which can be loaded into COBRA toolbox. The work was supported by State key basic research program (973) 2011CB910204, Research Program of CAS (KSCX2-EW-R-04), and the National Natural Science Foundation of China (30800199, 30900272).
This article has been published as part of BMC Systems Biology Volume 6 Supplement 2, 2012: Proceedings of the 23rd International Conference on Genome Informatics (GIW 2012). The full contents of the supplement are available online at http://www.biomedcentral.com/bmcsystbiol/supplements/6/S2.
- Kajala K, Covshoff S, Karki S, Woodfield H, Tolley BJ, Dionora MJ, Mogul RT, Mabilangan AE, Danila FR, Hibberd JM, Quick WP: Strategies for engineering a two-celled C4 photosynthetic pathway into rice. J Exp Bot. 2011, 62: 3001-3010. 10.1093/jxb/err022.View ArticlePubMedGoogle Scholar
- Majeran W, Friso G, Ponnala L, Connolly B, Huang M, Reidel E, Zhang C, Asakura Y, Bhuiyan NH, Sun Q, Turgeon R, van Wijk KJ: Structural and metabolic transitions of C4 leaf development and differentiation defined by microscopy and quantitative proteomics in maize. Plant Cell. 2010, 22: 3509-3542. 10.1105/tpc.110.079764.PubMed CentralView ArticlePubMedGoogle Scholar
- Hibberd JM, Sheehy JE, Langdale JA: Using C4 photosynthesis to increase the yield of rice-rationale and feasibility. CurrOpin Plant Biol. 2008, 11: 228-231. 10.1016/j.pbi.2007.11.002.Google Scholar
- Taniguchi Y, Ohkawa H, Masumoto C, Fukuda T, Tamai T, Lee K, Sudoh S, Tsuchida H, Sasaki H, Fukayama H, Miyao M: Overproduction of C4 photosynthetic enzymes in transgenic rice plants: an approach to introduce the C4-like photosynthetic pathway into rice. J Exp Bot. 2008, 59: 1799-1809.View ArticlePubMedGoogle Scholar
- Evans JR: Enhancing C3 photosynthesis. Plant Physiol. 2010, 154: 589-592. 10.1104/pp.110.160952.PubMed CentralView ArticlePubMedGoogle Scholar
- Sweetlove LJ, Last RL, Fernie AR: Predictive metabolic engineering: a goal for systems biology. Plant Physiol. 2003, 132: 420-425. 10.1104/pp.103.022004.PubMed CentralView ArticlePubMedGoogle Scholar
- Gutierrez RA, Shasha DE, Coruzzi GM: Systems biology for the virtual plant. Plant Physiol. 2005, 138: 550-554. 10.1104/pp.104.900150.PubMed CentralView ArticlePubMedGoogle Scholar
- DellaPenna D: Plant metabolic engineering. Plant Physiol. 2001, 125: 160-163. 10.1104/pp.125.1.160.PubMed CentralView ArticlePubMedGoogle Scholar
- Kitano H: Standards for modeling. Nat Biotechnol. 2002, 20: 337-View ArticlePubMedGoogle Scholar
- Kitano H: Systems biology: a brief overview. Science. 2002, 295: 1662-1664. 10.1126/science.1069492.View ArticlePubMedGoogle Scholar
- Dennis C, Surridge C: Arabidopsis thaliana genome. Introduction. Nature. 2000, 408: 791-View ArticlePubMedGoogle Scholar
- Paterson AH, Bowers JE, Bruggmann R, Dubchak I, Grimwood J, Gundlach H, Haberer G, Hellsten U, Mitros T, Poliakov A, Schmutz J, Spannagl M, Tang H, Wang X, Wicker T, Bharti AK, Chapman J, Feltus FA, Gowik U, Grigoriev IV, Lyons E, Maher CA, Martis M, Narechania A, Otillar RP, Penning BW, Salamov AA, Wang Y, Zhang L, Carpita NC: The Sorghum bicolor genome and the diversification of grasses. Nature. 2009, 457: 551-556. 10.1038/nature07723.View ArticlePubMedGoogle Scholar
- Becker SA, Feist AM, Mo ML, Hannum G, Palsson BØ, Herrgard MJ: Quantitative prediction of cellular metabolism with constraint-based models: the COBRA Toolbox. Nature Protocols. 2007, 2: 727-738. 10.1038/nprot.2007.99.View ArticlePubMedGoogle Scholar
- Boyle NR, Morgan JA: Flux balance analysis of primary metabolism in Chlamydomonasreinhardtii. BMC SystBiol. 2009, 3: 4-View ArticleGoogle Scholar
- Pramanik J, Keasling JD: Stoichiometric model of Escherichia coli metabolism: incorporation of growth-rate dependent biomass composition and mechanistic energy requirements. BiotechnolBioeng. 1997, 56: 398-421.Google Scholar
- Varma A, Palsson BO: Stoichiometric flux balance models quantitatively predict growth and metabolic by-product secretion in wild-type Escherichia coli W3110. Appl Environ Microbiol. 1994, 60: 3724-3731.PubMed CentralPubMedGoogle Scholar
- Price ND, Papin JA, Schilling CH, Palsson BO: Genome-scale microbial in silico models: the constraints-based approach. Trends Biotechnol. 2003, 21: 162-169. 10.1016/S0167-7799(03)00030-1.View ArticlePubMedGoogle Scholar
- Grafahrend-Belau E, Schreiber F, Koschutzki D, Junker BH: Flux balance analysis of barley seeds: a computational approach to study systemic properties of central metabolism. Plant Physiol. 2009, 149: 585-598. 10.1104/pp.108.129635.PubMed CentralView ArticlePubMedGoogle Scholar
- de Oliveira Dal'Molin CG, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK: AraGEM, a Genome-Scale Reconstruction of the Primary Metabolic Network in Arabidopsis. Plant Physiology. 2009, 152: 579-589.View ArticlePubMedGoogle Scholar
- Poolman MG, Miguet L, Sweetlove LJ, Fell DA: A genome-scale metabolic model of Arabidopsis and some of its properties. Plant Physiol. 2009, 151: 1570-1581. 10.1104/pp.109.141267.PubMed CentralView ArticlePubMedGoogle Scholar
- Radrich K, Tsuruoka Y, Dobson P, Gevorgyan A, Swainston N, Baart G, Schwartz JM: Integration of metabolic databases for the reconstruction of genome-scale metabolic networks. BMC SystBiol. 2010, 4: 114-View ArticleGoogle Scholar
- Williams TC, Poolman MG, Howden AJ, Schwarzlander M, Fell DA, Ratcliffe RG, Sweetlove LJ: A genome-scale metabolic model accurately predicts fluxes in central carbon metabolism under stress conditions. Plant Physiol. 2010, 154: 311-323. 10.1104/pp.110.158535.PubMed CentralView ArticlePubMedGoogle Scholar
- Knoop H, Zilliges Y, Lockau W, Steuer R: The metabolic network of Synechocystis sp. PCC 6803: systemic properties of autotrophic growth. Plant Physiol. 2010, 154: 410-422. 10.1104/pp.110.157198.PubMed CentralView ArticlePubMedGoogle Scholar
- Golomysova A, Gomelsky M, Ivanov PS: Flux balance analysis of photoheterotrophic growth of purple nonsulfur bacteria relevant to biohydrogen production. International Journal of Hydrogen Energy. 2010, 35: 12751-12760. 10.1016/j.ijhydene.2010.08.133.View ArticleGoogle Scholar
- de Oliveira Dal'Molin CG, Quek LE, Palfreyman RW, Brumbley SM, Nielsen LK: C4GEM, a Genome-Scale Metabolic Model to Study C4 Plant Metabolism. Plant Physiology. 2010, 154: 1871-1885. 10.1104/pp.110.166488.PubMed CentralView ArticleGoogle Scholar
- Mrvar A, Batagelj V: Exploratory network analysis with pajek. 2005, Mark Granovetter: Cambridge University PressGoogle Scholar
- Albert R, DasGupta B, Hegde R, Sivanathan GS, Gitter A, Gürsoy G, Paul P, Sontag E: A new computationally efficient measure of topological redundancy of biological and social networks. Physical Review E. 2011, 84: 036117-View ArticleGoogle Scholar
- Farquhar GD, Berry JA: A Biochemical Model of Photosynthetic CO2 Assimilation in Leaves of C3 Species. Planta. 1980, 149: 78-90. 10.1007/BF00386231.View ArticlePubMedGoogle Scholar
- Marri L, Sparla F, Pupillo P, Trost P: Co-ordinated gene expression of photosynthetic glyceraldehyde-3-phosphate dehydrogenase, phosphoribulokinase, and CP12 in Arabidopsis thaliana. J Exp Bot. 2005, 56: 73-80.PubMedGoogle Scholar
- GeneBank Database. [http://www.ncbi.nlm.nih.gov/gene/]
- Quick WP, Schurr U, Fichtner K, Schulze E-D, Rodermel SR, Bogorad L, Stitt M: The impact of decreased Rubisco on photosynthesis, growth, allocation and storage in tobacco plants which have been transformed with antisense rbcS. The Plant Journal. 1991, 1: 51-58. 10.1111/j.1365-313X.1991.00051.x.View ArticleGoogle Scholar
- Sicher RC, Bunce JA: Relationship of photosynthetic acclimation to changes of Rubisco activity in field-grown winter wheat and barley during growth in elevated carbon dioxide. PHOTOSYNTHESIS RESEARCH. 1997, 52: 27-38. 10.1023/A:1005874932233.View ArticleGoogle Scholar
- Debnam PM, Emes MJ: Subcellular distribution of enzymes of the oxidative pentose phosphate pathway in root and leaf tissues. Journal of Experimental Botany. 1999, 50: 1653-1661.View ArticleGoogle Scholar
- Zelitch I, Schultes NP, Peterson RB, Brown P, Brutnell TP: High glycolate oxidase activity is required for survival of maize in normal air. Plant Physiol. 2009, 149: 195-204. 10.1104/pp.108.128439.PubMed CentralView ArticlePubMedGoogle Scholar
- CLORE SMD AM, TINNIRELLO SMN: Increased levels of reactive oxygen species and expression of a cytoplasmic aconitase/iron regulatory protein 1 homolog during the early response of maize pulvini to gravistimulation. Plant, Cell & Environment. 2008, 31: 144-158.Google Scholar
- Schwarte S, Bauwe H: Identification of the photorespiratory 2-phosphoglycolate phosphatase, PGLP1, in Arabidopsis. Plant Physiol. 2007, 144: 1580-1586. 10.1104/pp.107.099192.PubMed CentralView ArticlePubMedGoogle Scholar
- Lunn JE, Ashton AR, Hatch MD, Heldt HW: Purification, molecular cloning, and sequence analysis of sucrose-6F-phosphate phosphohydrolase from plants. PNAS. 2000, 97: 12914-12919. 10.1073/pnas.230430197.PubMed CentralView ArticlePubMedGoogle Scholar
- Hernández JMGM, Castignolles P, Gidley MJ, Myers AM, Gilbert RG: Mechanistic investigation of a starch-branching enzyme using hydrodynamic volume SEC analysis. Biomacromolecules. 2008, 9: 954-965. 10.1021/bm701213p.View ArticlePubMedGoogle Scholar
- Monreal JA, McLoughlin F, Echevarria C, Garcia-Maurino S, Testerink C: Phosphoenolpyruvate carboxylase from C4 leaves is selectively targeted for inhibition by anionic phospholipids. Plant Physiol. 2010, 152: 634-638. 10.1104/pp.109.150326.PubMed CentralView ArticlePubMedGoogle Scholar
- Mechin V, Thevenot C, Le Guilloux M, Prioul JL, Damerval C: Developmental analysis of maize endosperm proteome suggests a pivotal role for pyruvate orthophosphate dikinase. Plant Physiol. 2007, 143: 1203-1219. 10.1104/pp.106.092148.PubMed CentralView ArticlePubMedGoogle Scholar
- Oberhuber W, Dai Z-Y, Edwards GE: Light dependence of quantum yields of Photosystem II and CO2 fixation in C3 and C4 plant. Photosythesis research. 1993, 35: 265-274. 10.1007/BF00016557.View ArticleGoogle Scholar
- Kanai R, Edwards GE: The biochemistry of C4 photosynthesis. Chapter 3 in C4 Plant Biology. 1999Google Scholar
- Fravolini A, Williams DG, Thompson TL: Carbon isotope discrimination and bundle sheath leakiness in three C4 subtypes grown under variable nitrogen, water and atmospheric CO2 supply. Journal of Experimental Botany. 2002, 53: 2261-2269. 10.1093/jxb/erf084.View ArticlePubMedGoogle Scholar
- Bowman WD: Inputs and Storage of Nitrogen in Winter Snowpack in an Alpine Ecosystem. Arctic and Alpine Research. 1992, 24: 211-215. 10.2307/1551659.View ArticleGoogle Scholar
- Buchman N, Brooks JR, Rapp KD, Ehleringer JR: Carbon isotope composition of C4 grasses is influenced by light and water supply. Plant, Cell & Environment. 1996, 19: 392-402. 10.1111/j.1365-3040.1996.tb00331.x.View ArticleGoogle Scholar
- Taub DR, Lerdau MT: Relationship between leaf nitrogen and photosynthetic rate for three NAD-ME and three NADP-ME C4 grasses. Am J Bot. 2000, 87: 412-417. 10.2307/2656637.View ArticlePubMedGoogle Scholar
- Zhu XG, Shan L, Wang Y, Quick WP: C4 rice - an ideal arena for systems biology research. J Integr Plant Biol. 2010, 52: 762-770. 10.1111/j.1744-7909.2010.00983.x.View ArticlePubMedGoogle Scholar
- Caemmerer SV: Modeling C4 photosynthesis. In Biochemical models of leaf photosynthesis. 2000, 91-122.Google Scholar
- Ziska LH, Bunce JA: Influence of increasing carbon dioxide concentration on the photosynthetic and growth stimulation of selected C4 crops and weeds. Photosynthesis Research. 1997, 54: 199-208. 10.1023/A:1005947802161.View ArticleGoogle Scholar
- Price ND, Schellenberger J, Palsson BO: Uniform sampling of steady-state flux spaces: means to design experiments and to interpret enzymopathies. Biophys J. 2004, 87: 2172-2186. 10.1529/biophysj.104.043000.PubMed CentralView ArticlePubMedGoogle Scholar
- Schellenberger J, Lewis NE, Palsson BO: Elimination of thermodynamically infeasible loops in steady-state metabolic models. Biophys J. 2011, 100: 544-553. 10.1016/j.bpj.2010.12.3707.PubMed CentralView ArticlePubMedGoogle Scholar
This article is published under license to BioMed Central Ltd. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/2.0), which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.