1. Computational and Systems Biology
  2. Plant Biology
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Evolution of C4 photosynthesis predicted by constraint-based modelling

  1. Mary-Ann Blätke  Is a corresponding author
  2. Andrea Bräutigam
  1. Leibniz Institute of Plant Genetics and Crop Plant Research (IPK), Germany
  2. Computational Biology, Faculty of Biology, Bielefeld University, Universitätsstraße, Germany
Research Article
Cite this article as: eLife 2019;8:e49305 doi: 10.7554/eLife.49305
6 figures, 4 tables and 1 additional file


Figure 1 with 2 supplements
Schematic representation of the primary subsystems in the one-cell model and the used input/output constraints; adapted from Arnold and Nikoloski (2014).
Figure 1—source data 1

SBML code of the one-cell model.

Figure 1—source data 2

Complete flux solution of the one-cell model.

Figure 1—source code 1

Jupyter notebook - Predicted fluxes of C3 metabolism.

Figure 1—source code 2

Jupyter notebook- Effect of the CO2 uptake rate on C3 metabolism.

Figure 1—source code 3

Jupyter notebook - Effect of the PPFD on C3 metabolism.

Figure 1—figure supplement 1
Effect of CO2 and PPFD variation.

(A) Dependence of the phloem output on CO2 input flux in the range 0 μmol/(m2s)–20 μmol/(m2s), (B) Dependence of phloem output on the PPFD in the range 0 μmol/(m2s)–400 μmol/(m2s). Sucrose and starch are produced in the same amounts, each of them consists of 12 C-atoms.

Figure 1—figure supplement 2
Energy Flux Distribution in the one-cell Model.

(A) ATP production and consumption, (B) NADPH production and consumption, (C) NADH production and consumption, (D) proportion of ATP, NADPH, NADH used as energy equivalent, (E) proportion of respiratory ATP used for maintenance.

Schematic representation of the primary subsystems in the two-cell model and the used input/output constraints; adapted from Arnold and Nikoloski (2014).
Figure 3 with 1 supplement
Effect of oxygenation : carboxylation ratio on the major steps in C4 cycle, including (A) activity of phosphoenolpyruvate carboxylase (PEPC), (B) metabolite transport to the bundle sheath, (C) activity of Rubisco, (D) activity of the decarboxylation enzymes, (E) metabolite transport to the mesophyll, and (F) activity of pyruvate phosphate dikinase (PPDK).
Figure 3—source code 1

Jupyter notebook - Analysing the effect of oxygenation : carboxylation ratio on the emergence of the C4 cycle.

Figure 3—figure supplement 1
Flux maps illustrating the effect of the oxygenation : carboxylation ratio of Rubisco on the C3-C4 trajectory.

Flux maps illustrating the effect of the proportion of photorespiratory flux through Rubisco. (A) Low photorespiratory flux; (B) Moderate photorespiratory flux; and (C) High photorespiratory flux. (Arc width and colour are set relative to flux values in flux, grey arcs - no flux).

Flux maps illustrating the effect of the C4 mode.

(A) NADP-ME, (B) PEP-CK, (C) NAD-ME. (Arc width and colour are set relative to flux values in flux, grey arcs - no flux).

Figure 4—source code 1

Jupyter notebook - Effect of C4 mode on the emergence of the C4 cycle.

Flux variability analysis of metabolite exchange with 1.5% deviation of the total flux minimum.

The upper bar defines the maximum exchange flux, while the lower bar defines the minimum exchange flux, points indicate the value of the original flux solution under minimal metabolic effort constraint. Positive flux values correspond to the transport direction from mesophyll to bundle sheath, negative values to the transport direction from bundle sheath to mesophyll, see also Figure 4—source code 1.

Figure 6 with 1 supplement
Effect of light on the C4 mode.

(A) CO2 uptake rate in dependence of the total PPFD, (B) Heat-maps illustrating the activity of the decarboxylation enzymes PEP-CK, NADP-ME, and NAD-ME relative to the CO2 uptake rate in dependence of the total PPFD and the photon distribution among mesophyll and bundle sheath.

Figure 6—source code 1

Jupyter notebook - Effect of light on the C4 mode.

Figure 6—source code 2

Jupyter notebook - Effect of NO3- limitation on the C4 mode.

Figure 6—source code 3

Jupyter notebook - Effect of H2O limitation on the C4 mode.

Figure 6—source code 4

Jupyter notebook - Effect of CO2 limitation on the C4 mode.

Figure 6—source code 5

Jupyter notebook - Effect of malate : aspartate transport ratio on the C4 mode.

Figure 6—figure supplement 1
Effect of other relevant factors on the C4 mode.

Effect of (A) NO3-, (B) H2O, and (C) CO2 limitation on the flux through the different decarboxylation enzymes, with each enzymes coded in color (blue PEPCK, light blue NADP-ME, and green NAD-ME); (D) effect of malate:aspartate transport ratio on the flux through the different decarboxylation enzymes with each enzymes coded in color (blue PEPCK, light blue NADP-ME, and green NAD-ME).


Table 1
Curation of the Arabidopsis core model from Arnold and Nikoloski (2014).
Arabidopsis core modelObservationone-cell modelReference
NADP-dependent malate dehydrogenases in all compartmentscycles through nitrate reductase to interconvert NAD and NADPNAD-dependent malate dehydrogenases in all compartments, NADP-dependent malate dehydrogenase only in chloroplast(Swarbreck et al., 2008)
Cyclic electron flowabsence of cyclic electron flowadded(Shikanai, 2016)
Alternative oxidasemissing alternative routes for electrons to pass the electron transport chain to reduce oxygenadded alternative oxidase reactions to the chloroplast and mitochondria(Vishwakarma et al., 2015)
Alanine transferaseNo alanine transferase in cytosol Alanine transferaseadded(Liepman and Olsen, 2003)
Transport chloroplastno maltose transporter by MEX1added(Linka and Weber, 2010)
no glucose transporter by MEX1 and pGlcT MEX1added
no unidirectional transport of ATP, ADP, AMP by BT-likeadded
no Mal/OAA, Mal/Pyr, and Mal/Glu exchange by DiTsadded
no folate transporter by FBT and FOLT1added
Transport Mitochondriano Mal/OAA, Cit/iCit, Mal/KG exchange by DTCadded(Linka and Weber, 2010)
no H+ importer by UCPs importadded
no OAA/Pi exchange by DIC1-3added
no ATP/Pi exchange by APCsadded
no NAD/ADP and NAD/AMP exchange by NDT2added
no ThPP/ATP exchange by TPCsadded
no Asp/Glu by AGCsadded
no uncoupled Ala exchangeadded
Transport peroxisomemissing NAD/NADH, NAD/ADP, NAD/AMP exchange by PXNadded(Linka and Weber, 2010)
no ATP/ADP and ATP/AMP exchange by PNCsadded
H+ sinks/sourcesH+ sinks/source reaction for the cytosol and futile transport cycles introduced by H+ -coupled transport reactionsH+ sinks/source reaction added for each compartment
ATPase stoichiometryFalse H+/ATP ratios for the plastidal and mitochondrial ATP synthaseH+/ATP ratio set to 3 : 1 (chloroplast) and 4:1 (mitochondria)(Petersen et al., 2012; Turina et al., 2016)
Alanine/aspartate transferaseno direct conversion of alanine and aspartateadded to cytosol, chloroplast and mitochondria(Schultz and Coruzzi, 1995; Duff et al., 2012)
Table 2
Input/output fluxes of one-cell model in comparison to physiological observations.
Molecular SpeciesFlux [µmol/(m2/s)]Physiological Range [µmol/(m2/s)]Reference
(i) Inputs
Photons193.7100 - 400Bailey et al. (2001)
CO22020Lacher (2003)
NO3-0.50.11 - 0.18Kiba et al. (2012)
(ii) Outputs
O220.916.5Sun et al. (1999)
Amino Acids0.3-
  1. Note: CO2 has one carbon per molecule while Sucrose has 12. Starch is configured to have the same number of carbons compared to sucrose while amino acids on average have 5.5 carbons.

Table 3
Flux boundary constraints of Im-/export reactions
Input (Reaction ID)Flux [μmol/(m2s)]
Lower boundUpper bound
Photons (Im_hnu)0inf
C02 (Im_CO2)020
NO3- (Im_NO3)0inf
NH4+ (Im_NH4)00
SO42- (Im_SO4)0inf
H2S (Im_H2S)0inf
H2O (Im_H2O)-infinf
O2 (Im_O2)-infinf
Amino Acids (Ex_AA)0inf
Surcose (Ex_Suc)0inf
Starch (Ex_starch)0inf
Other export reactions00
  1. -inf/inf is approximated by −106 / 106

Table 4
Maintenance costs by compartment
CompartmentFlux [μmol/(m2s)]

Data availability

All data generated or analysed during this study are included in the manuscript and supporting files. We provide jupyter notebooks as documentation for all the in silico experiments using constraint-based modelling and additional python code for Figure 1, 3, 4, 6, as well as the metabolic network used as source data for Figure 1 which can be accessed and executed from the GitHub repository https://github.com/ma-blaetke/CBM_C3_C4_Metabolism (copy archived at https://github.com/elifesciences-publications/CBM_C3_C4_Metabolism).

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