Photosynthesis Research

, Volume 90, Issue 1, pp 45–66 | Cite as

C3 photosynthesis in silico

Original Paper


A computer model comprising light reactions, electron–proton transport, enzymatic reactions, and regulatory functions of C3 photosynthesis has been developed as a system of differential budget equations for intermediate compounds. The emphasis is on electron transport through PSII and PSI and on the modeling of Chl fluorescence and 810 nm absorptance signals. Non-photochemical quenching of PSII excitation is controlled by lumenal pH. Alternative electron transport is modeled as the Mehler type O2 reduction plus the malate-oxaloacetate shuttle based on the chloroplast malate dehydrogenase. Carbon reduction enzymes are redox-controlled by the ferredoxin–thioredoxin system, sucrose synthesis is controlled by the fructose 2,6-bisphosphate inhibition of cytosolic FBPase, and starch synthesis is controlled by ADP-glucose pyrophosphorylase. Photorespiratory glycolate pathway is included in an integrated way, sufficient to reproduce steady-state rates of photorespiration. Rate-equations are designed on principles of multisubstrate-multiproduct enzyme kinetics. The parameters of the model were adopted from literature or were estimated from fitting the photosynthetic rate and pool sizes to experimental data. The model provided good simulations for steady-state photosynthesis, Chl fluorescence, and 810 nm transmittance signals under varying light, CO2 and O2 concentrations, as well as for the transients of post-illumination CO2 uptake, Chl fluorescence induction and the 810 nm signal. The modeling shows that the present understanding of photosynthesis incorporated in the model is basically correct, but still insufficient to reproduce the dark-light induction of photosynthesis, the time kinetics of non-photochemical quenching, ‘photosynthetic control’ of plastoquinone oxidation, cyclic electron flow around PSI, oscillations in photosynthesis. The model may find application for predicting the results of gene transformations, the analysis of kinetic experimental data, the training of students.


Photosynthesis Light reactions Mathematical model 



This work was supported by Targeted Financing Theme 0182535s03 from Estonian Government and by Grants 6607 and 6611 from Estonian Science Foundation.


  1. Badger MR, Lorimer GH (1981) Interaction of sugar phosphates with the catalytic site of ribulose-1,5-bisphosphate carboxylase. Biochemistry 20(8):2219–2225PubMedCrossRefGoogle Scholar
  2. Bassham JA, Jensen RG (1967) Photosynthesis of carbon compounds. In: San Pietro A, Greer FA, Army TJ (eds) Harvesting the Sun. Academic Press, New York/London, pp 79–110Google Scholar
  3. Brown HT, Escombe ELS (1900) Static diffusion of gases and liquids in relation to the assimilation of carbon and translocation in plants. Phil Trans 193:223–291CrossRefGoogle Scholar
  4. Buckley TN, Farquhar GD (2004) A new analytical model for whole-leaf electron transport rate. Plant Cell Environ 27:1487–1502CrossRefGoogle Scholar
  5. Bukhov N, Egorova E, Carpentier R (2002) Electron flow to photosystem I from stromal reductantsin vivo: the size of the pool of stromal reductants controls the rate of electron donation to both rapidly and slowly reducing photosystem I units. Planta 215:812–820PubMedCrossRefGoogle Scholar
  6. von Caemmerer S, Furbank RT (1999) Modelling C4 photosynthesis. In: Sage RF, Monson RK (eds) C4 plant biology. Academic Press, San Diego/London/Boston/NewYork/Sydney/Tokyo/Toronto, pp 173–211Google Scholar
  7. von Caemmerer S (2000) Biochemical models of leaf photosynthesis. Australia, CSIRO PublishingGoogle Scholar
  8. Chartier P (1966) Etude theorique de l’assimilation brute de la feuille. Ann Physiol Veg 8:167–195Google Scholar
  9. Cleland WW (1963) The kinetic of enzyme-catalyzed reactions with two or more substrates or products. I. Nomenclature and rate equations. Biochim Biophys Acta 767:432–443Google Scholar
  10. Cramer WA, Soriano GM, Ponomarev M, Huang D, Zhang H, Martinez SE, Smith JL (1996) Some new structural aspects and old controversies concenrning the cytochrome b 6 f complex of oxygenic photosynthesis. Annu Rev Plant Physiol Plant Mol Biol 47:477–508CrossRefGoogle Scholar
  11. Cruz JA, Sacksteder CA, Kanazawa A, Kramer DM (2001) Contribution of electric field (Δψ) to steady-state transthylakoid proton motive force (pmf) in vitro and in vivo. Control of pmf parsing into Δ ψ and ΔpH by ionic strength. Biochemistry 40:1226–1237PubMedCrossRefGoogle Scholar
  12. Eichelmann H, Laisk A (1999) Ribulose-1,5-bisphosphate carboxylase/oxygenase content, assimilatory charge and mesophyll conductance in leaves. Plant Physiol 119:179–189PubMedCrossRefGoogle Scholar
  13. Eichelmann H, Laisk A (2000) Cooperation of photosystems II and I in leaves as analysed by simultaneous measurements of chlorophyll fluorescence and transmittance at 800 nm. Plant Cell Physiol 41:138–147PubMedGoogle Scholar
  14. Eichelmann H, Weis E, Laisk A (1990) The effect of electron cycling around PSII on fluorescence induction mathematical modelling. In: Baltscheffsky M (ed) Current research in photosynthesis, vol I. Kluwer Academic Publishers, Dordrecht, the Netherlands, pp 663–666Google Scholar
  15. Farquhar GD (1979) Models describing the kinetics of ribulose bisphosphate carboxylase-oxygenase. Arch Biochem Biophys 2:456–468CrossRefGoogle Scholar
  16. Farquhar GD, von Caemmerer S (1982) Modelling of photosynthetic response to environmental conditions. In Lange OL, Nobel PS, Osmond CB, Ziegler H (eds) Physiological plant ecology. Encycl Plant Physiol, New Series, vol. 12B, pp 549–588. Springer-Verlag, BerlinGoogle Scholar
  17. Farquhar GD, von Caemmerer S, Berry JA (1980) A biochemical model of photosynthetic CO2 assimilation in leaves of C3 species. Planta 149:78–90CrossRefGoogle Scholar
  18. Feniouk BA, Mulkidjanian AY, Junge W (2005) Proton slip in the ATP synthase of Rhodobacter capsulatus: induction, proton conduction, and nucleotide dependence. Biochim Biophys Acta 1706:184–194PubMedCrossRefGoogle Scholar
  19. Flügge U-I (1991) Metabolite translocators of the chloroplast envelope. Annu Rev Plant Physiol Plant Mol Biol 42:129–144CrossRefGoogle Scholar
  20. Fridlyand LE, Backhausen JE, Scheibe R (1999) Homeostatic regulation upon changes of enzyme activities in the Calvin cycle as an example for general mechanisms of flux control. What can we expect from transgenic plants? Photosynth Res 61(3):227–239CrossRefGoogle Scholar
  21. Hahn BD (1987) A matemathical model of photorespiration and photosynthesis. Ann Bot 60:157–169Google Scholar
  22. Harbinson J, Hedley CL (1989) The kinetics of P700+ reduction in leaves: a novel in situ probe of thylakoid functioning. Plant Cell Environ 12:357–369CrossRefGoogle Scholar
  23. Heber U, Neimanis S, Dietz KJ, Viil J (1986) Assimilatory power as a driving force in photosynthesis. Biochem Biophys Acta 852: 144–155CrossRefGoogle Scholar
  24. Heimann S, Klughammer C, Schreiber U (1998) Two distinct states of the thylakoid bf complex. FEBS Lett 426:126–130PubMedCrossRefGoogle Scholar
  25. Holzhütter H-G (2004) The principle of flux minimization and its application to estimate stationary fluxes in metabolic networks. Eur J Biochem 271:2905–2922PubMedCrossRefGoogle Scholar
  26. Horton P, Ruban AV (1992) Regulation of photosystem II. Photosynth Res 34:375–385CrossRefGoogle Scholar
  27. Johnson G (2003) Thiol regulation of the thylakoid electron transport chain – a missing link in the regulation of photosynthesis. Biochemistry 42:3040–3044PubMedCrossRefGoogle Scholar
  28. Jordan DB, Chollet R, Ogren WL (1983) Binding of phosphorylated effectors by active and inactive forms of ribulose-1,5-bisphosphate carboxylase. Biochemistry 22:3410–3418CrossRefGoogle Scholar
  29. Kanazawa A, Kramer DM (2002) In vivomodulation of nonphotochemical exciton quenching (NPQ) by regulation of the chloroplast ATP synthase. PNAS 99:12789–12794PubMedCrossRefGoogle Scholar
  30. Kirchhoff H, Schöttler MA, Maurer J, Weis E (2004) Plastocyanin redox kinetics in spinach chloroplasts: evidence for disequilibrium in the high potential chain. Biochim Biophys Acta 1659:63–72PubMedCrossRefGoogle Scholar
  31. Klughammer C, Schreiber U (1994) An improved method, using saturating light pulses, for the determination of photosystem I quantum yield via P700+-absorbance changes at 830 nm. Planta 192:261–268CrossRefGoogle Scholar
  32. Krause GH, Heber U (1976) Energetics of intact chloroplasts. In: Barber J (ed) The intact chloroplast. Elsevier/North-Holland Biomedical Press, Amsterdam/New York/Oxford, pp 171–214Google Scholar
  33. Kull O, Kruijt B (1998) Leaf photosynthetic light response: a mechanistic model for scaling photosynthesis to leaves and canopies. Funct Ecol 12:767–777CrossRefGoogle Scholar
  34. Kull O, Kruijt B (1999) Acclimation of photosynthesis to light: a mechanistic approach. Functional Ecol 13(1): 24Google Scholar
  35. Laisk A (1970) A model of leaf photosynthesis and photorespiration. In: Shetlik I (ed) Prediction and measurement of photosynthetic productivity. PUDOC, Wageningen, pp 295–306Google Scholar
  36. Laisk A (1977) Modelling of the closed Calvin cycle. In: Unger K (ed) Biophysikalische Analyse Pflanzlicher Systeme. VEB Fischer-Verlag, Jena, DDR, pp 175–182Google Scholar
  37. Laisk A, Edwards GE (2000) A mathematical model of C4 photosynthesis: the mechanism of concentrating CO2 in NADP-malic enzyme type species. Photosynth Res 66:199–224PubMedCrossRefGoogle Scholar
  38. Laisk A, Eichelmann H (1989) Towards understanding oscillations: a mathematical model of the biochemistry of photosynthesis. Phil Trans R Soc Lond 323:369–384CrossRefGoogle Scholar
  39. Laisk A, Eichelmann H, Oja V, Eatherall A, Walker DA (1989) A mathematical model of the carbon metabolism in photosynthesis. Difficulties in explaining oscillations by fructose 2,6-bisphosphatase. Proc R Soc Lond B 237:389–415Google Scholar
  40. Laisk A, Eichelmann H, Oja V, Peterson RB (2005) Control of cytochrome b 6 f at low and high light intensity and cyclic electron transport in leaves. Biochim Biophys Acta 1708:79–90PubMedCrossRefGoogle Scholar
  41. Laisk A, Eichelmann H, Oja V, Rasulov B, Rämma H (2006) Photosystem II cycle and alternative electron flow in leaves. Plant Cell Physiol 47, in pressGoogle Scholar
  42. Laisk A, Kiirats O, Eichelmann H, Oja V (1987) Gas exchange studies of carboxylation kinetics in intact leaves. In: Biggins J (ed) Progress in photosynthesis research. Martinus Nijhoff Publishers, Dordrecht, the Netherlands, pp 245–252Google Scholar
  43. Laisk A, Laarin P (1983) Feedback regulation of the potential rate of photosynthesis. In: Margna U (ed) Regulation of Plant Growth and Metabolism. Valgus Publishing, Tallinn, pp 135–150 (in Russian)Google Scholar
  44. Laisk A, Oja V (1994) Range of the photosynthetic control of postillumination P700 reduction rate in sunflower leaves. Photosynth Res 39:39–50CrossRefGoogle Scholar
  45. Laisk A, Oja V (1995) Coregulation of electron transport through PS I by Cyt b 6 f, excitation capture by P700 and acceptor side reduction. Time kinetics and electron transport requirement. Photosynth Res 45:11–19CrossRefGoogle Scholar
  46. Laisk A, Oja V (1998) Dynamic gas exchange of leaf photosynthesis. Measurement and interpretation. CSIRO Publishing, CanberraGoogle Scholar
  47. Laisk A, Oja V (2000a) Alteration of PSII properties with non-photochemical excitation quenching. Phil Trans R Soc Lond B 355:1405–1418CrossRefGoogle Scholar
  48. Laisk A, Oja V (2000b) Electron transport through photosystem II in leaves during light pulses: acceptor resistance increases with nonphotochemical excitation quenching. Biochim Biophys Acta 1460:255–267CrossRefGoogle Scholar
  49. Laisk A, Oja V, Kiirats O (1984) Assimilatory power (post-illumination CO2 uptake) in leaves—measurement, environmental dependencies and kinetic properties. Plant Physiol 76:723–729PubMedGoogle Scholar
  50. Laisk A, Oja V, Rasulov B, Eichelmann H, Sumberg A (1997) Quantum yields and rate constants of photochemical and nonphotochemical excitation quenching. Experiment and model. Plant Physiol 115:803–815PubMedGoogle Scholar
  51. Laisk A, Oja V, Rasulov B, Rämma H, Eichelmann H, Kasparova I, Pettai H, Padu E, Vapaavuori E (2002) A computer-operated routine of gas exchange and optical measurements to diagnose photosynthetic apparatus in leaves. Plant Cell Environ 25:923–943CrossRefGoogle Scholar
  52. Laisk A, Walker DA (1986) Control of phosphate turnover as a rate-limiting factor and possible cause of oscillations in photosynthesis: a mathematical model. Proc R Soc Lond B 227:281–302Google Scholar
  53. Laisk A, Walker DA (1989) A mathematical model of electron transport. Thermodynamic necessity for photosystem II regulation: "light stomata". Proc R Soc Lond B 237:417–444CrossRefGoogle Scholar
  54. Makino A, Mae T, Ohira K (1987) Variation in the contents and kinetic properties of ribulose-1,5-bisphosphate carboxylases among rice species. Plant Cell Physiol 28:799–804Google Scholar
  55. Makino A, Miyake C, Yokota A (2002) Physiological functions of the water-water cycle (Mehler reaction) and the cyclic electron flow around PSI in rice leaves. Plant Cell Physiol 43:1017–1026PubMedCrossRefGoogle Scholar
  56. Mitchell P (1966) Chemiosmotic coupling in oxidative and photosynthetic phosphorylation. Biol Rev 41:445–502PubMedCrossRefGoogle Scholar
  57. Miyake C, Yokota A (2000) Determination of the rate of photoreduction of O2 in the water-water cycle in watermelon leaves and enhancement of the rate by limitation of photosynthesis. Plant Cell Physiol 41(3):335–343PubMedGoogle Scholar
  58. Mott KA, Woodrow IE (2000) Modelling the role of Rubisco activase in limiting non-steady-state photosynthesis. J Exp Bot 51:399–406PubMedCrossRefGoogle Scholar
  59. Niyogi KK, Li X-P, Rosenberg V, Jung H-S (2005) Is PsbS the site of non-photochemical quenching in photosynthesis? J Exp Bot 56:375–382PubMedCrossRefGoogle Scholar
  60. Oja V, Bichele I, Hüve K, Rasulov B, Laisk A (2004) Reductive titration of photosystem I and differential extinction coefficient of P700+ at 810–950 nm in leaves. Biochim Biophys Acta 1658:225–234PubMedCrossRefGoogle Scholar
  61. Oja V, Eichelmann H, Peterson RB, Rasulov B, Laisk A (2003) Decyphering the 820 nm signal: redox state of donor side and quantum yield of photosystem I in leaves. Photosynth Res 78:1–15PubMedCrossRefGoogle Scholar
  62. Oja V, Laisk A (1995) Gas system and method for CO2 titration of intact leaves. Photosynthetica 31:37–50Google Scholar
  63. Oja V, Laisk A (2000) Oxygen yield from single turnover flashes in leaves:non-photochemical excitation quenching and the number of active PSII. Biochim Biophys Acta 1460:291–301PubMedCrossRefGoogle Scholar
  64. Oja V, Laisk A, Heber U (1986) Light-induced alkalization of the chloroplast stroma in vivo as estimated from the CO2 capacity of intact sunflower leaves. Biochim Biophys Acta 849:355–365CrossRefGoogle Scholar
  65. Pärnik T, Keerberg O (1995) Decarboxylation of primary and end products of photosynthesis at different oxygen concentrations. J Exp Bot 46:1439–1447Google Scholar
  66. Peltier G, Cournac L (2002) Chlororespiration. Annu Rev Plant Biol 53:523–550PubMedCrossRefGoogle Scholar
  67. Pettai H, Oja V, Freiberg A, Laisk. A (2005) Photosynthetic activity of far-red light in green plants. Biochim Biophys Acta 1708:311–321PubMedCrossRefGoogle Scholar
  68. Pettersson G, Ryde-Pettersson U (1988) A mathematical model of the Calvin photosynthesis cycle. Eur J Biochem 175:661–672PubMedCrossRefGoogle Scholar
  69. Porcar-Castell A, Bäck J, Juurola E, Hari P (2006) Dynamics of the energy flow through photosystem II under changing light conditions: a model approach. Functional Plant Biol 33:229–239CrossRefGoogle Scholar
  70. Rabinowitch E (1953) Photosynthesis II. Publ. House of Foreign Liter., Moscow.Google Scholar
  71. Rees D, Noctor G, Ruban AV, Crofts J, Young A, Horton P (1992) pH dependent chlorophyll fluorescence quenching in spinach thylakoids from light treated or dark adapted leaves. Photosynth Res 31:11–19CrossRefGoogle Scholar
  72. Rumberg B, Schubert K, Strelow F, Tran-Anh T (1990) The H+/ATP coupling ratio at the H+-ATP-synthase of spinach chloroplasts is four. In: Baltscheffsky M (ed) Current research in photosynthesis, vol III. Kluwer Acad. Publ., the Netherlands, pp 125–128Google Scholar
  73. Sacksteder CA, Kanazawa A, Jacoby ME, Kramer DM (2000) The protonto electron stoichiometry of steady-state photosynthesis in living plants: a proton-pumping Q cycle is continuously engaged. PNAS 97:14283–14288PubMedCrossRefGoogle Scholar
  74. Scheibe R (1987) NADP+-malate dehydrogenase in C3-plants: Regulation and role of a light-activated enzyme. Physiol. Plantarum 71:393–400CrossRefGoogle Scholar
  75. Scheuring S, Fotiadis D, Möller C, Müller SA, Engel A, Müller DJ (2001) Single proteins observed by atomic force microscopy. Single Mol 2:59–67CrossRefGoogle Scholar
  76. Seelert H, Poetsch A, Dencher NA, Engel A, Stahlberg H, Müller DJ (2000) Proton powered turbine of a plant motor. Nature 405:418–419PubMedCrossRefGoogle Scholar
  77. Siebke K, Laisk A, Oja V, Kiirats O, Raschke K, Heber U (1990) Control of photosynthesis in leaves as revealed by rapid gas exchange and measurements of the assimilatory force F a. Planta 182:513–522CrossRefGoogle Scholar
  78. Siggel U (1974) The control of electron transport by two pH-sensitive sites. In: Avron M (ed) Proc. 3rd Internat. Congr. on Photosynth. Elsevier, Amsterdam, pp 645–654Google Scholar
  79. Stitt M (1987) Fructose 2,6-bisphosphate and plant carbohydrate metabolism. Plant Physiol 84:201–204PubMedCrossRefGoogle Scholar
  80. Vallon O, Bulte L, Dainese P, Olive J, Bassi R, Wollman F-A (1991) Lateral redistribution of cytochrome b6/f complexes along thylakoid membranes upon state transitions. Proc Natl Acad Sci USA 88:8262–8266PubMedCrossRefGoogle Scholar
  81. Viil J, Laisk A, Oja V, Pärnik T (1972) Positive influence of oxygen on photosynthesis. Doklady AN SSSR (Proc Acad Sci USSR) 204(5):1269–1271 (in Russian)Google Scholar
  82. Viil J, Laisk A, Oja V, Pärnik T (1977) Enchancement of photosynthesis caused by oxygen under saturating irradiance and high CO2 concentrations. Photosynthetica 11(3):251–259Google Scholar
  83. Winter H, Robinson DG, Heldt HW (1993) Subcellular volumes and metabolite concentrations in barley leaves. Planta 191:180–190CrossRefGoogle Scholar
  84. Winter H, Robinson DG, Heldt HW (1994) Subcellular volumes and metabolite concentrations in spinach leaves. Planta 193:530–535CrossRefGoogle Scholar
  85. Yin X, Harbinson J, Struk PC (2006) Mathematical review of literature to assess alternative electron transports and interphotosystem excitation partitioning of steady-state C3 photosynthesis under limiting light. Plant Cell Environ doi: 10.1111/j.1365-3040.2006.01554.x: 1–12 (in press)Google Scholar
  86. Yin X, van Oijen M, Schapendonk AHCM (2004) Extension of a biochemical model for the generalized stoichiometry of electron transport limited C3 photosynthesis. Plant Cell Environ 27:1211–1222CrossRefGoogle Scholar
  87. Zhu X-G, Govindjee, Baker NR, deSturler E, Ort DR, Long SP (2005) Chlorophyll a fluorescence induction kinetics in leaves predicted from a model describing each discrete step of excitation energy and electron transfer associated with photosystem II. Planta 223:114–133PubMedCrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media B.V. 2006

Authors and Affiliations

  1. 1.Institute for Molecular and Cell BiologyTartu UniversityTartuEstonia

Personalised recommendations