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Phloem pp 371-386 | Cite as

A Mechanistic Model to Predict Distribution of Carbon Among Multiple Sinks

  • André LacointeEmail author
  • Peter E. H. Minchin
Protocol
Part of the Methods in Molecular Biology book series (MIMB, volume 2014)

Abstract

Modeling is a fundamental part of quantitative science used to bring together several quantitative components, often developed though detailed reductionist approach on component parts, e.g., sucrose transport through a membrane osmotic relation. It is now generally accepted that phloem transport is the result of bulk solution flow generated by the difference in osmotic pressure between source and sink tissues. However, there is still little agreement on how different sink tissues compete for available carbohydrate. Furthermore, the impact of phloem pathway leakage (unloading) and reloading on source-to-sink carbon transport remains unclear. Moreover, it is debated to what degree the interactions between phloem and xylem flows influence carbohydrate source-sink relations. These aspects are extremely difficult to research by a reductionist approach, with modeling being an important tool to examine the consequences of proposed mechanisms, which can then be tested on whole plants.

Phloem/xylem modeling has been at the limits of quantitative modeling, especially when dynamic models are needed to explain tracer studies. Advances in computing now enable more realistic modeling, which are utilized by the PiafMunch approach described here. This model enables a high level of mechanistic detail to be incorporated and the observable effect of it to be tested. In the most recent version of the software with the introduction of tracer dynamics, it can now predict the effects of specific phloem mechanisms upon the shape of evolving tracer profiles.

Key words

Münch model Carbon allocation Carbon partitioning Sink priority Phloem Xylem Plant architecture Functional-structural plant modeling Source-sink relations 

References

  1. 1.
    Wardlaw IF (1990) The control of carbon partitioning in plants. New Phytol 116:341–381CrossRefGoogle Scholar
  2. 2.
    Lacointe A (2000) Carbon allocation among tree organs. A review of basic processes and representation in functional tree-models. Ann For Sci 57:521–533CrossRefGoogle Scholar
  3. 3.
    Hölltä T, Vesala T, Sevanto S, Perämäki M, Nikinmaa E (2006) Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis. Trees 20:67–78CrossRefGoogle Scholar
  4. 4.
    Nikinmaa E, Sievänen R, Hölttä T (2014) Dynamics of leaf gas exchange, xylem and phloem transport, water potential and carbohydrate concentration in a realistic 3-D model tree crown. Ann Bot 114:653–666CrossRefGoogle Scholar
  5. 5.
    Münch E (1928) Versuche über den Saftkreislauf. Deutsch Botanisch Gesellschaft 45:340–356Google Scholar
  6. 6.
    Christy AL, Ferrier JM (1973) A mathematical treatment of Munch’s pressure-flow hypothesis of phloem translocation. Plant Physiol 52:531–538CrossRefGoogle Scholar
  7. 7.
    Thompson MV, Holbrook NM (2003) Application of a single-solute non-steady-state phloem model to the study of long-distance assimilate transport. J Theor Biol 220:419–455CrossRefGoogle Scholar
  8. 8.
    Minchin PEH, Thorpe MR, Farrar JF (1993) A simple mechanistic model of phloem transport which explains sink priority. J Exp Bot 44:947–955CrossRefGoogle Scholar
  9. 9.
    Minchin PEH, Farrar JF, Thorpe MR (1994) Partitioning of carbon in split roots of barley: effect of temperature of the root. J Exp Bot 45:1103–1109CrossRefGoogle Scholar
  10. 10.
    Bidel LPR, Pages L, Riviere LM, Pelloux G, Lorendeau JY (2000) Mass Flow Dyn 1: a carbon transport and partitioning model for root system architecture. Ann Bot 85:869–886CrossRefGoogle Scholar
  11. 11.
    Daudet FA, Lacointe A, Gaudillère JP, Cruiziat P (2002) Generalized Münch coupling between sugar and water fluxes for modelling carbon allocation as affected by water status. J Theor Biol 214:481–498CrossRefGoogle Scholar
  12. 12.
    Lacointe A, Minchin PEH (2008) Modelling phloem and xylem transport within a complex architecture. Funct Plant Biol 35:772–780.  https://doi.org/10.1071/FP08085CrossRefGoogle Scholar
  13. 13.
    Hall AJ, Minchin PEH (2013) A closed-form solution for steady-state coupled phloem/xylem flow using the Lambert-W function. Plant Cell Environ 36:2150–2162CrossRefGoogle Scholar
  14. 14.
    Gilli R (1997) Evaluation de différentes données physico-chimiques relatives aux solutions sucrées. http://www.associationavh.com/fr/feuilles.html. Accessed 28 Mar 2018
  15. 15.
    Mathlouthi M, Génotelle J (1995) Rheological properties of sucrose solutions and suspensions. In: Mathlouthi M, Reiser P (eds) Sucrose. Properties and applications. Blackie Academic & Professional, GlasgowGoogle Scholar
  16. 16.
    Thornley JMH (1970) Respiration, growth and maintenance in plants. Nature 227:304–305CrossRefGoogle Scholar
  17. 17.
    Le Roux X, Lacointe A, Escobar-Gutiérrez A, Le Dizès S (2001) Carbon-based models of individual tree growth: a critical appraisal. Ann For Sci 58:469–506CrossRefGoogle Scholar
  18. 18.
    Davis TA, Palamadai Natarajan E (2010) Algorithm 907: KLU, a direct sparse solver for circuit simulation problems. ACM Trans Math Softw 37(36):1–17CrossRefGoogle Scholar
  19. 19.
    Hindmarsh AC, Brown PN, Grant KE, Lee SL, Serban R, Shumaker DE, Woodward CS (2005) SUNDIALS: suite of nonlinear and differential/algebraic equation solvers. ACM Trans Math Softw 31:363–396CrossRefGoogle Scholar
  20. 20.
    Bancal P, Soltani F (2002) Source-sink partitioning. Do we need Münch? J Exp Bot 53:1919–1928CrossRefGoogle Scholar
  21. 21.
    Thorpe MR, Lacointe A, Minchin PEH (2011) Modelling phloem transport with a pruned dwarf bean: a 2-source- 3-sink system. Funct Plant Biol 38:127–138CrossRefGoogle Scholar
  22. 22.
    Minchin PEH, Lacointe A (2017) Consequences of phloem pathway unloading/reloading on equilibrium flows between source and sink: a modelling approach. Funct Plant Biol 44:507–514CrossRefGoogle Scholar
  23. 23.
    Steppe K, Cochard H, Lacointe A, Ameglio T (2012) Could rapid diameter changes be facilitated by a variable hydraulic conductance? Plant Cell Environ 35(1):150–157CrossRefGoogle Scholar
  24. 24.
    Lockhart JA (1965) An analysis of irreversible plant cell elongation. J Theor Biol 8:264–227CrossRefGoogle Scholar

Copyright information

© Springer Science+Business Media, LLC, part of Springer Nature 2019

Authors and Affiliations

  1. 1.Université Clermont AuvergneINRA, PIAFClermont-FerrandFrance
  2. 2.New Zealand Institute for Plant and Food ResearchMotueka Research CentreMotuekaNew Zealand

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