Register      Login
Functional Plant Biology Functional Plant Biology Society
Plant function and evolutionary biology
RESEARCH ARTICLE

Modelling phloem and xylem transport within a complex architecture

André Lacointe A and Peter E. H. Minchin B C
+ Author Affiliations
- Author Affiliations

A INRA, UMR547 PIAF, F-63100 Clermont-Ferrand, France.

B The Horticulture and Food Research Institute of New Zealand Ltd, 412 No. 1 Road, RD2 Te Puke, New Zealand.

C Corresponding author. Email: pminchin@hortresearch.co.nz

This paper originates from a presentation at the 5th International Workshop on Functional–Structural Plant Models, Napier, New Zealand, November 2007.

Functional Plant Biology 35(10) 772-780 https://doi.org/10.1071/FP08085
Submitted: 18 March 2008  Accepted: 29 July 2008   Published: 11 November 2008

Abstract

The function of the plant’s vasculature, incorporating both phloem and xylem, is of fundamental importance to the survival of all higher plants. Although the physiological mechanism involved in these two transport pathways has been known for some time, quantitative modelling of this has been slow to develop. 1-D continuous models have shown that the proposed mechanisms are quantitatively plausible (Thompson and Holbrook 2003) but more complex geometries (architectures) have remained out of reach because of mathematical difficulties. In this work, we extend the alternative modular approach by Daudet et al. (2002) using recently developed numerical tools which allow us to model complex architectures. After a full description of the extended model, we first show that it efficiently reproduces the results of the continuous approach when applied to the same simple configurations. The model is then applied to a more complex configuration with two sinks, confirming that sink priority is an emergent property of the Münch flow as earlier found with a minimalist model (Minchin et al. 1993). It is further shown how source leaf transpiration can change the relative carbon allocation rates among sinks.

Additional keywords: carbon allocation, coupled water and carbon fluxes, functional–structural plant modelling, Münch model, phloem, plant architecture, sink priority, xylem.


Acknowledgements

AL is very grateful for travel support from the International Science and Technology Linkage Fund (contract ISATA07–45) of the New Zealand Ministry of Research, Science and Technology. PEHM was supported by PGSF funding, contract CO6X0706.


References


Anderson E , Bai Z , Bischof C , Blackford S , Demmel J , et al. (1999) ‘LAPACK users’ guide. 3rd edn.’ Available at http://www.netlib.org/lapack/lug/index.html, accessed 8 August 2008.

Bancal P, Soltani F (2002) Source–sink partitioning. Do we need Münch? Journal of Experimental Botany 53, 1919–1928.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Christy AL, Ferrier JM (1973) A mathematical treatment of Munch’s pressure-flow hypothesis of phloem translocation. Plant Physiology 52, 531–538.
PubMed |
open url image1

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. Journal of Theoretical Biology 214, 481–498.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Gilli R (1997) ‘Evaluation de différentes données physico-chimiques relatives aux solutions sucrées.’ Available at http://www.associationavh.com/fr/feuilles.html, accessed 8 August 2008.

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 Transactions on Mathematical Software 31, 363–396.
Crossref | GoogleScholarGoogle Scholar | open url image1

Hölttä 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, 67–78.
Crossref | GoogleScholarGoogle Scholar | open url image1

Le Roux X, Lacointe A, Escobar-Gutiérrez A, Le Dizès S (2001) Carbon-based models of individual tree growth: a critical appraisal. Annals of Forest Science 58, 469–506.
Crossref | GoogleScholarGoogle Scholar | open url image1

Mathlouthi M , Génotelle J (1995) Rheological properties of sucrose solutions and suspensions. In ‘Sucrose. Properties and applications’. (Eds M Mathlouthi, P Reiser) pp. 126–154. (Blackie Academic & Professional: Glasgow)

Minchin PEH, Thorpe MR, Farrar JF (1993) A simple mechanistic model of phloem transport which explains sink priority. Journal of Experimental Botany 44, 947–955.
Crossref | GoogleScholarGoogle Scholar | open url image1

Münch E (1928) Versuche über den Saftkreislauf. Deutsche botanische Gesellschaft 45, 340–356. open url image1

Nobel PS (1991) ‘Physicochemical and environmental plant physiology.’ (Academic Press Inc.: London)

Thompson MV, Holbrook NM (2003) Application of a single-solute non-steady-state phloem model to the study of long-distance assimilate transport. Journal of Theoretical Biology 220, 419–455.
Crossref | GoogleScholarGoogle Scholar | PubMed | open url image1

Thompson MV , Zwieniecki MA (2005) The role of potassium in long distance transport in plants. In ‘Vascular transport in plants’. (Eds NM Holbrook, MJ Zwieniecki) pp. 221–240. (Elsevier Academic Press: Boston)

Thornley JMH (1970) Respiration, growth and maintenance in plants. Nature 227, 304–305.
Crossref | GoogleScholarGoogle Scholar | open url image1

Van Bel AJE (2003) The phloem, a miracle of ingenuity. Plant, Cell & Environment 26, 125–147.
Crossref | GoogleScholarGoogle Scholar | open url image1