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Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis

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Abstract

Water and solute flows in the coupled system of xylem and phloem were modeled together with predictions for xylem and whole stem diameter changes. With the model we could produce water circulation between xylem and phloem as presented by the Münch hypothesis. Viscosity was modeled as an explicit function of solute concentration and this was found to vary the resistance of the phloem sap flow by many orders of magnitude in the possible physiological range of sap concentrations. Also, the sensitivity of the predicted phloem translocation to changes in the boundary conditions and parameters such as sugar loading, transpiration, and hydraulic conductivity were studied. The system was found to be quite sensitive to the sugar-loading rate, as too high sugar concentration, (approximately 7 MPa) would cause phloem translocation to be irreversibly hindered and soon totally blocked due to accumulation of sugar at the top of the phloem and the consequent rise in the viscosity of the phloem sap. Too low sugar loading rate, on the other hand, would not induce a sufficient axial water pressure gradient. The model also revealed the existence of Münch “counter flow”, i.e., xylem water flow in the absence of transpiration resulting from water circulation between the xylem and phloem. Modeled diameter changes of the stem were found to be compatible with actual stem diameter measurements from earlier studies. The diurnal diameter variation of the whole stem was approximately 0.1 mm of which the xylem constituted approximately one-third.

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References

  • Bancal P, Soltani F (2002) Source–sink partitioning. Do we need Münch? J Exp Bot 53:1919–1928

    Article  PubMed  CAS  Google Scholar 

  • Daudet FA, Lacointe A, Gaudillere JP, Cruiziat P (2002) Generalized Münch coupling between sugar and water fluxes for modelling carbon allocation as affected by water status. J Theor Biol 214:481–498

    Article  PubMed  CAS  Google Scholar 

  • Ferrier JM, Tyree MT, Christy AL (1975) The theoretical time-dependent behavior of a Münch pressure-flow system: the effect of sinusoidal time variation in sucrose loading and water potential. Can J Bot 53:1120–1127

    Google Scholar 

  • Génard M, Fishman S, Vercambre G, Huguet JG, Bussi C, Besset J, Habib R (2001) A biophysical analysis of stem and root diameter variations in woody plants. Plant Physiol 126:188–202

    Article  PubMed  Google Scholar 

  • Hari P, Mäkelä A, Korpilahti E, Holmberg M (1986) Optimal control of gas exchange. Tree Physiol 2:169–175

    PubMed  Google Scholar 

  • Hari P, Keronen P, Bäck J, Altimir N, Linkosalo T, Pohja T, Kulmala M, Vesala T (1999) An improvement of the method for calibrating measurements of photosynthetic C02 flux. Plant Cell Environ 22:1297–1301

    Article  Google Scholar 

  • Hubbard RM, Ryan MG, Stiller V, Sperry VS (2001) Stomatal conductance and photosynthesis vary linearly with plant hydraulic conductance in ponderosa pine. Plant Cell Environ 24:113–121

    Article  Google Scholar 

  • Irvine J, Grace J (1997) Continuous measurements of water tensions in the xylem of trees based on the elastic properties of wood. Planta 202:455–461

    Article  CAS  Google Scholar 

  • Knoblauch M, van Bel AJE (1998) Sieve tubes in action. Plant Cell 10:35–50

    Article  CAS  Google Scholar 

  • Kockenberger W, Pope JM, Xia Y, Jeffrey KR, Komor E, Callaghan PT (1997) A noninvasive measurement of phloem and xylem water flow in castor bean seedlings by nuclear magnetic resonance microimaging. Planta 201:53–63

    Article  Google Scholar 

  • Lalonde S, Tegeder M, Thorne-Holst M, Frommer WB, Patrick JW (2003) Phloem loading and unloading of sugars and amino acids. Plant Cell Environ 26:37–56

    Article  CAS  Google Scholar 

  • Mauseth J (2003) Botany: an introduction to plant biology, 3rd edn. Jones & Bartlett, Boston

    Google Scholar 

  • Mencuccini M, Grace J, Fioravanti M (1997) Biomechanical and hydraulic determinants of tree structure in Scots pine: anatomical characteristics. Tree Physiol 17:105–113

    PubMed  Google Scholar 

  • Milburn JA (1996) Sap ascent on vascular plants: challengers to the cohesion theory ignore the significance of immature xylem and recycling of Münch water. Ann Bot 78:399–407

    Article  Google Scholar 

  • Minchin P, Thorpe MR (1987) Measurement of unloading and reloading of photoassimilate within the stem of bean. J Exp Bot 38:211–220

    Article  Google Scholar 

  • Morison KR (2002) Viscosity equations for sucrose solutions: old and new 2002. In: Proceedings of the 9th APCChE Congress and CHEMECA 2002, Paper # 984

  • Nobel PS (1991) Physicochemical and environmental plant physiology, 4th edn. Academic, San Diego, CA

    Google Scholar 

  • Offenthaler I, Hietz P, Richter H (2001) Wood diameter indicates diurnal and long-term patterns of xylem water potential in Norway spruce. Trees 15:215–221

    Article  Google Scholar 

  • Pate JS, Jeschke WD (1995) Role of stems in transport, storage, and circulation of ions and metabolites by the whole plant. In: Gartner B (ed) Plant stems physiology and functional morphology. Academic, San Diego, CA, pp 177–204

    Google Scholar 

  • Pedersen O, Sand-Jensen K (1997) Transpiration does not control growth and nutrient supply in the amphibious plant Mentha aquatica. Plant Cell Environ 20:117–123

    Article  CAS  Google Scholar 

  • Perämäki M, Nikinmaa E, Sevanto S, Ilvesniemi H, Siivola E, Hari P, Vesala T (2001) Tree stem diameter variations and transpiration in Scots pine: an analysis using a dynamic sap flow model. Tree Physiol 21:889–897

    PubMed  Google Scholar 

  • Phillips RJ, Dungan SR (1993) Asymptotic analysis of flow in sieve tubes with semipermeable walls. J Theor Biol 162:465–485

    Article  Google Scholar 

  • Press WH, Flannery BP, Teukolsky SA, Wetterling WT (1989) Numerical recipes in Pascal: the art of scientific computing. Cambridge University Press, Cambridge, UK

    Google Scholar 

  • Salleo S, Assunta Lo Gullo M, De Paoli D, Zippo M (1996) Xylem recovery from cavitation-induced embolism in young plants of Laurus nobilis: a possible mechanism. New Phytol 132:47–56

    Article  Google Scholar 

  • Salleo S, Lo Gullo M, Trifiló P, Nardini A (2004) New evidence for a role of vessel-associated cells and phloem in the rapid xylem refilling of cavitated stems of Laurus nobilis. Plant Cell Environ 25:1065–1076

    Article  Google Scholar 

  • Schultze ED (1991) Water and nutrient interactions with plant water stress. In: Mooney HA, Winner WE, Pell EJ (eds) The book, response of plants to multiple schemes. Academic, San Diego, CA, pp 89–101

    Google Scholar 

  • Sevanto S, Vesala T, Perämäki M, Nikinmaa E (2002) Time lags for xylem and stem diameter variations in Scots pine tree. Plant Cell Environ 25:1071–1077

    Article  Google Scholar 

  • Sevanto S, Vesala T, Perämäki M, Nikinmaa E (2003) Sugar transport together with environmental conditions controls time lags between xylem and stem diameter changes. Plant Cell Environ 26:1257–1265

    Article  Google Scholar 

  • Sheehy JE, Mitchell PL, Durand JL, Gastal F, Woodward FI (1995) Calculation of translocation coefficients from phloem anatomy for use in crop models. Ann Bot 76:263–269

    Article  Google Scholar 

  • Siau JF (1984) Transport processes in wood. Springer-Verlag, Berlin Heidelberg New York, 211 p

    Google Scholar 

  • Smith KC, Magnuson CE, Goeschl JD, DeMichele DW (1980) A time-dependent mathematical expression of the Münch hypothesis of phloem transport. J Theor Biol 86:493–505

    Article  Google Scholar 

  • Sperry JS, Pockman WT (1993) Limitation of transpiration by hydraulic conductance and xylem cavitation in Betula occidentalis. Plant Cell Environ 16:279–287

    Article  Google Scholar 

  • Taiz L, Zeiger E (1998) Plant physiology, 2nd edn. Sineaur, Sunderland, MA

    Google Scholar 

  • Tanner W, Beevers H (2001) Transpiration, a prerequisite for long-distance transport of minerals in plants? Plant Biol 98:9443–9447

    CAS  Google Scholar 

  • Thompson VM, Holbrook M (2003a) Application of a single-solute nonsteady-state phloem model to the study of long-distance assimilate transport. J Theor Biol 220:419–455

    Article  Google Scholar 

  • Thompson NM, Holbrook NM (2003b) Scaling phloem transport water potential equilibrium and osmoregulatory flow. Plant Cell Environ 26:1561–1577

    Article  Google Scholar 

  • Thompson VM, Holbrook M (2004) Scaling phloem transport: information transmission. Plant Cell Environ 27:509–519

    Article  Google Scholar 

  • Tyree MT, Christy AL, Ferrier JM (1974) A simpler iterative steady state solution of Münch pressure-flow systems applied to long and short translocation paths. Plant Physiol 54:589–600

    Article  PubMed  Google Scholar 

  • Van Bel AJE (2003) The phloem, a miracle of ingenuity. Plant Cell Environ 26:125–149

    Article  Google Scholar 

  • Vesala T, Haataja J, Aalto P, Altimir N, Buzorius G, Garam E, Hämeri K, Ilvesniemi H, Jokinen V, Keronen P, Lahti T, Markkanen T, Mäkelä J, Nikinmaa E, Palmroth S, Palva L, Pohja T, Pumpanen J, Rannik Ü, Siivola E, Ylitalo H, Hari P, Kulmala M (1998) Long-term field measurements of atmosphere–surface interactions in boreal forest combining forest ecology, micrometeorology, aerosol physics, and atmospheric chemistry. Trends Heat Mass Momentum Transfer 4:17–35

    CAS  Google Scholar 

  • Vesala T, Hölttä T, Perämäki M, Nikinmaa E (2003) Refilling of a hydraulically isolated embolised vessel: model calculations. Ann Bot 91:419–428

    Article  PubMed  Google Scholar 

  • Zimmermann MH (1983) Xylem structure and the ascent of sap. Springer-Verlag, Berlin Heidelberg New York, 143 p

    Google Scholar 

  • Zwieniecki MA, Melcher PJ, Holbrook N (2001) Hydraulic properties of individual xylem vessels of Fraxinus americana. J Exp Bot 52:257–264

    Article  PubMed  CAS  Google Scholar 

Download references

Acknowledgements

We thank Magnus Ehrnrooth foundation and Academy of Finland (projects #200731 and #55107) for research funding.

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Author notes

  1. S. Sevanto

    Present address: Department of Organismic and Evolutionary Biology, Harvard University, 3083 Biological Laboratories 16 Divinity Avenue, Cambridge, 02138, MA, USA

Authors and Affiliations

  1. Department of Physical Sciences, University of Helsinki, P.O. Box 64, FIN-00014, Helsinki, Finland

    T. Hölttä, T. Vesala & S. Sevanto

  2. Department of Forest Ecology, University of Helsinki, P.O. Box 24, FIN-00014, Helsinki, Finland

    M. Perämäki & E. Nikinmaa

Authors
  1. T. Hölttä
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  2. T. Vesala
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  3. S. Sevanto
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  5. E. Nikinmaa
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Correspondence to T. Hölttä.

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Hölttä, T., Vesala, T., Sevanto, S. et al. Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis. Trees 20, 67–78 (2006). https://doi.org/10.1007/s00468-005-0014-6

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  • DOI: https://doi.org/10.1007/s00468-005-0014-6

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