Mathematical Biosciences and Engineering (MBE)

A surface model of nonlinear, non-steady-state phloem transport
Pages: 1055 - 1069, Issue 4, August 2017

doi:10.3934/mbe.2017055      Abstract        References        Full text (5425.3K)           Related Articles

Youcef Mammeri - Laboratoire Amiénois de Mathématique Fondamentale et Appliquée , CNRS UMR 7352, Université de Picardie Jules Verne, 80069 Amiens, France (email)
Damien Sellier - SCION, New Zealand Forest Research Institute, Private bag 3020, Rotorua 3046, New Zealand (email)

1 P. Cabrita, M. Thorpe and G. Huber, Hydrodynamics of steady state phloem transport with radial leakage of solute, Frontiers Plant Sci., 4 (2013), 531-543.
2 A. L. Christy and J. M. Ferrier, A mathematical treatment of Münch's pressure-flow hypothesis of phloem translocation, Plant Physio., 52 (1973), 531-538.
3 T. K. Dey and J. A. Levine, Delaunay meshing of isosurfaces, Visual Comput., 24 (2008), 411-422.
4 J. M. Ferrier, Further theoretical analysis of concentration-pressure-flux waves in phloem transport systems, Can. J. Bot., 56 (1978), 1086-1090.
5 F. G. Feugier and A. Satake, Dynamical feedback between circadian clock and sucrose availability explains adaptive response of starch metabolism to various photoperiods, Frontiers Plant Sci., 305 (2013), 1-11.
6 D. B. Fisher and C. Cash-Clark, Sieve tube unloading and post-phloemtransport of fluorescent tracers and proteins injected into sieve tubes via severed aphid stylets, Plant Physio., 123 (2000), 125-137.
7 J. D. Goeschl and C. E. Magnuson, Physiological implications of the Münch-Horwitz theory of phloem transport: effect of loading rates, Plant Cell Env., 9 (1986), 95-102.
8 J. Gričar, L. Krže and K. Čufar, Number of cells in xylem, phloem and dormant cambium in silver fir (Abies alba), in trees of different vitality, IAWA Journal, 30 (2009), 121-133.
9 J. Hansen and E. Beck, The fate and path of assimilation products in the stem of 8-year-old Scots pine (Pinus sylvestris L.) trees, Trees, 4 (1990), 16-21.
10 F. Hecht, New Developments in Freefem++, J. Num. Math., 20 (2012), 251-265.       
11 L. Horwitz, Some simplified mathematical treatments of translocation in plants, Plant Physio., 33 (1958), 81-93.
12 T. Hölttä, M. Mencuccini and E. Nikinmaa, Linking phloem function to structure: Analysis with a coupled xylem-phloem transport model, J. Theo. Bio., 259 (2009), 325-337.
13 T. Hölttä, T. Vesala, S. Sevanto, M. Perämäki and E. Nikinmaa, Modeling xylem and phloem water flows in trees according to cohesion theory and Münch hypothesis, Trees, 20 (2006), 67-78.
14 W. Hundsdorfer and J. G. Verwer, Numerical Solution of Time-Dependent Advection- Diffusion-Reaction Equations, Springer Series in Comput. Math., 33, Springer, 2003.       
15 K. H. Jensen, J. Lee, T. Bohr, H. Bruus, N. M. Holbrook and M. A. Zwieniecki, Optimality of the Münch mechanism for translocation of sugars in plants, J. R. Soc. Interface, 8 (2011), 1155-1165.
16 A. Kagawa, A. Sugimoto and T. C. Maximov, CO 2 pulse-labelling of photoassimilates reveals carbon allocation within and between tree rings, Plant Cell Env., 29 (2006), 1571-1584.
17 E. M. Kramer, Wood grain pattern formation: A brief review, J. Plant Growth Reg., 25 (2006), 290-301.
18 H.-O. Kreiss and J. Lorenz, Initial-Boundary Value Problems and the Navier-Stokes Equations, Classics in Applied Mathematics, SIAM, 2004.       
19 A. Lacointe and P. E. H. Minchin, Modelling phloem and xylem transport within a complex architecture, Funct. Plant Bio., 35 (2008), 772-780.
20 A. Lang, A model of mass flow in the phloem, Funct. Plant Bio., 5 (1978), 535-546.
21 P. E. H. Minchin, M. R. Thorpe and J. F. Farrar, A simple mechanistic model of phloem transport which explains sink priority, Journal of Experimental Botany, 44 (1993), 947-955.
22 E. Münch, Die Stoffbewegungen in der Pflanze, Jena, Gustav Fischer, 1930.
23 K. A. Nagel, B. Kastenholz, S. Jahnke, D. van Dusschoten, T. Aach, M. Mühlich, D. Truhn, H. Scharr, S. Terjung, A. Walter and U. Schurr, Temperature responses of roots: Impact on growth, root system architecture and implications for phenotyping, Funct. Plant Bio., 36 (2009), 947-959.
24 E. M. Ouhabaz, Analysis of Heat Equations on Domains, London Math. Soc. Monographs Series, Princeton University Press, 2005.       
25 S. Payvandi, K. R. Daly, K. C. Zygalakis and T. Roose, Mathematical modelling of the phloem: The importance of diffusion on sugar transport at osmotic equilibrium, Bull. Math Biol., 76 (2014), 2834-2865.       
26 S. Pfautsch, J. Renard, M. G. Tjoelker and A. Salih, Phloem as capacitor: Radial transfer of water into xylem of tree stems occurs via symplastic transport in ray parenchyma, Plant Physio., 167 (2015), 963-971.
27 O. Pironneau and M. Tabata, Stability and convergence of a Galerkin-characteristics finite element scheme of lumped mass type, Int. J. Num. Meth. Fluids, 64 (2000), 1240-1253.       
28 G. E. Phillips, J. Bodig and J. Goodman, Flow grain analogy, Wood Sci., 14 (1981), 55-64.
29 R. J. Phillips and S. R. Dungan, Asymptotic analysis of flow in sieve tubes with semi-permeable walls, J. Theor. Biol., 162 (1993), 465-485.
30 D. Rotsch, T. Brossard, S. Bihmidine, W. Ying, V. Gaddam, M. Harmata, J. D. Robertson, M. Swyers, S. S. Jurisson and D. M. Braun, Radiosynthesis of 6'-Deoxy-6'[18F]Fluorosucrose via automated synthesis and its utility to study in vivo sucrose transport in maize (Zea mays) leaves, PLoS ONE, 10 (2015), e0128989.
31 D. Sellier and J. J. Harrington, Phloem transport in trees: A generic surface model, Eco. Mod., 290 (2014), 102-109.
32 D. Sellier, M. J. Plank and J. J. Harrington, A mathematical framework for modelling cambial surface evolution using a level set method, Annals Bot., 108 (2011), 1001-1011.
33 R. Spicer, Symplasmic networks in secondary vascular tissues: Parenchyma distribution and activity supporting long-distance transport, J. Exp. Bot., 65 (2014), 1829-1848.
34 J. F. Swindells, C. F. Snyder, R. C. Hardy and P. E. Golden, Viscosities of sucrose solutions at various temperatures: Tables of recalculated values, NBS Circular, 440 (1958).
35 M. V. Thompson and N. M. Holbrook, Application of a single-solute non-steady-state phloem model to the study of long-distance assimilate transport, J. Theo. Bio., 220 (2003), 419-455.

Go to top