Mathematical modelling of the phloem: the importance of diffusion on sugar transport at osmotic equilibrium

S. Payvandi, K. R. Daly, K. C. Zygalakis, T. Roose

Research output: Contribution to journalArticlepeer-review

Abstract

Plants rely on the conducting vessels of the phloem to transport the products of photosynthesis from the leaves to the roots, or to any other organs, for growth, metabolism, and storage. Transport within the phloem is due to an osmotically-generated pressure gradient and is hence inherently nonlinear. Since convection dominates over diffusion in the main bulk flow, the effects of diffusive transport have generally been neglected by previous authors. However, diffusion is important due to boundary layers that form at the ends of the phloem, and at the leaf-stem and stem-root boundaries. We present a mathematical model of transport which includes the effects of diffusion. We solve the system analytically in the limit of high Münch number which corresponds to osmotic equilibrium and numerically for all parameter values. We find that the bulk solution is dependent on the diffusion-dominated boundary layers. Hence, even for large Péclet number, it is not always correct to neglect diffusion. We consider the cases of passive and active sugar loading and unloading. We show that for active unloading, the solutions diverge with increasing Péclet. For passive unloading, the convergence of the solutions is dependent on the magnitude of loading. Diffusion also permits the modelling of an axial efflux of sugar in the root zone which may be important for the growing root tip and for promoting symbiotic biological interactions in the soil. Therefore, diffusion is an essential mechanism for transport in the phloem and must be included to accurately predict flow.
Original languageEnglish
Pages (from-to)2834-2865
Number of pages32
JournalBulletin of Mathematical Biology
Volume76
Issue number11
Early online date28 Oct 2014
DOIs
Publication statusPublished - Nov 2014

Fingerprint

Dive into the research topics of 'Mathematical modelling of the phloem: the importance of diffusion on sugar transport at osmotic equilibrium'. Together they form a unique fingerprint.

Cite this