Hydrodynamics of steady state phloem transport with radial leakage of solute

Abstract

Long-distance phloem transport occurs under a pressure gradient generated by the osmotic exchange of water associated with solute exchange in source and sink regions. But these exchanges also occur along the pathway, and yet their physiological role has almost been ignored in mathematical models of phloem transport. Here we present a steady state model for transport phloem which allows solute leakage, based on the Navier-Stokes and convection-diffusion equations which describe fluid motion rigorously. Sieve tube membrane permeability Ps for passive solute exchange (and correspondingly, membrane reflection coefficient) influenced model results strongly, and had to lie in the bottom range of the values reported for plant cells for the results to be realistic. This smaller permeability reflects the efficient specialization of sieve tube elements, minimizing any diffusive solute loss favored by the large concentration difference across the sieve tube membrane. We also found there can be a specific reflection coefficient for which pressure profiles and sap velocities can both be similar to those predicted by the Hagen-Poiseuille equation for a completely impermeable tube.

Computational models evaluating the impact of sieve plates and radial water exchange on phloem pressure gradients

“…In addition, we found that increasing the membrane hydraulic conductivity values increases pressure profiles because higher inflow led to greater flow through the sieve tube. Previous studies have also shown non‐linear pressure profiles due to radial inflow (Cabrita et al, ; Phillips & Dungan, ) and also report pressure gradient increases due to increased radial water flows. In contrast to the current study, the aforementioned reports seem to show that when radial water flow ceases, pressure gradients are reduced.…”

“…Water and sugars may therefore be exchanged along the entire route, not just in the source and sink regions (De Schepper et al, ; Sevanto, ; Thompson, ). This may have implications for the regulation of phloem pressure (Sevanto, ; Van Bel, ), and it may also impact pressure and velocity profiles (Cabrita et al, ; Phillips & Dungan, ; Tyree & Dainty, ). Here, we asked how a semipermeable membrane with high water transport capacity would affect the pressure gradient in the sieve tube.…”

“…Structural models have assumed plates are perpendicular to side walls, sieve pores are circular, and both sieve plates and lumen are free of obstruction (Jensen, Mullendore, et al, 2012;Mullendore et al, 2010; Thompson & Holbrook, 2003a). Meanwhile, other models have presented the relative importance of radial water exchange on flow (Cabrita, Thorpe, & Huber, 2013;Hölttä, Mencuccini, & Nikinmaa, 2009;Jensen, Rio, Hansen, Clanet, & Bohr, 2009;Phillips & Dungan, 1993;Tyree & Dainty, 1975). Particularly important to these models is sieve tube pressure as a function of distance along the tube.…”

Plant-PET Scans: In Vivo Mapping of Xylem and Phloem Functioning

“…Phloem function and transport have been, and still are [9], an important subject of debate, and while ongoing research provides new insights on phloem traits and its operating principles, it lacks visualization of the fate of carbon inside plants (e.g., [7,10,15,21,53,55,[64][65][66][67]). To improve our knowledge about the ecological implications of xylem and phloem function, as well as their interactions, several missing links need to be deciphered.…”

Plants, Functions and Processes Adapt to Different Environments

“…Aquaporins membrane proteins are present in all living plants, which form a complex permeable to water. In drought conditions aquaporins activity is critical in regulating hydraulic conductivity [23] (structures inspection status of water, particularly during drought by changing the hydraulic conductivity). With moisture deficit aquaporins are phosphorylated to a lesser extent and permeability of membranes for water is reduced.…”