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.
Highlights
Phloem transport denotes long-distance transport, mainly of assimilates arising from photosynthesis, and is the movement of a solution in a continuum of interconnected cells, sieve elements, within the phloem of the vascular tissues in plants
It is currently accepted that solutes enter and exit the sieve tubes at sources and sinks, water enters and exits osmotically, and the solution moves in these sieve tubes due to the consequent osmotically generated pressure gradient: the theory of Münch pressure flow
In the case of a semipermeable membrane (σ = 1), concentration and pressure differences across the sieve tube membrane (c and p are higher than cout and pout) create a water potential difference, across the sieve tube membrane that always draws water into the sieve tube, causing a pronounced non-linearity of pressure in the direction of flow (Figure 2A)
Summary
Phloem transport denotes long-distance transport, mainly of assimilates arising from photosynthesis, and is the movement of a solution in a continuum of interconnected cells, sieve elements, within the phloem of the vascular tissues in plants. There is a considerable radial exchange of solutes between the sieve tubes and the adjacent cells along the longdistance pathway between source and sink regions, the so-called transport phloem (i.e., main veins, petioles, stems, and main roots) (Van Bel, 2003). This radial exchange has hardly been addressed in mechanistic modeling of phloem transport. Passive unloading of photosynthates into the apoplast has been estimated at about 6% cm−1 in bean (Phaseolus vulgaris) (Minchin and Thorpe, 1987; Van Bel, 1990) This passive radial exchange of solutes is coupled with radial water flux. The leakage of other metabolites shows similar behavior (Aloni et al, 1986)
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