Diffusion and bulk flow in phloem loading: A theoretical analysis of the polymer trap mechanism for sugar transport in plants

Abstract

Plants create sugar in the mesophyll cells of their leaves by photosynthesis. This sugar, mostly sucrose, has to be loaded via the bundle sheath into the phloem vascular system (the sieve elements), where it is distributed to growing parts of the plant. We analyze the feasibility of a particular loading mechanism, active symplasmic loading, also called the polymer trap mechanism, where sucrose is transformed into heavier sugars, such as raffinose and stachyose, in the intermediary-type companion cells bordering the sieve elements in the minor veins of the phloem. Keeping the heavier sugars from diffusing back requires that the plasmodesmata connecting the bundle sheath with the intermediary cell act as extremely precise filters, which are able to distinguish between molecules that differ by less than 20% in size. In our modeling, we take into account the coupled water and sugar movement across the relevant interfaces, without explicitly considering the chemical reactions transforming the sucrose into the heavier sugars. Based on the available data for plasmodesmata geometry, sugar concentrations and flux rates, we conclude that this mechanism can in principle function, but that it requires pores of molecular sizes. Comparing with the somewhat uncertain experimental values for sugar export rates, we expect the pores to be only 5-10% larger than the hydraulic radius of the sucrose molecules. We find that the water flow through the plasmodesmata, which has not been quantified before, contributes only 10-20% to the sucrose flux into the intermediary cells, while the main part is transported by diffusion. On the other hand, the subsequent sugar translocation into the sieve elements would very likely be carried predominantly by bulk water flow through the plasmodesmata. Thus, in contrast to apoplasmic loaders, all the necessary water for phloem translocation would be supplied in this way with no need for additional water uptake across the plasma membranes of the phloem.

Phloem Loading through Plasmodesmata: A Biophysical Analysis

“…Although segregation of RFOs based on a size exclusion mechanism has been proposed (Turgeon, 1991;Dölger et al, 2014), discrimination based only on hydrodynamic radii seems difficult considering that stachyose is only 40% larger than Suc (Liesche and Schulz, 2013), and raffinose is even smaller than stachyose. Even if the RFOs mass transfer coefficient is reduced by steric interaction with plasmodesmatal channels (Turgeon and Gowan, 1990;Dölger et al, 2014), back diffusion and leakage of RFOs into the mesophyll will eventually occur.…”

“…Even if the RFOs mass transfer coefficient is reduced by steric interaction with plasmodesmatal channels (Turgeon and Gowan, 1990;Dölger et al, 2014), back diffusion and leakage of RFOs into the mesophyll will eventually occur. Dölger et al (2014) presented a physical model of hindered transport of Suc through the plasmodesmata interface, concluding that the reentry of raffinose in the mesophyll could not be prevented by advective sweeping due to water flow through plasmodesmata. Here, we present an explicit model of advection and diffusion within the plasmodesmata ( Fig.…”

“…Suc and RFO are then exported via bulk flow in the transport phloem. Only a few models of phloem transport consider loading mechanisms and distinguish between mesophyll and phloem (Dölger et al, 2014;Lacointe and Minchin, 2008;Thompson and Holbrook, 2003). Other simplified modeling approaches (Jensen et al, 2011(Jensen et al, , 2012Jensen and Zwieniecki, 2013) have given insight into phloem traits at the plant scale but avoid the question of phloem loading by considering a fixed hydrostatic pressure in the phloem.…”

“…1B) and low levels of whole-leaf osmolarity ( pores from mesophyll to minor vein phloem, while simultaneously preventing the passage of larger RFOs in the opposite direction? One possibility is that the plasmodesmata in question are very narrow, allowing Suc to pass via diffusion (Haritatos and Turgeon, 1995;Liesche and Schulz, 2013;Turgeon and Gowan, 1990) or advection (Dölger et al, 2014;Voitsekhovskaja et al, 2006) while inhibiting RFO backflow on the basis of steric selectivity. However, coupling of local plasmodesmatal dynamics with whole-plant transport of water and sugars and the kinetics of polymerization has so far been neglected.…”

How Does Leaf Anatomy Influence Water Transport outside the Xylem?

“…This is discussed further in "Discussion." We also assumed that the quantitative contribution of plasmodesmatal flow to transpired water movement is negligible, consistent with its narrow circular slit (of width 1-2 nm) available for water flow between the membrane at its perimeter and the interior desmotubule of the endoplasmic reticulum (Doelger et al, 2014).…”