Sucrose transport to the root and shoot in the seedling phloem

In the seedling, sucrose synthesised within the leaves is transported via the phloem throughout the plant for growth and maintenance. Sucrose allocation between the root and shoot thus determines their relative growth; however, our understanding of how phloem characteristics affects sucrose allocation remains incomplete. In this paper, we develop and analyse a mathematical model that describes phloem sucrose transport in the Arabidopsis thaliana seedling, from a source region in a leaf to a sink region in either the root or shoot. Motivated by experimental observations in Arabidopsis seedlings, we assume sucrose unloading occurs via both bulk flow and diffusion. Moreover, we extend previous models by assuming that the phloem water and sucrose are unloaded via two different microscopic channels traversing the phloem boundary (plasmodesmata and aquaporins), the density of which vary along the phloem. Numerical solutions of our mathematical model predict that differences between the plasmodesmatal fluxes in the root or shoot (which are controlled by plasmodesmatal number and aperture) are the dominant mechanism controlling root-shoot sucrose allocation. We predict that while the sucrose concentration external to the phloem affects the relative diffusive and advective unloading, it has limited affect on sucrose allocation. Furthermore, we predict that negative pressure gradients external to the phloem (due to the xylem, for example) can inhibit sucrose allocation to the root. However, the model predicts that the Arabidopsis thaliana seedling modelled here can alleviate this effect by increasing the plasmodesmatal conductivity within the root.