The 2012 ASHS Annual Conference

A mathematical model to describe long distance transport envisions plants as organs or tissues, such as root, stem, and leaf, which are divided into the compartments: cytoplast, xylem, phloem, and apoplast. Short distance movement within each plant tissue is rapid and governed by diffusion of water and/or active transport of metabolites. This leads to a single water potential and a steady state distribution of water and metabolites within any one tissue. Long distance transport corresponds to a flux of water and solutes in xylem and phloem between organs or tissues of a plant. This movement is driven by hydrostatic pressure, related to a water potential gradient in the xylem, and to turgor pressure in the phloem. In the model plant, a conductance is defined for movement of water in xylem and phloem between each tissue.  Water flux is the pressure difference between tissues times the conductance. Long-distance flux of metabolites is the concentration in xylem or phloem times the flux of water. The model incorporated these processes as finite difference equations using the VENSIM dynamic simulation modeling tool. This model predicted a diurnal variation in both solute concentration and flow rate in the xylem. Flow of water was much greater in the light than in the dark, due to transpiration, and metabolite concentrations in the xylem were decreased, because there is a greater change in water movement than in uptake of solutes. Flow in the phloem showed an opposite variation with light. After a transition from dark to light, water potential in leaves decreased faster due to transpiration than it did in the phloem due to accumulation of sugars. Consequently, the turgor pressure decreased early in the day. If conductivity in phloem was sufficiently low, the flow varied relatively little from day to night, because sugar concentration remained high throughout. These diurnal variations in long distance transport altered the availability of nitrate in leaves and sugars in roots.