On the Efficacy of Water Transport in Leaves. A Coupled Xylem-Phloem Model of Water and Solute Transport

In this paper, we present and use a coupled xylem/phloem mathematical model of passive water and solute transport through a reticulated vascular system of an angiosperm leaf. We evaluate the effect of leaf width-to-length proportion and orientation of second-order veins on the indexes of water transport into the leaves and sucrose transport from the leaves. We found that the most important factor affecting the steady-state pattern of hydraulic pressure distribution in the xylem and solute concentration in the phloem was leaf shape: narrower/longer leaves are less efficient in convecting xylem water and phloem solutes than wider/shorter leaves under all conditions studied. The degree of efficiency of transport is greatly influenced by the orientation of second-order veins relative to the main vein for all leaf proportions considered; the dependence is non-monotonic with efficiency maximized when the angle is approximately 45° to the main vein, although the angle of peak efficiency depends on other conditions. The sensitivity of transport efficiency to vein orientation increases with increasing vein conductivity. The vein angle at which efficiency is maximum tended to be smaller (relative to the main vein direction) in narrower leaves. The results may help to explain, or at least contribute to our understanding of, the evolution of parallel vein systems in monocot leaves.