Optimal vein density in artificial and real leaves

Abstract

The long evolution of vascular plants has resulted in a tremendous variety of natural networks responsible for the evaporatively driven transport of water. Nevertheless, little is known about the physical principles that constrain vascular architecture. Inspired by plant leaves, we used microfluidic devices consisting of simple parallel channel networks in a polymeric material layer, permeable to water, to study the mechanisms of and the limits to evaporationdriven flow. We show that the flow rate through our biomimetic leaves increases linearly with channel density (1/d) until the distance between channels (d) is comparable with the thickness of the polymer layer (␦), above which the flow rate saturates. A comparison with the plant vascular networks shows that the same optimization criterion can be used to describe the placement of veins in leaves. These scaling relations for evaporatively driven flow through simple networks reveal basic design principles for the engineering of evaporation-permeation-driven devices, and highlight the role of physical constraints on the biological design of leaves.water transport ͉ microfluidic ͉ biomimetics ͉ leaf hydraulic properties ͉ evaporative pump L eaves are the main pumps for the upward movement of fluids in plants, which takes place in a network of conduits collectively called xylem (1). On warm, sunny days, the leaves of a large tree can transport hundreds of liters of water from the soil, corresponding to several milliliters per day per leaf. Although photosynthesis, rather than water loss, is the desideratum of living leaves, the shared diffusional pathway for CO 2 and water vapor and the regulation of this pathway by water status in the leaf implies that these two fluxes are closely coupled. Indeed, maximum rates of photosynthesis scale linearly with the transport capacity of the xylem (2-4). A key attribute of vascular design within leaves is to ensure that no portion of the leaf is under-supplied and thus unable to support the water losses associated with CO 2 uptake (5-8). However, studies of leaf venation have largely treated leaves as two-dimensional structures (8). Here, we account for the fact that leaves have a finite thickness and address the placement of veins within leaves in terms of both their spacing and their distance from the evaporative surface.Evaporation-driven flow in leaves is controlled by parameters such as wind, temperature, and stomatal aperture, all of which have been studied extensively (1, 9). However, the internal constraints imposed on evaporative transport by the architecture of the leaf hydraulic system have received relatively little attention (5, 6). Water utilizes two successive pathways as it flows from the veins of a leaf to the outside air, passing from the liquid to the vapor state. The first pathway is associated with capillary suction through the porous material-like network of cells and cell walls. One can describe the flux J using Darcy's law:grad ជ (P), where is the viscosity, is the permeability (linked to the characteri...

Weak coordination among petiole, leaf, vein, and gas‐exchange traits across Australian angiosperm species and its possible implications

“…Understanding this coordination has undoubtedly improved our understanding of water use and photosynthesis, and has provided an impetus for new theoretical work (Noblin et al. 2008; Boyce et al. 2009; Boyce and Zwieniecki 2012; Brodribb et al.…”

“…2007; Noblin et al. 2008; Zwieniecki and Boyce 2014), although this relationship is likely shifted by leaf thickness (Noblin et al. 2008; Sack et al.…”

Developmentally based scaling of leaf venation architecture explains global ecological patterns

“…Finally, Price et al 14 proposed that vein density should be independent from leaf size, because a constrained distance between the minor veins and thus a high vein density is needed for water and sugar transport. This idea comes from physiological studies that showed such an importance of high vein density but also adaptive variation across species 4,43,[51][52][53] . Indeed, we found here a considerably higher and more variable range of values for total vein density (Fig.…”

How Does Leaf Anatomy Influence Water Transport outside the Xylem?

“…High VLA may also be associated with shorter vertical path length if VLA is negatively correlated with leaf thickness, as is observed within certain species sets and lineages but not others (Noblin et al, 2008;Sack et al, , 2014Zwieniecki and Boyce, 2014). However, K ox might be correlated with VLA due to the influence of other traits that are structurally associated with veins and are positively correlated with K leaf , such as the size and hydraulic permeability of BS cells and the presence and size of bundle sheath extensions (BSEs).…”