The scaling of the hydraulic architecture in poplar leaves

Abstract

Although much is known about the hydraulics of xylem, the hydraulic interconnectivity and dimensional scaling of phloem with respect to xylem in leaves has not been adequately studied to test alternative hydraulic architectural rules such as da Vinci's rule or Murray's rule, or physiological models such as Münch's Pressure Flow hypothesis. Using confocal and electron microscopy as well as mathematical analyses, we examined the hydraulic architecture of the mature leaves of the model species Populus tremula × alba across all seven hierarchical orders of the vascular branching. We show that: phloem and xylem conductive areas increase from minor to major veins; the sum of the conductive areas for each vein order increases exponentially from major to minor veins; the volume of individual sieve tube and vessel members increases from minor to major veins; and phloem conductive area scales isometrically with respect to xylem area across all vein orders. The application of first principles to our data shows that conductive areas scale according to da Vinci's rule and not according to Murray's rule, and that the phloem network in poplar leaves can generate the pressure gradient envisioned in Münch's hypothesis.

Scaling of phloem hydraulic resistance in stems and leaves of the understory angiosperm shrub Illicium parviflorum

“…While having a higher proportion of sieve tubes in the petioles has consequences for mass transfer from the leaves to the stems, the 1:1 relationship between the phloem and the xylem in the leaves of I. parviflorum implies that the increasing total conductive area of the xylem and phloem in the major veins results from a higher number of conduits toward the petiole, similar to the described reduction in phloem conduit number in the single‐veined needles of pines (Ronellenfitsch et al., ). In addition, different vein hierarchies in the leaves of I. parviflorum have a scaling relationship of sieve tubes that is similar to what was recently reported for the reticulate‐veined leaves of poplar (Carvalho et al., ) and dichotomously veined Ginkgo (Carvalho et al., ). However, the sieve tube elements are shorter (and slightly thinner) at the petiole in Illicium parviflorum leaves than within the major leaf veins.…”

Phloem structure and development in Illicium parviflorum, a basal angiosperm shrub

“…While this has consequences for mass transfer from the leaves to the stems, the 1:1 relationship between the phloem and the xylem in the leaves of I. parviflorum implies that the increasing total conductive area of the xylem and phloem in the major veins results from a higher number of conduits towards the petiole, similar to the described reduction in phloem conduit number in the singled veined needles of pines (Ronellenfitsch et al ., 2015). In addition, different vein hierarchies in the leaves of I. parviflorum display a scaling relationship of sieve tubes that is similar to what was recently reported for the reticulate veined leaves of poplar (Carvalho et al ., 2017a) and the dichotomously veined Ginkgo (Carvalho et al ., 2017b). However, the sieve tube elements are shorter and thinner at the petiole in Illicium parviflorum leaves than within the leaf veins.…”

“…The directional flow in the sieve tubes of the major veins in Illicium leaves contrasts with the anatomy of the sieve tubes in the minor veins, where numerous sieve areas pervade their lateral walls. This is in line with the idea of a division of function between the minor veins, which mainly work as sugar loaders, and major veins, where directional transport occurs within leaves (Russin & Evert, 1985; Turgeon, 2006; Carvalho et al ., 2017a, 2018). A high number of symplasmic connections typically associate with passive sugar loading in the minor veins (van Bel et al ., 1992; Turgeon, 1996; Gamalei et al , 2000; Rennie & Turgeon, 2009; Turgeon, 2010; Davidson et al ., 2011; Zhang et al ., 2014), but the heterogeneity of the species evaluated leave this question still unresolved (Slewinski et al ., 2013).…”

“…2013; Rockwell et al ., 2018), the performance of the phloem in leaves is still poorly understood. With a recent exception (Carvalho et al ., 2017a), detailed evaluations of phloem architecture in leaves with reticulate venation are lacking. This is in part due to the challenging manipulations required to quantify the geometry of the sieve tubes in the tapering veins, as well as difficulties in evaluating the velocity of the sap inside the sieve tubes, typically measured by a fluorescent dye tracer (Jensen et al ., 2011, Etxeberria et al ., 2016) or radiolabeled compounds (Knoblauch et al ., 2016).…”

The hydraulic architecture of Ginkgo leaves

“…The structural linkages between phloem and xylem are also seen in the scaling relationships between the conductive transverse areas of both transport tissues in stems and leaves (Mencuccini et al, 2011; Jyske and Hölttä, 2015; Carvalho et al, 2017). However, the hydraulic, mechanical, and physiological implications of these scaling relationships remain unknown or at best poorly understood.…”