Development and verification of a water and sugar transport model using measured stem diameter variations

Abstract

In trees, water and sugars are transported by xylem and phloem conduits which are hydraulically linked. A simultaneous study of both flows is interesting, since they concurrently influence important processes such as stomatal regulation and growth. A few mathematical models have already been developed to investigate the influence of both hydraulically coupled flows. However, none of these models has so far been tested using real measured field data. In the present study, a comprehensive whole-tree model is developed that enables simulation of the stem diameter variations driven by both the water and sugar transport. Stem diameter variations are calculated as volume changes of both the xylem and the phloem tissue. These volume changes are dependent on: (i) water transport according to the cohesion-tension theory; (ii) sugar transport according to the Münch hypothesis; (iii) loading and unloading of sugars; and (iv) irreversible turgor-driven growth. The model considers three main compartments (crown, stem, and roots) and is verified by comparison with actual measured stem diameter variations and xylem sap flow rates. These measurements were performed on a young oak (Quercus robur L.) tree in controlled conditions and on an adult beech (Fagus sylvatica L.) tree in a natural forest. A good agreement was found between simulated and measured data. Hence, the model seemed to be a realistic representation of the processes observed in reality. Furthermore, the model is able to simulate several physiological variables which are relatively difficult to measure: phloem turgor, phloem osmotic pressure, and Münch's counterflow. Simulation of these variables revealed daily dynamics in their behaviour which were mainly induced by transpiration. Some of these dynamics are experimentally confirmed in the literature, while others are not.

Analytical model for long-distance tracer-transport in plants

“…Tyree and Zimmermann, 2002;Holbrook and Zwieniecki, 2005;Lacointe and Minchin, 2008;De Schepper and Steppe, 2010). Because of the delicate structure of the transport tissues, non-invasive techniques are needed to study the underlying mechanisms in intact plants.…”

Light on phloem transport (an MRI approach)

“…600 mol · m -2 · s -1 ). This diurnal phloem volume flow pattern with higher flow during the day is striking because it is in contradiction to modelled phloem flows which predict higher phloem flow at night (Hölttä et al, 2006;De Schepper & Steppe, 2010). However, those models were developed for trees, not for herbaceous plants like tomato.…”

“…(Note: MRI is also an imaging technique, although its resolution is much lower). These and other novel techniques are providing input and calibration parameters for phloem flow models which have the potential to unlock further insights into how phloem works (Hölttä et al, 2006;De Schepper & Steppe, 2010). …”

“…Xylem and phloem are hydraulically linked; this tight relation is reflected for example in the replenishment of water for the phloem stream by the xylem stream (a fraction of the Munch's counter-flow) (Hölttä et al, 2006;Windt et al, 2006;De Schepper & Steppe, 2010). When we compared the xylem/phloem average volume flow ratio for individual nights, this ratio decreased by 35 % during the nights following short photoperiod.…”

“…The use of non-conventional breeding techniques such as transgenesis may circumvent these issues (Chapter 5), although in practice they are currently, at least from a societal perspective, an unacceptable method of crop improvement. One possible solution could be the calibration of phloem transport models (derived from current models (Thompson & Holbrook, 2003a;Minchin & Lacointe, 2005;Hölttä et al, 2006;Pickard & Abraham-Shrauner, 2009;De Schepper & Steppe, 2010;De Swaef et al, 2013)) with in-depth phenotyping data. Such data could be generated using an integrated approach combining several independent plant sensors (as demonstrated in Chapter 3).…”