Laboratory of Plant Ecology, Department of Applied Ecology and Environmental Biology, Faculty of Bioscience Engineering, Ghent University, Coupure links 653, B-9000 Ghent, Belgium.
J Exp Bot. 2010 May;61(8):2083-99. doi: 10.1093/jxb/erq018. Epub 2010 Feb 22.
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.
在树木中，水和糖通过木质部和韧皮部导管进行运输，这些导管在水力上是相连的。同时研究这两种流动是很有趣的，因为它们同时影响着重要的过程，如气孔调节和生长。已经有一些数学模型来研究这两种水力耦合流的影响。然而，到目前为止，这些模型都没有使用实际测量的现场数据进行测试。在本研究中，开发了一个全面的整树模型，能够模拟由水和糖运输驱动的树干直径变化。树干直径的变化是通过木质部和韧皮部组织的体积变化来计算的。这些体积变化取决于：（i）根据水的凝聚力-张力理论进行的水运输；（ii）根据 Münch 假说进行的糖运输；（iii）糖的加载和卸载；以及（iv）不可逆膨压驱动的生长。该模型考虑了三个主要的隔室（树冠、树干和根系），并通过与实际测量的树干直径变化和木质部汁液流动速率进行比较进行了验证。这些测量是在受控条件下对一棵年轻的橡树（Quercus robur L.）和天然林里的一棵成年山毛榉（Fagus sylvatica L.）进行的。模拟数据与实测数据吻合较好。因此，该模型似乎是对实际观测到的过程的一种现实描述。此外，该模型还能够模拟一些相对难以测量的生理变量：韧皮部膨压、韧皮部渗透压和 Münch 反流动。这些变量的模拟揭示了它们行为的日动态，这些动态主要是由蒸腾作用引起的。这些动态中的一些在文献中有实验证实，而另一些则没有。
