When it comes to leaves, size matters

What shorter trees lack in height, they make up for in a wide range of leaf sizes suited to the environmental stresses that define their existence. For the tallest trees, though, the range of leaf sizes is far more limited, for reasons that until now have been largely unexplained.

A pair of scientists from Harvard University and UC Davis have shown in a recent study that the limitations on this particular feature of plant diversity may largely come down to basic physics.

The physical principles in question concern the movement of fluid throughout a tree’s vascular system. This network of specialized channel cells consists of xylem, which conduct water and minerals up from the roots, and phloem, which transport the products of photosynthesis generated in the leaves to the rest of the plant. Because these photosynthetic products are the sugars that power the plant’s metabolism, the movement of sugar-containing sap can be quantified as an energy flow.

In their paper published in the Jan. 4 issue of Physical Review Letters, authors Maciej Zwieniecki and Kaare Jensen argue that the length of leaves relative to tree height follows a mathematical relationship that optimizes the flow of energy through the tree.

“The way we do engineering, and [the way] nature does engineering, is we are [both] trying to make everything function efficiently,” said Zwieniecki, a plant physiologist at UC Davis.

To calculate efficiency in energy terms means understanding in detail how sugars are transported in trees. This understanding requires sensitive measurements in the hard-to-reach, microscopic phloem tubes. By comparing such measurements with data gathered from an artificial microfluidic device, the researchers had already developed a simplified quantitative model for sugar transport.

Unlike the vascular system of animals, trees have no heart to mechanically pump their vital fluids. In the phloem, fluid flow is believed to be driven by osmotic pressure generated by differences in the concentration of sugar molecules, which diffuse into the cells from their sources in leaf tissue. By taking into account a variety of factors, the authors could relate the sugar transport speed with leaf length and compare it to the energy costs of maintaining trees of a certain height and leaves of a certain length.

To test the model, Zwieniecki and Jensen used recorded data on leaf length in 1,925 species of trees mostly located in the diverse Sabah and Sarawak forests of Malaysia, as well as species from Australia and North America. The trees studied were all angiosperms, flowering plants, by far the most widespread and diverse group of land plants.

A plot of leaf length against tree height shows wide variability that tapers off sharply as trees approach 100 meters in height, the maximum observed for angiosperms in nature. This reflects the fact that the tallest trees grow only in the most forgiving environments, where environmental stresses don’t factor in, and leaf length is determined almost entirely by the intrinsic physical constraints of sugar transport. For the tallest trees, these limit leaf lengths to a narrow range of just 4 to 8 inches.

The observations fit closely within the bounds set by the authors’ theoretical calculations for minimum and maximum leaf length based on optimum flow speed and energy distribution, which they believe underscores the validity of their phloem flow model.

Karl Niklas, a Cornell University professor of plant biology and author of the book Plant Physics, called the study “elegant” in its use of simple mathematics to relate variables such as phloem radius and tree height to leaf length.

“As far as I know, this is the first time that anybody has actually emphasized phloem loading and the energy aspects of the leaf,” Niklas said. “And if this study withstands the test of experiment and additional analysis, it shows you can really understand a great deal about biology using comparatively simple physical principles.”

Other studies of biophysical limitations on plant growth have typically examined water flow from the roots to the leaves in the xylem, accomplished by the cohesion of the water column as it is pulled up and out of the leaves during transpiration.

“What in my opinion has been lacking is that you have to look at what the primary purpose of a leaf is,” said Jensen, a postdoctoral researcher in Harvard’s Department of Organismic and Evolutionary Biology. “The primary purpose will always be to produce energy for the plant. So any constraint related to that will be at least as important as any other hydrological constraint.”

Jensen said nailing down the exact mechanisms of transport in the phloem could also lead to improvements for osmotic pumps used in medical applications or even osmotic batteries used for generating power at a micro-scale. Nonetheless, a number of theoretical questions remain: For example, how the specific branching patterns of the vascular system allow trees to optimize energy flow.

“It’s a nice scientific question,” Jensen said. “And it’s almost certain that the solution will be surprising and elegant.”

OYANG TENG can be reached at science@theaggie.org.