Using an artificial model of a leaf, scientists have unveiled a mathematical principle underlying how leaf veins are arranged to enable water to perspire as fast as possible.

Because water perspiration is closely linked to how plants absorb CO₂, the findings could help researchers learn about past climates by studying the patterns of veins found on fossilized leaves.

Water evaporation helps leaves stay cool and provides the pull that lets plants lift nutrients from the soil. But during photosynthesis, when plants open up the pores on the underside of leaves to absorb CO₂, water escapes from those pores at an accelerated pace. "The same membranes that let CO₂ inside also let water outside,” says Maciej Zwieniecki of Harvard University’s Arnold Arboretum. Leaves then need abundant water flow to avoid dehydration. And the more CO₂ a plant absorbs, the more energy it can take in from the sun through photosynthesis, and the more it can grow. Evolution should thus favor a distribution of veins that can carry water through the leaves at a fast pace.

Zwieniecki and his collaborators write in the July 8 Proceedings of the National Academy of Sciences that, on average, the distance separating the veins that pump water through leaves is about the same as the distance separating the veins from the leaves’ surface.

This finely tuned geometry keeps water flowing quickly through the leaves, the team has found. Within species, leaf veins follow very uniform patterns, Zwieniecki says, suggesting that the geometry is a feature optimized through many generations of evolution.

The team’s results are “fascinating,” comments Lawren Sack, a biologist at the University of California, Los Angeles. “The finding implies that leaves are optimized during evolution by adjusting not only the length of vein per area [vein density], but also the thickness of tissues.”

The research could help scientists study past climate clues found in fossil leaves, Sack adds. “Venation patterns are often preserved,” he says, and could help reconstruct patterns of rainfall and availability of sunshine. The rate of evaporation from leaves is affected by humidity, and the amount of sunshine determines the energy available for photosynthesis.

The patterns could also inspire engineers to design better irrigation systems, he says.

Zwieniecki and his collaborators built a model of a leaf’s circulatory system by embedding a system of parallel microscopic channels into a layer of silicone. The researchers then let water circulate and measured the rate at which the water perspired from the material and evaporated through microscopic pores in the silicone.

The team repeated the experiment, changing the distance between channels and the thickness of the artificial leaf. Packing the channels closer together let water evaporate faster. But the rate of evaporation reached a plateau when the distance between channels was about the same as their distance from the outside surface. Zwieniecki says that, at that point, the channels become virtually indistinguishable and increasing their density would offered advantage.

The experiments suggest that for thin leaves, the vein density can be increased a great deal and still allow greater flow through the whole system. However, for thick leaves, increasing the vein density quickly loses any benefit for increasing flow.

The team confirmed its hypothesis by measuring the geometry of vein systems in the leaves of 32 plant species, ranging from thick-leaf succulents such as the Jade plant (Crassula ovata) to common trees with thin leaves, such as the red maple.

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