The world’s first mathematical formula for
weather forecasting included “leaf surface area.”
Early climate models were criticized for lack of
“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.”
June 30th, 2008
Plant leaf plumbing designed to move water fast
Optimizing leafy networks
By Davide Castelvecchi
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
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
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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