Tiny pores in leaves appear to organize veins in a surprising geometric arrangement
A common houseplant hides a pattern that can reveal the formation of certain leaf veins.
The leaves of the Chinese money plant (pilea peperomioides) display a geometric pattern called a Voronoi diagramreport the researchers on May 12 in Natural communications. This pattern can form when waves of plant hormones spread from tiny water-secreting pores and meet during leaf development. A similar mechanism could also shape the veins of other plants, the researchers say.
“This is a nice new extension of the principle that veins optimize in many functions and have so much to tell us,” says Lawren Sack, a plant biologist at the University of California, Los Angeles, who was not involved in the work.
This trend was discovered when Elijah Blum, then a high school intern at Cold Spring Harbor Laboratory in New York, noticed the phenomenon. Pilea fascinating leaves when planting for her sister. The leaves were dotted with water-shedding pores called hydathodes, each surrounded by veins to form a mosaic. Blum, now at New York University, turned the factory over to his supervisor, computer scientist Saket Navlakha.
“He showed me the plant and said, ‘Look, the veins look pretty interesting here,'” Navlakha said. “And we kind of brought it to light, and we saw this canonical Voronoi diagram.”
In a Voronoi diagram, a surface is divided around a set of points such that each point in an area is closer to the point in that area than any other. City planners use the same idea to map services such as fire departments, assigning homes to the nearest train station.
Voronoi-like patterns appear elsewhere in nature, notably in the fur tiling of giraffes and dragonfly wing scales. But in a real Voronoi diagram, the mosaic must be generated by a set of points. In the Chinese central currency, hydathodes serve as points. Using geometric and statistical tests, Navlakha, Blum and their colleagues determined that the relationships between pores and major veins met the conditions for a Voronoi diagram.
The team then explored how this model could develop. The conventional explanation for the formation of similar leaf veins is canalization, in which auxin, a plant development hormone, branches through leaves to create a network of tree-shaped canals that become veins. But channeling would not produce a Voronoi relationship with hydathodes. Computer simulations instead suggest that, as Pilea as leaves grow, auxin waves radiate from each hydathode, colliding to form fronts that eventually become major veins.
Mathematical biologist CiCi Zheng, formerly of Cold Spring Harbor Laboratory, says more research is needed to determine why Pilea the leaves follow this pattern. One possibility, she says, is that the Voronoi model retains major veins, which carry water, as far away as possible from the hydathodes, where water loss peaks. “You may want to place the veins near places where water evaporates very quickly,” says Zheng, now at the Allen Institute in Seattle.
Sack is excited about what this discovery could mean beyond plant biology. He says previous studies of leaf veins have helped improve technologies such as solar panels, electronic circuits and irrigation systems. by leading engineers to reimagine how distribution systems can be optimized.
“The more we know about leaf veins,” Sack says, “the more functional and aesthetic systems we can build around us.”