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The secret math of plants

UCLA biologists uncover rules that govern leaf design

UCLA | 10/31/2013, 1:33 p.m.
Transverse cross-section of a very thin sunflower leaf (Helianthus annuus) to a thick tea leaf (Camellia sasquana). Along with total leaf thickness and leaf area, the leaves differ dramatically in cell size and in the thickness of cell walls according to specific mathematical equations newly discovered by the UCLA research team. Lawren Sack, Grace John, Christine Scoffoni/UCLA Life Sciences

By contrast, a leaf’s area is unrelated to the sizes of the cells inside. This allows plants to produce leaves with a huge range of surface areas without the need for larger cells, which would be inefficient in function, the researchers said.

The team hypothesized that these strong mathematical relationships arise from leaf development — the process by which leaves form on the branch, growing from a few cells that divide into many, with cells then expanding until the leaf is fully mature. Because light can penetrate only so many layers of cells, leaves cannot vary much in the number of cells arranged vertically. The expansion of individual cells and their cell walls occurs simultaneously and is reflected in the thickness of the whole leaf. On the other hand, the number of cells arranged horizontally in the leaf continues to increase as leaves expand, regardless of the size of the individual cells.

The new ability to predict the internal anatomy of leaves from their thickness can give clues to the function of the leaf, because leaf thickness affects both the overall photosynthetic rate and the lifespan, said Sack.

“A minor difference in thickness tells us more about the layout inside the leaf than a much more dramatic difference in leaf area,” John said.

The design of the leaf provides insights into how larger structures can be constructed without losing function or stability.

“Fundamental discoveries like these highlight the elegant solutions evolved by natural systems,” Sack said. “Plant anatomy often has been perceived as boring. Quantitative discoveries like these prove how exciting this science can be. We need to start re-establishing skill sets in this type of fundamental science to extract practical lessons from the mysteries of nature.

“There are so many properties of leaves we cannot yet imitate synthetically,” he added. “Leaves are providing us with the blueprints for bigger, better things. We just have to look close enough to read them.”

The new allometric equations are an important step toward understanding the design of leaves on a cellular basis, John said. And because leaves are so diverse, she said, there is much to learn. In future research, the group will study species that are very closely related in an effort to uncover any evolutionary relationships between leaf design and function.

“What makes the cross-sections especially exciting is the huge variation from one species to the next,” John said. “Some have relatively enormous cells in certain tissues, and cell shapes vary from cylindrical to star-shaped. Each species is beautiful in its distinctiveness. All of this variation needs decoding.”

The research was federally funded by the National Science Foundation.

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