After performing an exhaustive quantitative research across numerous plant species, scientists at  UCLA’s College of Letters and Science  have found that leaf design is governed by a set of fundamental mathematical expressions, underling once again the elegance of nature.

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.
Credit: Lawren Sack, Grace John, Christine Scoffoni/UCLA Life Sciences

The basis of their research was  “allometric analysis”, that is to say the study of an object’s evolution in size by studying its constituting parts and how they vary in proportionality. While it is easy to observe major differences in leaf surface area among species, they said, differences in leaf thickness are less obvious but equally important. Leaf thickness is actually where the researchers struck gold.

Once you start rubbing leaves between your fingers, you can feel that some leaves are floppy and thin, while others are rigid and thick,” said Grace John, a UCLA doctoral student in ecology and evolutionary biology and lead author of the research. “We started with the simplest questions — but ones that had never been answered clearly — such as whether leaves that are thicker or larger in area are constructed of different sizes or types of cells.”

A leaf is made out of three distinct parts: the outer layer that makes the leaf surface also called an epidermis, the  mesophyll which is comprised of photosynthesis capable cells and vascular tissue, whose cells are involved in water and sugar transport. The team found, after cutting cross-sections thinner than a single cell to observe each leaf’s microscopic layout, that the thicker the leaf, the larger the size of the cells in all of its tissues — except in the vascular tissue.

These relationships can be described by new, simple mathematical equations, effectively allowing scientists to predict the dimension of cells and cell walls based on the thickness of a leaf.

“This means that if a leaf has a larger cell in one tissue, it has a larger cell in another tissue, in direct proportion, as if you blew up the leaf and all its cells using Photoshop,” said Christine Scoffoni, a doctoral student at UCLA and member of the research team.

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.