Uncovering the maths of leaf design

Scientists at UCLA have discovered a set of simple mathematical equations that allow plants to produce leaves that vary greatly in size.

Leaf anatomy varies across all plant species, not just in terms of surface area but also leaf thickness. Leaves comprise of three key tissues: the outer layer, the epidermis, the mesophyll for photosynthesis, and vascular tissue for water and sugar transport. Changes in the size of the leaf must rely on coordinated changes in each of these tissues to produce a functional lateral organ. This research reveals the rules responsible for ensuring proportional changes between all tissues of the leaf. Discovery of these rules leads Lawren Sack, Professor of ecology and evolutionary biology at UCLA, to call leaves “perfect machines”.

The team at UCLA used allometric analysis of 14 diverse angiosperm species with strong differentiation in leaf anatomy. This involves looking at how proportions of parts of the leaf change with difference in the total size of the leaf. It reveals an extraordinarily strong relationship linking cell size with cell wall thickness and leaf thickness. Generally relationships are isometric, so that changes in all aspects of the organ are proportional to one another, but leaf area remains unrelated to size of cells. This is so plants can produce leaves with a variety of surface areas without the need to change cell size which may be inefficient for the function of the cell.

This mathematical relationship can be used to infer the internal anatomy of a leaf from just leaf thickness alone. It also provides insight into how nature builds and changes the shape of structure without losing functionality; another example of the elegant solutions present within the natural world.

In future, the research group aims to uncover evolutionary relationships between leaf design and function in order to uncode the variation between species in the internal anatomy of their leaves. As Sack says “leaves are providing us with blueprints for bigger and better things – we just have to look closely to read them”.

Paper can be found at: http://www.amjbot.org/content/100/10/1936.full