L Mahadevan, the Lola England de Valpine Professor of Applied Mathematics, of Organismic and Evolutionary Biology, and of Physics at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) and a team of mathematicians and physicists have used observations, lab experiments, theory and computation to understand the growth and form of the cusp of an apple.
The team collected apples at various growth stages from an orchard at Peterhouse College at University of Cambridge in the U.K. They then mapped the growth of the dimple, or cusp as they called it, over time. To understand the evolution of the shape of the apple and the cusp in particular, the researchers applied the mathematical theory known as singularity theory. Singularity theory is used to describe many different phenomena. "The apple cusp has nothing in common with light patterns in a swimming pool, or a droplet breaking off from a column of water, yet it makes the same shape as they do,” said Thomas Michaels, a former postdoctoral fellow at SEAS and co-lead author of the paper, now at University College London.
The study published in Nature Physics used numerical simulation to understand how differential growth between the fruit cortex and the core drives formation of the cusp. The researchers corroborated the simulations with experiments which mimicked the growth of apples using gel that swelled over time. The experiments showed that different rates of growth between the bulk of the apple and the stalk region resulted in the dimple-like cusp and the team found that the underlying fruit anatomy along with mechanical instability may play joint roles in giving rise to multiple cusps in fruits.
“Morphogenesis, literally the origin of shape, is one of the grand questions in biology,” said Mahadevan. “The shape of the humble apple has allowed us to probe some physical aspects of a biological singularity. Of course, we now need to understand the molecular and cellular mechanisms behind the formation of the cusp, as we move slowly towards a broader theory of biological shape.”