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Apples are among the oldest and most recognizable fruits in the world. But have you ever really thought about the shape of an apple? Apples are relatively spherical, except for that characteristic dimple at the top where the stem grows.
How do apples grow this distinctive shape?
Today, a team of mathematicians and physicists used observations, lab experiments, theory, and calculus to understand the growth and shape of an apple’s cusp.
The article is published in Nature Physics.
“Biological forms are often organized by the presence of structures that serve as focal points,” said L Mahadevan, Lola England Valpine professor of applied mathematics, organic and evolutionary biology, and physics at the Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS) and lead author of the study. “These foci can sometimes take the form of singularities where the deformations are located. A ubiquitous example is seen in the cusp of an apple, the inner dimple where the stem meets the fruit.
Mahadevan had already developed a simple theory to explain the shape and growth of apples, but the project began to bear fruit when researchers were able to link observations of real apples at different stages of growth and gel experiments to mimic the growth with theory and calculations.
The research team began by harvesting apples at different stages of growth from an orchard at Peterhouse College at Cambridge University in the UK (the alma mater of another famous apple lover, Sir Isaac Newton) .
Using these apples, the team 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, researchers turned to an ancient mathematical theory known as the theory of singularity. Singularity Theory is used to describe a multitude of different phenomena, from black holes to more mundane examples such as light patterns at the bottom of a swimming pool, the rupture of droplets and the propagation of cracks.
“What’s exciting about singularities is that they are universal. The cusp of the apple has nothing to do with the light patterns of a swimming pool or a droplet that comes off a column of water, but it has the same shape as them, ”said Thomas Michaels, former postdoctoral fellow at SEAS and co-lead author of the article, now at University College London. “The concept of universality is very deep and can be very useful because it links singular phenomena observed in very different physical systems.
From this theoretical framework, the researchers used numerical simulation to understand how the differential growth between the fruit cortex and the stone leads to the formation of the cusp. They then corroborated the simulations with experiments that mimicked the growth of apples using a gel that swelled over time. Experiments showed that different growth rates between the bulk of the apple and the stem region resulted in a dimple-shaped cusp.
“Being able to control and replay the morphogenesis of singular cusps in the lab with simple hardware toolkits was particularly exciting,” said Aditi Chakrabarti, postdoctoral researcher at SEAS and co-author of the article. “The variation in the geometry and composition of the gel mimics showed how multiple cusps are formed, as seen in some apples and other drupes, such as peaches, apricots, cherries and plums.”
The team found that the underlying anatomy of the fruit as well as mechanical instability may play a joint role in giving rise to multiple cusps in the fruit.
“Morphogenesis, literally the origin of form, is one of the big questions in biology,” Mahadevan said. “The shape of the humble apple allowed us to probe certain physical aspects of a biological singularity. Of course, now we need to understand the molecular and cellular mechanisms behind cusp formation, as we slowly move towards a larger theory of biological form. “
This research was co-authored by Sifan Yin, a visiting student from Tsinghua University and Eric Sun, a former undergrad in the lab.
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