Over 350 Years After Newton, Physicists Analyse Apples To Discover A New Theory

Physicists have recently conducted a study to understand the distinctive shapes of apples, and have found that certain special structures can be attributed to the cusp shape of the fruit

The cusp of an apple | Photo: Getty

New Delhi: Have you ever wondered how apples get their distinctive shape? What is responsible for the depression at the top of the sphere-shaped fruit where it has the stalk?

A team of researchers has recently conducted experiments to understand the growth and formation of the cusp of an apple. 

The study was recently published in the Nature Physics journal.

Odd traits, also called singularities, are commonly observed in diverse physical systems, and result in universal structures. Singularities are found in black holes, and in the light patterns at the bottom of a water body. Singularities also naturally arise in biological systems, such as an apple, which physicists have analysed using computations.

What are the findings?

Mahadevan, one of the lead authors of the study, explained that the presence of certain structures determine how biological shapes are organised, according to a statement by the Harvard School of Engineering and Applied Sciences. These structures, which act as focal points, can sometimes turn into singularities, he noted. 

Deformations are localised at these points, and an apple is a predominant example of this. Mahadevan said that the inward dimple in the cusp of an apple, where the stalk meets the fruit, is an instance of such singularities. 

Although he had earlier tried to explain the formation and growth of apples using a simple theory, it did not bear much fruit.  Mahadevan, along with his team, later studied apples at different growth stages using gel experiments.

The geometry of an apple is axisymmetric, which means the fruit is symmetrical about an axis, and the researchers analysed this with simulations of a physical gel that resembles an apple. The gel swells over time, and was used in order to mimic the growth of an apple. 

The experiments conducted in swelling gels show that axisymmetric cusps can lose stability and attain the shape of a lobe. The ratio of the stalk size to the sphere's size determines the number of lobes in an apple's cusp, the scientists note. In other words, difference in the growth rates between the bulk of the apple, and the stalk region results in the dimple-like cusp.

Multiple cusps may arise in other fruits such as peaches, apricots, cherries, and plums due to this connection between fruit anatomy and the loss of stability in the fruit, known as mechanical instability.

How was the study conducted?

The scientists studied the morphogenesis of the cusp of an apple, which refers to the biological process that causes a tissue to develop its characteristics shape by controlling cellular distribution at the embryonic stage. 

The scientists collected apples at various growth stages from an orchard at Peterhouse College at University of Cambridge in the UK. Interestingly, this is the college where a popular apple lover, Sir Isaac Newton, studied. It is famously said that Newton discovered gravity after an apple fell on his head. 355 years after the discovery of gravity due to an apple, physicists have analysed the fruit to understand its distinctive shape. 

The researchers used a mechanical theory which explains the heterogeneous growth of a soft sphere, in order to understand how the axisymmetric cusp came to be. They mapped the growth of the cusp at different stages.

This mathematical theory, known as the singularity theory, was used to understand the evolution of the shape and cusp of an apple. 

There is a difference in the pattern of growth occurring at the fruit cortex (outer layer), and at the core, and this is what drives the formation of the cusp, the study explains. This was understood using numerical simulations, which were then corroborated using other experiments. 

Mahadevan said that morphogenesis is an important question in biology, as it is the shape of a biological structure originates due to this phenomenon.

He added that they had only understood the physical aspects of a biological singularity, and were yet to understand the molecular and cellular mechanisms which cause the apple to be cusp-shaped.