Study shows how apples got their shape


Apples are usually round, flattened, or oblong in shape. They taper towards the bottom, which is categorized as conical. There is also a dimple at the top where the stem grows.

How do apples develop this distinctive shape?

With the help of observations, laboratory experiments, theory and computer methods, a team of mathematicians and physicists understood the growth and shape of an apple tip.

A simple theory has already been developed to explain the shape and growth of apples. This new project began when scientists combined observations of real apples at various stages of growth and gel experiments to mimic the growth and theory and calculations.

Scientists began collecting apples at various stages of growth from an orchard at Peterhouse College, University of Cambridge in the UK (the alma mater of another famous apple lover, Sir Isaac Newton).

With these apples, the team mapped the growth of the dimple, or hump, as they called it, over time.

Experimental measurements of apple cross-sections in different growth stages. (Source: Thomas Michaels / Aditi Chakrabarti / Harvard SEAS)

Using a long-standing mathematical theory, the singularity theory, scientists have determined the evolution of the shape of the apple and the tip in particular. Singularity describes a variety of different phenomena, from black holes to more mundane examples like the patterns of light at the bottom of a swimming pool, the breaking up of droplets, and the propagation of cracks.

Thomas Michaels, a former SEAS postdoctoral fellow and co-lead author of the paper, now at University College Londonvvvv, said: “The exciting thing about singularities is that they are universal. The apple humps have nothing to do with patterns of light in a swimming pool or a drop breaking off from a column of water, yet they have the same shape as them. The concept of universality goes very deep and can be very useful because it connects singular phenomena that are observed in very different physical systems. “

Building on this theoretical framework, the scientists used numerical simulations to see how the different development between the fruit rind and the core drives the formation of the bumps.

They then verified the simulations with experiments that mimicked the growth of apples with a gel that swelled over time. The experiments showed that different growth rates between the mass of the apple and the stem region led to the dimple-like tip.

Aditi Chakrabarti, postdoctoral fellow at SEAS and co-author of the work, said: “It was particularly exciting to be able to control and reproduce the morphogenesis of individual cusps in the laboratory with simple material toolkits. The variation in the geometry and composition of the gel imitations showed how several bumps form, as can be seen in some apples and other stone fruits such as peaches, apricots, cherries and plums. “

In addition to mechanical instability, the underlying fruit anatomy is crucial for the formation of multiple bumps in fruit.

L. Mahadevan, Lola England de Valpine Professor of Applied Mathematics, Organismic and Evolutionary Biology and Physics at Harvard John A. Paulson School of Engineering and Applied Sciences (SEAS), called, “Morphogenesis, literally the origin of form, is one of the big questions in biology. The shape of the humble apple has enabled us to study some physical aspects of a biological singularity. Of course, we now need to understand the molecular and cellular mechanisms behind hump formation as we slowly approach a broader theory of biological form. “

Journal reference:
  1. Aditi Chakrabartiet al. The tip of an apple, Natural Physics (2021). DOI: 10.1038 / s41567-021-01335-8


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