How apples get their shapes
Using theory and experiments, researchers show how apples get their
distinct cusp-like features

Date:
October 4, 2021
Source:
Harvard John A. Paulson School of Engineering and Applied Sciences
Summary:
How do apples grow that distinctive shape? Now, 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.



FULL STORY ========================================================================== Apples are among the oldest and most recognizable fruits in the world. But
have you ever really considered an apple's shape? Apples are relatively spherical except for that characteristic dimple at the top where the
stem grows.


==========================================================================
How do apples grow that distinctive shape? Now, 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 paper is published inNature Physics.

"Biological shapes are often organized by the presence of structures that
serve as focal points," said 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 senior author of the study. "These focal
points can sometimes take the form of singularities where deformations
are localized. A ubiquitous example is seen in the cusp of an apple, the
inward dimple where the stalk meets the fruit." Mahadevan had already developed a simple theory to explain the form and growth of apples
but the project began to bear fruit when the researchers were able to
connect observations of real apples at different growth stages and gel experiments to mimic the growth along with theory and computations.



==========================================================================
The research team began by collecting apples at various growth stages from
an orchard at Peterhouse College at University of Cambridge in the U.K.,
(the alma mater of another famous apple lover, Sir Isaac Newton).

Using those 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, the researchers turned to a long-standing mathematical theory
known as singularity theory. Singularity theory is used to describe a
host of different phenomena, from black holes, to more mundane examples
such as the light patterns at the bottom of a swimming pool, droplet
breakup and crack propagation.

"What is exciting about singularities is that they are universal. 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 concept of universality goes very deep and can
be very useful because it connects singular phenomena observed in very different physical systems." Building from this theoretical framework,
the researchers used numerical simulation to understand how differential
growth between the fruit cortex and the core drives formation of the
cusp. They then 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.

"Being able to control and replay morphogenesis of singular cusps in the laboratory with simple material toolkits was particularly exciting,"
said Aditi Chakrabarti, a postdoctoral fellow at SEAS and co-author
of the paper. "Varying the geometry and composition of the gel mimics
showed how multiple cusps form, as seen in some apples and other drupes,
such as peaches, apricots, cherries and plums." 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." This research was co-authored by Sifan
Yin, a visiting student from Tsinghua University and Eric Sun, a former undergraduate in the lab.

========================================================================== Story Source: Materials provided by Harvard_John_A._Paulson_School_of_Engineering_and_Applied
Sciences. Original written by Leah Burrows. Note: Content may be edited
for style and length.


========================================================================== Journal Reference:
1. Chakrabarti, A., Michaels, T.C.T., Yin, S. et al. The cusp of
an apple.

Nat. Phys., 2021 DOI: 10.1038/s41567-021-01335-8 ==========================================================================

Link to news story: https://www.sciencedaily.com/releases/2021/10/211004115131.htm

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