Explain the shape of the apples starting with the black holes

The theory of singularities is used to describe numerous physical phenomena, from the fall of water droplets to black holes. A Harvard University study used it to understand the shape of apples

Photo: Pranjall Kumar | Unsplash Apples and physics: since the time of Isaac Newton, it is not the first time that the former have helped to understand the latter. Now the opposite is also true: a team of mathematicians and physicists from Harvard University, led by Lakshminarayanan Mahadevan, has developed a method to explain the shape of apples, in particular the hollow, called the cusp, from which the petiole then grows. . This would follow the mathematical theory of singularities, used to describe numerous natural phenomena, from the propagation of cracks to black holes.

The results of the study, published in the journal Nature Physics, are the fruit of theory, calculation, experiments in laboratory and direct observations. The starting point? An orchard of the University of Cambridge's Peterhouse College, where apples are known to have inspired Newton's law of universal gravitation.

From black holes to biology

Researchers, therefore, have set as a basis for understanding the evolution of the shape of apples the mathematical theory known as the theory of singularities: singularities, sudden breaking points between two conditions, are common in physical systems and can be applied to numerous contexts of real life. The theory of singularities, in fact, is used to describe numerous extremely different phenomena, from black holes, to the refraction patterns of light on the bottom of a swimming pool, to the fall of water drops, to the propagation of cracks on a wall.

“The exciting thing about singularities is that they are universal. The apple cusp has nothing in common with the bright patterns in a swimming pool, or with a drop falling off a water column, yet it has the same shape, "said Thomas Michaels, co-author of the study:" The concept of universality goes very deep and can be very useful because it connects singular phenomena observed in very different physical systems ”. A model so universal that the researchers thought of applying it also to living beings, in particular to morphogenesis, the biological process in which growth and movement over a period of time determine the shape and size of a biological entity, such as a fruit.

Reaping the fruits of research

Starting from this theoretical assumption, the research team used several mathematical simulations to understand how the growth of an apple could guide the construction of its characteristic shape, in particular of the cusp. The project, however, began to pay off - in the true sense of the word - when scientists corroborated the results of the simulations with laboratory experiments done on gel spheres and observations on real apples. The latter came from the orchard of the Peterhouse College of the University of Cambridge in the United Kingdom, Isaac Newton's alma mater, to whom the fall of an apple inspired the formulation of the theory of universal gravitation.

Through experiments with the Apples in gel and observations on real apples, the scientists mapped the growth of the hollow on top of the fruit, showing that the cusp formation is due to a difference between the growth of the petiole region and the rest of the apple. >
"Being able to control and reproduce the morphogenesis of the cusps in the laboratory with simple tools was particularly exciting", said Aditi Chakrabarti, co-author of the article: "Varying the geometry and composition of the gel spheres we have shown how more cusps can form, as seen in some apples and other fruits, such as peaches, apricots, cherries and plums ".

The study confirms that the and biological entities often possess structures that act as focal points, and that understanding them can help clarify both the processes of morphogenesis and singularities in biological systems at the same time. "Morphogenesis, literally the origin of form, is one of the great questions in biology - concludes 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 underlying cusp formation as we slowly move towards a broader theory of biological form. ”


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