Cauliflower and Chaos, Fractals in Every Flower


Monks once hoped to turn lead into gold through alchemy. But consider cauliflower instead. Just two genes are all it takes to transform the ordinary stems, stems, and flowers of the herbaceous, tasteless Brassica oleracea strain into such a wondrous creation as this fractal, cloudy vegetable.

This is real alchemy, says Christophe Godin, senior researcher at the National Research Institute of Digital Science and Technology in Lyon, France.

Dr. Godin studies plant architecture by virtually modeling the evolution of forms of different species in three dimensions. He wondered what genetic modification lurked behind the intertwined helices of cauliflower and the logarithmic schematic fractals of Romanesco, a variety of cauliflower that could almost be mistaken for a crystal.

“How can nature build such unexpected objects?” He asked. “What could be the rules behind this?”

Fifteen years ago, Dr. Godin met François Parcy, a plant biologist at the National Center for Scientific Research in Grenoble, France. Dr. At Parcy, Dr. Godin recognized a friend for fractal flowers.

Dr. “You cannot fail to notice that it is such an amazing vegetable,” Parcy said, referring to Romanesco.

Driven by his passion for Brassica, Dr. Godin and Dr. Parcy explored the genetic mystery of fractal geometry in both Romanesco and standard cauliflower, animating plants in mathematical models and also growing them in real life. Their results, which suggest that fractals form in response to changes in gene networks that govern flower development, were published Thursday. Science.

“It’s a very nice integration of genetics on the one hand and meticulous modeling on the other,” said Michael Purugganan, a biologist at New York University who was not involved in the research. “They’re trying to show that you can achieve dramatic changes in a plant by changing the rules of how genes interact.”

In the early 2000s, Dr. Parcy believed she understood cauliflower. He even gave lectures on flower development. “What is cauliflower? How can it grow? Why does it look like this?” said.

Like Brussels sprouts, cauliflower has been around for centuries. selective breeding oleracea People have grown brussels sprouts for side buds and cauliflower for inflorescences. However, cauliflower does not produce flower buds; inflorescences or flowering shoots are never mature enough to produce flowers. Instead, cauliflower florets form copies of themselves in a spiral, forming clumps of curd like plant-based cottage cheese.

While two researchers were discussing cauliflower, Dr. Godin, if Dr. He suggested that if Parcy truly understood the plant, it would be easy to model the morphological development of the vegetable. As it turns out, it wasn’t.

The two first faced the curled-up swamp on the blackboard and drew various genetic network diagrams that could explain how the vegetable morphed into its current shape. Their muse was Arabidopsis thaliana, a well-studied herb from the same family as cauliflower and its many cousins.

If a cauliflower plant has a single cauliflower at the base, Arabidopsis has many cauliflower-like structures along its long stem. But what genes can turn these little cauliflowers into a single large, compact cauliflower? And if they identified these genes, could they bend these cauliflowers towards the hills formed by Romanescos?

To answer these questions, the researchers would alter the gene network and run it through mathematical models, reproduce it in 3D and mutate it in real life. Dr. “You imagine something, but you don’t know what it’s going to look like until you program it,” Parcy said.

(During the research, Dr. Parcy also collected several Romanesco samples from the local farmer’s market, sorted and dissected them. He and his colleagues then ate their meal along with a glass of beer, often with different dips, raw.)

Many early models failed with little resemblance to cauliflowers. At first, researchers believed that the key to cauliflower was the length of the stem. But when they programmed Arabidopsis with short stems and no stems, they realized that cauliflowers didn’t need to reduce stem size, neither in 3D models nor in real life.

And the cauliflowers they simulated and grown weren’t fractal enough. The patterns could only be seen at two fractal scales, for example, as if one spiral was placed inside another spiral. In contrast, a normal cauliflower usually shows self-similarity on at least seven fractal scales; this means a helix nested in a helix, a helix nested in a helix nested in a helix, a helix nested in a helix, a helix nested in a helix, ultimately a helix nested within another helix.

So, instead of focusing on the stem, they concentrated on the meristem, the region of plant tissue at the tip of each stem, where actively dividing cells produce new growth. They hypothesized that enlarging the meristem would increase the number of shoots produced.

The only problem was that the researchers did not know which gene could control the rate of shoot production of the meristem.

One day, at that time, Dr. Eugenio Azpeitia, a postdoctoral researcher in Godin’s lab, recalled a gene known to change the size of the meristem central region. The three researchers enjoyed a brief moment of enthusiasm and then patiently waited for months for their newly modified Arabidopsis to grow. When the shoots sprouted, they had distinctive conical-tipped cauliflowers.

“Very reminiscent of what happened in Romanesco,” said Godin proudly.

Normally, when a plant has a flower, the flowering end of the plant inhibits further growth from the stem. A cauliflower curd is a bud that was designed to become a flower but never gets there and instead makes a shoot. But the researchers’ experiments on the meristem found that this shoot was exposed to a gene that triggered its growth as it went through a temporary flower stage. Dr. “Since you are a flower, you are free to grow and you can shoot,” Parcy said.

This process creates a chain reaction in which the meristem produces many shoots and more shoots, invigorating the fractal geometry of a cauliflower.

“This is not a normal torso,” said Dr. godin. “A leafless stem. A non-blocking root.”

Dr. “It’s the only way to make cauliflower,” Parcy said.

Other mutations are likely responsible for Romanesco’s magnificent shape, the researchers say. Ning Guo, a researcher at the Beijing Vegetable Research Center who also studies the potential genetic mechanism behind the architecture of the cauliflower clot, says the paper offers “a lot of inspiration.”

“The story isn’t over yet,” Godin said, and he and Dr. He added that they will continue to develop Parcy’s cauliflower models. But we know we are on the right track.”

But they say they are open to scrutiny of anything that blooms.


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