Cauliflower and Chaos, Fractals in Each Floret

Monks once hoped to turn lead into gold through alchemy. Instead, consider the cauliflower. It only takes two genes to transform the common stems, stems and flowers of the herbaceous, tasteless species Brassica oleracea into such a wonderful formation as this fractal, cloud-like vegetable.

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

Dr. Godin examines plant architecture by virtually modeling the evolution of the shapes of different species in three dimensions. He wondered what genetic mutations lurked behind the nested spirals of cauliflower and the logarithmic chartreuse fractals of romanesco, a type of cauliflower that could almost be mistaken for a crystal.

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

15 years ago, Dr. Godin François Parcy, a plant biologist at the National Center for Scientific Research in Grenoble, France. In Dr. Parcy recognized Dr. Godin ‘a fellow man for fractal flowers.

“There is absolutely no way you can tell that it is such a wonderful vegetable,” said Dr. Parcy in relation to Romanesco.

Inspired by a passion for Brassica, Dr. Godin and Dr. Parcy found the genetic secret of fractal geometry in both romanesco and standard cauliflower, conjured up the plants in mathematical models and also bred them in real life. Their findings, which suggest the fractals form in response to changes in the networks of genes that control flower development, will be published in Science on Thursday.

“It’s such a beautiful integration of genetics on the one hand and rigorous modeling on the other,” said Michael Purugganan, a biologist at New York University who was not involved in the research. “They are trying to show that by optimizing the rules for how genes interact, you can make dramatic changes in a plant.”

In the early 2000s, Dr. Parcy to understand the cauliflower. He even taught courses on flower development. “What is a cauliflower? How can it grow? Why does it look like this? ”He said.

Like Brussels sprouts, cauliflower comes from the selective breeding of Brassica oleracea for centuries. Man grew Brussels sprouts for side buds and cauliflowers for flower clusters. However, cauliflower does not produce flower buds; their inflorescences or flower-bearing shoots never mature to produce flowers. Instead, cauliflower inflorescences create spiral replicas of themselves, creating clusters of curd cheese like plant-based cottage cheese.

When the two researchers were discussing cauliflower, Dr. Godin suggested that if Dr. Parcy really understands the plant, it should be easy to model the morphological evolution of the vegetable. As it turned out, it wasn’t.

The two first confronted the curdled swamp on the blackboard and sketched various diagrams of genetic networks that could explain how the vegetable mutated into its present form. Her muse was Arabidopsis thaliana, a well-studied weed from the same family as cauliflower and its many cousins.

When a cauliflower has a single cauliflower at the base of the plant, Arabidopsis has many cauliflower-like structures along its elongated stem. But what genes could refine this small cauliflower into a large, compact cauliflower? And if they identified these genes, could they deform this cauliflower into the peaks that form Romanescos?

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

(In the course of his research, Dr. Parcy also collected several copies of Romanesco from his local farmers’ market, sequenced and dissected them. He and his colleagues then ate the leftovers, mostly raw with various dips, along with glasses of beer.)

Many of the early models flopped and bore little resemblance to cauliflower. At first, researchers believed that the key to cauliflower lies in the length of the stem. But when they programmed Arabidopsis with and without a short stem, they found that they didn’t need to reduce the stem size of the cauliflower in either the 3D models or in real life.

And the cauliflowers they simulated and grew just weren’t fractal enough. The patterns were only visible on two fractal scales, such as a spiral embedded in another spiral. In contrast, a regular cauliflower often shows self-similarity in at least seven fractal scales, meaning that a spiral nested in a spiral nested in a spiral nested in a spiral nested in a spiral eventually nested in another spiral.

Instead of focusing on the stem, they focused on the meristem, a region of plant tissue at the top of each stem where actively dividing cells create new growth. They hypothesized that increasing the size of the meristem would increase the number of shoots produced.

The only problem was that the researchers didn’t know which gene could control the rate at which the meristem sprouts sprout.

One day, Eugenio Azpeitia, then a postdoctoral fellow in Dr. Godin’s lab, working on a gene known to resize the central zone of the meristem. The three researchers enjoyed a brief moment of euphoria and then waited patiently for months for their newly modified Arabidopsis to grow. When the shoots germinated, they had cauliflowers with pronounced conical tips.

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

Usually, when a plant sprouts a flower, the flower tip of the plant prevents more growth from the stem. A cauliflower curd is a bud that was designed to become a flower, but never makes it, instead forms a shoot. However, the researchers’ experiments in the meristem showed that since this sprout has gone through a temporary flowering stage, it is exposed to a gene that triggers its growth. “Because you were a flower, you can grow and shoot freely,” said Dr. Parcy.

This process creates a chain reaction in which the meristem creates many shoots, which in turn create many more shoots, mimicking the fractal geometry of a cauliflower.

“It’s not a normal stem,” said Dr. Godin. “It’s a stem without a leaf. A tribe without inhibitions. “

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

The researchers say that other mutations are likely responsible for the spectacular shape of romanesco. Ning Guo, a researcher at the Beijing Vegetable Research Center who is also studying the potential genetic mechanism behind the architecture of cauliflower curd, says the paper was “a lot of inspiration”.

“The story isn’t finished yet,” said Dr. Godin, adding that he and Dr. Parcy will continue to refine their cauliflower models. “But we know that we are on the right track.”

But they are open to study anything that blooms.

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