Cauliflower and chaos, fractals in every bloom
The monks once hoped to turn lead into gold through alchemy. But instead consider cauliflower. It only takes two genes to transform the stalk, stalk and ordinary flowers of the bad, tasteless Brassica oleracea into a formation as wonderful as this fractured vegetable, like a cloud.
This is true alchemy, says Christophe Godin, a senior fellow at the National Institute for Research in Digital Science and Technology in Lyon, France.
Dr. Godin studies plant architecture by practically modeling the development of forms of different species in three dimensions. He wondered what genetic modification was hidden behind the nested cauliflower coils and logarithmic logarithmic fractures of Romanesco, a cauliflower cultivar that could almost be mistaken for a crystal.
“How is nature able to build such unexpected objects?” he asked. “What could be the rules behind this?”
Fifteen years ago, Dr. Godin met François Parcy, a plant biologist with the National Center for Scientific Research in Grenoble, France. In Dr. Parcy, Dr. Godin met another friend about fractal flowers.
“There is no way you can not notice that it is such a wonderful vegetable,” said Dr. Parcy, referring to Romanesco.
Enjoyed by a passion for Brassica, Dr. Godin and Dr. Parcy explored the genetic mystery of fractal geometry in both Romanesco and standard cauliflower, bringing plants to life in mathematical models and also growing them in real life. Their results, which suggest the shape of fractals in response to changes in the gene networks that regulate flower development, were published Thursday in science.
“It’s such a good 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 changing the rules of how genes interact you can get dramatic changes to a plant.”
In the early 2000s, Dr. Parcy believed he understood cauliflower. He even gave lessons on the development of its flowers. “What is cauliflower? How can it be grown? Why does it look like that? He said.
Cauliflower, like Brussels sprouts, has been around for centuries selective education of Brassica oleracea. People bred brussels sprouts for side buds and cauliflower for bouquets. Cauliflower, however, does not produce flower buds; their flower clusters, or flower buds, never ripen to produce flowers. Instead, cauliflower flowers generate their own replicas in a spiral, creating groups of cheeses like plant-based cottage cheese.
As the two researchers discussed cauliflower, Dr. Godin suggested that if Dr. Parcy really understood the plant, it would be easy to model the morphological development of vegetables. As it turned out, it was not so.
The two first encountered the noisy swamp on the blackboard, sketching out various diagrams of genetic networks that could explain how vegetables were transformed into its current form. Their muse was Arabidopsis thaliana, a poorly studied herb in the same family as cauliflower and its numerous cousins.
If a cauliflower has a single cauliflower at the base of the plant, Arabidopsis has many cauliflower-like structures along its elongated stalk. But what genes can perfect these smaller cauliflowers in a large, compact cauliflower? And if they were to identify those genes, could they break these cauliflowers on the tops that form Romanescos?
To answer these questions, researchers would uproot the gene network and steer it through mathematical models, generate it in 3-D, and translate it into real life. “You imagine something, but until you program it you do not know what it will look like,” said Dr. Parcy.
(During the study, Dr. Parcy also collected some Romanesco specimens from his local farmer’s market, sorted and shredded them. He and his colleagues then dined at the leftovers, often raw with various dips, along with glasses of beer.)
Many early models returned, bearing little resemblance to cauliflower. At first, researchers believed that the key to cauliflower lay in the length of the stalk. But when they programmed Arabidopsis with and without a short stalk, they realized they did not need to reduce the stalk size of the cauliflower, either in 3-D models or in real life.
And the cauliflowers they simulated and grew were not simply fractal. The patterns were only visible on two fractal scales, such as one spiral placed on another spiral. In contrast, an ordinary cauliflower often exhibits resemblance to itself in at least seven fractal scales, meaning a coil placed in a coil placed in a nested coil in a nested coil in a nested coil embedded in a nested coil, after all, in another coil.
So instead of focusing on the stem, they focused on the meristem, a region of plant tissue at the top of each stem, where the dividing cells actively produce new growth. They hypothesized that making the largest 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 meristem shoot production.
One day, Eugenio Azpeitia, then a postdoctoral collaborator in the laboratory of Dr. Godin, recalled a gene that was known to change the size of the central meristem area. The three researchers enjoyed a brief moment of euphoria and then waited patiently for months for their newly modified Arabidopsis to grow. When the buds sprouted, they had cauliflower with distinct conical tips.
“It reminds you a lot of what happens in Romanesco,” Dr. Godin said proudly.
Normally, when a plant sprouts a flower, the flowering top of the plant prevents more growth from the stalk. A cauliflower curd is a bud that is designed to become a flower, but never makes it up there, and instead makes a shoot. But meristem researchers’ experiments revealed that because this shoot has gone through a temporary flowering stage, it is exposed to a gene that causes it to grow. “Since you were a flower, you are free to grow and can make a jump,” said Dr. Parcy.
This process creates a chain reaction where the meristem is creating many shoots which, in turn, creates many more shoots, applying the fractal geometry of a cauliflower.
“It’s not a normal flow,” said Dr. Godin. “It is a leafless stalk. A stalk without braking. ”
“This is the only way to make a cauliflower,” said Dr. Parcy.
Researchers say there are likely to be other mutations responsible for Romanesco’s spectacular shape. Ning Guo, a researcher at the Vegetable Research Center in Beijing who is also studying the possible genetic mechanism behind the cauliflower cottage cheese architecture, says the paper has provided “a lot of inspiration”.
“The story is not over yet,” said Dr. Godin, adding that he and Dr. Parcy will continue to refine their cauliflower patterns. “But we know we are on the right track.”
But they are open, they say, to studying everything that thrives.