Life sciences : the formation of biological fractals

Plants are comprised of roots, stems, buds, leaves and flowers. So far, so simple. And yet, researchers across the world have spent decades trying to unravel the mysteries of the process which explains the development of plants - morphogenesis.Their aim has been to establish connections between the visible transformations of plants and the genetic activity which triggers these transformations.

“Arabidopsis thaliana, the plant dealt with in our publication, has 25,000 genes”,explains François Parcy, CNRS director of research and one of the authors of the paper published in Science. “We selected seven of these based on the key role they play in the formation of flowers. The way they interact with each other is so complex that it is beyond human intelligence.”

We needed a computer simulation in order to describe it and to understand it.

That said, this was far from an easy task. François Parcy began developing models in 2008 with Christophe Godin, Inria director of research with the Mosaic project team at the Inria Lyon research centre, a project that was supposed to last three years. In the end, twelve years had passed by the time their paper was published in Science, one of the world’s most influential scientific journals.

“Every advance made in modelling revealed shortcomings or weaknesses in our hypotheses”, explains François Parcy. “For example, I knew that the flower buds of plants such as cabbages and cauliflowers lost the activity of the floral genes and became stem buds, but I didn’t know why. Our model didn’t work until we were able to identify new regulations which stimulated the stem genes and caused this change in the nature of the buds.” 

Assisted by four foreign teams*, the French researchers were successfully able to develop a model that was more reliable and more sophisticated than anything that had been developed before. It simulates the growth dynamic of Arabidopsis thalianain three dimensions and over time, bringing together the way in which the gene networks operate and how the shape of the plant changes.

This model, which was calibrated using lab-produced plants, is capable of reproducing either natural or genetically-modified growth.

Disrupting a complex system and seeing if we can explain what happens as a result enables us to understand the system as a whole, explains Christophe Godin.

As it transpired, with Arabidopsis thaliana, the model explained how two mutations were enough to bring about a major morphological change: instead of producing flowers, the plant started to produce small cabbages!

At this stage, it bears repeating that plant organs emerge from groups of stem cells, meristems, which are located at the tip of each stem. Normally, the local activity of their genes would lead to the formation of leaves, stems or flowers. But the two cauliflower mutations in Arabidopsis thalianawere found to modify this process:the meristem, which had previously been engaged in a floral genetic programme, reverted back to the status of a stem.

However, it retained a “memory” of its brief foray into the floral programme and began producing a practically infinite succession of stems, giving the appearance of a cabbage.

The seven genes referred to earlier are involved in these transformations. One in particular, christened LEAFY, plays a vital role: instead of being active over a long period of time, which would produce a flower, it experiences a brief peak in activity before fading away. This peak has an irreversible effect on the meristem, leading to a chain reaction that responsible for the number of stems that are produced.

This was an important result for several reasons. First and foremost, it reveals the very essence of how plants are constructed, in their purest form. If you inhibit the genetic mechanisms which transform these meristems into differentiated organs (flowers and leaves), the plant will grow like a small tree, producing stems which will also produce stems themselves. However, in wild plants or crops that are the result of lengthy selection processes, this elementary process is modified by other layers of genetic control.

The paper published in Sciencealso raises more earthly questions, which could have a significant impact on our diet. “It features an additional model for understanding the genetic phenomena governing the growth of the cauliflower”, explains François Parcy. “Their domestication by humans has made them far more complex thanArabidopsis thaliana, even if they do have much in common. But agriculture is faced with an emergency.” 

Spells of hot weather linked to climate change sometimes result in strange, elongated cauliflowers which customers don't want to buy. A research programme has been launched in the Netherlands aimed at developing varieties which tolerate heat better. In France, l’Organisation bretonne de sélection (a union of agricultural cooperatives based in Brittany) is overseeing a project on this subject, and the scientists involved enlisted the support of François Parcy as a consultant.

The paper published in Sciencealso put forward an explanation for the unique shape of Romanesco, which is formed of rows of small identical pyramids over different levels. “In mathematics this is what’s known as a fractal pattern”, explains Christophe Godin. 

But why does the Romanesco have this fractal appearance while the cauliflower doesn’t, despite the two being formed of meristems that are harvested before they flower?

Their answer is that while the meristems of the Romanesco produce new meristems at an increasing rate, with the cauliflower this rate remains constant.  The researchers found a way of testing this hypothesis in an experiment, producing small, conical cauliflowers that were similar to Romanesco in their fractal appearance.

This work on the Romanesco had one unexpected consequence for Christophe Godin, giving him inspiration for new ways of designing mathematical models for generating fractals based on growing, regulated structures. As for François Parcy, he also believes that this collaboration between a biologist and a mathematician was very fruitful. “Because he is not an expert in my field, Christophe wasn’t encumbered by bias, and some of the questions he asked really got me thinking. Some would have been too difficult to explore, while for others I had the data available in my lab, but I would never have thought about using it had it not been for Christophe.” 

Christophe Godin co-authored another scientific paper that was published in Science in 2020, on the subject of the dynamic behaviour of the embryo cells of a small marine animal from the ascidian class , with a particular focus on the molecular signals they exchange, which can be likened to “cries”. Five French and two foreign research teams (from Germany and the USA) put their names to the paper.

François Parcy is the author of “L’histoire secrète des fleurs” (“The secret history of flowers”), which was published in 2019 by Humensciences.

*Instituto de Biología Molecular y Celular de Plantas (Valence, Espagne), Università degli Studi di Milano (Italie), California Institute of Technology(États-Unis) et John Innes Centre (Royaume-Uni)