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From stable rules to complex shapes in plant modelling

A challenge for plant modelling is to capture the variation in phenotype, the physical form and timing of development, from a stable set of rules. Plants can be thought of as a set of building blocks, phytomers. Phytomers are a leaf and an internode, a length of stem running from one leaf to the next. Effectively, phytomers repeat up the plant. If you can model how plants build phytomers, then you have the start of modelling a plant’s development.

Models have assumed that whole shoot development has been led by the leaf appearance rate, and this is reliant on thermal time. The warmer it is, the less time it takes for the leaves to appear. Vidal and Andrieu have looked at this and found a problem. Leaf appearance actually results from leaf extension, so it’s not a direct way of characterizing shoot development. They have been working with maize on a revised set of rules to improve plant modelling.

Maize growing in a field.
Maize. Image: Canva.

“Maize is also both a model plant in Plant Science and an important economic crop. This means that a lot of data is available from literature and conversely new data/knowledge are of interest for a large community,” says co-author Bruno Andrieu. He also adds that it has some traits that make it very useful for checking models. “It is a large plant, so easy to dissect and measure the size of leaves or internode at the very beginning of their growth.”

Vidal and Andrieu have developed work by Junqi Zhu and colleagues, (of which Bruno Andrieu was one). This work laid out the principles of the relationship of thermal time and leaf emergence. “Among existing models based on co-ordination rules, the model proposed by Zhu et al. (2014) for maize is the most comprehensive, being the only one that covers the vegetative and reproductive stages of plant development and considers both leaf and stem extension,” write Vidal and Andrieu.

The key is the progress of developing phytomers. The plant develops by adding on these units as it develops and the development of phytomers follows regular patterns. A good model will be able to generate these patterns as emerging properties. If you can do that, then you’ll be identifying some of the critical mechanisms in growing a plant. Vidal and Andrieu have been looking at these repetitive steps, and have turned around an important assumption in their model. “You may see plants producing regular rhythms as if the plants are behaving like a clock. In usual models, this is formalized as plants ‘obeying’ a clock. However, with this model, we propose that the plant body itself is a clock. What is interesting is that by behaving as a clock, the plants produce the beautiful patterns of size,” says Andrieu.

While the model is not yet predictive, Vidal and Andrieu write “…several inputs, such as blade, internode and sheath RERs [relative elongation rates], could be considered as variables driven by plant status instead of being input parameters.” These would be factors driven by nutrients, and water Andrieu said.

While maize is the model plant, Andrieu says that this approach can be adapted to other grasses. “If you think to the model as assembling a set of mechanisms, then most of them have been proven to exist for various grass species. And I do not know any example where one of the mechanisms would have been rejected. Maize is simply today the species for which the most complete set of evidence has been collected.”

“In most grasses, the coordination has been investigated only for early stages of growth and focusing on leaves, whereas in maize, data have been collected for the full growth cycle and including internodes. We have unpublished data on wheat for the full cycle, which are consistent with those on maize. Certainly, most grass species follow most of the rules. This leaves space for some alterations in some places, which remain to be identified.”

The model uses a common feature to grasses that they share with other monocots says Andrieu. “One specificity in grass and monocots is that young organs grow hidden within a pseudostem. Emergence occurs quite late in their development.”

“Emergence is a key event in our model. It triggers major changes in growth behaviour. This is consistent with the fact that emergence corresponds to an instant dramatic change in the environment perceived by tissues, in term of light, humidity, the composition of the gaseous environment, mechanical constraint and so on.”

“In dicots, there is no pseudostem, so growing organs are exposed to the external environment at a much earlier stage of their development.”

So while this model will apply to monocots, it cannot be easily transferred to a dicot model. “Dicots also produce regular rhythms and patterns, but they are more diverse. The model of a monocot is certainly something to have in mind, but it would be more than being a simple transposition.”

Andrieu says that the mechanism, which evaluates the length of leaves and internodes along the shoot will be useful to other modellers. “One of the implications is how a phytomer is impacted by growth conditions does not depend only on the conditions perceived by the phytomer, but also the size of the whorl it grows in. So, the size of the whorl should be amongst the variables to be collected and included in the analysis in responses. Simple comparisons between different conditions can only be made between plants having the same whorl dimension.”

“A related implication is that when a stress is over a long period, this results in a smaller whorl, which in turn, results in smaller leaves or internodes, even if the stress has stopped. The whorl is a kind of memory, that impacts the potential of growth of young organs.”

The memory that stress creates is an example of the ‘clock’ of the plant changing the speed of its metaphorical pendulum. “If we go to modelling, this shows the limitation that occurs from the very much used approach in which there is an a priori potential size of organs with stress acting by reducing growth below the potential. The potential size is built dynamically by the plant. Considering an a priori potential is certainly one important source of inaccuracy of current models when considering responses to stresses.”

This difference, that the plant defines its own potential as it grows, is a topic that intrigues Andrieu. “An interesting research project would be to integrate, in a simplified way, this idea in crop models. In effect, by not describing crops as having a predefined potential that they try to follow, but rather as building their potential dynamically. That would make models more flexible and more faithful to real plants.”

Written by Alun Salt

Alun is the Producer for Botany One. It's his job to keep the server running. He's not a botanist, but started running into them on a regular basis while working on writing modules for an Interdisciplinary Science course and, later, helping teach mathematics to Biologists. His degrees are in archaeology and ancient history.

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