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Plants Solving the Da Vinci Code

Por: | 24 de abril de 2014

FOTO 64_resized

By Henrik Jönsson, Lund University

“Sunflower seeds grow in opposing spirals. Can you guess the ratio of each rotation's diameter to the next?”The number that Professor Robert Langdon, the main character of Dan Brown’s The Da Vinci Code, is asking his students for is the golden ratio, or 1.6180339887(...). How can it be that the symmetric patterns seen in plants connect to this almost magical number? With the help of new microscopy technology and the use of mathematical modelling, scientists have today started to resolve this question in great detail.

Unlike most animals, which do not form a new pair of legs or arms once they are born, plants continue to grow and form new organs throughout their lives. Growth appears at the plant shoot, and new leaves and flowers are initiated at the shoot periphery. This does not happen randomly, but the plant positions these organs in a symmetric pattern. Various patterns appear in different plants, and a common pattern is to place the leaves in a spiral arrangement around the stem, where the length of the arc between consecutive leaves divides the circumference according to the golden ratio.

The golden ratio has been regarded as somewhat of a perfect ratio. It appears in many places in nature, and a classic definition was produced by Euclid in ancient Greece. The mysterious properties of this number have also inspired human creativity and you find it in paintings, buildings and even in musical pieces. The reason a plant positions its leaves with this angle is that it tries to position them as far as possible from earlier leaves, most likely to avoid shade and increase the intake of sunlight.

The idea that plant organs form away from previous organs is not new. It had been proposed by the German botanist Wilhelm Hofmeister in the nineteenth century, but at that time it was not possible to show whether this rule lead to golden ratio symmetries, or to determine what signals the plant uses to form these patterns.

One would assume that if leaves avoid each other, they should be positioned on the opposite side of the stem from the previous leaf and not according to the golden ratio. This is also true for many plants. However, in plants where leaves form close to each other, the newest leaf avoids not only the last one, but also leaves formed earlier. Twenty years ago, scientists started to build simple geometrical models that could show that this naturally leads to a placement of leaves according to the golden ratio.

Even if the scientists had a clue for why the positions of the leaves give the golden ratio, the most important question was still unanswered. How is the plant actually doing this? What signals and rules are used to make a plant grow new leaves at these specific positions? It was not until recently that scientists have been able to study fully the processes leading to these organised patterns of plant growth. Newly developed microscopy techniques have made it possible to follow the growth of individual plant cells in the living plant. These experiments have shown that it is the plant hormone auxin that is responsible for the growth of new organs. The hormone is transported to the site where a new organ is to be initiated, and the higher auxin concentration at the site then causes a new leaf or flower to grow.

But what makes the cells transport auxin to the site where the new organ is to be formed? This is not a trivial task to solve for the plant cells. They need to organise themselves so that a large number of cells act together, relying only on information from themselves and their nearest neighbours. This was, again, not an easy task for the scientists to solve; they had to use computer simulations to test different possibilities. Finally, they found the solution — a plant cell increases its transport to neighbours with higher auxin.

The interesting thing we could see in our simulations was that this local rule of auxin transport automatically led to a spacing mechanism where auxin peaks formed away from each other. Hence the local cell rule of increasing auxin transport towards cells with high auxin explains the formation of new organs away from earlier ones — which is exactly how the plant develops.

Scientists now understand the ancient question of how and why plants grow and develop the way they do. This knowledge might make it possible to alter the behaviour of plants in the future, such that more or larger organs can be formed. The increased number or size of fruit, for example, would lead to a better yield in agriculture, which is essential for an ever-growing world population.

But these possibilities are only a positive side effect for me as a researcher. My main goal is to understand the logics of life, including how plants are able to solve the da Vinci code.

Henrik Jönsson
Lund University

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