Modeling Whorls of Leaves

Computer simulation helps explain how plants grow

The petals of every flower and the leaves sprouting from every plant stalk have characteristic arrangements, a phenomenon called phyllotaxis. For two centuries, botanists have puzzled over the force driving such regularity.


A computer simulation of the growing tip of a seedling of Arabidopsis thaliana, viewed from above. PIN1 proteins (red) facilitate transport of the plant hormone auxin (green), which in high concentrations promotes budding of leaves, seen here bulging out from the stalk. The feedback interaction of the protein and hormone produce the characteristic spiral pattern of leaves that form as the plant grows. “If you want to understand how plants acquire their form, this is one of the very key questions,” says Przemyslaw Prusinkiewicz, PhD, professor in computer science at the University of Calgary in Alberta, Canada. He and his colleagues recently presented a new celluar-level computer model of the process. The work appeared January 31, 2006, issue of the Proceedings of the National Academy of Sciences.


Previous experimental work by Prusinkiewicz’s Swiss collaborators had shown that a plant hormone, auxin, plays a crucial role in phyllotaxis, as does a protein called PIN1, which regulates the transport of auxin. The team hypothesized that there was a feedback mechanism in which the distribution of auxin determined the location of the PIN1 proteins, the position of which, in turn, governed the flow of auxin.


They devised a computer model to test the theory quantitatively by simulating the properties of individual cells during the growth of a small flowering plant of the mustard family, Arabidopsis.


The model assumes that the tip of the stem develops at the same time that the pattern of leaves is forming, all of which relates to the pattern of cell division. The results of the simulation confirmed that the proposed interplay of auxin and PIN1 on the molecular level could produce the characteristic spiral leaf pattern found in Arabidopsis, but also yielded some surprises.


Though the researchers initially assumed auxin was produced in the basal tissues of the stem and flowed up to the growing tip, they were only able to get the leaf patterns observed in nature when they altered the model to have auxin produced locally at the tip.
They also found that by varying the parameters of the model, they could produce the leaf patterns found in other plants, which, Prusenkiewicz says, “reinforces our belief that what we have shown is actually true, and it is not just true in Arabidopsis, but also in other plants.”


Prusenkiewicz characterizes their model as part of a broader inquiry into how genes and molecular level processes determine the macroscopic forms of organisms, which he calls “one of the most fascinating questions in develop- mental biology right now.”



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