Fibonacci numbers are notorious for appearing in the most unlikely places, including the architecture of plants. Elsewhere in this issue, Didier Reinhardt and colleagues describe the role of the plant hormone auxin in phyllotaxis, the positioning of leaves around a stem (Nature 426, 255–260; 2003). In so doing, they reveal a mechanism by which Fibonacci numbers can emerge.
Fibonacci was the nickname of the Italian mathematician Leonardo Pisano (1170–1250), who introduced the Arabic number system into Europe. In 1202, he also posed a seemingly inconsequential problem concerning the breeding of rabbits. Its solution required the use of a series of numbers whose members are the sum of the two preceding entries (1, 1, 2, 3, 5, 8, 13, 21, 34, 55,...). This series now bears his name.
The Fibonacci series occurs in the arrangement of many plant organs. The seeds of sunflowers, Helianthus annuus, and the leaves of cacti and succulents (such as Mammillaria myrtax, upper image here, and Sempervivum hybrida, lower image) are arranged in both left- and right-handed spirals. The numbers of leaves, or seeds, in these spirals are consecutive Fibonacci numbers.
Leaves are also spirally distributed around the stems of less exotic plants. Here they tend to be separated by an angle of 137.5°. This is the radial equivalent of the golden ratio, ≈1.618, the ultimate proportional increase between successive Fibonacci numbers. Many hypotheses, ranging from the prosaic to the mystical, have been proposed to explain why leaves should stick out at this angle. Some invoke physical properties of the stem, whereas others propose that growing leaves emit an inhibitory field to prevent new leaves from arising in their vicinity, but none has had direct supporting evidence.
Leaves originate at the tips of growing shoots in a self-renewing region known as the shoot apical meristem. Using the thale cress, Arabidopsis thaliana, Reinhardt and colleagues saw that new leaves formed where the concentration of auxin was highest. Indeed, artificially adding auxin to specific points on the surface of the meristem caused leaves to be produced at those points.
Auxin is a growth stimulator that is propelled through plant tissues by specific influx and efflux transporters. Reinhardt et al. looked at the distribution of one of the most important of these, the efflux protein PIN1, as well as mutants in which it was missing, and deduced that auxin is moved towards the shoot tip through the outer layers of the shoot apical meristem. Existing leaf buds act as sinks, preventing auxin from continuing its progress directly above them. The maximum auxin concentration, and so the site of new leaf formation, is thus as far away as possible from already-formed leaves.
Reinhardt et al. have therefore uncovered a mechanism in which the position of leaves is determined neither by a physical property of the stem, nor by an inhibitory field produced by growing leaves. Instead, the gaps between leaves, by allowing the free flow of auxin, mark out the position of each new leaf.
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Surridge, C. Leaves by number. Nature 426, 237 (2003). https://doi.org/10.1038/426237a