Credit: H. KOBAYASHI ET AL.

Next time you pack for a scientific conference, consider how much more you can cram into a suitcase if your clothes are neatly folded. Problems of packing are common in biology — examples include DNA in chromatin, brain architecture and the arrangement of alveoli in the lung. An entertaining example from functional ecology is addressed by H. Kobayashi et al. in Proceedings of the Royal Society (265, 147-154; 1998). They have looked at the geometry of unfolding tree leaves from tightly packed buds.

The design of the leaves is reminiscent of man-made structures such as solar panels and the lightweight antennae of satellites, which have to be packed optimally to ensure fail-safe deployment. The authors have used techniques borrowed from engineering to model the leaves of two species of deciduous tree, the hornbeam Carpinus betulus, and the beech Fagus synaticus. These species have oval, corrugated leaves with a central midrib, which develop from scaled buds.

The leaf is modelled as a plain surface with straight parallel folds. Conveniently, the creases or folds of the leaves run along lateral veins, angled at 30-50° from the midrib of the expanded leaf. Using vector analysis, the authors calculate the effect of varying the ‘vein angle’ and leaf shape on packing efficiency and leaf expansion. Increasing the vein angle allows more compact folding within the bud, but only at the cost of energetically less efficient, slower leaf expansion. By getting the balance of design parameters right, natural selection may optimize the timing of leaf deployment, maximizing photosynthesis while minimizing damage caused by late frosts and leaf-eating larvae.