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The filling law: a general framework for leaf folding and its consequences on leaf shape diversity
Etienne Couturier1, Sylvain Courrech du Pont, Stéphane Douady
1Laboratoire Matières et Systèmes Complexes (MSC), UMR 7057 CNRS/Université Paris-Diderot, 10 Rue Alice Domon & Léonie Duquet, 75205 Paris Cedex 13, France. etienne.couturier@polytech.univ-mrs.fr
Journal of Theoretical Biology
|August 31, 2011
Summary
Leaf packing in buds follows a "filling law," dictating folded leaf shapes and symmetries. This geometric principle influences leaf lobe and sinus sizes, demonstrating pervasive developmental constraints.
Area of Science:
- Plant morphology
- Developmental biology
- Biophysics
Background:
- Leaves are packed within buds in various configurations (flat, rolled, folded) but always occupy the entire bud volume.
- This consistent bud-filling behavior, termed the "filling law," has significant implications for the development and final shape of growing leaves.
Purpose of the Study:
- To investigate the geometric consequences of the leaf bud
- filling law
- on the shapes of developing folded leaves.
Main Methods:
- Analysis of different leaf folding and packing types.
- Geometric modeling of folded leaf volumes, considering vein and margin placement.
- Observation of symmetries and quantitative relationships in leaf shapes.
Main Results:
- Folded leaf volumes approximate ellipsoidal segments, with veins typically on the outer convex surface and margins on the adaxial plane.
- Leaf development under space constraints results in characteristic symmetries and predictable ratios between lobe and sinus sizes.
- Specific geometries lead to unique leaf margin features, such as spoon-like lobes or asymmetrical wavy edges, influenced by lateral veins or tangent cuts.
Conclusions:
- The
- filling law
- is a fundamental constraint shaping mature leaf morphology.
- Observed symmetries and quantitative relationships in leaf shape are direct geometric consequences of this packing principle.
- Variations in bud packing among cultivars correlate with distinct mature leaf shapes, highlighting the law's pervasive influence.
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