title: Conformal growth of Arabidopsis leaves.
abstract: I show that Arabidopsis leaf growth can be described with good precision by a conformal map, where expansion is locally isotropic (the same in all directions) but the amount of expansion can vary with position. Data obtained by tracking leaf growth over time can be reproduced with almost 90% accuracy by such a map. The growth follows a Möbius transformation, which is a type of conformal map that would arise if there were an underlying linear gradient of growth rate. From the data one can derive the parameters that describe this linear gradient and show how it changes over time. Such a rule has the property of maintaining the flatness of a leaf.
authors.affiliation: Sainsbury Laboratory, Cambridge University, Cambridge, UK. Electronic address: gjm12@cam.ac.uk.
authors.forename: Graeme
authors.initials: G
authors.lastname: Mitchison
mesh_terms: D017360:Arabidopsis / Q000254:growth & development; D008954:Models, Biological; D010641:Phenotype; D018515:Plant Leaves / Q000033:anatomy & histology / Q000254:growth & development
keywords: Conformal map; Gradient; Growth control; Leaf growth; Möbius transformation