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.

Code and data availability

The paper's analysis is built on publicly available Arabidopsis leaf bead-tracking data (from Remmler & Rolland-Lagan 2012 and Rolland-Lagan et al. 2014), which the authors state are deposited with a package of Matlab leaf-shape analysis programs at a public repository handle. This is a paper-specific, publicly and行动可及