Curvature analysis reveals new functions for ethylene signalling pathway in shape determination of seed poles and root apices.

IN MATHEMATICS, CURVATURE IS AN IMPORTANT MAGNITUDE IN THE DESCRIPTION OF PLANE CURVES: it represents the rate of change of direction of a curve with respect to distance along the curve. By looking at root tips of Arabidopsis, we observed that their shape is altered in ethylene insensitive mutants. Here we describe the mathematical meaning of the concept of curvature and how it has been adapted in the analysis of root apex and seed poles shapes in Arabidopsis. Ethylene signalling effects on shapes and curvatures are assessed using ethylene mutants. Departing from an image of an Arabidopsis plant, the curve that represents the profile of the root tip was obtained and the curvature value of the root apex was calculated. Observed curvature values in root apices of ethylene insensitive mutants were smaller than in the wild-type Columbia. Curvature values were also used in the description of Arabidopsis seeds. For a dry seed, curvature values are similar in both seed poles. During imbibition, curvature values tend to decrease in the seed poles. The reduction is more pronounced in ethylene mutants than in the wild-type Columbia seeds, in which reduction occurs predominantly in the basal pole resulting in marked polarity after imbibition.