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A new model for the description of Arabidopsis seed shape based on the comparison of the outline of its longitudinal section with a transformed cardioid is presented. The transformation consists of scaling the horizontal axis by a factor equal to the Golden Ratio. The elongated cardioid approximates the shape of the Arabidopsis seed with more accuracy than other figures. The length to width ratio in wild-type Columbia Arabidopsis dry seeds is close to the Golden Ratio and decreases over the course of imbibition. Dry seeds of etr1-1 mutants presented a reduced length to width ratio. Application of the new model based on the cardioid allows for comparison of shape between wild-type and mutant genotypes, revealing other general alterations in the seeds in ethylene signaling pathway mutants (etr1-1).

Curvature of a plane curve is a measurement related to its shape. A Mathematica code was developed [Cervantes E, Tocino A. J Plant Physiol 2005;162:1038-1045] to obtain parametric equations from microscopic images of the Arabidopsis thaliana root apex. In addition, curvature values for these curves were given. It was shown that ethylene-insensitive mutants (etr1-1 and ein2-1) have reduced curvature values in the root apex. It has also been shown that blocking ethylene action by norbornadiene, an ethylene inhibitor, results in reduced curvature values in the two outer cell layers of the root apex [Noriega A, Cervantes E, Tocino A. J Plant Physiol 2008, in press]. Because ethylene action has been related with hydrogen peroxide [Desikan R, Hancock JT, Bright J, Harrison J, Weir I, Hooley R, Neill SJ. Plant Physiol 2005;137:831-834], the effect of a treatment with hydrogen peroxide in the curvature values of three successive layers of the root apex in Arabidopsis thaliana was investigated by confocal microscopy. Treatment with 10mM hydrogen peroxide resulted in reduced curvature values in the three layers. The effect was associated with smaller cells having higher circularity indices. The results are discussed in the context of the role of ethylene in development.

7 pages, 5 figures.-- PMID: 18023916 [PubMed].-- Available online 19 November 2007., Recently, curvature was described as a new trait useful in the analysis of root apex shape. Treating the root profile as a geometric curve revealed that root apex curvature values are lower in ethylene-insensitive mutants (Cervantes E, Tocino A. Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development. J Plant Physiol 2005;162:1038–45). This fact suggests that curvature is regulated by ethylene. In this work, we have determined the curvature values in embryonic roots of wild-type Columbia as well as in ethylene signal-transduction mutants, and found smaller values in embryos of the mutants. We also report on the evolution of root curvature during early development after seed germination. The line Lt16b that expresses GFP in the cell wall has allowed us to investigate the evolution of curvature values in three successive cell layers of seedling roots by confocal microscopy. Treatment of seedlings with norbornadiene resulted in lower curvature values.