Infraspecific Variation in Silene Seed Tubercles.

The seeds of many species in the order Caryophyllales exhibit surface protuberances called tubercles. While tubercle shape and distribution have often been proposed as taxonomic criteria, paradoxically, their description has primarily relied on adjectives, with quantitative data on tubercle width, height, and other measurements lacking in the literature. Recently, a quantitative analysis of seed surface tubercles based on tubercle width, height, and curvature values (maximum and average curvature, and maximum to average curvature ratio) was proposed and applied to individual populations of a total of 31 species, with 12 belonging to Silene subg. Behenantha and 19 to S. subg. Silene. Tubercles were classified into two categories: echinate and rugose. Echinate tubercles exhibited higher values of height and curvature, and lower width, and were more prevalent in species of S. subg. Behenantha, while the rugose type was more abundant in S. subg. Silene. This work explored infraspecific differences in tubercle size and shape. For this, measurements of tubercle width, height and curvature were applied to 31 populations of eight species of Silene. Significant differences between populations were observed for most of the species examined. A particular tubercle type, previously described as umbonate or mammillate, was identified in S. nocturna seeds, characterized by high curvature values.

Curvature Analysis of Seed Silhouettes in Silene L.

The application of seed morphology to descriptive systematics requires methods for shape analysis and quantification. The complexity of lateral and dorsal views of seeds of Silene species is investigated here by the application of the Elliptic Fourier Transform (EFT) to representative seeds of four morphological types: smooth, rugose, echinate and papillose. The silhouettes of seed images in the lateral and dorsal views are converted to trigonometric functions, whose graphical representations reproduce them with different levels of accuracy depending on the number of harmonics. A general definition of seed shape in Silene species is obtained by equations based on 40 points and 20 harmonics, while the detailed representation of individual tubercles in each seed image requires between 100 and 200 points and 60-80 harmonics depending on their number and complexity. Smooth-type seeds are accurately represented with a low number of harmonics, while rugose, echinate and papillose seeds require a higher number. Fourier equations provide information about tubercle number and distribution and allow the analysis of curvature. Further estimation of curvature values in individual tubercles reveals differences between seeds, with higher values of curvature in S. latifolia, representative of echinate seeds, and lower in S. chlorifolia with rugose seeds.

Quantitative Analysis of Seed Surface Tubercles in Silene Species.

In the Caryophyllaceae, seed surfaces contain cell protrusions, of varying sizes and shapes, called tubercles. Tubercles have long been described in many species, but quantitative analyses with measurements of size and shape are lacking in the literature. Based on optical photography, the seeds of Silene were classified into four types: smooth, rugose, echinate and papillose. Seeds in each of these groups have characteristic geometrical properties: smooth seeds lack tubercles and have the highest values of circularity and solidity in their lateral views, while papillose seeds have the largest tubercles and lowest values of circularity and solidity both in lateral and dorsal views. Here, tubercle width, height and slope, maximum and mean curvature values and maximum to mean curvature ratio were obtained for representative seeds of a total of 31 species, 12 belonging to Silene subg. Behenantha and 19 to S. subg. Silene. The seeds of the rugose type had lower values of curvature. Additionally, lower values of curvature were found in species of S. subg. Silene in comparison with S. subg. Behenantha. The seeds of S. subg. Behenantha had higher values of tubercle height and slope and higher values of maximum and average curvature and maximum to mean curvature ratio.

New Geometric Models for Shape Quantification of the Dorsal View in Seeds of Silene Species.

The description of shape in Silene seeds is based on adjectives coined by naturalists in the 19th century. The expressions reniform, dorso plana, and dorso canaliculata were applied in reference to lateral or dorsal views of seeds, but the characters described can be submitted now to an analytical description by quantitative methods, allowing shape quantification and the comparison between species or populations. A quantitative morphological analysis is based on the comparison with geometric models that adjust to the shape of seeds. Morphological analysis of the dorsal view of Silene seeds based on geometric models is applied here to 26 seed populations belonging to 12 species. According to their dorsal views, the seeds are classified as convex and non-convex. New geometric models are presented for both types, including figures such as super-ellipses and modified ellipses. The values of J index (percent of similarity of a seed image with the model) are obtained in representative seed samples from diverse populations and species. The quantitative description of seed shape based on the comparison with geometric models allows the study of variation in shape between species and in populations, as well as the identification of seeds in Silene species. The method is of application to other plant species.

The Outline of Seed Silhouettes: A Morphological Approach to Silene (Caryophyllaceae).

Seed morphology is an important source of information for plant taxonomy. Nevertheless, the characters under study are diverse, and a simple, unified method is lacking in the literature. A new method for the classification of seeds of the genus Silene based on optical images and image analysis has recently been described on the basis of morphological measurements of the lateral seed views. According to the outline of their silhouettes, seeds from 52 species (49 of Silene and three related species) were classified in three groups: smooth, rugose and echinate, revealing remarkable differences between these groups. This methodology has been applied here to 51 new species, making a total of 100 species of Silene analyzed so far. According to our data, a new group was described, termed papillose. The results showed morphological differences between the four mentioned seed groups, with reduced values of circularity for dorsal and lateral seed views in the papillose and echinate groups and reduced values of solidity in the papillose seeds. The method was applied to the analysis of individual as well as to average seed silhouettes and some of the differences between groups were maintained in both cases.

Seed Geometry in the Vitaceae.

The Vitaceae Juss., in the basal lineages of Rosids, contains sixteen genera and 950 species, mainly of tropical lianas. The family has been divided in five tribes: Ampelopsideae, Cisseae, Cayratieae, Parthenocisseae and Viteae. Seed shape is variable in this family. Based on new models derived from equations representing heart and water drop curves, we describe seed shape in species of the Vitaceae. According to their similarity to geometric models, the seeds of the Vitaceae have been classified in ten groups. Three of them correspond to models before described and shared with the Arecaceae (lenses, superellipses and elongated water drops), while in the seven groups remaining, four correspond to general models (waterdrops, heart curves, elongated heart curves and other elongated models) and three adjust to the silhouettes of seeds in particular genera (heart curves of Cayratia and Pseudocayratia, heart curves of the Squared Heart Curve (SqHC) type of Ampelocissus and Ampelopsis and Elongated Superellipse-Heart Curves (ESHCs), frequent in Tetrastigma species and observed also in Cissus species and Rhoicissus rhomboidea). The utilities of the application of geometric models for seed description and shape quantification in this family are discussed.

Geometric Models for Seed Shape Description and Quantification in the Cactaceae.

Seed shape in species of the Cactaceae is described by comparison with geometric models. Three new groups of models are presented, two for symmetric seeds, and a third group for asymmetric seeds. The first two groups correspond, respectively, to superellipses and the combined equations of two semi-ellipses. The third group contains models derived from the representation of polar equations of Archimedean spirals that define the shape of asymmetric seeds in genera of different subfamilies. Some of the new models are geometric curves, while others are composed with a part resulting from the average silhouettes of seeds. The application of models to seed shape quantification permits the analysis of variation in seed populations, as well as the comparison of shape between species. The embryos of the Cactaceae are of the peripheral type, strongly curved and in contact with the inner surface of the seed coat. A relationship is found between seed elongation and the models, in which the genera with elongated seeds are represented by models with longer trajectories of the spiral. The analysis of seed shape opens new opportunities for taxonomy and allows quantification of seed shape in species of the Cactaceae.

Geometric analysis of Arabidopsis root apex reveals a new aspect of the ethylene signal transduction pathway in development.

Structurally, ethylene is the simplest phytohormone and regulates multiple aspects of plant growth and development. Its effects are mediated by a signal transduction cascade involving receptors, MAP kinases and transcription factors. Many morphological effects of ethylene in plant development, including root size, have been previously described. In this article a combined geometric and algebraic approach has been used to analyse the shape and the curvature in the root apex of Arabidopsis seedlings. The process requires the fitting of Bézier curves that reproduce the root apex shape, and the calculation of the corresponding curvatures. The application of the method has allowed us to identify significant differences in the root curvatures of ethylene insensitive mutants (ein2-1 and etr1-1) with respect to the wild-type Columbia.

Seed shape in model legumes: approximation by a cardioid reveals differences in ethylene insensitive mutants of Lotus japonicus and Medicago truncatula.

Seed shape in the model legumes Lotus japonicus and Medicago truncatula is described. Based in previous work with Arabidopsis, the outline of the longitudinal sections of seeds is compared with a cardioid curve. L. japonicus seeds adjust well to an unmodified cardioid, whereas accurate adjustment in M. truncatula is obtained by the simple transformation of scaling the vertical axis by a factor equal to the Golden Ratio. Adjustments of seed shape measurements with simple geometrical forms are essential tools for the statistical analysis of variations in seed shape under different conditions or in mutants. The efficiency of the adjustment to a cardioid in the model plants suggests that seed morphology may be related to genome complexity. Seeds of ethylene insensitive mutants present differences in size and shape as well as altered responses to imbibition. The biological implication and meaning of these relationships are discussed.

Modeling the Arabidopsis seed shape by a cardioid: efficacy of the adjustment with a scale change with factor equal to the Golden Ratio and analysis of seed shape in ethylene mutants.

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).

Ethylene, free radicals and the transition between stable states in plant morphology.

Treatment with hydrogen peroxide has notable effects in the morphology of the root apex in Arabidopsis seedlings. The result was described as consisting in two aspects: first, a reduction in curvature values in the root profile. Second, alterations in size and shape of the cells in the root cap. Cells of the root cap were smaller and had higher circularity index (Fig. 1). The results of peroxide treatment were similar to alterations in the root apex of ethylene insensitive mutants and wild-type seedlings treated with ethylene inhibitors. This brings new evidence in favour of the association between ethylene and hydrogen peroxide signalling that was recently demonstrated in stomatal cells. Notable changes in morphology under peroxide treatment were previously reported in other biological systems (Fig. 2). In the following paragraphs we make emphasis on the need of an accurate analysis of morphology. This aspect has not received the attention required in biology, a discipline dominated by functional analysis. We suggest that the observed morphological characteristics in the root apex treated with peroxide may be the manifestation of global processes of adaptation in the organism. Alternative forms of roots grown in water or in peroxide are stable situations representing different global configurations that may have other (genomic, physiological) traits associated. Each form represents a different mode of adaptation to environmental change. The accurate description of morphology in organisms, with particular emphasis in model systems, and their variations under stress, is needed to identify and understand the basis of genomic organization and plasticity.

Hydrogen peroxide treatment results in reduced curvature values in the Arabidopsis root apex.

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.

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.

Morphological analysis of seed shape in Arabidopsis thaliana reveals altered polarity in mutants of the ethylene signaling pathway.

The shape of Arabidopsis thaliana dry seed is described here as a prolate spheroid. The accuracy of this approximation is discussed. Considering its limitations, it allows a geometric approximation to the analysis of changes occurring in seed shape during imbibition prior to seed germination as well as the differences in shape between genotypes and their changes during imbibition. The triple mutant ein2-1, ers1-2, etr1-7 presents notable alterations in seed shape. In addition, seeds of this and other mutants in the ethylene signaling pathway (ctr1-1, eto1-1, etr1-1, ein2-1) show different response to imbibition than the wild type. Imbibed seeds of the wild type increase their asymmetry compared with the dry seeds. This is detected by the relative changes in the curvature values in both poles. Thus, during imbibition of the wild-type seeds, the reduction in curvature values observed in the basal pole gives them an ovoid shape. In contrast, in the seeds of the ethylene mutants, reduction in curvature values occurs in both basal and apical poles, and its shape remains as a prolate spheroid. Our data indicate that the ethylene signaling pathway is involved, in general, in the complex regulation of seed shape and, in particular, in the establishment of polarity in seeds, controlling curvature values in the seed poles.

Ethylene responses in Arabidopsis seedlings include the reduction of curvature values in the root cap.

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. Our results show details illustrating the effect of ethylene in root curvature.