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 high throughput method for egg size measurement in Drosophila

Life-history traits are used as proxies of fitness in insects including Drosophila. Egg size is an adaptive and ecologically important trait potentially with genetic variation across different populations. However, the low throughput of manual measurement of egg size has hampered the widespread use of this trait in evolutionary biology and population genetics. We established a method for accurate and high throughput measurement of Drosophila egg size using large particle flow cytometry (LPFC). The size estimates using LPFC are accurate and highly correlated with the manual measurements. The measurement of egg size is high throughput (average of 214 eggs measured per minute) and viable eggs of a specific size can be sorted rapidly (average of 70 eggs per minute). Sorting by LPFC does not reduce the survival of eggs making it a suitable approach for sorting eggs for downstream analyses. This protocol can be applied to any organism within the detectable size range (10-1500 µm) of the large particle flow cytometers. We discuss the potential applications of this method and provide recommendations for optimizing the protocol for other organisms.

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.

Seed Morphology in Species from the Silene mollissima Aggregate (Caryophyllaceae) by Comparison with Geometric Models

The description of seed shape by comparison with geometric models allows shape quantification, providing the means for an accurate comparison between different species or populations. Geometric models described for the lateral and dorsal views of the seeds of Silene species are applied to the quantification of the shape in the seeds belonging to twenty populations of the eleven taxa of S. mollissima aggregate. Cardioid models LM1, LM5 and LM6 adjust differentially to the lateral views of the seeds, while models DM1, DM5 and DM6 are applied to the dorsal views of the seeds. Quantification of the lateral view of seeds with LM5 results in two groups of species of different geographic origin. The seeds more resembling DM5 include S. andryalifolia, S. badaroi, S. gazulensis, S. hifacensis and S. tomentosa, i.e., the taxa with a continental distribution from southern Spain to northern Italy; in contrast, the group of seeds with lower similarity to DM5 includes those from species in northern Africa and the Mediterranean Tyrrhenian islands: S. auricolifolia, S. hicesiae, S. ichnusae, S. mollissima, S. oenotriae and S. velutina. The description of the seed shape based on geometric models contributes to investigating the relationships between related species and constitutes a promising technique for taxonomy.

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.

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.

Seed Morphology in Silene Based on Geometric Models

Seed description in morphology is often based on adjectives such as “spherical”, “globular”, or “reniform”, but this does not provide a quantitative method. A new morphological approach based on the comparison of seed images with geometric models provides a seed description in Silene species on a quantitative basis. The novelty of the proposed method is based in the comparison of the seed images with geometric models according to a cardioid shape. The J index is a measurement that indicates the seed percentage of similarity with a cardioid or cardioid-derived figures used as models. The seeds of Silene species have high values of similarity with the cardioid and cardioid-derived models (J index superior to 90). The comparison with different figures allows species description and differentiation. The method is applied here to seeds of 21 species and models are proposed for some of them including S. diclinis, an endangered species. The method is discussed in the context of previous comparison with the measures used in traditional morphometric analysis. The similarity of seed images with geometric figures opens a new perspective for the automatized taxonomical evaluation of samples linking seed morphology to functional traits in endangered Silene species.

A high throughput method for quantifying number and size distribution of Arabidopsis seeds using large particle flow cytometry

BACKGROUND

Seed size and number are important plant traits from an ecological and horticultural/agronomic perspective. However, in small-seeded species such as Arabidopsis thaliana, research on seed size and number is limited by the absence of suitable high throughput phenotyping methods.

RESULTS

We report on the development of a high throughput method for counting seeds and measuring individual seed sizes. The method uses a large-particle flow cytometer to count individual seeds and sort them according to size, allowing an average of 12,000 seeds/hour to be processed. To achieve this high throughput, post harvested seeds are first separated from remaining plant material (dust and chaff) using a rapid sedimentation-based method. Then, classification algorithms are used to refine the separation process in silico. Accurate identification of all seeds in the samples was achieved, with relative errors below 2%.

CONCLUSION

The tests performed reveal that there is no single classification algorithm that performs best for all samples, so the recommended strategy is to train and use multiple algorithms and use the median predictions of seed size and number across all algorithms. To facilitate the use of this method, an R package (SeedSorter) that implements the methodology has been developed and made freely available. The method was validated with seed samples from several natural accessions of Arabidopsis thaliana, but our analysis pipeline is applicable to any species with seed sizes smaller than 1.5 mm.

Statistical methods for identification of golden ratio

Several biological systems such as the biomechanics of human heart, locomotion, and phyllotaxis of plants present a harmonic behavior because their fractal structure are associated to the golden ratio. The golden ratio (Φ = 1.618033988749…), also known as Phi, golden mean, golden section or divine proportion, is an irrational constant found in various forms in nature and recently has been used in many health areas. However, there is no literature on a specific statistical test to identify the golden ratio structures. To validate the results from each survey, it is necessary that statistical techniques be correctly selected and implemented, and the absence of a test to identify the golden ratio may undermines the scientific papers which have this goal. Since the golden number is a ratio, some tests have been wrongly applied in its identification. The objective of this paper is to present and to evaluate methods for identification of golden ratio. Four tests were evaluated: t-Student with ratio statistic (TR), with delta statistic (TΔ), with difference statistic (TED), and Wilcoxon test with statistic difference (WD). Data simulating different samples sizes (n = 2-200) and variability scenarios were used. The tests were assessed regarding type I error rate and power. For TΔ, type I error rate increased along with sample size and variability, achieving 50% in the scenario of relative standard deviation of 12.5% and 20.0% for line segments of lengths a and b, and sample size equal 200. This test also showed lower power when compared to the others in all scenarios. Similarly, for TR, the type I error rate was sensitive to the increasing in sample size, varying from 5 to 60%. On the other hand, WD and TED were associated to low type I error rates (around 5%) and high power (6.1% for sample size equal 2-100% for sample size equal 200). The TΔ and TR were inadequate to identify the golden ratio, since they did not controlled the type I error rate and/or presented low power, leading to possible erroneous conclusions. Therefore WD and TED, both with statistical of difference, appeared as the most appropriate methods to test golden ratio structures.

An Angiosperm Species Dataset Reveals Relationships between Seed Size and Two-Dimensional Shape

Datasets containing information on seed size have been published and are currently available. Nevertheless, there is a lack in the literature of a dataset dedicated to seed shape. We present a preliminary version for a dataset on seed morphology based on a comparison of seed shape with geometric figures. Similarity of the outline of seed images with geometric models is considered as a basis to classify seeds according to the geometric figures they resemble (e.g., ellipse, oval, cardioid). This allows, first, the classification of plant species according to their geometric type of seed, and second, seed shape quantification. For each seed image, the percent of similarity of their outline with a geometric figure can be calculated as a J index. Similarity in absolute terms is considered only when the J index >90. This criterion is important to avoid ambiguity and increase discrimination. The dataset opens the possibility of studying the relationship between seed shape and other variables such as seed size, genome complexity, life form or adaptive responses.

Seed Shape Description and Quantification by Comparison with Geometric Models

Modern methods of image analysis are based on the coordinates of the points making the silhouette of an image and allow the comparison between seed shape in different species and varieties. Nevertheless, these methods miss an important reference point because they do not take into consideration the similarity of seeds with geometrical figures. We propose a method based on the comparison of the bi-dimensional images of seeds with geometric figures. First, we describe six geometric figures that may be used as models for shape description and quantification and later on, we give an overview with examples of some of the types of seed morphology in angiosperms including families of horticultural plants and addressing the question of how is the distribution of seed shape in these families. The relationship between seed shape and other characteristics of plant species is discussed.

Updated Methods for Seed Shape Analysis

Morphological variation in seed characters includes differences in seed size and shape. Seed shape is an important trait in plant identification and classification. In addition it has agronomic importance because it reflects genetic, physiological, and ecological components and affects yield, quality, and market price. The use of digital technologies, together with development of quantification and modeling methods, allows a better description of seed shape. Image processing systems are used in the automatic determination of seed size and shape, becoming a basic tool in the study of diversity. Seed shape is determined by a variety of indexes (circularity, roundness, and J index). The comparison of the seed images to a geometrical figure (circle, cardioid, ellipse, ellipsoid, etc.) provides a precise quantification of shape. The methods of shape quantification based on these models are useful for an accurate description allowing to compare between genotypes or along developmental phases as well as to establish the level of variation in different sets of seeds.

Identification of rice ethylene-response mutants and characterization of MHZ7/OsEIN2 in distinct ethylene response and yield trait regulation

Ethylene plays essential roles in adaptive growth of rice plants in water-saturating environment; however, ethylene signaling pathway in rice is largely unclear. In this study, we report identification and characterization of ethylene-response mutants based on the specific ethylene-response phenotypes of etiolated rice seedlings, including ethylene-inhibited root growth and ethylene-promoted coleoptile elongation, which is different from the ethylene triple-response phenotype in Arabidopsis. We establish an efficient system for screening and a set of rice mutants have been identified. Genetic analysis reveals that these mutants form eight complementation groups. All the mutants show insensitivity or reduced sensitivity to ethylene in root growth but exhibit differential responses in coleoptile growth. One mutant group mhz7 has insensitivity to ethylene in both root and coleoptile growth. We identified the corresponding gene by a map-based cloning method. MHZ7 encodes a membrane protein homologous to EIN2, a central component of ethylene signaling in Arabidopsis. Upon ethylene treatment, etiolated MHZ7-overexpressing seedlings exhibit enhanced coleoptile elongation, increased mesocotyl growth and extremely twisted short roots, featuring enhanced ethylene-response phenotypes in rice. Grain length was promoted in MHZ7-transgenic plants and 1000-grain weight was reduced in mhz7 mutants. Leaf senescent process was also affected by MHZ7 expression. Manipulation of ethylene signaling may improve adaptive growth and yield-related traits in rice.

Brassinosteroid functions in Arabidopsis seed development

Seed development of flowering plant is a complicated process controlled by a signal network. Double fertilization generates 2 zygotic products (embryo and endosperm). Embryo gives rise to a daughter plant while endosperm provides nutrients for embryo during embryogenesis and germination. Seed coat differentiates from maternally derived integument and encloses embryo and endosperm. Seed size/mass and number comprise final seed yield, and seed shape also contributes to seed development and weight. Seed size is coordinated by communication among endosperm, embryo, and integument. Seed number determination is more complex to investigate and shows differences between monocot and eudicot. Total seed number depends on sillique number and seed number per sillique in Arabidopsis. Seed comes from fertilized ovule, hence the ovule number per flower determines the maximal seed number per sillique. Early studies reported that engineering BR levels increased the yield of ovule and seed; however the molecular mechanism of BR regulation in seed development still remained unclear. Our recent studies demonstrated that BR regulated seed size, shape, and number by transcriptionally modulating specific seed developmental pathways. This review summarizes roles of BR in Arabidopsis seed development and gives clues for future application of BR in agricultural production.

Universal natural shapes: from unifying shape description to simple methods for shape analysis and boundary value problems

Gielis curves and surfaces can describe a wide range of natural shapes and they have been used in various studies in biology and physics as descriptive tool. This has stimulated the generalization of widely used computational methods. Here we show that proper normalization of the Levenberg-Marquardt algorithm allows for efficient and robust reconstruction of Gielis curves, including self-intersecting and asymmetric curves, without increasing the overall complexity of the algorithm. Then, we show how complex curves of k-type can be constructed and how solutions to the Dirichlet problem for the Laplace equation on these complex domains can be derived using a semi-Fourier method. In all three methods, descriptive and computational power and efficiency is obtained in a surprisingly simple way.

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.