Tessellations and Pattern Formation in Plant Growth and Development

The shoot apical meristem (SAM) is a dome-shaped collection of cells at the apex of growing plants from which all above-ground tissue ultimately derives. In Arabidopsis thaliana (thale cress), a small flowering weed of the Brassicaceae family (related to mustard and cabbage), the SAM typically contains some three to five hundred cells that range from five to ten microns in diameter. These cells are organized into several distinct zones that maintain their topological and functional relationships throughout the life of the plant. As the plant grows, organs (primordia) form on its surface flanks in a phyllotactic pattern that develop into new shoots, leaves, and flowers. Cross-sections through the meristem reveal a pattern of polygonal tessellation that is suggestive of Voronoi diagrams derived from the centroids of cellular nuclei. In this chapter we explore some of the properties of these patterns within the meristem and explore the applicability of simple, standard mathematical models of their geometry.Comment: Originally presented at: "The World is a Jigsaw: Tessellations in the Sciences," Lorentz Center, Leiden, The Netherlands, March 200

Cell cycle regulates cell type in the Arabidopsis sepal

The formation of cellular patterns during development requires the coordination of cell division with cell identity specification. This coordination is essential in patterning the highly elongated giant cells, which are interspersed between small cells, in the outer epidermis of the Arabidopsis thaliana sepal. Giant cells undergo endocycles, replicating their DNA without dividing, whereas small cells divide mitotically. We show that distinct enhancers are expressed in giant cells and small cells, indicating that these cell types have different identities as well as different sizes. We find that members of the epidermal specification pathway, DEFECTIVE KERNEL1 (DEK1), MERISTEM LAYER1 (ATML1), Arabidopsis CRINKLY4 (ACR4) and HOMEODOMAIN GLABROUS11 (HDG11), control the identity of giant cells. Giant cell identity is established upstream of cell cycle regulation. Conversely, endoreduplication represses small cell identity. These results show not only that cell type affects cell cycle regulation, but also that changes in the cell cycle can regulate cell type

Local cues and asymmetric cell divisions underpin body plan transitions in the moss Physcomitrella patens

Background: Land plants evolved from aquatic algae more than 450 million years ago. Algal sisters of land plants grow through the activity of apical initial cells that cleave either in one plane to generate filaments or in two planes to generate mats. Acquisition of the capacity for cell cleavage in three planes facilitated the formation of upright bushy body plans and enabled the invasion of land. Evolutionary transitions between filamentous, planar, and bushy growth are mimicked within moss life cycles. Results: We have developed lineage analysis techniques to assess how transitions between growth forms occur in the moss Physcomitrella patens. We show that initial cells giving rise either to new filaments or bushy shoots are frequently juxtaposed on a single parent filament, suggesting a role for short-range cues in specifying differences in cell fate. Shoot initials cleave four times to establish a tetrahedral shape and subsequently cleave in three planes, generating bushy growth. Asymmetric and self-replacing divisions from the tetrahedral initial generate leaf initials that divide asymmetrically to self-replace and to produce daughter cells with restricted fate. The cessation of division in the leaf is distributed unevenly and contributes to final leaf shape. Conclusions: In contrast to flowering plants, changes in body plan in P. patens are regulated by cues acting at the level of single cells and are mediated through asymmetric divisions. Genetic mechanisms regulating shoot and leaf development in P. patens are therefore likely to differ substantially from mechanisms operating in plants with more recent evolutionary origins

Variability in the control of cell division underlies sepal epidermal patterning in Arabidopsis thaliana

How growth and proliferation are precisely controlled in organs during development and how the regulation of cell division contributes to the formation of complex cell type patterns are important questions in developmental biology. Such a pattern of diverse cell sizes is characteristic of the sepals, the outermost floral organs, of the plant Arabidopsis thaliana. To determine how the cell size pattern is formed in the sepal epidermis, we iterate between generating predictions from a computational model and testing these predictions through time-lapse imaging. We show that the cell size diversity is due to the variability in decisions of individual cells about when to divide and when to stop dividing and enter the specialized endoreduplication cell cycle. We further show that altering the activity of cell cycle inhibitors biases the timing and changes the cell size pattern as our model predicts. Models and observations together demonstrate that variability in the time of cell division is a major determinant in the formation of a characteristic pattern

Computational morphodynamics of plants: integrating development over space and time

The emerging field of computational morphodynamics aims to understand the changes that occur in space and time during development by combining three technical strategies: live imaging to observe development as it happens; image processing and analysis to extract quantitative information; and computational modelling to express and test time-dependent hypotheses. The strength of the field comes from the iterative and combined use of these techniques, which has provided important insights into plant development

Segmenting the sepal and shoot apical meristem of Arabidopsis thaliana

We present methods for segmenting the sepal and shoot apical meristem of the Arabidopsis thaliana plant. We propose a mathematical morphology pipeline and a modified numerical scheme for the active contours without edges algorithm to extract the geometry and topology of plant cells imaged using confocal laser scanning microscopy. We demonstrate our methods in typical images used in the studies of cell endoreduplication and hormone transport and show that in practice they produce highly accurate results requiring little human intervention to cope with image aberrations

Control of Fruit Patterning in Arabidopsis by INDEHISCENT

AbstractThe Arabidopsis seedpod opens through a spring-loaded mechanism known as pod shatter, which is essential for dispersal of the seeds. Here, we identify INDEHISCENT (IND), an atypical bHLH protein, that is necessary for fruit opening and is involved in patterning each of the three fruit cell types required for seed dispersal. Previous studies suggested that FRUITFULL (FUL), a member of the MADS-domain transcription factor family, is required for fruit growth since ful mutant fruit fail to undergo the dramatic enlargement that normally occurs after fertilization. Here we show, however, that FUL is not directly required for fruit elongation and instead is required to prevent ectopic activity of IND. Our molecular and genetic studies suggest a model for the regulatory interactions among the genes that control fruit development and the mechanism that results in the expression of IND in a narrow stripe of cells

Computational Morphodynamics: A Modeling Framework to Understand Plant Growth

Computational morphodynamics utilizes computer modeling to understand the development of living organisms over space and time. Results from biological experiments are used to construct accurate and predictive models of growth. These models are then used to make novel predictions that provide further insight into the processes involved, which can be tested experimentally to either confirm or rule out the validity of the computational models. This review highlights two fundamental challenges: (a) to understand the feedback between mechanics of growth and chemical or molecular signaling, and (b) to design models that span and integrate single cell behavior with tissue development. We review different approaches to model plant growth and discuss a variety of model types that can be implemented to demonstrate how the interplay between computational modeling and experimentation can be used to explore the morphodynamics of plant development

What determines cell size?

AbstractFirst paragraph (this article has no abstract) For well over 100 years, cell biologists have been wondering what determines the size of cells. In modern times, we know all of the molecules that control the cell cycle and cell division, but we still do not understand how cell size is determined. To check whether modern cell biology has made any inroads on this age-old question, BMC Biology asked several heavyweights in the field to tell us how they think cell size is controlled, drawing on a range of different cell types. The essays in this collection address two related questions - why does cell size matter, and how do cells control it