Cell size and growth regulation in the Arabidopsis thaliana apical stem cell niche

Heterogeneity and Robustness in Plant Morphogenesis: From Cells to Organs

Development is remarkably reproducible, producing organs with the same size, shape, and function repeatedly from individual to individual. For example, every flower on the Antirrhinum stalk has the same snapping dragon mouth. This reproducibility has allowed taxonomists to classify plants and animals according to their morphology. Yet these reproducible organs are composed of highly variable cells. For example, neighboring cells grow at different rates in Arabidopsis leaves, sepals, and shoot apical meristems. This cellular variability occurs in normal, wild-type organisms, indicating that cellular heterogeneity (or diversity in a characteristic such as growth rate) is either actively maintained or, at a minimum, not entirely suppressed. In fact, cellular heterogeneity can contribute to producing invariant organs. Here, we focus on how plant organs are reproducibly created during development from these highly variable cells.

The growth of a stable stationary structure: coordinating cell behavior and patterning at the shoot apical meristem

Plants are characterized by their ability to produce new organs post-embryonically throughout their entire life cycle. In particular development of all above-ground organs relies almost entirely on the function of the shoot apical meristem (SAM). The SAM performs a dual role by maintaining a pool of undifferentiated cells and simultaneously driving cell differentiation to initiate organogenesis. Both processes require strict coordination between individual cells which leads to formation of reproducible morphological and molecular patterns within SAM. The patterns are formed and maintained in large part due to spatio-temporal variation in signaling of plant hormones auxin and cytokinin resulting in tissue-specific transcriptional regulation. Integration of these mechanisms into computational models further identifies the key regulatory interactions involved in SAM function.

A Sizer model for cell differentiation in Arabidopsis thaliana root growth

Plant roots grow due to cell division in the meristem and subsequent cell elongation and differentiation, a tightly coordinated process that ensures growth and adaptation to the changing environment. How the newly formed cells decide to stop elongating becoming fully differentiated is not yet understood. To address this question, we established a novel approach that combines the quantitative phenotypic variability of wild‐type Arabidopsis roots with computational data from mathematical models. Our analyses reveal that primary root growth is consistent with a Sizer mechanism, in which cells sense their length and stop elongating when reaching a threshold value. The local expression of brassinosteroid receptors only in the meristem is sufficient to set this value. Analysis of roots insensitive to BR signaling and of roots with gibberellin biosynthesis inhibited suggests distinct roles of these hormones on cell expansion termination. Overall, our study underscores the value of using computational modeling together with quantitative data to understand root growth.

Clones of cells switch from reduction to enhancement of size variability in Arabidopsis sepals

Organs form with remarkably consistent sizes and shapes during development, whereas a high variability in growth is observed at the cell level. Given this contrast, it is unclear how such consistency in organ scale can emerge from cellular behavior. Here, we examine an intermediate scale, the growth of clones of cells in Arabidopsis sepals. Each clone consists of the progeny of a single progenitor cell. At early stages, we find that clones derived from a small progenitor cell grow faster than those derived from a large progenitor cell. This results in a reduction in clone size variability, a phenomenon we refer to as size uniformization. By contrast, at later stages of clone growth, clones change their growth pattern to enhance size variability, when clones derived from larger progenitor cells grow faster than those derived from smaller progenitor cells. Finally, we find that, at early stages, fast growing clones exhibit greater cell growth heterogeneity. Thus, cellular variability in growth might contribute to a decrease in the variability of clones throughout the sepal.

Summary: Growth analyses of Arabidopsis sepals identify a tipping point in organ development, at which clones of cells change their growth pattern from size uniformization to size variability enhancement.

Pavement cells and the topology puzzle

D'Arcy Thompson emphasised the importance of surface tension as a potential driving force in establishing cell shape and topology within tissues. Leaf epidermal pavement cells grow into jigsaw-piece shapes, highly deviating from such classical forms. We investigate the topology of developing Arabidopsis leaves composed solely of pavement cells. Image analysis of around 50,000 cells reveals a clear and unique topological signature, deviating from previously studied epidermal tissues. This topological distribution is established early during leaf development, already before the typical pavement cell shapes emerge, with topological homeostasis maintained throughout growth and unaltered between division and maturation zones. Simulating graph models, we identify a heuristic cellular division rule that reproduces the observed topology. Our parsimonious model predicts how and when cells effectively place their division plane with respect to their neighbours. We verify the predicted dynamics through in vivo tracking of 800 mitotic events, and conclude that the distinct topology is not a direct consequence of the jigsaw piece-like shape of the cells, but rather owes itself to a strongly life history-driven process, with limited impact from cell-surface mechanics.

Cell size control - a mechanism for maintaining fitness and function

The maintenance of cell size homeostasis has been studied for years in different cellular systems. With the focus on 'what regulates cell size', the question 'why cell size needs to be maintained' has been largely overlooked. Recent evidence indicates that animal cells exhibit nonlinear cell size dependent growth rates and mitochondrial metabolism, which are maximal in intermediate sized cells within each cell population. Increases in intracellular distances and changes in the relative cell surface area impose biophysical limitations on cells, which can explain why growth and metabolic rates are maximal in a specific cell size range. Consistently, aberrant increases in cell size, for example through polyploidy, are typically disadvantageous to cellular metabolism, fitness and functionality. Accordingly, cellular hypertrophy can potentially predispose to or worsen metabolic diseases. We propose that cell size control may have emerged as a guardian of cellular fitness and metabolic activity.

Topological analysis of multicellular complexity in the plant hypocotyl

Multicellularity arose as a result of adaptive advantages conferred to complex cellular assemblies. The arrangement of cells within organs endows higher-order functionality through a structure-function relationship, though the organizational properties of these multicellular configurations remain poorly understood. We investigated the topological properties of complex organ architecture by digitally capturing global cellular interactions in the plant embryonic stem (hypocotyl), and analyzing these using quantitative network analysis. This revealed the presence of coherent conduits of reduced path length across epidermal atrichoblast cell files. The preferential movement of small molecules along this cell type was demonstrated using fluorescence transport assays. Both robustness and plasticity in this higher order property of atrichoblast patterning was observed across diverse genetic backgrounds, and the analysis of genetic patterning mutants identified the contribution of gene activity towards their construction. This topological analysis of multicellular structural organization reveals higher order functions for patterning and principles of complex organ construction.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

Morphological Plant Modeling: Unleashing Geometric and Topological Potential within the Plant Sciences

The geometries and topologies of leaves, flowers, roots, shoots, and their arrangements have fascinated plant biologists and mathematicians alike. As such, plant morphology is inherently mathematical in that it describes plant form and architecture with geometrical and topological techniques. Gaining an understanding of how to modify plant morphology, through molecular biology and breeding, aided by a mathematical perspective, is critical to improving agriculture, and the monitoring of ecosystems is vital to modeling a future with fewer natural resources. In this white paper, we begin with an overview in quantifying the form of plants and mathematical models of patterning in plants. We then explore the fundamental challenges that remain unanswered concerning plant morphology, from the barriers preventing the prediction of phenotype from genotype to modeling the movement of leaves in air streams. We end with a discussion concerning the education of plant morphology synthesizing biological and mathematical approaches and ways to facilitate research advances through outreach, cross-disciplinary training, and open science. Unleashing the potential of geometric and topological approaches in the plant sciences promises to transform our understanding of both plants and mathematics.

A method to generate the surface cell layer of the 3D virtual shoot apex from apical initials

BACKGROUND

The development of cell pattern in the surface cell layer of the shoot apex can be investigated in vivo by use of a time-lapse confocal images, showing naked meristem in 3D in successive times. However, how this layer is originated from apical initials and develops as a result of growth and divisions of their descendants, remains unknown. This is an open area for computer modelling. A method to generate the surface cell layer is presented on the example of the 3D paraboloidal shoot apical dome. In the used model the layer originates from three apical initials that meet at the dome summit and develops through growth and cell divisions under the isotropic surface growth, defined by the growth tensor. The cells, which are described by polyhedrons, divide anticlinally with the smallest division plane that passes depending on the used mode through the cell center, or the point found randomly near this center. The formation of the surface cell pattern is described with the attention being paid to activity of the apical initials and fates of their descendants.

RESULTS

The computer generated surface layer that included about 350 cells required about 1200 divisions of the apical initials and their derivatives. The derivatives were arranged into three more or less equal clonal sectors composed of cellular clones at different age. Each apical initial renewed itself 7-8 times to produce the sector. In the shape and location and the cellular clones the following divisions of the initial were manifested. The application of the random factor resulted in more realistic cell pattern in comparison to the pure mode. The cell divisions were analyzed statistically on the top view. When all of the division walls were considered, their angular distribution was uniform, whereas in the distribution that was limited to apical initials only, some preferences related to their arrangement at the dome summit were observed.

CONCLUSIONS

The realistic surface cell pattern was obtained. The present method is a useful tool to generate surface cell layer, study activity of initial cells and their derivatives, and how cell expansion and division are coordinated during growth. We expect its further application to clarify the question of a number and permanence or impermanence of initial cells, and possible relationship between their shape and oriented divisions, both on the ground of the growth tensor approach.