Cauliflowers or how the perseverance of a plant to make flowers produces an amazing fractal structure.

Biological organisms have an immense diversity of forms. Some of them exhibit conspicuous and fascinating fractal structures that present self-similar patterns at all scales. How such structures are produced by biological processes is intriguing. In a recent publication, we used a multi-scale modelling approach to understand how gene activity can produce macroscopic cauliflower curds. Our work provides a plausible explanation for the appearance of fractal-like structures in plants, linking gene activity with development.

Les organismes biologiques possèdent une immense diversité de formes. Certains d'entre eux arborent des structures fractales remarquables et fascinantes présentant des motifs similaires à toutes les échelles. La manière dont ces structures sont produites par des processus biologiques est intrigante. Dans une publication récente, nous avons utilisé une approche de modélisation multi-échelle pour comprendre comment l'activité de certains gènes peut engendrer des pommes de chou-fleur macroscopiques. Notre travail fournit une explication plausible quant à l'apparition de structures de type fractal chez les plantes, en reliant l'activité des gènes au développement.

A graph-based approach for simultaneous semantic and instance segmentation of plant 3D point clouds.

Accurate simultaneous semantic and instance segmentation of a plant 3D point cloud is critical for automatic plant phenotyping. Classically, each organ of the plant is detected based on the local geometry of the point cloud, but the consistency of the global structure of the plant is rarely assessed. We propose a two-level, graph-based approach for the automatic, fast and accurate segmentation of a plant into each of its organs with structural guarantees. We compute local geometric and spectral features on a neighbourhood graph of the points to distinguish between linear organs (main stem, branches, petioles) and two-dimensional ones (leaf blades) and even 3-dimensional ones (apices). Then a quotient graph connecting each detected macroscopic organ to its neighbors is used both to refine the labelling of the organs and to check the overall consistency of the segmentation. A refinement loop allows to correct segmentation defects. The method is assessed on both synthetic and real 3D point-cloud data sets of Chenopodium album (wild spinach) and Solanum lycopersicum (tomato plant).

Post-transcriptional regulation of transcription factor codes in immature neurons drives neuronal diversity.

How the vast array of neuronal diversity is generated remains an unsolved problem. Here, we investigate how 29 morphologically distinct leg motoneurons are generated from a single stem cell in Drosophila. We identify 19 transcription factor (TF) codes expressed in immature motoneurons just before their morphological differentiation. Using genetic manipulations and a computational tool, we demonstrate that the TF codes are progressively established in immature motoneurons according to their birth order. Comparing RNA and protein expression patterns of multiple TFs reveals that post-transcriptional regulation plays an essential role in shaping these TF codes. Two RNA-binding proteins, Imp and Syp, expressed in opposing gradients in immature motoneurons, control the translation of multiple TFs. The varying sensitivity of TF mRNAs to the opposing gradients of Imp and Syp in immature motoneurons decrypts these gradients into distinct TF codes, establishing the connectome between motoneuron axons and their target muscles.

Phenotyping and modeling of root hydraulic architecture reveal critical determinants of axial water transport.

Water uptake by roots is a key adaptation of plants to aerial life. Water uptake depends on root system architecture (RSA) and tissue hydraulic properties that, together, shape the root hydraulic architecture. This work investigates how the interplay between conductivities along radial (e.g. aquaporins) and axial (e.g. xylem vessels) pathways determines the water transport properties of highly branched RSAs as found in adult Arabidopsis (Arabidopsis thaliana) plants. A hydraulic model named HydroRoot was developed, based on multi-scale tree graph representations of RSAs. Root water flow was measured by the pressure chamber technique after successive cuts of a same root system from the tip toward the base. HydroRoot model inversion in corresponding RSAs allowed us to concomitantly determine radial and axial conductivities, providing evidence that the latter is often overestimated by classical evaluation based on the Hagen-Poiseuille law. Organizing principles of Arabidopsis primary and lateral root growth and branching were determined and used to apply the HydroRoot model to an extended set of simulated RSAs. Sensitivity analyses revealed that water transport can be co-limited by radial and axial conductances throughout the whole RSA. The number of roots that can be sectioned (intercepted) at a given distance from the base was defined as an accessible and informative indicator of RSA. The overall set of experimental and theoretical procedures was applied to plants mutated in ESKIMO1 and previously shown to have xylem collapse. This approach will be instrumental to dissect the root water transport phenotype of plants with intricate alterations in root growth or transport functions.

Benchmarking of deep learning algorithms for 3D instance segmentation of confocal image datasets.

Segmenting three-dimensional (3D) microscopy images is essential for understanding phenomena like morphogenesis, cell division, cellular growth, and genetic expression patterns. Recently, deep learning (DL) pipelines have been developed, which claim to provide high accuracy segmentation of cellular images and are increasingly considered as the state of the art for image segmentation problems. However, it remains difficult to define their relative performances as the concurrent diversity and lack of uniform evaluation strategies makes it difficult to know how their results compare. In this paper, we first made an inventory of the available DL methods for 3D cell segmentation. We next implemented and quantitatively compared a number of representative DL pipelines, alongside a highly efficient non-DL method named MARS. The DL methods were trained on a common dataset of 3D cellular confocal microscopy images. Their segmentation accuracies were also tested in the presence of different image artifacts. A specific method for segmentation quality evaluation was adopted, which isolates segmentation errors due to under- or oversegmentation. This is complemented with a 3D visualization strategy for interactive exploration of segmentation quality. Our analysis shows that the DL pipelines have different levels of accuracy. Two of them, which are end-to-end 3D and were originally designed for cell boundary detection, show high performance and offer clear advantages in terms of adaptability to new data.

Introduction to Computational Modeling of Multicellular Tissues.

The study of biological tissues is extremely complicated, as they comprise mechanisms and properties at many different temporal and spatial scales. For this reason, modeling is becoming one of the most active and important research fields for the analysis and understanding of tissues. However, this is not a simple task, as it requires mathematical and computational skills, as well as the development of software tools for its implementation. Here, we provide an introduction covering some of the most important and basic issues for modeling tissues. In particular, we focus on both the chemical and cellular properties of a tissue. We explain how to represent and couple these properties within a virtual tissue. All our examples were done using Multicell, a Python library that simplifies their reproducibility, even by readers with little experience in biological modeling.

Cauliflower fractal forms arise from perturbations of floral gene networks.

Throughout development, plant meristems regularly produce organs in defined spiral, opposite, or whorl patterns. Cauliflowers present an unusual organ arrangement with a multitude of spirals nested over a wide range of scales. How such a fractal, self-similar organization emerges from developmental mechanisms has remained elusive. Combining experimental analyses in an Arabidopsis thaliana cauliflower-like mutant with modeling, we found that curd self-similarity arises because the meristems fail to form flowers but keep the "memory" of their transient passage in a floral state. Additional mutations affecting meristem growth can induce the production of conical structures reminiscent of the conspicuous fractal Romanesco shape. This study reveals how fractal-like forms may emerge from the combination of key, defined perturbations of floral developmental programs and growth dynamics.

What shoots can teach about theories of plant form.

Plants generate a large variety of shoot forms with regular geometries. These forms emerge primarily from the activity of a stem cell niche at the shoot tip. Recent efforts have established a theoretical framework of form emergence at the shoot tip, which has empowered the use of modelling in conjunction with biological approaches to begin to disentangle the biochemical and physical mechanisms controlling form development at the shoot tip. Here, we discuss how these advances get us closer to identifying the construction principles of plant shoot tips. Considering the current limits of our knowledge, we propose a roadmap for developing a general theory of form development at the shoot tip.

Organ geometry channels reproductive cell fate in the Arabidopsis ovule primordium.

In multicellular organisms, sexual reproduction requires the separation of the germline from the soma. In flowering plants, the female germline precursor differentiates as a single spore mother cell (SMC) as the ovule primordium forms. Here, we explored how organ growth contributes to SMC differentiation. We generated 92 annotated 3D images at cellular resolution in Arabidopsis. We identified the spatio-temporal pattern of cell division that acts in a domain-specific manner as the primordium forms. Tissue growth models uncovered plausible morphogenetic principles involving a spatially confined growth signal, differential mechanical properties, and cell growth anisotropy. Our analysis revealed that SMC characteristics first arise in more than one cell but SMC fate becomes progressively restricted to a single cell during organ growth. Altered primordium geometry coincided with a delay in the fate restriction process in katanin mutants. Altogether, our study suggests that tissue geometry channels reproductive cell fate in the Arabidopsis ovule primordium.

A multiscale analysis of early flower development in Arabidopsis provides an integrated view of molecular regulation and growth control.

We have analyzed the link between the gene regulation and growth during the early stages of flower development in Arabidopsis. Starting from time-lapse images, we generated a 4D atlas of early flower development, including cell lineage, cellular growth rates, and the expression patterns of regulatory genes. This information was introduced in MorphoNet, a web-based platform. Using computational models, we found that the literature-based molecular network only explained a minority of the gene expression patterns. This was substantially improved by adding regulatory hypotheses for individual genes. Correlating growth with the combinatorial expression of multiple regulators led to a set of hypotheses for the action of individual genes in morphogenesis. This identified the central factor LEAFY as a potential regulator of heterogeneous growth, which was supported by quantifying growth patterns in a leafy mutant. By providing an integrated view, this atlas should represent a fundamental step toward mechanistic models of flower development.

Cortical tension overrides geometrical cues to orient microtubules in confined protoplasts.

In plant cells, cortical microtubules (CMTs) generally control morphogenesis by guiding cellulose synthesis. CMT alignment has been proposed to depend on geometrical cues, with microtubules aligning with the cell long axis in silico and in vitro. Yet, CMTs are usually transverse in vivo, i.e., along predicted maximal tension, which is transverse for cylindrical pressurized vessels. Here, we adapted a microwell setup to test these predictions in a single-cell system. We confined protoplasts laterally to impose a curvature ratio and modulated pressurization through osmotic changes. We find that CMTs can be longitudinal or transverse in wallless protoplasts and that the switch in CMT orientation depends on pressurization. In particular, longitudinal CMTs become transverse when cortical tension increases. This explains the dual behavior of CMTs in planta: CMTs become longitudinal when stress levels become low, while stable transverse CMT alignments in tissues result from their autonomous response to tensile stress fluctuations.

Phyllotaxis as geometric canalization during plant development.

Why living forms develop in a relatively robust manner, despite various sources of internal or external variability, is a fundamental question in developmental biology. Part of the answer relies on the notion of developmental constraints: at any stage of ontogenesis, morphogenetic processes are constrained to operate within the context of the current organism being built. One such universal constraint is the shape of the organism itself, which progressively channels the development of the organism toward its final shape. Here, we illustrate this notion with plants, where strikingly symmetric patterns (phyllotaxis) are formed by lateral organs. This Hypothesis article aims first to provide an accessible overview of phyllotaxis, and second to argue that the spiral patterns in plants are progressively canalized from local interactions of nascent organs. The relative uniformity of the organogenesis process across all plants then explains the prevalence of certain patterns in plants, i.e. Fibonacci phyllotaxis.

Microtubule-Mediated Wall Anisotropy Contributes to Leaf Blade Flattening.

Plant organs can adopt a wide range of shapes, resulting from highly directional cell growth and divisions. We focus here on leaves and leaf-like organs in Arabidopsis and tomato, characterized by the formation of thin, flat laminae. Combining experimental approaches with 3D mechanical modeling, we provide evidence that leaf shape depends on cortical microtubule mediated cellulose deposition along the main predicted stress orientations, in particular, along the adaxial-abaxial axis in internal cell walls. This behavior can be explained by a mechanical feedback and has the potential to sustain and even amplify a preexisting degree of flatness, which in turn depends on genes involved in the control of organ polarity and leaf margin formation.

Skeletonization of Plant Point Cloud Data Using Stochastic Optimization Framework.

Skeleton extraction from 3D plant point cloud data is an essential prior for myriads of phenotyping studies. Although skeleton extraction from 3D shapes have been studied extensively in the computer vision and graphics literature, handling the case of plants is still an open problem. Drawbacks of the existing approaches include the zigzag structure of the skeleton, nonuniform density of skeleton points, lack of points in the areas having complex geometry structure, and most importantly the lack of biological relevance. With the aim to improve existing skeleton structures of state-of-the-art, we propose a stochastic framework which is supported by the biological structure of the original plant (we consider plants without any leaves). Initially we estimate the branching structure of the plant by the notion of ß-splines to form a curve tree defined as a finite set of curves joined in a tree topology with certain level of smoothness. In the next phase, we force the discrete points in the curve tree to move toward the original point cloud by treating each point in the curve tree as a center of Gaussian, and points in the input cloud data as observations from the Gaussians. The task is to find the correct locations of the Gaussian centroids by maximizing a likelihood. The optimization technique is iterative and is based on the Expectation Maximization (EM) algorithm. The E-step estimates which Gaussian the observed point cloud was sampled from, and the M-step maximizes the negative log-likelihood that the observed points were sampled from the Gaussian Mixture Model (GMM) with respect to the model parameters. We experiment with several real world and synthetic datasets and demonstrate the robustness of the approach over the state-of-the-art.

Contact area-dependent cell communication and the morphological invariance of ascidian embryogenesis.

Marine invertebrate ascidians display embryonic reproducibility: Their early embryonic cell lineages are considered invariant and are conserved between distantly related species, despite rapid genomic divergence. Here, we address the drivers of this reproducibility. We used light-sheet imaging and automated cell segmentation and tracking procedures to systematically quantify the behavior of individual cells every 2 minutes during Phallusia mammillata embryogenesis. Interindividual reproducibility was observed down to the area of individual cell contacts. We found tight links between the reproducibility of embryonic geometries and asymmetric cell divisions, controlled by differential sister cell inductions. We combined modeling and experimental manipulations to show that the area of contact between signaling and responding cells is a key determinant of cell communication. Our work establishes the geometric control of embryonic inductions as an alternative to classical morphogen gradients and suggests that the range of cell signaling sets the scale at which embryonic reproducibility is observed.

Temporal integration of auxin information for the regulation of patterning.

Positional information is essential for coordinating the development of multicellular organisms. In plants, positional information provided by the hormone auxin regulates rhythmic organ production at the shoot apex, but the spatio-temporal dynamics of auxin gradients is unknown. We used quantitative imaging to demonstrate that auxin carries high-definition graded information not only in space but also in time. We show that, during organogenesis, temporal patterns of auxin arise from rhythmic centrifugal waves of high auxin travelling through the tissue faster than growth. We further demonstrate that temporal integration of auxin concentration is required to trigger the auxin-dependent transcription associated with organogenesis. This provides a mechanism to temporally differentiate sites of organ initiation and exemplifies how spatio-temporal positional information can be used to create rhythmicity.

Plants, like animals and many other multicellular organisms, control their body architecture by creating organized patterns of cells. These patterns are generally defined by signal molecules whose levels differ across the tissue and change over time. This tells the cells where they are located in the tissue and therefore helps them know what tasks to perform. A plant hormone called auxin is one such signal molecule and it controls when and where plants produce new leaves and flowers. Over time, this process gives rise to the dashing arrangements of spiraling organs exhibited by many plant species. The leaves and flowers form from a relatively small group of cells at the tip of a growing stem known as the shoot apical meristem. Auxin accumulates at precise locations within the shoot apical meristem before cells activate the genes required to make a new leaf or flower. However, the precise role of auxin in forming these new organs remained unclear because the tools to observe the process in enough detail were lacking. Galvan-Ampudia, Cerutti et al. have now developed new microscopy and computational approaches to observe auxin in a small plant known as Arabidopsis thaliana. This showed that dozens of shoot apical meristems exhibited very similar patterns of auxin. Images taken over a period of several hours showed that the locations where auxin accumulated were not fixed on a group of cells but instead shifted away from the center of the shoot apical meristems faster than the tissue grew. This suggested the cells experience rapidly changing levels of auxin. Further experiments revealed that the cells needed to be exposed to a high level of auxin over time to activate genes required to form an organ. This mechanism sheds a new light on how auxin regulates when and where plants make new leaves and flowers. The tools developed by Galvan-Ampudia, Cerutti et al. could be used to study the role of auxin in other plant tissues, and to investigate how plants regulate the response to other plant hormones.

Cellular Heterogeneity in Pressure and Growth Emerges from Tissue Topology and Geometry.

Cell-to-cell heterogeneity prevails in many systems, as exemplified by cell growth, although the origin and function of such heterogeneity are often unclear. In plants, growth is physically controlled by cell wall mechanics and cell hydrostatic pressure, alias turgor pressure. Whereas cell wall heterogeneity has received extensive attention, the spatial variation of turgor pressure is often overlooked. Here, combining atomic force microscopy and a physical model of pressurized cells, we show that turgor pressure is heterogeneous in the Arabidopsis shoot apical meristem, a population of stem cells that generates all plant aerial organs. In contrast with cell wall mechanical properties that appear to vary stochastically between neighboring cells, turgor pressure anticorrelates with cell size and cell neighbor number (local topology), in agreement with the prediction by our model of tissue expansion, which couples cell wall mechanics and tissue hydraulics. Additionally, our model predicts two types of correlations between pressure and cellular growth rate, where high pressure may lead to faster- or slower-than-average growth, depending on cell wall extensibility, yield threshold, osmotic pressure, and hydraulic conductivity. The meristem exhibits one of these two regimes, depending on conditions, suggesting that, in this tissue, water conductivity may contribute to growth control. Our results unravel cell pressure as a source of patterned heterogeneity and illustrate links between local topology, cell mechanical state, and cell growth, with potential roles in tissue homeostasis.

Sugar availability suppresses the auxin-induced strigolactone pathway to promote bud outgrowth.

Apical dominance occurs when the growing shoot tip inhibits the outgrowth of axillary buds. Apically-derived auxin in the nodal stem indirectly inhibits bud outgrowth via cytokinins and strigolactones. Recently, sugar deprivation was found to contribute to this phenomenon. Using rose and pea, we investigated whether sugar availability interacts with auxin in bud outgrowth control, and the role of cytokinins and strigolactones, in vitro and in planta. We show that sucrose antagonises auxin's effect on bud outgrowth, in a dose-dependent and coupled manner. Sucrose also suppresses strigolactone inhibition of outgrowth and the rms3 strigolactone-perception mutant is less affected by reducing sucrose supply. However, sucrose does not interfere with the regulation of cytokinin levels by auxin and stimulates outgrowth even with optimal cytokinin supply. These observations were assembled into a computational model in which sucrose represses bud response to strigolactones, largely independently of cytokinin levels. It quantitatively captures our observed dose-dependent sucrose-hormones effects on bud outgrowth and allows us to express outgrowth response to various combinations of auxin and sucrose levels as a simple quantitative law. This study places sugars in the bud outgrowth regulatory network and paves the way for a better understanding of branching plasticity in response to environmental and genotypic factors.

Light Regulation of Axillary Bud Outgrowth Along Plant Axes: An Overview of the Roles of Sugars and Hormones.

Apical dominance, the process by which the growing apical zone of the shoot inhibits bud outgrowth, involves an intricate network of several signals in the shoot. Auxin originating from plant apical region inhibits bud outgrowth indirectly. This inhibition is in particular mediated by cytokinins and strigolactones, which move from the stem to the bud and that respectively stimulate and repress bud outgrowth. The action of this hormonal network is itself modulated by sugar levels as competition for sugars, caused by the growing apical sugar sink, may deprive buds from sugars and prevents bud outgrowth partly by their signaling role. In this review, we analyze recent findings on the interaction between light, in terms of quantity and quality, and apical dominance regulation. Depending on growth conditions, light may trigger different pathways of the apical dominance regulatory network. Studies pinpoint to the key role of shoot-located cytokinin synthesis for light intensity and abscisic acid synthesis in the bud for R:FR in the regulation of bud outgrowth by light. Our analysis provides three major research lines to get a more comprehensive understanding of light effects on bud outgrowth. This would undoubtedly benefit from the use of computer modeling associated with experimental observations to deal with a regulatory system that involves several interacting signals, feedbacks, and quantitative effects.