Plant cells control their volume by regulating the osmotic potential of their cytoplasm and vacuole. Water is attracted into the cell as the result of a cascade of solute exchanges between the cell subcompartments and the cell surroundings, which are governed by chemical, electrostatic and mechanical forces. Due to this multi-physics aspect and to couplings between volume changes and chemical effects, modeling these exchanges remains a challenge that has only been partially addressed. As interest for multi-compartment models grows in the plant cell community, this challenge calls for new modeling strategies. In this paper, we introduce an energy-based approach to couple chemical, electrical and mechanical processes taking place between several subcompartments of a plant cell. The contributions of all physical effects are gathered in an energy function, which allows us to derive the equations satisfied by each variable in a systematic way. We illustrate the properties of this modular, unified approach on the modeling of ion and water transport in a guard cell during stoma opening. We represent the stoma opening process as a quasi-static evolution driven by hydrogen pumps in the plasma and vacuolar membranes, and we show that the new formalism explains why the system varies in a particular direction in response to perturbations. Additional numerical simulations allow us to investigate the role of each hydrogen pump in this process. Altogether, we show that this energy-based approach highlights a hierarchy between the forces involved in the system, and to dissect the role of each physical effect in the complex behavior of the system.

In Arabidopsis thaliana, successful fertilisation relies on the precise guidance of the pollen tube as it navigates through the female tissues to deliver sperm cells to ovules. While prior research has focused on pistil signals directing pollen tubes towards the ovules, the pollen tube growth within the stigmatic epidermis has received limited attention. Our recent work comparing wild-type pollen tube paths on wild-type and katanin1-5 stigmatic cells, revealed a tight connection between pollen tube directionality and mechanical properties of the invaded stigmatic cell. Given that most mechanical properties of the stigmatic tissue are experimentally challenging to access, we used mathematical modelling to investigate the mechanisms underlying early pollen tube guidance through the papilla cell wall. We found that in ktn1-5, the wild-type pollen tube navigates freely across the curved papilla surface, following curves close to geodesics, whereas the wild-type papilla imposes directional guidance. The order of magnitude analysis of the mechanical forces required for pollen tubes to progress at the papilla surface indicates that both the elongated geometry of the papilla and the difference in rigidity of its cell wall layers combine to efficiently orient the pollen tube towards the papilla base.

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.

The class of self-nested trees presents remarkable compression properties because of the systematic repetition of subtrees in their structure. In this paper, we provide a better combinatorial characterization of this specific family of trees. In particular, we show from both theoretical and practical viewpoints that complex queries can be quickly answered in self-nested trees compared to general trees. We also present an approximation algorithm of a tree by a self-nested one that can be used in fast prediction of edit distance between two trees.

The growth of plant organs is a complex process powered by osmosis that attracts water inside the cells; this influx induces simultaneously an elastic extension of the walls and pressure in the cells, called turgor pressure; above a threshold, the walls yield and the cells grow. Based on Lockhart's seminal work, various models of plant morphogenesis have been proposed, either for single cells, or focusing on the wall mechanical properties. However, the synergistic coupling of fluxes and wall mechanics has not yet been fully addressed in a multicellular model. This work lays the foundations of such a model, by simplifying as much as possible each process and putting emphasis on the coupling itself. Its emergent properties are rich and can help to understand plant morphogenesis. In particular, we show that the model can display a new type of lateral inhibitory mechanism that amplifies growth heterogeneities due e.g to cell wall loosening.

A classical compression method for trees is to exploit subtree repeats in the structure by representing them by directed acyclic graphs. We propose a lossy compression method that consists in computing a structure with high redundancy that approximates the initial data.

The goal of this paper is the reconstruction of topologically accurate 3-dimensional triangular meshes representing a complex, multi-layered plant tissue structure. Based on time sequences of meristem images of the model plant Arabidopsis thaliana, displaying fluorescence markers on either cell membranes or cell nuclei under confocal laser scanning microscopy, we aim at obtaining faithful reconstructions of all the cell walls in the tissue. In the presented method, the problem is tackled under the angle of topology, and the shape of the cells is seen as the dual geometry of a 3-d simplicial complex accounting for their adjacency relationships. We present a method for optimizing such complexes using an energy minimization process, designed to make them fit to the actual adjacencies in the tissue. The resulting dual meshes constitute a light discrete representation of the cell surfaces that enables fast visualization, and quantitative analysis, and allows in silico physical and mechanical simulations on real-world data.

The link between genetic regulation and the definition of form and size during morphogenesis remains largely an open question in both plant and animal biology. This is partially due to the complexity of the process, involving extensive molecular networks, multiple feedbacks between different scales of organization and physical forces operating at multiple levels. Here we present a conceptual and modeling framework aimed at generating an integrated understanding of morphogenesis in plants. This framework is based on the biophysical properties of plant cells, which are under high internal turgor pressure, and are prevented from bursting because of the presence of a rigid cell wall. To control cell growth, the underlying molecular networks must interfere locally with the elastic and/or plastic extensibility of this cell wall. We present a model in the form of a three dimensional (3D) virtual tissue, where growth depends on the local modulation of wall mechanical properties and turgor pressure. The model shows how forces generated by turgor-pressure can act both cell autonomously and non-cell autonomously to drive growth in different directions. We use simulations to explore lateral organ formation at the shoot apical meristem. Although different scenarios lead to similar shape changes, they are not equivalent and lead to different, testable predictions regarding the mechanical and geometrical properties of the growing lateral organs. Using flower development as an example, we further show how a limited number of gene activities can explain the complex shape changes that accompany organ outgrowth.

In this paper, we are interested in the problem of approximating trees by trees with a particular self-nested structure. Self-nested trees are such that all their subtrees of a given height are isomorphic. We show that these trees present remarkable compression properties, with high compression rates. In order to measure how far a tree is from being a self-nested tree, we then study how to quantify the degree of self-nestedness of any tree. For this, we define a measure of the self-nestedness of a tree by constructing a self-nested tree that minimizes the distance of the original tree to the set of self-nested trees that embed the initial tree. We show that this measure can be computed in polynomial time and depict the corresponding algorithm. The distance to this nearest embedding self-nested tree (NEST) is then used to define compression coefficients that reflect the compressibility of a tree. To illustrate this approach, we then apply these notions to the analysis of plant branching structures. Based on a database of simulated theoretical plants in which different levels of noise have been introduced, we evaluate the method and show that the NESTs of such branching structures restore partly or completely the original, noiseless, branching structures. The whole approach is then applied to the analysis of a real plant (a rice panicle) whose topological structure was completely measured. We show that the NEST of this plant may be interpreted in biological terms and may be used to reveal important aspects of the plant growth.

This paper presents a reconstruction pipeline for recovering branching structure of trees from laser scanned data points. The process is made up of two main blocks: segmentation and reconstruction. Based on a variational k-means clustering algorithm, cylindrical components and ramified regions of data points are identified and located. An adjacency graph is then built from neighborhood information of components. Simple heuristics allow us to extract a skeleton structure and identify branches from the graph. Finally, a B-spline model is computed to give a compact and accurate reconstruction of the branching system.

Abstract Modeling natural elements such as trees in a plausible way, while offering simple and rapid user control, is a challenge. This paper presents a method based on a new structurefrom silhouettesparadigm. We claim that sketching the silhouettes of foliage at multiple scales is quicker and more intuitive for a user than having to sketch each branch of a tree. This choice allows us to incorporate botanical knowledge, enabling us to infer branches that connect in a plausible way to their parent branch and have a correct distribution in 3D. We illustrate these ideas by presenting a seamless sketch‐based interface, used for sketching foliage silhouettes from the scale of an entire tree to the scale of a leaf. Each sketch serves for inferring both the branches at that level and construction lines to serve as support for sub‐silhouette refinement. When the user finally zooms out, the style inferred for the branching systems he has refined (in terms of branch density, angle, length distribution and shape) is duplicated to the unspecified branching systems at the same level. Meanwhile, knowledge from botany is again used for extending the branch distribution to 3D, resulting in a full, plausible 3D tree that fits the user‐sketched contours. As our results show, this system can be of interest to both experts and novice users. While experts can fully specify all parts of a tree and over‐sketch specific branches if required, any user can design a basic 3D tree in one or two minutes, as easily as sketching it with paper and pen.

Plants continuously generate new organs through the activity of populations of stem cells called meristems. The shoot apical meristem initiates leaves, flowers, and lateral meristems in highly ordered, spiralled, or whorled patterns via a process called phyllotaxis. It is commonly accepted that the active transport of the plant hormone auxin plays a major role in this process. Current hypotheses propose that cellular hormone transporters of the PIN family would create local auxin maxima at precise positions, which in turn would lead to organ initiation. To explain how auxin transporters could create hormone fluxes to distinct regions within the plant, different concepts have been proposed. A major hypothesis, canalization, proposes that the auxin transporters act by amplifying and stabilizing existing fluxes, which could be initiated, for example, by local diffusion. This convincingly explains the organised auxin fluxes during vein formation, but for the shoot apical meristem a second hypothesis was proposed, where the hormone would be systematically transported towards the areas with the highest concentrations. This implies the coexistence of two radically different mechanisms for PIN allocation in the membrane, one based on flux sensing and the other on local concentration sensing. Because these patterning processes require the interaction of hundreds of cells, it is impossible to estimate on a purely intuitive basis if a particular scenario is plausible or not. Therefore, computational modelling provides a powerful means to test this type of complex hypothesis. Here, using a dedicated computer simulation tool, we show that a flux-based polarization hypothesis is able to explain auxin transport at the shoot meristem as well, thus providing a unifying concept for the control of auxin distribution in the plant. Further experiments are now required to distinguish between flux-based polarization and other hypotheses.

Abstract Because of their complexity, plant models used in computer graphics are commonly created with proceduralmethods. A difficult problem is the user control of these models: a small number of parameters is insufficient tospecify plant characteristics in detail, while large numbers of parameters are tedious to manipulate and difficultto comprehend. To address this problem, we propose a method for managing parameters involved in plant modelmanipulation. Specifically, we introduce decomposition graphs as multiscale representations of plant structuresand present interactive tools for designing trees that operate on decomposition graphs. The supported operationsinclude browsing of the parameter space, editing of generalized parameters (scalars, functions, and branchingsystem silhouettes), and the definition of dependencies between parameters. We illustrate our method by creatingmodels of bonsai trees. Categories and Subject Descriptors (according to ACM CCS): I.3.6 [Computer Graphics]: Methodology and Techniques